Soil and Environmental Chemistry-2012

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Soil and Environmental ChemistryWilliam F. BleamUniversity of Wisconsin, MadisonAMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORDPARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYOAcademic Press is an imprint of ElsevierSoil and EnvironmentalChemistryAcademic Press is an imprint of Elsevierpermission, further information about the Publishers permissions policies and our arrangementswith organizations such as the Copyright Clearance Center and the Copyright Licensing Agency,can be found at our website: www.elsevier.com/permissions.This book and the individual contributions contained in it are protected under copyright by thePublisher (other than as may be noted herein).NoticesKnowledge and best practice in this field are constantly changing. As new research andexperience broaden our understanding, changes in research methods, professional practices, ormedical treatment may become necessary.Practitioners and researchers must always rely on their own experience and knowledge inevaluating and using any information, methods, compounds, or experiments described herein. Inusing such information or methods they should be mindful of their own safety and the safety ofothers, including parties for whom they have a professional responsibility.To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors,assume any liability for any injury and/or damage to persons or property as a matter of productliability, negligence or otherwise, or from any use or operation of any methods, products,instructions, or ideas contained in the material herein.Library of Congress Cataloging-in-Publication DataBleam, W. F. (William F.)Soil and environmental chemistry / William F. Bleam.p. cm.Reprinted with corrections.Includes bibliographical references and index.ISBN 978-0-12-415797-2 (alk. paper)1. Soil chemistry. 2. Environmental chemistry. I. Title.S592.5.B565 2012b631.41dc232011028878British Library Cataloguing-in-Publication DataA catalogue record for this book is available from the British Library.For information on all Academic Press publications,visit our website: www.elsevierdirect.comTransferred to Digital Printing in 201230 Corporate Drive, Suite 400, Burlington, MA 01803, USAThe Boulevard, Langford Lane, Kidlington, Oxford, OX5 1GB, UK# 2012 Elsevier Inc. All rights reserved.No part of this publication may be reproduced or transmitted in any form or by any means,electronic or mechanical, including photocopying, recording, or any information storage andretrieval system, without permission in writing from the publisher. Details on how to seekTo Wilbert F. Bleam, my father and so much more.develop problem-solving skills. Examples and problems rely on actual exper-imental data when available, supplemented by data gleaned from the USDANatural Resources Conservation Service Soil Data Mart, the United StatesEnvironmental Protection Agency PBT Profiler and Integrated Risk Infor-mation System, and the National Atmospheric Deposition Program, to namea few. These examples are designed to develop key problem-solving skillsPrefaceThe Earth, atmosphere, water, and living things abide intimately and insepar-ably in a place we call the soil. Any attempt to describe the chemistry of thispeculiar corner of the environment inevitably sets boundaries. Hydrology sitsbeyond the boundary for many soil chemists; but certain chemical processestake decades to develop, making residence time an important variable, tosay nothing of belowground water transport. Again, soil microbiology maylay beyond the black stump separating chemistry from its cousin biology;yet respiratory processes drive redox chemistry wherever microbes are foundin nature. Is there sufficient chemistry in risk assessment to warrant its inclu-sion despite differences in scientific dialect?Moving the boundaries outward to include Soil Moisture & Hydrology andRisk Assessment forces compensating choices. Herein Clay Mineralogy & ClayChemistry embraces layer silicates and swelling behavior, but demurs thebroader discussion of structural crystallography. Mineral weathering makes itsappearance in Acid-Base Chemistry as the ultimate source of basicity, butdetailed chemical mechanisms receive scant attention. Ion exchange is strippedto its bare essentialsthe exchange isotherm and the factors determining itsappearance. Natural Organic Matter & Humic Colloids adds content related tocarbon turnover and colloidal behavior, but does not take on the humificationprocess or the primary structure of humic molecules. Water Chemistry down-plays algebraic methods in favor of model validation, reflecting my experiencethat students attain more success applying their chemical knowledge to validat-ing simulation results than slogging through mathematically complex and sym-bolically unfamiliar coupled equilibrium expressions. The hallmark of Acid-Base Chemistry is integrationpulling together water chemistry, ion exchange,and fundamental acid-base principles to develop an understanding of two chem-ically complex topics: exchangeable acidity and sodicity.Each chapter includes insofar as possible: actual experimental data plottedin graphic form, one or more simple models designed to explain the chemicalbehavior manifest in experimental data, and quantitative examples designed toxvand to demonstrate methods for making sound estimates and predictions usingbasic chemistry principles, proven chemical models, and readily accessiblesoil, environmental, and chemical data.I wish to acknowledge several individuals who contributed to the planning,writing, and completion of this book. Philip Helmke and Phillip Barak, mychemistry colleagues at Madison, influenced uncounted choices of contentand emphasis. Birl Lowery, John Norman, and Bill Bland, my soil physicscolleagues, guided my choice to include hydrology. Robin Harris and BillHickey fed my interest and passion in environmental microbiology. Dr. BeatMuller of EAWAG (Das Schweizer Eidgenossischen Technischen Hochschulenund Forschung) was most helpful on all questions regarding ChemEQL. RobertW. Taylor, a friend dating from my Philadelphia days, exemplified encourage-ment. My graduate advisorsRoscoe Ellis, Murray B. McBride, and RoaldHoffmanguided my development as a young scientist, setting me on a coursethat ultimately led to writing this book. Edna J. Cash, a dear friend, diligentlyedited final drafts and proofs. Sharonmy wifewas always patient, alwayssupportive.William F. Will Bleam,October 2010PrefacexviElements: Their OriginaElements 161.12 Estimating the Most ProbableConcentration andAppendix 1F. The Estimate ofCentral Tendency andVariation of a Log-NormalPopular Science published an electronic version of the Periodic Table of theElements in November 2006 (http://www.popsci.com/files/periodic_popup.html) that contained pictures of virtually all of the elements in pure form. Nota-bly absent are the radioactive elements: promethium Pm, astatine At, radon Rn,francium Fr, actinium Ac, protactinium Pa, and elemSoil and Environmental Chemistry.# 2012 Elsevier Inc. All rights reserved.Concentration Range Using Distribution 371.1. INTRODUCTION1.11 Concentration FrequencyDistributions of theDilutions and the Law ofProportionate Effect 35nd AbundanceChapter Outline1.1 Introduction 11.2 A Brief History of the SolarSystem and Planet Earth 21.3 The Composition of EarthsCrust and Soils 31.4 The Abundance of Elementsin the Solar System, EarthsCrust, and Soils 31.5 Elements and Isotopes 41.6 Nuclear Binding Energy 61.7 Enrichment and Depletionduring Planetary Formation 81.8 Planetary Accretion 91.9 The Rock Cycle 121.10 Soil Formation 13the LogarithmicTransformation 181.13 Summary 21Appendix 1A.Factors Governing NuclearStability and IsotopeAbundance 22Appendix 1B.Nucleosynthesis 25Appendix 1C. ThermonuclearFusion Cycles 32Appendix 1D. Neutron-EmittingReactions that Sustain theS-Process 34Appendix 1E. Random SequentialChapter 1ents beyond uranium U.1Soil and Environmental Chemistry2There is a reason images of these elements are absent: every one of them is unsta-ble and, therefore, extremely rare. The Periodic Table of the Elements asserts thatall elements exist in principle, but this particular table correctly implies that all ofthe elements from hydrogen to uranium exist on planet Earth. In fact, every sam-ple of water, rock, sediment, and soil contains every stable elementand proba-bly most of the unstable elementsfrom hydrogen to uranium.The Environmental Working Group published an article in October 2008entitled Bottled Water Quality Investigation: 10 Major Brands, 38 Pollutants(Naidenko, Leiba et al., 2008). Among the contaminants found in bottled watersold in the United States were the radioactive strontium isotope Sr-90 (0.02Bq L1), radioactive radium (isotopes Ra-286 plus Ra-288; 0.02Bq L1), boron(6090 mg L1), and arsenic (1 mg L1). These concentrations, combined with acommentary listing the potential and actual toxicity of these substances, can bealarming. The important question is not whether drinking water, food, air, soil,or dust contains toxic elements; it most certainly does! The important questionis: is the level of any toxic element in drinking water, food, or soils harmful?The United States Environmental Protection Agency (USEPA) has estab-lished a maximum contaminant level (MCL) for beta emitterssuch as stron-tium-90 or radiumin public drinking water: 0.296 Bq L1 (8 pCi L1). Thecurrent USEPA drinking water MCL for arsenic is 10 mg L1; the mean arse-nic concentration in U.S. groundwater (based on over 20,000 samples) is2 mg L1. The USEPA does not have a drinking water standard for boron,but the World Health Organization (WHO) recommends boron levels indrinking water less than 500 mg L1, and in 1998 the European Unionadopted a drinking water standard of 100 mg L1. Typical boron concentra-tions in U.S. groundwater fall below 100 mg L1 and 90% below 40mg L1. Evaluated in context, the contaminants found in bottled water areless threatening and raise the question of whether it is reasonable to entirelyeliminate trace elements from water and food.1.2. A BRIEF HISTORY OF THE SOLAR SYSTEM AND PLANETEARTHThe gravitational collapse of a primordial cloud of gas and dust gave birth tothe present-day Solar System. The conservation of angular momentum in theprimordial dust cloud explains the rotation of the Sun (25-day rotation periodat the equator) and a primordial accretion disk that spawned the planets andother bodies that orbit the Sun. The primordial gas and dust cloud was wellmixed and uniform in composition. Gravitational accretion and radioactivedecay released sufficient heat to melt the early Earth, leading segregation intoa solid metallic core, a molten mantle, and a crystalline crust. Planetary for-mation and segregation altered the composition of Earths crust relative tothe primordial cloud and imposed variability in the composition of each ele-ment as a direct consequence of each separation process.Chapter 1 Elements 3Throughout its entire history, planet Earth has experienced continual trans-formation as plate tectonics generate new inner (oceanic) crust and shift platesof outer (continental) crust around like pieces of a jigsaw puzzle. Plate tecton-ics and the hydrologic cycle drive a rock cycle that reworks portions of theouter crust through weathering, erosion, and sedimentation. The rock cycleimposes a new round of geochemical separation processes that alters the com-position of the terrestrial land surface relative to the outer crust from which itderives. The rock cycle and soil development, much like planetary formationand segregation early in Earths history scale, impose additional variability inthe composition of each element. Transformations in the overall compositionof planet Earth and the imposition of composition variability relative to theprimordial gas cloud are the central themes of this chapter.1.3. THE COMPOSITION OF EARTHS CRUST AND SOILSMost books on geology, soil science, or environmental science include a tablelisting the composition of Earths crust or soil. There are several reasons forlisting the elemental composition of Earth materials. The composition of soilconstrains the biological availability of each element essential for livingorganisms. Soils develop from the weathering of rocks and sediments andinherit much of their composition from the local geology. The most commonelementsthose accounting for 9095% of the total compositiondetermine the dominant mineralogy of rocks and materials that form whenrocks weather (residuum, sediments, and soils).The soil at a particular location develops in starting or parentmaterialrockor sedimentsunder a variety of local influenceslandform relief, climate, andbiological community over a period of decades or centuries. Not surprisingly,the composition of soil is largely inherited from the parent material. The rocksor sediments in which a soil develops are usually not the basement rocks thatcompose the bulk of Earths crust. Regardless of geologic history, virtuallyevery rock exposed at the Earths terrestrial surface owes its composition tothe crystalline igneous rock of the continental crust. The Earths outer crustinherits its composition from the overall composition of the planet and, byextension, the gas and dust cloud that gave rise to the Solar System as a whole.How much do the composition of soil, Earths crust, and the Solar Systemhave in common? What can we learn about the processes of planetary forma-tion, the rock cycle, and soil development from any differencesin composition? What determines the relative abundance of elements in soil?1.4. THE ABUNDANCE OF ELEMENTS IN THE SOLAR SYSTEM,EARTHS CRUST, AND SOILSWe are looking for patterns, and, unfortunately, data in tabular form usuallydo not reveal patterns in their most compelling form. Patterns in the elementalabundance of the Solar System, Earths crust, and soils are best understood4when abundance is plotted as a function of atomic number Z. Astronomersbelieve the composition of the Suns photosphere is a good representationof the primordial gas and dust cloud that gave rise to the Solar System. Usu-ally the composition of the Solar System is recorded as the atom mole fractionof each element, normalized by the atom mole fraction of silicon.The composition of Earths crust and soil is usually recorded as the massfraction of each element. If we are to compare the compositions of the SolarSystem, Earths crust, and soils, the abundance data must have the same units.Since atoms combine to form compounds based on atomic mole ratios, theatom mole fraction is the most informative. The atom mole fraction is foundby dividing the mass fraction of each elementin crust or soilby its atomicmass and then normalized by the atom mole fraction of silicon.An abundance plot of the Solar System, Earths crust, and soil using a lin-ear atomic mole fraction scale reveals little because 99.86% of the SolarSystem consists of hydrogen and helium. A plot using a logarithmic atommole fraction scale for the Solar System, Earths crust, and soil reveals threeimportant features. First, the abundance of the elements decreases exponen-tially with increasing atomic number Z (the decrease appears roughly linearwhen plotted using a logarithmic scale). Second, a zigzag pattern is superim-posed on this general tread, known as the even-odd effect: elements with aneven atomic number are consistently more abundant than elements withan odd atomic number. Third, while the data set for soil composition is miss-ing many of the elements recorded for the Solar System and Earths crust,the exponential decrease in abundance with atomic number (Figure 1.1) andthe even-odd effect (Figure 1.2) appear in all three data sets.Cosmological processes, beginning with the so-called Big Bang, deter-mined Solar System composition. The cosmological imprintthe exponentialdecrease in abundance with atomic number and the even-odd effectisclearly discernible in the composition of the Earths crust and terrestrial soilsdespite the profound changes resulting from planetary formation, the rockcycle, and soil development.1.5. ELEMENTS AND ISOTOPESThe Periodic Table of the Elements organizes all known elements into groups andperiods. Elements in the same chemical grouphave the samenumber of electrons inthe outermost electronic shell but differ in the number of occupied electronic shells.Elements in the same chemical periodhave the samenumber of occupied electronicshells but differ in the number of electrons in the partially filled outermost electronicshell. Period 1 contains elements H and He, the filling of atomic shell 1s. Atomicshell 2s is filled in groups 1 and 2 of period 2elements Li and Bewhile 2p isfilled in groups 1318 of the same period. Elements of the same period exhibit sim-ilar chemical properties because their outermost or valence electronic shell has theSoil and Environmental Chemistrysame number of electrons. It is this characteristicthe valence electron configura-tionthat has the greatest influence on the chemistry of each element.FIGURE 1.1 Elemental abundance of the Solar System, Earths crust, and soil decreases expo-nentially with atomic number Z (Shacklette, 1984; Lide, 2005).FIGURE 1.2 Elemental abundance of the Solar System, Earths crust, and soil from calcium(atomic number Z 20) to zirconium (atomic number Z 40), showing the even-odd effect(Shacklette, 1984; Lide, 2005).Chapter 1 Elements 56FIGURE 1.3 Periodic Table of the Elements: the abundance of each element in the bulk silicateEarth (i.e., mantle plus crust) plotted on the vertical scale in logarithmic units. Source: Repro-duced with permission from Anders, E., and N. Grevesse, 1989. Abundance of the elements: mete-Soil and Environmental ChemistryThe Periodic Table of the Elements always lists the symbol, and usuallythe atomic number Z and atomic weight, of each element. The atomic numberZ is an integer equal to the number of positively charged protons in thenucleus of that element. The atomic weight, unlike Z, is not an integer but adecimal number larger than Z. The atomic weight is the mass of one moleof the pure element and accounts for the relative abundance of the stableand long-lived radioactive isotopes for that element (see Appendix 1A).Figure 1.3 is an unusual Periodic Table of the Elements because it plots therelative abundance of each element in the Earths outermost layersthe mantleand the cruston a logarithmic vertical scale. We will have more to say aboutthe segregation of the Earth later, but for now we are most concerned with theprocesses that determine why some elements are more abundant than others.You will notice that the abundance of elements in a given periodsay, period4fluctuate; Ca is more abundant than K or Sc, and Ti is more abundant thanSc or V. This is the even-odd effect mentioned earlier and results from thenuclear stability of each element, a topic discussed further in Appendix 1A.1.6. NUCLEAR BINDING ENERGYThe even-odd effect fails to explain the abundance of iron (Z 26) or, to bemore precise, 5626Fe. Figure 1.4 is a plot of the nuclear binding energy pernucleon for all known isotopes. It clearly shows 5626Fe is the isotope with theoric and solar. Geochim. Cosmochim. Acta. 53, 197214.greatest binding energy per nucleon. The fusion of lighter nuclei to formheavier nuclei is exothermic when the product has a mass number A 56FIGURE 1.4 Binding energy per nucleon of each isotope as a function of the mass number A.bueninblmainThinofExapter 1 ElementsCh 7t is endothermic for all heavier isotopes. You will also notice that theergy release from fusion reactions diminishes rapidly as the mass numbercreases to 20 and then gradually in the range from 20 to 56.The mass of an electron (0.000549 unified atomic mass units u) is negligi-e compared to that of protons (1.007276 u) and neutrons (1.008665 u). Thess number A of each isotope is an integral sum of protons Z and neutrons Nthe nucleus, while the isotope mass is the mass of one mole of pure isotope.e mass of an isotope with mass number A is always lower than the mass of Z-dependent protons and N-independent neutrons. The nuclear binding energyhydrogen isotope 21H (Example 1.1) illustrates the so-called mass defect.ample 1.1 Calculate the Nuclear Binding Energy for Deuterium 21H , anIsotope of Hydrogen.The nucleus of a deuterium atomconsists of one proton and one neutron. Themassesof the constituents, in unified atomic mass units u (1 u 1.66053886 10-27 kg):mproton 1:007276 umneutron 1:008665 umproton mneutron 2:015941 uThe mass of one mole of pure 21H , however, is 2.014102 u0.001839 u lessthan the mass found by adding the rest mass of a proton and a neutron. The massdifference, multiplied by 931.494 MeV u-1 and divided by 2 to account for thetwo nucleons of 21H , is the binding energy per nucleon for21H : 0.8565 MeV.the transformation from a homogeneous state to a heterogeneous stateonSoil and Environmental Chemistry8scales ranging from the scale of the Solar System itself to the smallest micro-scopic scale we can characterize experimentally.Homogeneity in the primordial gas cloud that ultimately became the SolarSystem resulted from the random motion of gas molecules and dust particles.If we collected samples from the primordial cloud for elemental analysis, thesample population would yield a frequency distribution consistent with theconditions existing in the gas cloud. A homogenous, well-mixed cloud ofgas and dust would yield a normal distribution of concentrations for each ele-ment (Figure 1.5). The average (or central tendency) concentration of eachelement is estimated by calculating the arithmetic mean concentration forthe sample population.A consequence of the various separation processes during planetary accre-tion and segregation, the rock cycle on planet Earth, and, ultimately, soil for-mation is more than the enrichment and depletion of individual elements,altering the abundance profile (see Figures 1.2 and 1.3). Elemental analysisshows that the weathered rock materials and soils that blanket the Earths con-tinental crust bear the imprint of numerous separation processes and, as wewill presently discover, yield abundance distributions that differ markedlyExothermic fusion reactions are the source of the energy output from stars,beginning with 11H nuclei and other nuclei produced during the early stagesof the universe following the Big Bang. Figure 1.4 shows that exothermicfusion becomes increasingly inefficient as an energy source. Simply put: astars nuclear fuel is depleted during its lifetime and is eventually exhausted.Appendix 1B describes the nuclear processes that formed every isotope foundin our Solar System and the Earth today. Some of those processes occurredduring the early moments of the universe under conditions that no longerexist. Other processes continue to occur throughout the universe because thenecessary conditions exist in active stars or in the interstellar medium.Nucleosynthesis is an accumulation process that gradually produces heaviernuclides from lighter nuclides, principally by exothermic fusion or neutroncapture. Lighter nuclides are generally more abundant than heavier nuclides.The extraordinary energies required for exothermic nuclear fusion and thecomplex interplay of neutron-capture and radioactive decay, the principalnucleosynthesis processes, translate into an abundance profile (see Figure 1.1)that embodies the relative stability of each nuclide.1.7. ENRICHMENT AND DEPLETION DURING PLANETARYFORMATIONGravitational collapse of a primordial cloud of gas and dust and subsequentplanetary formation in the Solar System was a process of differentiationfrom the normal distribution shown in Figure 1.5.Chapter 1 Elements 91.8. PLANETARY ACCRETIONThe Solar System formed during the gravitational collapse of a gas cloud thatultimately became the Sun. Preservation of angular momentum within the col-lapsing gas cloud concentrated dust particles into a dense rotating centralFIGURE 1.5 The frequency of concentrations from a sample population (bar graph) closelyapproximates a normal probability density function (line). The mean (or central tendency) for anormal probability distribution equals the arithmetic mean for the sample population. Source:Image generated using Sample versus Theoretical Distribution (Wolfram Demonstration Project)using 40 bins and a sample size n 4118.bodythe Sunand a diffuse disc (Figure 1.6, left) perpendicular to the axisof the Suns rotation. Gravity led to the accretion of planetesimals within thedisc that grew in size as they collided with one another.The Solar System formed about 4 billion years ago and contains 8 majorplanets and 153 confirmed moons, asteroids, meteors, comets, and uncountedplanetesimals at its outer fringe. The innermost planetsMercury, Venus,Earth, and Marsare rocky (density 5 Mg m-3), while the outermostFIGURE 1.6 Planetesimal formation in the accretion disc of a protosun (left) and the presentSolar System (right) resulted in the differentiation and segregation of the primordial gas cloud.planetsJupiter, Saturn, Uranus, and Neptuneare icy (density Chapter 1 Elements 11molten mantle and crust of crystalline silicate rock (Figure 1.8). The silicate-rich crust is further segregated into an inner or oceanic crust and an outer orcontinental crust. The inner crust has a composition and density very similarto the mantle, while the outer crust is less dense, thicker, and far more rigidthan the inner crust. The composition of the outer crust reflects the effect ofsegregation on the planetary scale but bears little imprint from the rock cyclebecause the mean age of the outer crust is roughly the same as the age ofFIGURE 1.8 Segregated Earth: core, mantle, and crust.planet Earth.The ferromagnetic elements comprise four transition metals from thefourth period: manganese Mn, iron Fe, cobalt Co, and nickel Ni. These fourmetals are depleted in Earths crust (see Figure 1.7), having become majorcomponents of the Earths metallic core. The noble metalsruthenium Ru,rhodium Rh, palladium Pd, silver Ag, rhenium Re, osmium Os, iridium Ir,platinum Pt, and gold Auhave little tendency to react with either oxygenor sulfur. These elements are depleted from the basic silicate Earth, enrichingthe metallic core. Goldschmidt (1937) grouped the ferromagnetic transitionmetals and noble metals together as siderophilic metals.The lithophilic elements (Goldschmidt, 1937) consist of all elements in theperiodic table characterized by their strong tendency to react with oxygen.The chalcophilic elementswhich include sulfur and the elements from per-iods 4 (copper through selenium), 5 (silver through tellurium), and 6 (mercurythrough polonium)combine strongly with sulfur. The chalcophilic and litho-philic elements would be enriched in basic silicate Earth after the segregationof the metallic core.Given the atomic mass of oxygen and sulfur and the relative atomic massof lithophilic chalcophilic elements in the same period; it should not besurprising that sulfide minerals are significantly denser than oxide minerals.Buoyancy in the Earths gravitational field would cause lithophilic magmato migrate toward the Earths surface, while chalcophilic magma would tendto sink toward the Earths core, thereby depleting the crust of chalcophilic ele-ments (see Figure 1.7).1.9. THE ROCK CYCLEThe Earths crust is in a state of continual flux because convection currents inthe mantle form new inner crust along midoceanic ridges. The spreading ofnewly formed oceanic crust drives the edges of the inner crust underneaththe more buoyant outer crust along their boundaries, propelling slabs of outercrust against each other. This movementplate tectonicsdrives the rockcycle (Figure 1.9).If we take a global view, the outer crust is largely composed of granite,while the inner crust is primarily basalt. Granite is a coarse-grained rock thatcrystallizes slowly and at much higher temperatures than basalt. Basalt rockhas a density comparable to the mantle; it solidifies along midoceanic ridges,where convection currents in the mantle carry magma to the surface. Geolo-gists classify granite, basalt, and other rocks that solidify from the moltenstate as igneous rocks.Soil and Environmental Chemistry12MeltingCrystallizationMETAMORPHICROCKSMAGMAWeatheringUplift & ExposureTransportationDepositionLithification(Compaction andcementation)MetamorphismConsolidationSEDIMENTSSEDIMENTARYROCKSIGNEOUS ROCKS(INTRUSIVE)IGNEOUS ROCKS(EXTRUSIVE)FIGURE 1.9 The rock cycle.for liquid water to penetrate igneous and metamorphic rock formations. Freez-Chapter 1 Elements 13ing and thawing accelerate fracturing, exfoliating layers of rock and exposingit to erosion by flowing water, wind, gravity, and ice at the Earth surface. Thewater itself, along with oxygen, carbon dioxide, and other compounds dis-solved in water, promotes reactions that chemically degrade minerals formedat high temperatures in the absence of liquid water, precipitating new mineralsthat are stable in the presence of liquid water.Burial, combined with chemical cementation by the action of pore water,eventually transforms sedimentary deposits into sedimentary rocks. Primarymineralsminerals that crystallize at high temperatures where liquid waterdoes not existcomprise igneous and metamorphic rocks. Secondary miner-alsthose that form through the action of liquid waterform in surfacedeposits and sedimentary rocks.The rock cycle (see Figure 1.9) is completed as plate tectonics carryoceanic crust and their sedimentary overburden downward into the mantleat the continental margins, or magma melting upward from the mantle returnsrock into its original molten state.1.10. SOIL FORMATIONThe rock cycle leaves much of the outer crust untouched. Soil developmentoccurs as rock weathering alters rocks exposed on the terrestrial surface ofthe Earths crust. Weathered rock materials, sediments and saprolite, undergofurther differentiation during the process of soil formation. Picture freshlydeposited or exposed geologic formations (sediments deposited following aflood or landslide, terrain exposed by a retreating glacier, fresh volcanic ashand lava deposits following a volcanic eruption). This fresh parent materialtransforms through the process of chemical weathering, whose intensitydepends on climate (rainfall and temperature), vegetation characteristic ofthe climate zone, and topography (drainage and erosion). Over time theseprocesses and unique characteristics of the setting lead to the developmentA more detailed view of the crust on the scale of kilometers to tens of kilo-meters reveals other rocks that owe their existence to volcanic activity,weathering, erosion, and sedimentation. Magma welling up from the mantlemelts through the crust. Rock formations along the margin of the melted zoneare annealed; minerals in the rock recrystallize in a process geologists callmetamorphism. Both the mineralogy and texture of metamorphic rocks revealradical transformation under conditions just short of melting. Metamorphicrocks provide geologists with valuable clues about Earth history, but theyare far less abundant than igneous rocks.Inspection on the kilometer scale reveals a zone of rock weathering andsediment deposits covering both the continental and oceanic crusts. Stressfractures, caused by thermal expansion and contraction, create a pathwayof soil.Soil and Environmental Chemistry14The excavation of a pit into the soil reveals a sequence of layers or soilhorizons with depth (Figure 1.10). This sequence of soil horizons is knownas the soil profile for that site. Soil horizons vary in depth, thickness, compo-sition, physical properties, particle size distribution, color, and other proper-ties. Soil formation takes hundreds to thousands of years, and, provided theFIGURE 1.10 A northern temperate forest soil developed in glacial till (Northern Ireland).site has remained undisturbed for that length of time, the soil profile reflectsthe natural history of the setting.Plotting the abundance of each element in the Earths crust divided by itsabundance in the Solar System reveals those elements enriched or depletedduring formation of planet Earth and the formation of the outer crust duringthe segregation of the Earth (see Figure 1.7). Plotting the abundance of eachelement soil divided by its abundance in the Earths crust reveals those ele-ments enriched or depleted during the rock cycle and soil development. Whenboth are displayed together on the same graph (Figure 1.11), plotting the log-arithm of the abundance ratio of crust to the Solar System and the ratio of soilto crust, an important and not surprising result is immediately apparent:enrichment and depletion during planetary formation and segregation areorders of magnitude greater than those that take place during the rock cycleand soil formation. This explains the findings (Helmke, 2000) that a charac-teristic soil composition cannot be related to geographic region or soil taxo-nomic group.Enrichment from biological activity is clearly apparent when plotting thelogarithm of the atom mole fraction ratio soil-to-crust (Figure 1.12). Carbonand nitrogen, two elements strongly depleted in the Earths crust relative tothe Solar System, are the most enriched in soil relative to the crust. BothFIGURE 1.11 Elemental abundance of the Solar System relative to the Earths crust and soilrelative to the Earths crust reveal the magnitude of planetary formation, the rock cycle, and soilformation (Shacklette, 1984; Lide, 2005).FIGURE 1.12 Elemental abundance of soil relative to the Earths crust, showing enrichment ofcarbon, nitrogen, and sulfur caused by biological activity (Shacklette, 1984).Chapter 1 Elements 15are major constituents of biomass. Selenium, sulfur, and boronamong the topSoil and Environmental Chemistry16sixmost enriched elements in soilare essential for plant and animal growth. Therelative enrichment of arsenic, which is not a nutrient, may have much to do withits chemical similarity with phosphorusanother essential element.1.11. CONCENTRATION FREQUENCY DISTRIBUTIONS OF THEELEMENTSNo element is distributed uniformly in Earth materials because separation pro-cesses tend to enrich an element in certain zones while depleting it in others(see Figures 1.10 and 1.11). Geologists, soil scientists, environmental che-mists, and others often wish to identify zones of enrichment or depletion. Thisrequires collecting samples representative of the site under study, chemicallyanalyzing the sample collection (or sample population), and performing a sta-tistical analysis of the sample data set to estimate the mean1 concentration andvariability of each element analyzed.Geologists delineate zones of enrichment (or depletion) using thisapproach while prospecting for economic mining deposits or reconstructingthe geologic history of rock formations. Soil scientists rely on chemicalanalysis to classify certain soil horizons characterized by either the loss oraccumulation (see Figure 1.10). Environmental chemists map contaminationand assess the effectiveness of remediation treatments by analyzing samplepopulations. In short, statistical analysis of a representative sample popula-tion will establish whether enrichment or depletion is significant.Natural variation at the field site results in an abundance distributionfor each element in the sample population. Understanding the abundance dis-tribution typical of environmental samples enables us to identify appropriatestatistical methods for estimating the central tendency and variation for eachelement in the sample population.Figures 1.13 and 1.14 illustrate typical abundance distributions for envi-ronmental samples. The data in Figure 1.13 represent samples where geo-chemical processes dominate, while Figure 1.14 shows samples where thedominant processes are biological. Table 1.1 lists a number of studies report-ing abundance distributions from the chemical analysis of rock, soil, water,and atmospheric samples. The results in Figures 1.13 and 1.14, along withthe studies listed in Table 1.1, clearly show a characteristic property of fre-quency distributions for environmental samples: they tend to be skewed ratherthan symmetric (see Figure 1.8).Ahrens (1954) discovered that the skewed frequency distributions usuallyencountered by geochemists tend to follow a logarithmic-transformed normal(or more commonly, log-normal) distribution. Biologists consider log-normal1. The mean is one measure of the central tendency of a distribution. Median and mode are otherstatistics that serve as central tendency indicators.Chapter 1 Elements 17distributions typical of biological processes (Limpert, Stahel et al., 2001).A logarithmic-transformed normal concentration distribution is a skewed dis-tribution that under a logarithmic-transformation (i.e., a plot of logarithm ofsample concentrations) becomes a symmetric normal distribution. Many envi-ronmental chemists, geochemists, and biologists estimate the geometric meanconcentration (i.e., a central tendency statistic for log-normal distributions)and geometric standard deviation for their data sets.Some of the studies listed in Table 1.1 assume their data set follows a log-normal distribution (Dudka, Ponce-Hernandez et al., 1995; Chen, Ma et al.,1999; Budtz-Jrgensen, Keiding et al., 2002), while others perform a statisti-cal analysis to verify that the concentration distribution is best described by alog-normal distribution function (Hadley and Toumi, 2003). In some cases theconcentration distributions may not conform to a true log-normal distribution,yet they clearly deviate from a normal distribution (Yang and Chang, 2005;Zhang, Manheim et al., 2005).FIGURE 1.13 Abundance distributions for the elements Pb in Canadian granite (Ahrens, 1954),soil Cd from Taiwan (Yang and Chang, 2005), and Fe and P from the USGS National Geochemi-cal Survey data set of U.S. soils and sediments (Zhang, Manheim et al., 2005). The number ofsamples n in each study is, respectively, 32 (Pb), 918 (Cd), and 16,511 (Fe and P).Soil and Environmental Chemistry18Appendix 1E describes two models of environmental processes that resultin log-normal concentration frequency distributions. The simplest to understandis the sequential random dilution model (Ott, 1990). The second model, knownas the law of proportionate effect (Kapteyn, 1903), is completely general.1.12. ESTIMATING THE MOST PROBABLE CONCENTRATIONAND CONCENTRATION RANGE USING THE LOGARITHMICTRANSFORMATIONEach type of frequency distribution results from processes with specific char-acteristics. For now we will rely on the same assumption as Ahrens (1954); alog-normal distribution is a reasonable representation of the abundance distri-bution of trace elements in the environment.FIGURE 1.14 Frequency distributions for nitrate nitrogen leaching from German soils (Borkenand Matzner, 2004), soil organic carbon from China (Liu, Wang et al., 2006), urinary mercurylevels in a human population in Rio-Rato, Brazil (Silva, Nyland et al., 2004), and Cs-127 levelsin a species of tree frogs (Hyla cinerea) near a nuclear facility in South Carolina (Dapson andKaplan, 1975). The number of samples n in each study is, respectively, 57 (nitrate-nitrogen),354 (soil organic carbon), 98 (Hg), and 141 (Cs-137).Chapter 1 Elements 19TABLE 1.1 Studies Reporting Frequency Distributions for EnvironmentalSamplesMedium Elements Analyzed SampleSizeReferenceThe best way to understand log-normal distributions is to consider a realexample. The example we will use is the data set published by Ahrens(1954) consisting of Pb concentrations from a sample population of Canadiangranites (Table 1.2; see Figures 1.13 and 1.15). The upper portion of Table 1.2lists the original data set based on Pb concentrations in parts per million(mg kg1). The lower portion of Table 1.2 lists the transformed data set basedon the natural logarithm of Pb concentrations in the original data set. TheRock K, Rb, Sc, V, Co, Ga, Cr, Zr, La, Cs,F, Mo158 (Ahrens, 1966)SurfaceMaterialAl, Ca, Fe, K, Mg, Na, P, Ti, Ba, Ce,Co, Cr, Cu, Ga, La, Li, Mn, Nb, Nd,Ni, Pb, Sc, Sr, Th, V, Y, Zn16,511 (Zhang, Manheimet al., 2005)Soil Cd, Co, Cu, Cr, Fe, Mn, Ni, S, Zn 73 (Dudka, Ponce-Hernandez et al.,1995)Soil Ag, As, Ba, Be, Cd, Cr, Cu, Hg, Mn,Mo, Ni, Pb, Sb, Se, Zn448 (Chen, Ma et al.,1999)Soil Cd 918 (Yang and Chang,2005)Soil C 354 (Liu, Wang et al.,2006)Groundwater Ag, As, Ba, Be, Cd, Co, Cr, Cu, Hg,Ni, Pb, Sb, Se, Tl, Sn, V, Zn104,280 (Newcomb andRimstidt, 2002)Groundwater N 57 (Borken andMatzner, 2004)Atmosphere SO2 >365 (Hadley andToumi, 2003)HumanTissueHg 98140 (Silva, Nylandet al., 2004)HumanTissuemethylmercury 1022 (Budtz-Jrgensen,Keiding et al., 2002)Green TreeFrogsCs-137 141 (Dapson andKaplan, 1975)Soil and Environmental Chemistry20TABLE 1.2 Estimates of the Central Tendency and the VariationEncompassing 95.5% of the Pb Concentrations in Canadian GraniteSamplesOriginal Data SetData Set(mg kg1){2.0, 3.8, 5.5, 6.0, 6.0, 6.5, 7.5, 7.7, 8.0, 8.0, 8.5, 8.5, 9.0, 9.0, 9.0, 10.0,10.0, 11.0, 12.0, 14.0, 14.0, 15.0, 17.0, 18.0, 20.0, 20.0, 22.0, 24.0, 26.0,29.0, 39.0, 68.0}ArithmeticMeanx 1n Pi xi x 14:8ArithmeticStandards 1n Pi xi x 2q s 12:7arithmetic mean and arithmetic standard deviation are central tendencyand variation statistics of the original data set, while the transformed dataset employs the geometric mean and geometric standard deviation. SeeAppendix 1F for another example from Ahrens (1954).Figure 1.15 plots the Pb abundance distribution on a linear concentrationscale and the log-normal distribution using the data sets in Table 1.2.Although the arithmetic and geometric means do not differ much from oneanother, the geometric mean is clearly a better estimate of the average Pbconcentration than the arithmetic mean, regardless of which concentrationscale is used for plotting. The major difference, a difference crucial for estab-lishing whether the most probable values of two different sample populationsare significantly different from one another, is the range estimate.Range estimates are designed to cover a specified interval for the variablein question. Normal distributions are symmetric about the arithmetic mean, soDeviation95.5% Range x 2 s x x 2 s 2:1mg kg1 x 27:5mg kg1 Logarithmic-Transformed Data SetTransformedData Set{0.69, 1.34, 1.70, 1.79, 1.79, 1.87, 2.01, 2.04, 2.08, 2.08, 2.14, 2.14,2.20, 2.20, 2.20, 2.30, 2.30, 2.40, 2.48, 2.64, 2.64, 2.71, 2.83, 2.89,3.00, 3.00, 3.09, 3.18, 3.26, 3.37, 3.66, 4.22}GeometricMeanxG exp 1n Pi lnxi Qi xi 1n xG 11:5 exp 2:45 GeometricStandardDeviationsG exp1n Pi lnxi lnxG 2q sG 2:02 exp 0:702 95.5% Range xG s2G x xG s2G 2:9mg kg1 x 46:0mg kg1 Source: Ahrens, 1954.Chapter 1 Elements 21the range is symmetric about the mean. For example, a range extending fromone standard deviation below the mean to one standard deviation above themean covers 68.3% of the population, while a range spanning two standarddeviations from the mean covers 95.5% (see Table 1.2). Log-normal distribu-tions are asymmetric about the geometric mean. The lower limit of a rangecovering 68.3% of the population is the geometric mean divided by thegeometric standard deviation while the upper limit is the geometric meanmultiplied by the geometric standard deviation. Table 1.2 lists the 95.5%range for our logarithmic-transformed data set. The skewed nature of the Pbconcentrations (see Figure 1.15, left) clearly demands the skewed range esti-FIGURE 1.15 Frequency distributions of Pb in Canadian granite (Ahrens, 1954): original distri-bution (left) and logarithmic-transformed distribution (right). The appropriate central tendencyconcentration and variation appear in Table 1.2.mate provided by log-normal distribution statistics rather than the symmetricrange estimate based on normal distribution statistics.1.13. SUMMARYThe evolution of the universe and the Solar System, ultimately, determinedthe composition of planet Earth. Gravitational collapse of primordial gasclouds formed first-generation stars, triggering exothermic fusion reactionsthat generated sufficient heat to forestall complete collapse and producing aseries of heavier elements culminating in the isotope 5626Fe. The sequentialburning of lighter elements produces heavier elements with less efficiencyin each subsequent stage. Eventually the first-generation stars depleted theirnuclear fuel, either collapsing into obscurity or exploding into supernovae thatseeded the interstellar medium with heavy elements.Later stellar generations repeat the process, producing still heavierelements by neutron capture and beta decay either slowly throughout thelifetime of the star (s-process) or in the paroxysm of a supernova (r-process).R-process neutron capture generates a host of radioactive isotopes, some ofSoil and Environmental Chemistry22which have survived the formation of the Solar System and are found on Earthtoday, and others that decayed to lighter isotopes by the present time.Solar System segregation occurred during planetary accretion, resulting inthe formation of the four inner terrestrial planets, including Earth. Further seg-regation took place as the Earth separated into layers: core, mantle, and crust.Separation processes continue to the present day, the result of the rock cycleand soil formation. Segregation transformed the original homogeneous elementdistribution inherited from the collapsing gas cloud into the heterogeneous dis-tributions we find in the Earths terrestrial environment.Samples drawn from the environmentrocks, weathered surface deposits,soils, and groundwaterreflect this heterogeneity. Efforts to detect enrich-ment or depletion require statistical analysis of sample populations of suffi-cient size to capture natural variability. Chemical analysis of environmentalsamples typically yields data sets with skewed frequency distributions.Estimates of the mean concentration of an element and the concentration var-iation of the sample population usually rely on the logarithmic transformationof the data set, a practice justified because log-normal distributions are gener-ally good representations of natural abundance distributions.APPENDIX 1A. FACTORS GOVERNING NUCLEAR STABILITYAND ISOTOPE ABUNDANCE1A.1. The Table of Isotopes and Nuclear Magic NumbersThe Table of Isotopes (Figure 1A.1) organizes all known isotopes andelements into columns and rows, listing important information about each iso-tope: atomic number Z, neutron number N, mass number A, isotopic rest mass,binding energy, stability, half-life, and abundance.Stable isotopes (black squares in Figure 1A.1) occupy a narrow band passingthrough the center of the known isotopes in the Table of Isotopes. Borderingthis narrow peninsula of stability is a zone of radioactive (i.e., unstable) isotopesthat are increasingly less stable (i.e., shorter half-lives) as the isotopes becomeincreasingly proton-rich or neutron-rich. Lighter shades of gray in Figure 1A.1represent increasingly less stable isotopes. Physicists and nuclear chemists callthe several processes that form elements and isotopes nucleosynthesis.There are parallels between the Periodic Table of the Elements and theTable of Isotopes. Protons and neutrons in the nucleus are also organized intoshells; isotopes exhibit significantly greater stability when a nuclear shell iscompletely filled by either protons or neutrons or when there is an even num-ber of protons or neutrons.1A.2. Nuclear Magic NumbersThe Periodic Table of the Elements owes its periodicity to the filling of elec-tronic shells. It takes 2, 8, 10, and 14 electrons to complete electronic shellsChapter 1 Elements 23N = 8 N = 20N = 28N = 50N = 82N = 126Z = 82Z = 50Z = 28Z = 20Z = 8FIGURE 1A.1 The Table of Isotopes, with each square representing a known isotope and thedesignated s, p, d, and f. Chemists noticed that when elements react, they tendto lose, gain, or share a certain number of electrons. The Octet Rule associatesunusual chemical stability with the sharing or transfer of electrons that resultin completely filled s and p electronic shells. The preferred oxidation states ofan element or charge of an ion can usually be explained by stability conferredby a filled electron shell. A filled electron shell and covalent chemical bondsincrement by two spin-paired electrons.Completely filled nuclear shells contain a magic number (2, 8, 20, 28, 50,82, and 126) of nucleons. Nucleons are either protons or neutrons. Thefilling of proton nuclear shells is independent of the filling of neutron nuclearshells. Isotopes with completely filled nuclear shells have significantly greaterstabilityand greater abundancethan isotopes with partially filled nuclearshells. Isotopes with half-filled nuclear shells or shells with an even numberof spin-paired nucleons represent stable nuclear configurations and explainthe even-odd effect seen so clearly in the composition of the Solar System(Figure 1A.2) and, to a lesser degree in the Earths crust and soil(Figure 1A.3), and in the number of stable isotopes for each element.Lets make this very clear: atomic number Z or proton count determinesthe identity of each element, while neutron count N identifies each isotope.A magic atomic number Z or a half-filled nuclear proton shell (an atomicnumber Z of 1, 4, 10, 14, etc.) or an even number of protons confers addedshade representing stability. Source: Reproduced with permission from NDDC, 2009. InteractiveChart of Nuclides. Retrieved August 26, 2009, from http://www.nndc.bnl.gov/chart/.FIGURE 1A.2 Isotope abundance decreases with increasing mass number A. The abundance isthe isotope mole fraction normalized by 2814Si (Anders and Grevesse, 1989).Half-Lifehttp://atom.kaeri.re.kr/Neutron Number NAtomic Number ZStable100 000 a>10 a>100 d>10 d>1 d>1 h>60 sFIGURE 1A.3 A portion of the Table of Isotopes: the darkest shade of gray identifies stable iso-topes, while lighter shades of gray indicate radioactive isotopes with progressively shorter half-lives. Source: Reproduced with permission from NDDC, 2009. Interactive Chart of Nuclides.Retrieved August 26, 2009, from http://www.nndc.bnl.gov/chart/.Soil and Environmental Chemistry24Chapter 1 Elements 25stability to the element that translates into greater abundance than elementslacking those characteristics. A magic neutron number N or a half-fillednuclear neutron shell (a neutron number N of 1, 4, 10, 14, etc.) or an evennumber of neutrons confers added stability to the isotope, which translatesinto greater stability than isotopes lacking those characteristics.A portion of the Table of Isotopes appears in Figure 1A.3. The elements,represented by their atomic number Z, appear as columns in this version,while the isotopes, represented by the number of neutrons in the nucleusN, appear as rows. The columns and rows are not completely filled becauseonly known isotopes are shown. Stable isotopes appear in the darkest shadeof gray, while unstable isotopes are shaded in lighter shades of gray andwhite, depending on the half-life of each radioactive isotope. The half-lifeof a radioactive isotope is the time it takes for half of the isotope to undergoradioactive decay into another isotope. Figure 1A.3 helps us understand howisotope stability contributes to element abundance.Hydrogen isotope 31HN 2, a magic neutron numberis the onlyrecognized unstable hydrogen isotope. Helium isotopes span a range from32HeN 1, a half-filled nuclear neutron shellto 102 HeN 8, a magicneutron number. Oxygen isotopes span a range from 128 ON 4, a half-fillednuclear neutron shell and an even numberto 248 ON 16, an even num-berwith the most abundant isotope being 168 O with a magic atomic numberZ and a magic neutron number N.APPENDIX 1B. NUCLEOSYNTHESIS1B.1. Nuclear ReactionsThe particles that make up each elementprotons, neutrons, and electronscondensed from more fundamental particles in the early instants of the universefollowing the Big Bang. In those early moments, none of the elements that nowfill the Periodic Table of the Elements existed other than the precursors ofhydrogen: protons, neutrons, and electrons. All of the elements that now existin the universe result from the nuclear reactions listed in Table 1B.1.The last three nuclear reactions, along with fission reactions, result fromthe spontaneous decay of unstable or radioactive isotopes. Radioactive decayresults in the emission of alpha particles (42He nuclei), electrons (beta-minusparticles: 01e), positrons (beta-plus particles:01e), or gamma rays (g).Fusion reactions produce proton-rich isotopes that, if they are unstable,decay by positron emission (beta plus decay)a process that effectivelyconverts a proton to a neutron in the nucleus coupled with the emission of apositron 01e and an electron neutrino ne to preserve charge and nuclear spin.Neutron-capture reactions produce neutron-rich isotopes that are oftenunstable, leading to spontaneous beta decay emitting an electron 01e and anelectron antineutrino ne while converting a neutron to a proton in the nucleus.Soil and Environmental Chemistry26TABLE 1B.1 Nucleosynthesis Reactions Yielding Elements and IsotopesNuclear Reaction ExampleFusion 21H 11H !nuclearfusion 32He g11H 11H !nuclearfusion 21H 01e ne42He 136C !nuclearfusion 168O 10nElectron Capture 74Be 01e !electroncapture 73L i neNeutron Capture 5926Fe 10n !neutroncapture 6026Fe gSpallation 11H 147N !cosmicspallation 94Be 42He 2 11HFission 23892U !spontaneousfission 14355Cs 9037Rb 3 10n gPositron Emission 13positronemission 13 0Thus, fusion is often coupled with positron emission, while neutron capturecommonly leads to beta decay.1B.2. Nuclear FusionThe early universe was very hot and denseideal conditions for nucleosyn-thesis but short-lived because the universe was also rapidly expanding. Rapidexpansion cooled the early universe to temperatures that could no longer sus-tain nuclear fusion within a few minutes after the Big Bang. The compositionof the universe was limited to the handful of elements that formed during theearly minutes of its existence until about 100 million years later (Larson andBromm, 2001), when the first stars formed and the second stage of stellarnucleosynthesis began.Primordial nucleosynthesis began a fraction of a second after the BigBang, when the temperature of the universe had dropped to 109 K, lowenough for protons to capture neutrons, forming hydrogen isotopes andheavier elements through nuclear fusion. The absence of stable isotopes withA 5 and A 8 (black boxes on diagonal, Figure 1A.3) created a bottleneckfor primordial nucleosynthesis beyond 73Li and74Be.7N ! 6C 1e neBeta Decay 6026Fe !betadecay 6027Co 01e neAlpha Decay 21084Po!alphadecay 20682Pb 42HeChapter 1 Elements 27Free protons and electrons are stable, but neutrons can survive only 10.3 min an unbound state. The neutron-capture rate drops as the temperature of theexpanding universe cools below 109 K, resulting in the decay of unbound neu-trons to protons, electrons, and electron antineutrinos ne, bringing primordialnucleosynthesis to a close.10n !t1=210:3m 11H 01e neAbout 100250 million years after the Big Bang, gravitational collapse of gasclouds led to the first generation of stars (Larson and Bromm, 2001). The coretemperature in collapsing gas clouds rose until, once again, they reachedabout 109 K.A collapsing gas cloud emits infrared radiation as its temperature rises.Radiation emission is a cooling process that controls the eventual size ofthe star. Population III (first-generation) stars did not cool as efficiently aslater-generation stars because they lacked heavy elements. As a result, Popu-lation III stars with masses of 100 solar masses or higher were much morecommon (Larson and Bromm, 2001). Massive Population III stars meant thatsupernovae were more commona star must have a mass greater than 9 solarmasses to produce a core-collapse or Type II supernova.The Sun derives 98 to 99% of its energy output by the so-called proton-proton I cycle, depicted in the following reactions:11H 11H !nuclearfusion21H 01e ne21H 11H !nuclearfusion32He g32He 32He!nuclearfusion42He 211HThe intermediate isotopes in these reactions21H and32Hedo not accumu-late. The net product of the proton-proton I process is production of alphaparticles:411H !net 42He 2 01e 2ne g26:7 MeVRegardless of the specific process, the temperatures in the stellar coreproduced by hydrogen burning are insufficient to fuse alpha particles intoheavier elements. Hydrogen burning ceases once nearly all of the hydrogenin the stellar core is gone and gravity causes the core to collapse. This secondSoil and Environmental Chemistry28collapse increases core temperatures above 109 K, sufficient for a secondstage of stellar nucleosynthesis: helium burning.A sequence of nuclear fusion reactions unfolds as heavier elementsform and burn at ever-increasing temperatures as the stellar core continuesto collapse (see Appendixes 1A and 1C). Each collapse and core tempera-ture increase makes it possible to fuse heavier nuclei that resist fusion atlower temperatures. The sequential fusion of alpha particles with heaviernuclei tends to produce isotopes with even atomic numbers Z and massnumbers A of 32, 36, 40, 48, 52, and 56. About 97% of the stars in our gal-FIGURE 1B.1 False color images at two wavelengths of the Trifid Nebula.axy lack sufficient mass to sustain fusion reactions beyond the triple-alphaprocess (see Appendix 1C). These stars evolve into white dwarfs and do noteject heavy elements into interstellar space. Stars exceeding 9 solar massesundergo a series of collapses, leading to higher temperatures and densitiescapable of sustaining carbon, oxygen, and silicon burning. Each stage isless efficient, producing less energy and fewer nuclei. The fusion reactionsin this sequence are all exothermic up to 5626Fe. The final collapse of thesemassive stars triggers a core-collapse or Type II supernova (Figure 1B.1),seeding the interstellar medium with dust containing heavy elements thateventually collapse to form second-generation Population II stars.1B.3. Neutron CaptureNot only is the fusion of nuclei heavier than 5626Fe endothermic, consuming theenergy released by the fusion of lighter nuclei, but also stellar core tempera-tures are too low to overcome Coulomb repulsions that resist the fusion ofheavy elements. The nucleosynthesis of heavier elements must follow a dif-ferent pathway that avoids Coulomb repulsion: neutron capture.Chapter 1 Elements 29Neutron capture occurs simultaneously with exothermic nuclear fusion inthe stellar core but under low flux conditions know as the slow- or s-processbecause the timescale for neutron capture tn under low neutron flux condi-tions in the stellar core is on the order of 1001000 years. Unstable neu-tron-rich isotopes undergo beta decay to form more stable isotopes withfewer neutrons. Only those beta decay reactions with timescales tb tn cansustain s-process nucleosynthesis. The following neutron capture and betadecay reaction sequence illustrate s-process nuclear reactions:5926 Fe 10n!neutroncapture6026Fe g6026Fe!betadecay6027Co 01e ne6027Co 10n !neutroncapture6127Co g6127Co!betadecay6128Ni 01e neS-process nucleosynthesis is very sensitive to unstable, short-lived isotopes,confining it to reaction pathways involving relatively stable isotopes. Thes-process terminates with the production of 20983 Bi, unable to produce elementswith atomic masses between Po and Ac (84 Z 89) because all of theelements in this range are extremely unstable and very short-lived. The moststable radium isotope22688 Rahas a half-life of 1600 years, while the moststable francium isotope22387 Frhas a half-life of a mere 21.8 minutes.Not all of the elements present before the final collapse survive a super-nova. Astronomers believe photodisintegration in the superheated conditionsof the supernova destroys much of the 5626Fe formed in first-generation stars.In reality, supernova photodisintegration reactions affect all heavy nuclei,not just 5626Fe, and reach equilibrium during the brief supernova episode:5626Fe g !photodisintegrationneutron capture5526Fe 10nThe brief but intense (on the order of 1022 neutrons cm-2 s-1) supernova neutronflux triggers rapid-process (r-process) neutron capture that occurs at a muchfaster rate than the decay rate of unstable isotopes (tb 82 and isotopes with mass numbers A as highas 270. Super-heavy elements are so unstable that their nuclei fragment throughnuclear fission reactions as rapidly as r-process neutron capture produces them.3The presence of thorium and uranium on Earth is proof that the Solar System isa third-generation Population I stellar system because uranium could only formduring the supernova of a massive second-generation Population II star.1B.4. Cosmic Ray SpallationThe interstellar medium consists of gas and dust left over from the BigBang and subsequent star formation eras bathed in cosmic rays, mostly protonsand alpha particles traveling at extremely high velocities (10-1 the speed oflight). When cosmic rays strike heavy elements in the interstellar medium, thecollision causes the fragmentation or spallation of the heavier nuclei.Primordial and stellar nucleosynthesis is unable to account for the abun-dance of three light elementsLi, Be, and Bin the interstellar mediumand Solar System. These three elements are unable to withstand the high tem-peratures and densities that sustain nuclear fusion reactions; the quantitiesformed during the initial few minutes following the Big Bang would havebeen destroyed in first-generation stars. Cosmic ray spallation, however,occurs at low enough temperatures and densities to allow Li, Be, and B iso-topes to survive once they have formed. The following reactions are represen-tative of cosmic ray spallation and account for the higher interstellarabundance of Li, Be, and B compared to their Solar System abundances:42He 42He!cosmicspallation63Li 11H 10n11H 126C!cosmicspallation115 B 2 11H11H 147N !cosmicspallation94Be 42He 2 11H42He 126C!cosmicspallation73Li 2 42He 11H11H 147N !cosmicspallation105B 3 11H 2 10n1B.5. Transuranium ElementsAlthough elements heavier than uranium (Z > 92) either do not exist or areextremely rare on Earth, they are not synthetic elements, as they are oftencalled. All transuranic elements comprise isotopes that are short-lived com-pared to the age of the Solar System 4 106a . The transuranium elementsSoil and Environmental Chemistry0and several other elements lacking stable isotopes are extinct, the quantitiespresent in the primordial Solar System having decayed long ago.Technetium, element 43, has no stable isotopes; the longest-lived9843Tchas a half-life t1/2 on the order of 106 years. Polonium, Z 84, isanother element with no stable isotopes; all radioactive Po isotopes havehalf-lives less than 102 years. The most long-lived isotopes of the nextthree heavier elementsastatine (Z 85), radon (Z 86), and francium(Z 87)have half-lives ranging from 22 minutes to 3.8 days. None ofthe elements heavier than Pb form stable isotopes, and all are radioactive.Though unstable, thorium (Z 90), and uranium (Z 92) have isotopeswith half-lives greater than the age of the Solar System (Table 1B.2).How can we explain the presence of radon and other unstable elements inthe environment with half-lives less than the age of the Solar System? Thetrace level of elements lacking stable isotopes results from the radioactivedecay of 23892U , a portion of which appears in Table 1B.3, and23290Th.Trace amounts of transuranium isotopes are also found in nature, believedto be the products of the spontaneous or stimulated fission of long-liveduranium isotopes. Rather than emitting a simple alpha or beta particle,the nuclei of heavy uranium and transuranium isotopes disintegrate into twolarge fragments containing many neutrons and protons (Figure 1B.2). Nuclearfission may be spontaneous, requiring no external excitation:Chapter 1 Elements 3123692U !spontaneousfission14355Cs 9037Rb 3 10n gTABLE 1B.2 The Long-Lived Isotopes 23291Th and23892UElement Isotope Half-Life, t1/2Thorium 23290T h 1:405 1010aUranium 23892U 4:468 1010aTABLE 1B.3 A Portion of the Radioactive Decay Series for 23893UReaction Half-Life, t1/2 Reaction Half-Life, t1/223892U !a 23490T h 4:468 109a 23490T h!a 22688Ra 8 104a23490T h!b 23491Pa 24 d 22688Ra!a 22286Rn 1:6 103a23491Pa!b 23492U 1 m 22286Rn!a 21884Po 3.8 d23492U !a 23090T h 2:4 105a 21884Po!b 21885At 3.1 mSoil and Environmental Chemistry32Thermal Neutron Fission of U-235101Sr-90I-131Cs-137101102Fission Yield, Percent10360 80 100 120 140 160 180Certain uranium isotopes undergo fission when stimulated by neutron capture:23592U 10n !thermal neutronfission13756Ba 9536Kr 3 10n g23592U 10n !thermal neutronfission13954Xe 9538Sr 2 10n gNuclear reactors rely on the stimulated nuclear fission of radioactive uraniumand transuranium isotopes to generate high neutron fluxes that mimic ther-process. Nuclear reactors produce a variety of neutron-rich isotopes by neu-tron capture. Some fission reactions release more than one neutron, a neces-sary condition for fission chain reactions that rely on neutrons to stimulatefission.APPENDIX 1C. THERMONUCLEAR FUSION CYCLES1C.1. The CNO CycleAbout 1% of the Suns energy output and nearly all of the output of massivePopulation III stars is by the CNO cycle depicted below. Some of the productsMass Number AFIGURE 1B.2 Fission yield of 23592U .1H 7N ! 8O g7:35 MeV158O!positronemission157N 01e ne11H 157N !nuclearfusion126C 42HeThe carbon, nitrogen, and oxygen isotopes in these reactions also do not accu-mulate. The net product of the CNO cycle is nearly identical to the proton-proton I processproduction of alpha particlesthe only difference beingthe net energy output:411H!net 42He 2 01e 2ne g16:84 MeV1C.2. The Triple-Alpha ProcessHelium burning (triple-alpha process) follows the core collapse once hydro-gen is depleted. Unlike hydrogen burning (e.g., proton-proton I or CNOcycles) the triple-alpha process faces a bottleneck. The fusion of two alphaparticles produces a very unstable isotope 84Be with a lifetime of about 10-16 s.If 84Be fuses with another alpha particle before it decays it will form a stable126C that can sustain further fusion reactions. The two fusion reactions must benearly simultaneous:42 He 42He!nuclearfusion84Be 1016 sg4He 8Be !nuclearfusion 12C g(137N and158O ) are unstable because they have too many neutrons and decayby positron emission:11H 126C !nuclearfusion137N g1:95 MeV137N !positronemission136C 01e ne11H 136C !nuclearfusion147N g7:54 MeV1 14nuclearfusion15Chapter 1 Elements 332 41016 s6Soil and Environmental Chemistry34APPENDIX 1D. NEUTRON-EMITTING REACTIONS THATSUSTAIN THE S-PROCESSNumerous nuclear reactions in the stellar core, represented by the reactionsequences below, create a low neutron flux on the order of 105 to1011 neutrons cm2 s1 that supports s-process neutron capture in the stellarcore. These neutron-producing nuclear reactions occurred in first-generationstars but in the absence of the heavy elements found in second and subsequent-generation stars:126 C 11H !nuclearfusion137N g137N !positronemission136C 01e ne42He 136C!nuclearfusion168O 10n42 He 147 N !nuclearfusion189F gThe 84Be bottleneck means helium burning is much slower than hydrogenburning.1C.3. Carbon BurningCarbon burning follows the core collapse once helium is depleted. Fusion of twocarbon nuclei must overcome significant Coulombic repulsions, requiring highertemperatures (6 109 K) and densities that are needed to sustain helium burning:126 C 126C!nuclearfusion2010Ne 42He4:617MeV126C 126C!nuclearfusion2311Na 11 H2:241MeV126C 126C!nuclearfusion2312Mg 10 n2:599 MeVThese fusion reactions are all exothermic, the heat released as the kineticenergy of particles emitted from the nucleus (42He,11H , and10n ).189F!positronemission188O 01e ne42He 188 O!nuclearfusion2210Ne g42He 2210Ne!nuclearfusion2512Mg 10nAPPENDIX 1E. RANDOM SEQUENTIAL DILUTIONS AND THEChapter 1 Elements 35C0 C1 C2 C3 C4n1n1d1 = Vn2 n3 n4n2d2 = V Vn3d3 = Vn4d4 =FIGURE 1E.1 A four-step sequen-tial random dilution series beginswith an initial concentration C0and uses a fixed volume V. The vol-ume transferred in each step vi is arandom value, as is the resultingdilution factor di.type of environmental process that would yield a log-normal concentration dis-tribution. The random sequential dilution model is actually a special case of amore general process known as the law of proportionate effect first describedby the Dutch astronomer and mathematician K. C. Kapteyn (Kapteyn, 1903).Ott described two simple random processes that, in the limit of a largenumber of transformations, consistently yield log-normal concentration distri-bution. The first example imagines a sequential random dilution, in which thedilution factor 0 < di 1 at each step is a random value.The sequential random dilution (Figure 1E.1) begins with an initial con-centration C0 and transfers a random volume vi in each step. The concentra-tion at each stage Ci is a function of the transferred volume vi, theconcentration of the previous stage Ci1, and a fixed volume V:Ci viV Ci1 di Ci1The concentration Cn after n random volume transfers is a function of the ini-tial concentration C0 and the random transfer volumes vi in all previous stepsin the dilution sequence:LAW OF PROPORTIONATE EFFECTOtt (1990) published a simple random sequential dilution model to illustrate the0 1Soil and Environmental Chemistry36cal substance from the initial concentration C0 to some final concentrationCn results when n random pulses of fluid enter the chamber. The chambercould be a pore in or an arbitrary volume of soil, sediment, or aquifer.The sequential random dilution model (Ott, 1990) restricts the range ofeach random dilution factor: 0 < di 1. A more general formulation, knownas the law of proportionate effect (Kapteyn, 1903), imposes no such restrictionon the random scaling factors fi:arithm of a random number. Of course, it makes no difference whether the sum isbased on random numbers or the logarithm of a random number.Ott (1990) described a second example: a fluid-filled chamber (gasor liquid) of volume V and a chemical substance in the chamber at aninitial concentration C0. The chamber has two openings: an entrance andan exit. Through the entrance a random volume of pure fluid v1 enters,forcing the expulsion of an equal volume and a quantity of the chemical sub-stance v1 C0 through the exit. A random sequential dilution of the chemi-C1 v1V@ A C0 d1 C0C2 d2 C1 d2 d1 C0 Cn dn Cn1 dn dn1 d2 d1 C0 A logarithmic transformation of the product of these random dilutions yields asum of logarithmic term. Since each dilution factor di is a random number, thelogarithm of the dilution factor ln di is itself a random number:ln Cn ln dn ln dn1 . . . ln d2 ln d1 ln C0 ln Cn ln C0 Xni1ln di The Central Limit Theorem states that a sample population in which eachvalue is a sum of random numbers yields a normal distribution. You can ver-ify this by using a spreadsheet computer application to generate a large popu-lation of numbers (say, 100) in which each number is the sum of randomnumbers (say, 100 each). A plot of the frequency distribution of the numbersin this population of sums has the characteristics of a normal distribution.Conversely, if you use the spreadsheet application to generate a large popula-tion of numbers (say, 100, as before) in which each number is the product of ran-dom numbers (say, 100 each), the plot of the frequency distribution of numbersgenerated by this population of products has the characteristics of a log-normaldistribution. A logarithmic transformation of each product in the populationgenerates a sum of random numbers, entirely analogous to the sums yielding anormal distribution, except the random numbers in each sum are actually the log-C f CThe arit e a s deviation s are easily com-puted using d i r program:Chapter 1 Elements 37ni1s 1n0@1A Xni1xi 40:1 2vuuut 78:9 ppmThe geometric mean xG is simply the exponential transform of an arithmeticmean computed from the (natural) logarithm transforms of the concentrations:x 1n Xni1xi 40:1 ppms 10@1A Xn xi x 2vuuutstandar functions n any sp eadsheethmetic m an x and rithmetic tandardKB-13 15KB-12 24 48-490 2KB-11 2 48-489 27KB-10 410 48-485 5.5KB-9 22 48-118 6KB-8 17 48-158 3KB-7 5.8 48-115 7KB-6 5.3 48-63 19KB-5 3.5 KB-19 17KB-4 25 KB-18 38KB-3 120 KB-17 59KB-2 30 KB-16 95KB-1 40 KB-153528C2 f2 C1 f2 f 1 C0 Cn fn Cn1 fn f n1 f 2 f 1 C0 ln Cn ln C0 Xni1ln f i APPENDIX 1F. THE ESTIMATE OF CENTRAL TENDENCY ANDVARIATION OF A LOG-NORMAL DISTRIBUTIONThe following data set consists of chromium concentrations in 27 samples ofCanadian granite (Ahrens, 1954).Sample Cr, ppm Sample Cr, ppmG-1 22 KB-141 1 0The geometric st -arithm transform llogarithm of the eavy38c. nuclear fusion: 188 O 42He ! 2210Ne gd. positron emission: 189 F ! 01e ne3. List the number of stable isotopes for the period 3 elements (Na through Ar).Explain why some elements have more stable isotopes than others.Solutionabundance in percent.The nucleus of lithium-6 contains 3 protons and 3 neutrons. Followingthe example given in the chapter, the rest mass of the protons and neutronsin the nucleus is:The isotope mass of 63Li is 6.015122 u0.032701 u less than themass found by adding the rest mass of 3 protons and 3 neutrons. The massdifference, multiplied by 931.494 MeV u-1 and divided by 6 nucleons, isthe binding energy per nucleon for 63Li: 5.077 MeV. This value can bechecked against the value plotted in Figure 1.5.2. Complete the following nuclear reactions:a. neutron capture: 5826Fe 10n ! 5926Fe b. beta (minus) decay: 5926Fe ! 5927Co 01e ne3website, typing in the atomic number Z for Li: 3. The page also lists the iso-tope mass (relative atomic mass) of the two stable Li isotopes and their relativeerage of the differences, and taking the exponential of the square root:sG exp1n0@1A Xni1ln xi ln xG 2vuuut0B@1CAsG exp1n0@1A Xni1ln xi 2:85 2vuuut0B@1CA 3:56 ppmProblems1. Calculate the binding energy in MeV for the following isotopes: 42He,63Li,126 C ,and 136 C . Proton mass mproton is 1.007276 u, and the neutron mass mneutron is1.008865 u. Convert the mass difference to a binding energy using 931.494MeV u-1. You can obtain a complete list of isotope masses from a websitemaintained by the National Institute of Standards and Technology: http://www.physics.nist.gov/PhysRefData/Compositions/index.html.SolutionThe isotope mass for 6Li is 6.015122 u (6.015122 g mol-1) found at the NISTSodium hasElementali1andard deviation sG is computed by performing a natural logation of each chromium concentration, subtracting the naturageometric mean ln xG , squaring the difference, finding thxG exp 1n Xnln xi ! exp 2:85 17:2 ppmSoil and Environmental Chemistronly one stable isotope with an odd number of protons: 2311Na.abundances are listed on the National Physical Laboratorywebsite: habundance(1010) atomMagnesnumber oftron. Magnatoms-Mg/2Partiallysodium lessMg-26. Natope becau4. List the hal(84 < Z dances ofConstants,atomic_and5. The followi(Ahrens, 19ation fromChapter 1 Elements 39KB-6 30KB-7 33KB-8 27KB-9 34KB-10 42KB-11 10KB-12 52KB-13 51KB-14 182KB-15 630KB-16 144KB-17 94KB-18 94KB-19 2948-63 848-115 1148-158 5.548-118 2348-485 1948-489 748-490 5.6ttp://www.kayelaby.npl.co.uk/chemistry/3_1/3_1_3.html. Sodiumin the Solar System is 2.0 (10-6) 5.7 (104) atoms-Na 2.8s-H.ium has three stable isotopes: Mg-24 and Mg-26 have an evenprotons and neutrons, while Mg-25 has an unpaired (odd) neu-esium abundance in the Solar System is 3.9 (10-5) (1.1 (106).8 (1010) atoms-H).filled nuclear shells and an unpaired proton in the nucleus makestable than magnesium and Mg-25 less stable than Mg-24 andis less abundant than Mg, and Mg-25 is the least abundant Mg iso-se of isotope stability.f-life of the longest-lived isotope for each element from Po to Th90). A complete Table of the Isotopes is available on the Abun-the Elements (Kaye and Laby Tables of Physical and ChemicalNational Physics Laboratory): http://www.kayelaby.npl.co.uk/_nuclear_physics/4_6/4_6_1.html.ng data are the vanadium content of samples of Canadian granite54). Determine the geometric mean and geometric standard devi-this data set.Sample V, ppmG-1 21KB-1 75KB-2 43KB-3 200KB-4 50KB-5 7.52.3 Water Budgets 43 in the Derivation of theRetardation Coefficient Model2.1W tsthr n-ing biological availability. This chapter examines the properties and behaviorsof freshwater, both aboveground in lakes and streams and belowground,where it is confined to pores in soil and rocks. The selection of topics reflectsexposure to soil and aquifers. Residence time, regardless of aquifer chemicalproperties, influences pore water chemistry because mineral dissolution andprecipitation reactions are often slow relative to residence time. Water resi-dence time estimates require an understanding of both the water volume inconnected hydrologic environments and the water flux between thoseenvironments.Soil and Environmental Chemistry.# 2012 Elsevier Inc. All rights reserved.our primary interest: chemical hydrology.Chemical hydrology focuses on the changes in water chemistry caused byater is the primary medium that transports nutrients and contaminanough terrestrial environments and a major environmental factor determi2.4 Residence Time andRunoff Ratios 432.5 Groundwater Hydrology 452.6 Vadose Zone Hydrology 582.7 Elementary SoluteTransport Models 622.8 Summary 71Appendix 2A. Soil MoistureRecharge and Loss 71Appendix 2B. The Water-HoldingCapacity of a Soil Profile 72. INTRODUCTIONof Solute Transport 76Appendix 2E. Symbols and Units inthe Derivation of the PlateTheory Model of SoluteTransport 77Appendix 2F. Empirical WaterCharacteristic Function andUnsaturated HydraulicConductivity 79Chapter 2Soil Moisture and HydrologyChapter Outline2.1 Introduction 412.2 Water Resources and theHydrologic Cycle 42Appendix 2C. PredictingCapillary Rise 75Appendix 2D. Symbols and Units41Groundwater flow paths control the migration pathway of dissolved andsuspended substances. Flow paths above and at the water table are quitedifferent from flow paths below the water table. Changes in aquifer texturealter water flow rates and, potentially, the direction of flow. Dissolved andsuspended substances typically migrate more slowly than pore water itselfbecause interactions with the aquifer retard migration.2.2. WATER RESOURCES AND THE HYDROLOGIC CYCLEFreshwater accounts for about 0.26% of the total water on Earths surface(Table 2.1); 70% of the freshwater is frozen in glaciers and polar icecaps.The remaining 30% of the fresh terrestrial water is either stored abovegroundin lakes, rivers, and wetlands or belowground confined in the pores of soil andaquifers (water-bearing rock formations). The hydrologic cycle describes theexchanges of water between these reservoirs through precipitation, infiltra-tion, evaporation, transpiration (water vapor loss from vegetation), surfacerunoff, and groundwater discharge.TABLE 2.1 World Water Resources from MaidmentVolume, km3 Percent ofTotal{Percent ofFreshwater{Terrestrial Water 47,971,700 0.36%{Soil and Environmental Chemistry42Fresh Lakes 91,000 0.0007% 0.26%Saline Lakes 85,400 0.0006%Rivers{ 2,100 0.00002% 0.01%Wetlands{ 11,500 0.00009% 0.03%Soils{ 16,500 0.00012% 0.05%Fresh Groundwater{ 10,530,000 0.079% 30.07%Saline Groundwater 12,870,000 0.097%Biomass Water{ 1,100 0.000008% 0.003%Glaciers & Icecaps{ 24,364,100 0.183% 69.58%Oceans 13,238,000,000 99.28%Atmosphere{ 12,900 0.00010% 0.04%Total{ 13,333,956,300 100.00%Source: Data reproduced with permission from Maidment, D.R., 1993. Handbook of Hydrology.McGraw-Hill, New York, NY, pp. 1.11.15.Chapter 2 Soil Moisture and Hydrology 432.3. WATER BUDGETSHydrologists use water budgets to quantify water exchange in the hydrologiccycle. The conservation of mass ensures the total volume does not change atsteady state. The example of a lake surrounded by a catchment (watershed)serves to illustrate how a water budget is used. At steady state the lake volumedoes not change, provided we neglect daily and seasonal fluctuations:DVDt 0 2:1Steady state does not mean that the lake and its catchment are static. Waterenters the lake through mean annual precipitation P m3 y1 , groundwaterinflow Qg, in m3 y1 , and surface inflow (runoff) Qs, in m3 y1 and is lostthrough evaporation and transpiration ET m3 y1 , groundwater outflowQg, out m3 y1 , and surface outflow Qs, out m3 y1 . The annual steady-statewater budget for the lake is given by Eq. (2.2):DVlakeDt 0 P Qg, in Qs, in ET Qg, out Qs, out 2:2The rate of groundwater inflow and outflow is usually negligible when com-pared to the other exchange processes, leading to a simplified annual lakebudget where surface inflow (surface runoff and stream flow) and outfloware combined in the mean annual surface discharge Ds m3 y1 :P ET Qs, out Qs, in ET Ds 2:3You can imagine an alternative water budget for catchments where water isstored in the soil rather than aboveground in a lake or wetland. The catchmentwater budget might cover a growing season measured in months, or it mayrepresent an annual average. Water budget adds a term for soil moisture stor-age Sstorage m3 yr1 . Later, we will learn how to determine the plant-avail-able water storage capacity. Details on the calculation of soil moisturerecharge appear in Appendix 2A. Appendix 2B provides details on the calcu-lation of soil water storage capacity:P ET Ds Sstorage 2:42.4. RESIDENCE TIME AND RUNOFF RATIOSHydrologists use water budgets to estimate two important parameters of watersystems: runoff ratio Ds=P and residence time TR for water in a particular reser-voir. These parameters can be defined on many scales, ranging from the smallestcatchment to the global scale. Table 2.2 lists the runoff ratios for the continents.TABLE 2.2 Annual Continental Water Budgets and Runoff Ratios Ds=PContinent P Ds ET Ds=PAfrica 690mm 140 mm 550 mm 0.20Asia 720mm 290 mm 430 mm 0.40Australia 740mm 230 mm 510 mm 0.31Europe 730mm 320 mm 410 mm 0.44North America 670mm 290 mm 380 mm 0.43South America 1650mm 590 mm 1060mm 0.36Source: Data reproduced with permission from Lvovich, M.I., 1979. World Water Resources.American Geophysical Union, Washington, DC.Soil and Environmental Chemistry44losses of 0.61.Residence time TR is the average time a particular reservoir in a water sys-tem retains water:TR VQin VQout2:5Using the reservoir volumes listed in Table 2.1 and the flow rates in Table 2.3,we can estimate the residence time for water in the atmosphere (0.02 year or 7days), oceans (2650 years), subsurface aquifers (20,000 years), and surfaceThe average global runoff ratio Ds=P is 0.39, with evaporation-transpirationwaters (4 years).TABLE 2.3 Global Hydrologic Cycle Flow RatesProcess Flow Rate Q, km3 yr1Terrestrial Precipitation 119,000Terrestrial ET 72,600Oceanic Precipitation 458,200Oceanic ET 504,600Surface Discharge 452,000Groundwater Discharge 1200Source: Data reproduced with permission from Maidment, D.R., 1993. Handbook of Hydrology.McGraw-Hill, New York, NY, pp. 1.11.15.Chapter 2 Soil Moisture and Hydrology 45FIGURE 2.1 Lake water alkalinity increases the longer groundwater discharging into the lakeremains in contact with aquifer formations. Source: Reproduced with permission from Wolock,D.M., Hornberger, G.M., et al., 1989. The relationship of catchment topography and soil hydrau-Suppose we want to estimate the residence time for soil moisture, definedas subsurface water within the plant root zone. If we assume terrestrialevaporation-transpiration water flow comes primarily from soil (see Table 2.3)and use the global soil moisture volume listed in Table 2.1, the residence timeof soil moisture is about 0.2 years, or 70 days.Figure 2.1 illustrates the effect that groundwater residence time has onlake alkalinity. A portion of the inflow that sustains lake volume comes fromsurface runoff, and a portion comes from groundwater discharge, the latteraccounting for lake water alkalinity. As the groundwater residence timeincreases, the alkalinity of the groundwater discharge and, consequently, lakewater alkalinity increases. Alkalinity arises from the dissolution of carbonatemineralsprincipally calcite CaCO3into groundwater permeating the aqui-fer. The time scale on Figure 2.1 illustrates the time scale required for mineraldissolution reactions. Notice a 25-year residence time is still insufficient foralkalinity to reach a steady state.2.5. GROUNDWATER HYDROLOGY2.5.1. Water in the PorosphereWe can define the porosphere as that portion of the Earth surface where wefind water-filled pores. This section considers a number of parameters usedlic characteristics to lake alkalinity in the northeastern United States. Water Resour. Res. 25:829837.to characterize the porosphere. Porosity fa dimensionless numberis thefraction of the total volume occupied by pore spaces, as shown in Eq. (2.6).Related to the porosity f of porous Earth materials is the bulk density rB inEq. (2.7).f Vair VwaterVsolids Vair Vwater Vair VwaterVtotal2:6rB MdryVtotal MsolidsVair Vsolids 2:7Soil and Environmental Chemistry46Hydrologists and soil scientists use an average mineral density rmineral of 2.65Mg m-3 for the density of the rocks and rock grains that make up theporosphere, this density being the density of the mineral quartz. Porous rocks,sediments, and soils will have bulk densities rB less than 2.65 Mg m3,depending on the total porosity:f 1 rBrmineral2:8The method for measuring bulk density suggests a simple method for measur-ing gravimetric water content yM, which is simply mass loss caused by ovendrying:yM MwaterMsolids Mmoist MdryMdry2:9In many cases, soil scientists and hydrologists need to know the volume ofwater in a subsurface material, requiring conversion from gravimetric to vol-umetric water content yV :yV VwaterVsolids Vair Vwater 2:10Box 2.1 Measuring Bulk Density rBIf the sample is unconsolidated, the volume is simply the volume of a canisterdriven into in situ soil or sediment to extract the sample. A dry bulk measurementrequires the drying of the sample to eliminate pore water, which is accomplishedby drying the sample in an oven at about 100C until mass loss with further dryingis negligible. The bulk density is simply the dry mass of the sample dividedby the sample volume. The exterior of both consolidated and unconsolidatedsamples can be sealed after drying to prevent water entry, permitting volumemeasurement by immersion.Although it may not seem obvious at first, conversion from gravimetric watercontent yM to volumetric water content yV requires the bulk density rB of theEarth material and the density of water rW. Dividing a mass of a substance byits density yields the volume, as illustrated by the dimensional analysis:yVm3waterm3dry soil" # yM MgwaterMgdry soil rBrWMgdry soil=m3dry soilMgwater=m3water" #2:11Often soil scientists and hydrologists wish to determine water content relativeto the water-holding capacity, a proportion called the degree of saturation S:S VwaterVair Vwater Vwater=VtotalVair Vwater =Vtotal yf2:12Appendix 2B illustrates the conversion of gravimetric to volumetric watercontent to estimate the water-holding capacity of soil profiles.2.5.2. Hydrologic UnitsHydrologists distinguish geologic formations in the saturated (or phreatic)zone, whose water-holding capacity and hydraulic conductivities are relevantto groundwater flow (Figure 2.2). Formations that are effectively nonporous,Chapter 2 Soil Moisture and Hydrology 47FIGURE 2.2 Different aquifer formations: aquiclude, aquifuge, unconfined aquifer, and con-fined aquifer. The critical zone extends from the land surface to the lower boundary of the uncon-fined (or water table) aquifer. Source: Reproduced with permission from Environment Canada,2008. Nitrate Levels in the Abbotsford Aquifer an indicator of groundwater contamination inthe Lower Fraser Valley. Retrieved November 2, 2010 from http://www.ecoinfo.org/env_ind/region/nitrate/nitrate_e.cfm.holding negligible amounts of water and unable to conduct water, are calledaquifuges. Certain formations, usually containing significant amounts ofclay, may hold substantial amounts of water, but their low permeabilityimpedes water movement. These formations are called aquicludes. Manyhydrologists denote any formation with low permeability, regardless of poros-ity, as aquitards. An aquifer is any geologic formation, either consolidatedrock or unconsolidated sediments, with substantial water-holding capacityand relatively high permeability. An unconfined, or water table, aquifer refersto any aquifer that is saturated in its lower depths but terminates at an unsatu-rated or vadose zone in its upper reaches, the two zones being separated by awater table. A confined, or artesian, aquifer is overlain by an aquitard. Thehydrostatic pressure in a confined aquifer can be substantial, causing waterin wells drilled into the aquifer to rise above the top of the aquifer.2.5.3. Darcys LawFigure 2.3 shows the experimental apparatus used by Henry Darcy in 1856 tomeasure water flow rates QD through sand and other unconsolidated porousEarth materials. Darcy discovered that the water flow rate QD (Eq. (2.13))Soil and Environmental Chemistry48FIGURE 2.3 The experimental apparatus Darcy used to measure water flow under a hydraulicgradient through porous material. Source: Reproduced with permission from Dingman, S.L.,1994. Physical Hydrology. Macmillan, New York.Chapter 2 Soil Moisture and Hydrology 49QD /L2:13QD m3 s1 Kh m s1 A m2 h1 h2 m L m 2:142.5.4. Hydrostatic Heads and Hydrostatic GradientsThe hydraulic head h is central to Darcys Law and the dynamics of waterflow in the saturated aquifers. Hydrostatic pressure p is a component of thehydraulic head. Pressure is force per unit area and increases with depth d ina fluid. The downward-acting force in a column of fluid is simply the massof the fluid in the column times the acceleration due to gravity g. The massof the fluid at any given depth d is simply the density of the liquid r timesthe depth d, which yields the hydrostatic pressure p:phydrostatic N m2 F N A m2 mfluid Mg g m s2 A m2 phydrostatic mfluidA d d g1 rfluid Mg m3 g m s2 d m dhydrostatic phydrostaticrfluid g2:15Elementary thermodynamics from general chemistry tells us that the compres-sion or expansion of a gas involves a type of work called pressure-volumework. Pressure-volume work involving a gas is usually illustrated by a changein volume at constant pressure, but it can also occur when there is a change inpressure at constant volume. Fluid flow associated with a change in hydro-static pressure involves pressure-volume work:work p DV V Dp 2:16Any change in elevation z represents a change in potential energy. The Ber-noulli equation for fluid dynamics includes two primary contributions to thetotal hydraulic head h in groundwater systems: the pressure head that accountstaining the porous material and the difference in the hydraulic headDh between the two ends of the cylinder and inversely proportional to thelength L of the cylinder. The proportionality coefficient Kh (Eq. (2.14)) iscalled the hydraulic conductivity of the porous medium. Darcy could rotatethe cylinder to vary the difference in the hydraulic head Dh, read by measur-ing the water level in two standpipes at either end of the cylinder relative to adatum (see Figure 2.3).A h1 h2 is directly proportional to both the cross-sectional area A of the cylinder con-for pressure-volume work during water flow p= rW g and the elevation(gravitational) head z that accounts for changes in potential energy duringwater flow:htotal hhydrostatic helevation phydrostaticrW g z 2:17Hydrologists and soil scientists measure pressure relative to atmospheric pres-sure. The hydrostatic head hhydrostatic is zero at the surface of free water (Fig-ure 2.4, points A and B; Figure 2.4, points R and S). The water table in anunconfined aquifer (Figure 2.4, point R) is, by definition, the point where thehydrostatic head hhydrostatic is zero.Figure 2.4 also illustrates the difference between hydrostatic headhhydrostatic and elevation head helevation. A pressure measurement taken at thewater surface above a dam (Figure 2.4, point A) and at the water surfacebelow a dam (Figure 2.4, point B) both record atmospheric pressure, whichon our pressure gauge reads as zero ( pgauge 0):hApressure hBpressure pgagerW g 0Soil and Environmental Chemistry50FIGURE 2.4 Impounded water (upper) and an unconfined aquifer (lower) illustrating referencepoints and components of the total head (hydrostatic and elevation). The elevation of a waterlevel is denoted zA and zR, while the difference in the elevation of two water levels is denotedas zAB and zRS.Chapter 2 Soil Moisture and Hydrology 51The water at point A above the dam is at a higher potential energy due to thedifference in elevation zAB between point A and point B, so the elevation headhelevation at point A is higher than point B:hAelevation hBelevation zABThe hydrostatic pressure at point C is greater than zero and equal to the grav-itation force (i.e., weight) of the overlying water column:pChydrostatic rW g zAChChydrostatic pChydrostaticrW g zACThe total hydraulic head htotal at point C relative to point B in Figure 2.4includes contributions from both hydrostatic head hhydrostatic and elevationhead helevation:hCtotal hBtotal hChydrostatic hCelevation hBhydrostatic hBelevation hCtotal hBtotal zAC zBC 0 0 zABAs the depth zAC below the water surface increases, the hydrostatic headhhydrostatic becomes more positive at exactly the same rate as the elevation headhelevation decreases. Consequently, the total hydraulic head htotal remainsunchanged.Now, consider the saturated zone at and below the water table in Figure 2.4(points R and T). Pressure measurements taken at the water table (Figure 2.4,point R) and at the water surface of a stream in the valley bottom (Figure 2.4,point S) both record atmospheric pressure:hRhydrostatic hShydrostatic pgagerW g 0The water at point R at the water table up slope is at a higher potential energydue to the difference in elevation zRS between point R and point S, so theelevation head helevation at point R is higher than point S:hRelevation hSelevation zRSThe hydrostatic pressure at point T is greater than zero and equal to the gravi-tation force (i.e., weight) of the overlying pore water. Unlike the case shownin Figure 2.4 (point C), the hydrostatic pressure phydrostatic (and therefore thehydrostatic head hhydrostatic) at point T depends on the porosity of the aquiferand, therefore, must be measured rather than inferred from the depth zRTbelow the water table:pThydrostatic 6 rW g zRThThydrostatic pThydrostaticrW gThe total hydraulic head htotal at point T relative to point R in Figure 2.4 includescontributions from both hydrostatic head hhydrostatic and elevation head helevation:hTtotal hRtotal hThydrostatic hRhydrostatic hTelevation hRelevation hTtotal hRtotal pThydrostaticrW g 0 ! zRS zRT pThydrostaticrW g ! zSTAs the depth zRT below the water table increases, the hydrostatic headSoil and Environmental Chemistry52FIGURE 2.5 The hydrostatic gradient Dh=DL zAB=dAB between two points at the watertable of an unconfined aquifer is typically defined relative to an elevation datum. The elevationsof water levels relative to a datum are denoted zA and zB, while the difference in the elevation ofhhydrostatic becomes more positive but not at the same rate as the elevationhead helevation decreases.Darcys Law can be applied directly to the example in Figure 2.5. As youcompare Figures 2.4 and 2.5, note that the only contribution to the hydraulicgradient Dh between points A and B in Figure 2.5 is the difference in elevationbetween the two points zA zB . Following the convention adopted inFigure 2.2, the elevations of points A and B are measured relative to a datum.The hydrostatic head is zero at both points because A is located at the watertable and B is located at the water surface in the valley bottom. The dischargeqD between points A and B depends on the distance L between the two pointstwo water levels is denoted zAB.d2AB z2ABp, the hydraulic conductivity of the formation Kh, and the totalhydraulic gradient Dh:qD m s1 QD m3 s1 A m2 Kh m s1 hAhB d2ABz2ABp Kh m s1 DhDL 2:18The effect of porosity requires the direct measurement of the hydrostatic headusing either stand tubes (see Figure 2.3), which was how Darcy made themeasurement, or piezometers (Figure 2.6). Piezometers are basically standtubes that are inserted into the saturated zone at or below the water table.A piezometer has a screened opening at its lower end that allows water toenter the tube. The water level in the piezometermeasured from thescreenis the hydrostatic head hhydrostatic at the depth of the screened opening.Figure 2.7 illustrates the measurement of the hydraulic gradient whenboth points are below the water table. The hydraulic gradient Dh simplyreduces to the difference in the water levels of the two piezometers atChapter 2 Soil Moisture and Hydrology 53FIGURE 2.6 The components and placement of a piezometer used to measure hydrostatic gra-dient Dh/DL. On the left are the screen and the water level in the piezometer tube, and on the rightthe screen depth is denoted by the heavy line and the water level denoted by a heavy crossbar.Source: Reproduced with permission from Environment Canada, 2008. Nitrate Levels in the Abbots-ford Aquifer an indicator of groundwater contamination in the Lower Fraser Valley. Retrieved onNovember 2, 2010 from http://www.ecoinfo.gc.ca/env_ind/region/nitrate/nitrate_ref_e.cfm.Soil and Environmental Chemistry54points C and D. The relevance of the hydrostatic head hhydrostatic will becomeclearer when we use it to sketch hydrostatic equipotential contours and flownets in the saturated zone:C DpChydrostatic !pDhydrostatic !FIGURE 2.7 The hydrostatic gradient Dh=DL hCD=d2CD h2CDqbetween two points C and Dbelow the water table in an unconfined aquifer requires piezometer measurements. The elevationsof piezometer water levels relative to a datum are denoted hC and hD, while the difference in theelevation of two piezometer water levels is denoted hCD. The elevations of the piezometer screensrelative to a datum are denoted zC and zD.htotal htotal rW grW g hCD 2:192.5.5. Intrinsic PermeabilityThe hydraulic conductivity Kh in Darcys Law is simply an empirical param-eter. Hydrologists have derived an empirical expression (see Eq. (2.20)) forthe hydraulic conductivity Kh that attempts to separate the contributions aris-ing from the porous mediumparameter ki in Eq. (2.20) and representedby terms enclosed by the second set of brackets in Eq. (2.21)and thefluidthe terms enclosed by the second set of brackets in Eq. (2.21):Kh m s1 ki m2 rw Mg m3 g m s2 m Mg m1 s1 2:20The parameter d (see Eq. (2.21)) is the mean grain diameter and is a measureof intrinsic pore diameter, while N is a dimensionless empirical fitting param-eter. The viscosity m and density of the fluid r appear in the second set ofterms. The empirical parameter ki is called the intrinsic permeability of theporous medium and has units of area (m2).Freeze and Cherry (1979) measured the intrinsic permeability of a varietyof rock types and unconsolidated materials. The median intrinsic permeabilityChapter 2 Soil Moisture and Hydrology 55Box 2.2 Determining Groundwater Flow Using Water Table Elevations.The illustration below shows the elevation of the water table in meters (relative tomean sea level). Indicate the direction of groundwater flow on this illustration.of gravel, sand, silt, and clay ranges 9 orders of magnitude from 10-9 m2, 10-11m2, 10-14 m2, and 10-18 m2:qD N d2 r gm DhDL k r gm DhDL2:21Before we leave this section on Darcys Law, we need to discuss one finalparameter that is relevant to chemical transport in the saturated zone. The spe-cific discharge qD (Eqs. (2.18) and (2.21)) has the dimensions of distance perTo determine the direction of groundwater flow at the water table, make arough sketch of water table elevations.Water flow at the water table is downhill at right angles to the water tablecontours.Soil and Environmental Chemistry56unit time (m s-1), equivalent to a velocity, and represents the fluid velocityaveraged over the entire cross-sectional area of the measurement. The specificdischarge qD, however, is not a good representation of pore water velocitybecause a significant fraction of the cross-sectional area does not contributeto measurable water flow. There are no pores in a significant fraction of thecross-sectional area of any porous medium, and some of the pores have sucha small diameter that water flow through their combined area is negligible.Scaling the specific discharge qD by the porosity f of the porous medium pro-vides a better estimate of pore water velocity qP:qP qDf 2:222.5.6. Groundwater Flow NetsWater flow in aquifers is toward a lower total hydraulic head htotal. By way ofanalogy, imagine two gas spheres connected through a tube fitted with a valve.Gas pressure in sphere A is higher than gas pressure in sphere B. Gas will flowfrom sphere A to sphere B when the valve is opened. This occurs regardless ofwhether the gas pressure in the spheres is greater than atmospheric pressure(pgauge > patmospheric) or less than atmospheric pressure (pgauge < patmospheric).The hydrostatic pressure in the saturated zone is greater than zero(phydrostatic > patmospheric) at depths below the water table and zero, by definition,at the water table (phydrostatic patmospheric). In the next section we will learnabout water behavior in the unsaturated (vadose) zone, where the hydrostaticpressure phydrostaticand the hydrostatic head hhydrostaticare negative. Regard-less of whether the hydrostatic head hhydrostatic is positive or negative, water flowsin the direction of lower total hydraulic head htotal.Hydrologists can measure the total hydraulic head htotal at any point at orbelow the water table using piezometers (see Figure 2.6). The measuredhydraulic head htotal applies to the location of the screen at the bottom of thepiezometer. Hydrologists typically insert nests of piezometers at selected loca-tions on the land surface, each piezometer in the nest representing a differentdepth below the land surface. All measurements are relative to some elevationdatum, whether it is mean sea level (MSL) or some convenient local datum.The total hydraulic head htotal of the piezometer (see Figure 2.6) is the heightof the water level in the piezometer tube relative to the datum. The elevationhead z of the piezometer is the position of the screen, referenced to the datum.The hydrostatic head hhydrostatic ( phydrostatic=r g) at the depth of the screen is theelevation of the water level in the piezometer tube relative to the screen.These components are also illustrated in Figure 2.7. The elevation of thedatum is assigned a value of zero. Mean sea level is a very useful datum becauseland surface elevations are usually reported relative toMSL. The hydraulic gradi-ent Dh is not an absolute value and, as such, is independent of the datum.Chapter 2 Soil Moisture and Hydrology 57Figure 2.8 is an illustration adapted from Hubbert (1940) showing a landsurface and the water table below it. A nest of three piezometers is locatedto the left of the center, and the water levels in the leftmost and center piezo-meters (indicated by the crossbar) are the same; both are lower than the right-most piezometer. Water is flowing from the right piezometer toward theFIGURE 2.8 Groundwater flow follows the flow net in an unconfined aquifer. The streamlinesindicate the direction of groundwater flow. Vertical streamlines indicate groundwater divides.Note the relation between equipotential contours and piezometer water levels. Source: Repro-duced with permission from Hubbert, M.K., 1940. The theory of ground-water motion. J. Geol.48 (8): 785944.center and left piezometers because the hydraulic gradient Dh decreases inthat direction. Although the water levels are the same in the center and leftpiezometers, the screens are not at the same depth. The dashed line runningthrough the bottom of these two piezometers is an equipotential line connect-ing subsurface points with the same total hydraulic head h. The right piezom-eter indicates a higher hydraulic head and, therefore, lies on a differentequipotential contour connecting points at a higher hydraulic head.Several other dashed equipotential contours appear in Figure 2.8 radiatingoutward from the position where the water table elevation is highest (gener-ally in the uplands) and converging where the water table elevation is lowest(generally in the lowlands). The illustration also plots a set of streamlines thatintersect successive equipotential contours at right angles. The system ofhydraulic equipotential contours and streamlines constitutes a groundwaterflow net.Streamlines diverge from groundwater recharge areas and converge at dis-charge areas. A groundwater divide occurs where streamlines are vertical,centered on recharge and discharge areas. In reality, Figure 2.8 illustratestwo complete local flow cells, bordered by three groundwater divides, andportions of two more local flow cells on the left and right sides of the illustra-tion. If the illustration is expanded vertically and horizontally to include52.6. VADOSE ZONE HYDROLOGY2.6.1. Capillary ForcesCapillary forcesinteractions between thin films of water and mineralsurfacesdominate water behavior in the unsaturated or vadose zone abovethe water table in unconfined aquifers and soils. The basic principles behindcapillary forces are illustrated by a simple experiment in which the tip of asmall-diameter glass tube is inserted into a dish of water (Figure 2.9).As soon as the tip of the capillary tube touches the water surface, water isdrawn into the tube and rises to a certain level before it stops. The adhesion ofwater molecules to the glass surface and the cohesion binding water mole-cules to one another accounts for the capillary forces that draw water intosmall-diameter glass tubes. Soil pores behave like capillary tubes, drawingin water and, like the experiment illustrated in Figure 2.9, holding the waterin the pore against the force of gravity.Our simplified description of capillary forces is cast in the same languageused to describe forces in the saturated zone. The hydrostatic pressure at thewater surface in the dish is zerorelative to atmospheric pressureand incre-ases with depth below the water surface, as we have already seen. The phe-nomenon we are interested in, however, is hydrostatic pressure within thecapillary tube (or by analogy, within a small pore in the vadose zone). A clueregional trends in land surface elevation, then the features of regional ground-water flow would appear.Local groundwater flow is dominated by water table topography and dis-plays a complex pattern of local groundwater recharge and discharge areas.Regional groundwater flow is dominated by the orientation of geologic forma-tions and large-scale changes in elevation. Regional groundwater flow is morestrongly expressed in the lower depths of unconfined aquifers, while localgroundwater flow is most evident in the vicinity of the water table.The elevation of the water level in a piezometer h is, in general, not equal tothe water table elevation (see Figure 2.6) because the water level is the hydrau-lic head h corresponding to conditions at the screen opening of the piezometer.The piezometer water level in Figure 2.6 is lower than the water table, indicat-ing the hydraulic head at the bottom of the piezometer is lower than at the watertable. This condition tells us water flow is downward at the piezometer screenand the piezometer is located in a groundwater recharge area.In summary, piezometer measurements allow hydrologists to determinethe hydraulic head anywhere in an aquifer. Groundwater flow nets are mappedusing piezometer nests. Flow nets reveal seepage forces and the direction ofgroundwater flow. Environmental scientists working with hydrologists canpredict the direction and rate of contaminant migration using flow nets.Soil and Environmental Chemistry8emerges if we withdraw the capillary tube vertically from the water dish. Thehydrostatic pressure at the bottom tip of the capillary tube (point B, Figure 2.9)is zerorelative to atmospheric pressurethe same as the surface of the wateroutside the capillary tube (water table symbol indicates phydrostatic patmospheric).If the hydrostatic pressure at a distance k below the water surface (point C,Figure 2.9) is positive because of the gravitational force acting on the watercolumn above, how can the hydrostatic pressure at the bottom of the watercolumn in the capillary tube (point B, Figure 2.9) be zero?The gravitational force per unit area in unconfined water at a depth kFIGURE 2.9 The hydrostatic pressures within and below a capil-lary tube illustrate capillary rise.Chapter 2 Soil Moisture and Hydrology 59below the water surface (point C, Figure 2.9) is the compressive force we callhydrostatic pressure pC (23), reflecting the downward force of the watercolumn at the depth k. We are selecting a depth k equal to the height a ofwater rise in the capillary tube:pC rW g k > 0 2:23Consider the change in hydrostatic pressure along the vertical axis of the cap-illary from point C at depth k, through point B at the level of the water surfaceoutside the capillary, upward to point A inside the capillary at a height a. Sincethe hydrostatic pressure at any depth is uniform, and the hydrostatic pressure atthe unconfined water surface is atmospheric pressure, then the hydrostatic pres-sure at point B, pB, must be 0neglecting atmospheric pressure patmospheric:pB rW g 0 0 2:24The hydrostatic pressure at the bottom tip of the capillary tube at point B is0 regardless of whether the water is confined in the capillary tube or unconfined(outside the tube). The water in the capillary tube is suspended in the tube bycapillary forces, and those forces are balanced at the bottom tip. The force sus-pending the column of water in the capillary tube against the force of gravity isa tensional force. This means the hydrostatic pressure at the meniscus height aSoil and Environmental Chemistry60sion): ptension < patmospheric. The capillary fringe is in direct contact with thewater table where the hydrostatic pressure equals atmospheric pressure:phydrostatic patmospheric. The soil-water zone occupies the upper edge of thevadose zone and, by definition, is the vadose zone inhabited by plant roots.The soil-water zone undergoes significant changes in water content as plantsabsorb water through their roots and transpire it into the atmosphere throughtheir leaf canopy and as water infiltrates into the soil following precipitation.in the capillary tube (pA at point A, Figure 2.9) must be equal in magnitude tothe hydrostatic pressure at an equivalent distance k below the surface of thewater dish (pC at point C, Figure 2.9) but negative in sign:pA rW g a 2:25A negative hydrostatic pressure may seem counterintuitive, but the forceacting on the water is a tension force that, were it not for the cohesive forcesthat bind water molecules together, would tend to pull water molecules apart.Positive hydrostatic pressure is a compressive force that tends to push watermolecules closer together. The compressive hydrostatic force will increasethe density of water, while tensional force (caused by the pull of gravity) willdecrease the density of water in the capillary tube. Appendix 2C describeshow to predict capillary rise based on the balance of forces involved.Henceforth we will refer to the negative hydrostatic pressure (relative toatmospheric pressure) in the vadose zone as ptension to emphasize the dominantrole that tension forces play in the vadose zone. We reserve hydrostatic pres-sure phydrostatic for the saturated zone where pore water hydrostatic pressure ispositive relative to atmospheric pressure.The tension force acting on water in a capillary tube (see Eq. (2.25))depends on meniscus height a and capillary tube radius R (see Appendix2C). The water tension ptension in an unsaturated porous medium is a complexfunction of the water content yV and texture of the medium as it influencesporosity f and the mean pore radius rpore (see Appendix 2C).Soil scientists often use the symbol c Pa rather than p Pa when referringto water under tension. The International System of Units (SI) uses Pascal asthe preferred pressure unit 1N m2 1 Pa . To avoid unnecessary confu-sion, we do not use the symbol c Pa to represent water tension:Vadose Zone : ptension Pa < 0 2:262.6.2. Soil Moisture ZonesFigure 2.10 illustrates the upper edge of an unconfined aquifer. An unsatu-rated or vadose zone lies between the land surface and the water table. Lyingabove the water table is a zone, called the capillary fringe zone, where thepores are mostly saturated but the water pressure is negative (i.e., under ten-An intermediate zone often lies between the saturated zone and the soil-waterFIGURE 2.10 The unsaturated zoneChapter 2 Soil Moisture and Hydrology 61zonebelow the plant root zone and above the water tablewhere littlechange in water content takes place.Soil scientists recognize three water contents with special significance towater behavior in the vadose zone: saturation, field-capacity FC, and thewilting point WP. Saturation is self-explanatory and usually does not persistlong in upland sites but can persist at lowland sites where groundwater dis-charge occurs. Field capacity1 is the water content of a soil after gravity hasdrained as much water from the soil as possible. Soil water at field capacityis held by capillary forces against the force of gravity and, by definition,represents a water tension of approximately 10 kPa (Eq. (2.27)) or tensionhead of 1.02 m (Eq. (2.28)):pFC 10 kPa 2:27pFC 10 103 kg m1 s2 extends from the land surface to the watertable. The zone below the water table issaturated. Source: Reproduced with per-mission from Egger, A.E., 2003. TheHydrologic Cycle: Waters journeythrough time. Retrieved November 2,2010 from http://visionlearning.com/library/module_viewer.php?mid=99&l=.hFC rW g1:0 103 kg m3 9:807 m s2 1:02 m 2:28The wilting point is also self-explanatory to a degreeit being the water con-tent at which plants can no longer extract water from the soil. Needless to say,the WP of desert plants is different from plant species adapted to wetter cli-mates, so the WP is defined as a water tension of 1500 kPa (Eq. (2.29))or a tension head 153.0 m (Eq. (2.30)):pWP 1500 kPa 2:29hWP pWPrW g 1500 103 kg m1 s2 1:0 103 kg m3 9:807 m s2 153:0 m 2:301. The United States Department of Agriculture Natural Resources Conservation Service definesfield moisture capacity as the soil moisture content at a water tension of 33 kPa or 10 kPa.ptension ptension y < 0 2:326Likewise, the soil hydraulic conductivity Kh y varies with the soil-water con-tent y because the mean pore velocity decreases with pore diameter, and themaximum pore diameter filled with water decreases with water content.2.7. ELEMENTARY SOLUTE TRANSPORT MODELS2.7.1. The Retardation Coefficient ModelWater percolating downward through the vadose zone or groundwater flowthrough the saturated zone carries dissolved chemical agents. Most agentsdo not travel at the same velocity as the water because interactions with thesoil, saprolite, sediments, or aquifer retard their movement. Bouwer (1991)derived a simple expression for the retardation coefficient Rf that firstappeared as an empirical expression for solute transport through an adsorbent(Vermeulen, 1952; Higgins, 1959). The following section, using the defini-tions in Appendix 2D, recapitulates the derivation by Bouwer and evaluatesits limitations.The retardation coefficient Rf expression derived by Bouwer is applicableto both saturated and unsaturated flow. Bouwer lists a single assumption: thetimescale for water flow must be long relative to the timescale of the sorptionreaction that binds the agent to the solid phase of the soil or aquifer. In thisassumption the distribution coefficient KD is an accurate representation ofthe sorption reaction.The plant-available water content AWC in a soil is the amount of waterstored in a soil between field capacity yFC and the permanent wiltingpoint yWP:yAWC yFC yWP 2:312.6.3. The Water Characteristic Curve and Vadose ZoneHydraulic ConductivityThe soil tension ptension is a measure of how strongly capillary forces holdwater in soil pores. Water rises higher in small-diameter capillaries, whichshows that small-diameter pores hold water more strongly than large-diameterpores. As the water content of a soil decreases, water drains from the largestpores first, followed by the pores with progressively smaller diameters.Consequently, the soil tension ptension varies with the soil water content y ina manner that is characteristic of the soil or porous medium. The watercharacteristic curve reflects the unique pore size distribution of each soil:Soil and Environmental Chemistry2The retardation coefficient Rf (Eq. (2.33)) is defined as groundwatervelocity divided by agent velocity or, alternatively, the distance groundwaterW St (Figure 2.11, right):Rf LWLS2:33LW qD t 2:34Consider a cylindrical volume of soil or aquifer centered on a streamline of waterflow (see Figure 2.11). The base of the flow cylinder has an arbitrary area A. Thetravels L (Eq. (2.34)) divided by the distance substance S travels L in timeFIGURE 2.11 Flow paths (streamlines) tracing groundwater movement through an unconfinedaquifer (left). Each streamline forms the axis of a cylindrical volume element. The retardationcoefficient model represents interactions between the solute and aquifer delaying movement ofa solute S, resulting in a shorter travel distance LS than groundwater LW during time interval t.Chapter 2 Soil Moisture and Hydrology 63total mass of agent S entering the volume during a time interval t equals the prod-uct of the concentrationCS of agent S dissolved inwater and the volume swept outby water flowing along the streamline during time t. This volume is proportionalto the distancewater flows through the aquifer during time t.The volumetricwatercontent yV makes this expression valid for both saturated and unsaturated flow:mtotalS Mg LW m A m2 yV CS Mg m3 mtotalS LW A yV CS 2:35The total dissolved mass of agent S in the flow cylinder is the product of con-centration CS and the volume swept out by solute flowing along the axis of theflow cylinder during time t. This volume is proportional to the distance LS thatagent S travels through the aquifer during time t:mmS Mg LS m A m2 yV CS MgS m3 mmS LS A yV CS 2:36The total mass of agent S retained by solid aquifer during time interval t issimply the difference between the total mass in the flow cylinder mtotalS andthe dissolved mass mmS . Designating the dissolved agent as mobile m and the6fm3m3 Vw VaVw Va Vs VvoidsVtotalyVm3m3 VwVw Va Vs VwVtotalKD r KD r yVLWLS Rf 1 KD rbulkyV 2:41The retardation coefficient Rf applies to both saturated and unsaturated flow, theformer using porosity f and the latter using the volumetric water content yV : KD LW LS yVLS rbulk2:40Equation (2.40) is rearranged to yield the retardation factor Rf as defined bythe ratio Lw=LS:LW yV LS yV KD LS rbulkLW LS 1 KD rbulk The sorption coefficient KD is the ratio between sorbed and dissolved concen-trations of agent S in the flow cylinder: qS and CS, respectively:KD qSCS 1CS LW LS yV CSLS rbulk qS LW LS yV CSLS rbulk2:39solid aquifer is the product of the volume accessible to agent S during timeinterval t and the bulk density rB of the aquifer:maquifer Mg LS m A m2 rbulk Mg m3 2:38The total concentration of agent S immobilized through sorption by solid aquiferin the flow cylinder qS is msS divided bymaquifer. The arbitrary area A cancels out:qS msSmaquifer AA LW LS yV CSLS rbulkaquifer-bound agent as stationary s allows us to use a common set of symbolsfor the retardation coefficient and plate theory models of solute transport:msS mtotalS mmS LW LS A yV CS 2:37The aquifer (adsorbent) mass maquifer in the flow cylinder encompassed by dis-tance LS is needed to determine the sorption coefficient KD. The mass of theSoil and Environmental Chemistry41 Bf 1 ByV RfChapter 2 Soil Moisture and Hydrology 65Box 2.3 Estimating the Retardation Coefficient for a Soil Based on ItsPropertiesA soil from Illinois has a bulk density of 1.34 Mg m3 and a porosity of 0.49.Calculate the saturated-zone retardation coefficient Rf, for cyanazine, given aKD 12 m3 Mg1 for cyanazine adsorption by the soil.Rf 1rB KDf 1 1:34Mg m3 12 m3 Mg1 0:49 33:8Box 2.4 Estimating Contaminant Movement Based on Soil Properties andThe retardation coefficient model assumes the dissolved agent concentrationis uniform everywhere behind the solute front and zero in advance of the sol-ute front (see Figure 2.11). The plate theory model uses multiple sequentialpartitioning to represent dispersion at the solute front.2.7.2. Plate Theory: Multiple Sequential PartitioningAnother model for solute transport comes from the field of separation chemistry,where it is known as the plate theorymodel. Plate theory is used to model affinitychromatography that relies on the partitioning of compounds dissolved ina mobile liquid phase onto a stationary phase; the mobile phase flows through acolumn filled with the porous stationary phase. The migration of the compound isdetermined by its relative affinity for the mobile and stationary phases. Plate the-ory uses a discrete representation of the flow cylinder (Figure 2.12)dividingthe cylinder into n cylindrical sections or plates of equal lengthwith waterthe Retardation CoefficientEstimate the depth of cyanazine leaching from the soil surface after a 5 cm rainfall(assume no runoff or evaporation). The soil has a porosity of 0.49 and a volumet-ric water content of 0.25 at field capacity.Since the water content is not given, we will assume that the water content ofthe soil is 0.25, the water-holding capacity at field capacity. A 5 cm rainfall willsaturate the soil to a depth of 5.0/0.25 20 cm. Since the depth of water move-ment is 20 cm, the depth of cyanazine leaching is at least that depth divided bythe retardation coefficient.Rf LwaterLcyanazine 65:3Lcyanazine Lwater65:3 20 cm65:3 0:30 cmFIGURE 2.12 Flow paths (streamlines) tracing groundwater movement through an unconfinedaquifer (left). Each streamline forms the axis of cylindrical volume element. Plate theory dividesthe flow cylinder into a series of plates of thickness Lp. Groundwater travel distance LW during timeinterval t is equivalent to LW n Lp. Solute S undergoes partitioning between water and aquifer ineach plate before water movement carries a fraction of dissolved solute to the next plate.Soil and Environmental Chemistry66being the mobile phase and soil or aquifer material being the stationary phase.This model assumes that equilibrium partitioning is established in each platebefore the fluid carries dissolved agent to the next plate.Figure 2.13 illustrates the partitioning that occurs in plate 1 when the dis-solved agent enters the first of a sequence of plates. A separatory funnel illus-trates the agent partitioning that occurs in each plate; the upper solution is themobile phasethe solution transferred to the next separatory funnel in eachstepand the lower solution is the stationary phase.FIGURE 2.13 Partitioning of a solute in plate 1 (represented by a separatory funnel): initial statebefore partitioning (left), mixing of two phases (middle), and final state after partitioning (right).The volume transferred is n 0.Chapter 2 Soil Moisture and Hydrology 67msS1j1jinitial 1 a m0Final concentrations for the mobile and stationary phases in funnel 1 appearfollowing and in Figure 2.14 (plate 1, upper right): njp 1j1 :mmS 1j1 jfinal a 1 a m0msS1j1jfinal 1 a 1 a m0 1 a 2 m0As before, partitioning occurs during mixing (Figure 2.14, upper middle andlower middle), with the resulting agent concentrations in funnel 1 (Figure 2.14,plate 1, upper right) and funnel 2 (Figure 2.14, plate 2, lower right). Noticeferred; consequently the initial stationary phase agent concentration (Figure 2.14,plate 1, upper left) is the same as final stationary phase concentration inFigure 2.13 (right). Initial concentrations for the mobile and stationary phasesin funnel 1 appear below and in Figure 2.14 (plate 1, upper left): njp 1j1 :mmS1j1jinitial 0msS0j1jinitial 0Partitioning during mixing of the two phases (Figure 2.13, middle), where thetotal volume accessible to the agent is the sum of the stationary and mobilephases, is vplate vm vs.m0vm vsThe final state after partitioning (Figure 2.13, right) consists of a fractiona m0 of the agent in the mobile phase m and the remainder 1 a m0 inthe stationary phase s.Figure 2.14 illustrates the transfer of the mobile phase from the firstseparatory funnel (plate 1) to the second separatory funnel (plate 2). Thetransfer illustrated in Figure 2.14 is equivalent to water movement to the nextin the sequence of plates, carrying agent to the next plate.Rather than tracking concentrations, as in Figure 2.13, Figure 2.14 displaysthe agent fraction in each phase. Fresh solvent containing no dissolved agentreplaces the mobile phase volume in the first funnel (Figure 2.14, plate 1, upperleft), while the stationary phase in the second funnel initially contains no agent(Figure 2.14, plate 2, lower left). The stationary phase in funnel 1 is not trans-in the mobile (upper) phase m; the stationary (lower) phase s does not containany agent. The initial mass of agent added is m0. The index njp 0j1 indicates that the agent has not advanced beyond the first plate (volume trans-fer index n 0), and the concentrations apply to the first plate p 1.mmS0j1jinitial m0The initial state before partitioning (Figure 2.13, left) consists of the agentthe relative partitioning is the same as in Figure 2.13.6 Soil and Environmental Chemistry8One more transfer (n 1) will suffice to establish the pattern. Thisrequires adding a third funnel: adding fresh mobile phase solvent to funnel 1,transferring the final mobile phase from funnel 1 (Figure 2.14, plate 1, upperright) to funnel 2, and transferring the mobile phase from funnel 2 (Figure 2.14,plate 2, lower right) to funnel 3. The stationary phases in funnel 1 (Figure 2.14,plate 1, upper right) and funnel 2 (Figure 2.14, plate 1, lower right) remain inplace, which means the stationary phase in funnel 3 initially contains no agent.After partitioning, the mobile and stationary phases appear in Table 2.4.FIGURE 2.14 Partitioning of a solute in funnel 1 (plate 1) and funnel 2 (plate 2): initial statebefore partitioning (left), mixing of two phases (middle), and final state after partitioning (right).The volume transferred is n 1.TABLE 2.4 Initial (before Partitioning) and Final (after Partitioning)Distribution of Agent between Mobile and Stationary Phases afterVolume Transfer n 2 for Plate 1, Index 2 1j ; Plate 2, Index 2 2j ; andPlate 3, Index 2 3j Initial FinalmmS 2j1 initial a 0msS1j1 mmS 2j1 final a 1 a 2 m0 a 1 a 2 m0msS 2j1 initial 1 a 0msS 1j1 msS 2j1 final 1 a 1 a 2 m0 1 a 3 m0Chapter 2 Soil Moisture and Hydrology 69mmS 2j2 initial a mmS1j1 msS1j2 mmS 2j2 final a 2 a 1 a m0 2 a2 1 a m0msS 2j2 initial 1 a mmS1j1 msS1j2 msS 2j2 final 1 a 2 a 1 a m0 2 a 1 a 2 m0mmS 2j3 initial a mmS1j2 0 mmS 2j3 final a a2 m0 a3 m0msS 2j3 initial a mmS 1j2 0 msS 2j3 final 1 a a2 m0 a2 1 a m0If you were to proceed to volume transfer n 3, you would discover that theamount of agent in each plate follows a binomial expansion of the distribution ofa and (1 a), as shown in Table 2.5. This was the result reported by Martin andSynge (1941) in their landmark paper on the theory of chromatography:B n,k n! 1a nk a kk! nk ! ! n!k! nk ! binomial coefficient 1a nk a k 2:42TABLE 2.5 Total Agent Mass after Volume Transfer n 3 for Plate 1,Index 3 1j ; Plate 2, Index 3 2j ; Plate 3, Index 3 3j , and Plate 4, Index 3 4j FinalmmS3 1j msS3 1j 3! 1a 30 a 00! 30 ! m0 1 a 3 m0mmS3 2j msS3 2j 3! 1a 31 a 11! 31 ! m0 3 1 a 2 a m0mmS3 3j msS3 3j 3! 1a 32 a 22! 32 ! m0 3 1 a a2 m0mmS3 4j msS3 4j 3! 1a 30 a 00! 30 ! m0 1 a 3 m0The index n represents the number of volume transfers that advance theagent through a series of plates (funnels in this illustration), p is theplate index p k 1; 0 k n , and a represents the dimensionless frac-tion of total agent in each plate that partitions into the mobile phase (seeAppendix 2E).The binomial expansion is based on a discrete model of solute flow through aflow cylinder (see Figure 2.12). The flow cylinder is divided into a series of dis-crete increments representing water (and solute movement) as discrete advancesindicated by the volume transfer index n. The binomial distribution probabilityfunction defines the probability of the agent appearing in some plate p n,wheren is the number of plates through which the mobile phase has advanced, equiva-lent to LW in the retardation coefficient model (see Figure 2.12).Figure 2.15 plots agent distributions predicted by plate theory for three dif-ferent distances LW. Plate theoryusing a distribution coefficient a equiva-lent to the inverse of the retardation coefficient a 1=Rf (Appendix 2E)yields an agent distribution with the highest concentration being in the platecorresponding to LS a n Lplate .The retardation coefficient model would set LW n Lplate and, given the Soil and Environmental Chemistry70retardation coefficient Rf used in Figure 2.14, LS n Lplate =Rf . Plate the-ory, using a distribution coefficient a equivalent to the retardation coefficientRf used in Figure 2.14, yields a probability distribution with a most probablevalue corresponding to LS a n Lplate . Plate theory offers a more accuraterepresentation of solute movement and dispersion as it advances along theflow cylinder.FIGURE 2.15 Solute probability distributions for three different water advancement distances:2 Lplate, 10 Lplate, 20 Lplate for a distribution coefficient a R1f .estiFintheChapter 2 Soil Moisture and Hydrology 71saturated zones caused by chemical interactions with the aquifer.APPENDIX 2A. SOIL MOISTURE RECHARGE AND LOSSExample 1-AVegetation at the North Carolina Agricultural Experiment Station inOxford used an average 4.2 mm of water per day during May 2008. The soilsnear Oxford are about 60 cm deep and store 0.437 cm of water per cm of soildepth. At the beginning of May, the soil in the watershed held an average of0.412 mm of water per mm of soil depth. Predict the net soil storage at Oxfordat the end of May after a monthly total precipitation of 66.9 mm.Precipitation: P 66:9 mmEvapotranspiration: ET 30 d 4:2 mm d1 126 mmTotal soil storage: Sstorage 600 mmdepth 0:437 mm mm 1depth 262 mmNet soil storage: Sstorage 600 mmdepth 0:025 mm mm 1depth 15 mmSurface discharge: Ds P Sstorage ET 66:9 mm 141 mm 74 mmThe water budget is negative, indicating a loss of soil moisture.74 mm600 mmdepth 0:123 mmmmdepth The average soil moisture is drawn down by soil moisture loss throughevapotranspiration.0:412 0:124 mm mm1depth 0:289 mm mm1depthThe North Carolina Agricultural Station at Oxford reported an average soilmoally, this chapter introduced two elementary transport models that predictretardation of solute migration along flow paths with both the vadose andraulic conductivity (Appendix 2F). Darcys Law provides a means tomate pore water velocity that, in turn, influences solute transport rates.2.8. SUMMARYResidence time, water-holding capacity, groundwater flow paths and rates, andtransport models all contribute to our capacity to predict the impact of aquiferproperties onwater chemistry. This chapter introducedwater budgets as ameansto estimate groundwater residence time, a key factor in determining groundwa-ter chemistry. Changes in hydraulic head within the saturated zone determinegroundwater flow paths that vary at several spatial scales, although environmen-tal chemists are most interested in local flow paths. Variation in water content inthe vadose zone influences water retention by capillary forces and unsaturatedhydisture content of 0:350 mm mm1depth on May 30, 2008.mm of soil depth. At the beginning of June, the soil in the watershed holdsan average of 0.2 mm of water per mm of soil depth. Predict surface dischargeinto Gordon Creek during a month when 306 mm of precipitation falls.Precipitation: P 306 mmEvapotranspiration: ET 30 d 3:3 mm d1 99 mmTotal soil storage: Sstorage 500 mmdepth 0:4 mm mm 1depth 200 mmNet soil storage: Sstorage 500 mmdepth 0:2 mm mm 1depth 100 mmSurface discharge: Ds P Sstorage ET 306 mm 199 mm 107 mmRoughly one-third of the rainfall during this particular June appears asrunoff into Gordon Creek.HSoil and Environmental Chemistry72To estimate the total available water-holding capacity (AWC) of the soilprofile, begin by converting the gravimetric water of each horizon (seeTable 2B.1) into the plant-available mass water content for each horizon(Table 2B.2). Plant-available water is the water content at field capacity (pFC rB Mgdrysoil m3 A 030 1.28 0.28 0.20 0.08B 3070 1.40 0.30 0.25 0.15C 70120 1.95 0.20 0.15 0.051ym MgwaterMgdrysoilorizon Depth, cm Bulk density, 10 kPa 100 kPa 1500 kPaABLE 2B.1 Gravimetric Water Contents ym as a Function of Tension (kPa)nd Bulk Density rB of a Soil Profile APPENDIX 2B. THE WATER-HOLDING CAPACITY OF A SOILPROFILEExample 1-BTable 2B.1 lists the physical and water retention data for a soil.TaExample 2-AThe vegetation covering the 200 km2 Gordon Creek watershed in DaneCounty, Wisconsin uses an average of 3.3 mm of water per day during a typi-cal June. The average soil depth is 50 cm and can store 0.4 mm of water per0 kPa) minus the water content at the wilting point (pPWP 1500 kPa).The available water content is not the same for each horizon, and, further-more, each horizon differs in thickness. The AWC for the profile is the cumu-lative AWC accounting for the contribution from each horizon.Horizon A: The A-horizon bulk density rAB is 1.28Mgdrysoil m3. ConversionDepth, cm ym, FC ym, PWP ym,AWC030 0.28 0.08 0.203070 0.30 0.15 0.1570120 0.20 0.05 0.15yV m3dry soil4 5 0:20Mgdry soil4 51:00@ AMgwater=m3water4 5yAV 0:256 m3water m3dry soilImagine a volume of soil with an area of 1 m2 and a depth equal to theA-horizon: 30 cm 0.3 m. Multiplying the volumetric water content yAV timesthe volume of the A-horizon yields the available water volume V for theA-horizona volume equivalent to a water depth of 0.077 meter for everysquare meter of soil (Table 2B.3).TABLE 2B.3 Available Water Content of a Soil ProfileDepth, cm rB Mgdrysoil m3 yV,AWC m3water m3drysoilh iAWC cmwater from gravimetric to volumetric units requires Eq. (2.11): multiplying the gravi-metric water content by the soil bulk density yields the volumetric water content.A m3water2 3Mgwater2 31:280 1Mgdry soil=m3dry soil2 3TABLE 2B.2 Derived Gravimetric Water Contents (Field Capacity,Permanent Wilting Point, Available Water) of a Soil ProfileChapter 2 Soil Moisture and Hydrology 73dAwater 0:256mwatermdry soil2435 0:3 mdry soil dAwater 0:077 mwater030 1.28 0.256 7.73070 1.40 0.210 8.470120 1.95 0.293 14.6Total Profile 30.7for the profile is the cumulative AWC accounting for the contribution fromeach horizon.HorizonA:The A-horizon bulk density rAB is 1.25Mgdrysoil m3. Conversionfrom gravimetric to volumetric units requires Eq. (2.11): multiplying the gravi-metric water content by the soil bulk density yields the volumetric water content.yAVm3waterm3dry soil2435 0:19 MgwaterMgdry soil2435 1:251:000@1A Mgdry soil=m3dry soilMgwater=m3water2435yAV 0:24 m3water m3dry soilSoil and Environmental Chemistry74Multiplying the volumetric water content of each horizon yhorizonV times thevolume of each horizon (depth dhorizonsoil per square meter) yields the availablewater depth dhorizonwater . The volumetric water content of 0:24 m3water m3dry soil isequivalent to water depth of 0.24 meter for every meter of A-horizon (or0.12 meter of water for an A-horizon 0.5 meter in depth).dAwater 0:24mwatermdry soil2435 0:5 mdry soil dAwater 0:12 mwaterity (AWC) in centimeters of water for the entire soil profile.The available water content and thickness of each horizon vary. The AWCTABLE 2B.4 Gravimetric Available Water Holding Capacity and Bulk DensityrB of Each Horizon (A: 050 cm, B: 50135 cm, A: 135150 cm) in a Soildsoil cmsoil rB Mgdry soil m3total ym,AWC Mg3water Mg3dry soilh i050 1.25 0.1950135 1.45 0.15135150 1.55 0.13In fact, the plant-available water content of the A-horizon of this soil is equiv-alent to a water depth of 0.077, or 7.7 cm, regardless of area. There is practicalvalue in expressing water content this way. A 7.7 cm rainfall would saturatethe A-horizon AWC of this soil because the rainfall is expressed as a depthregardless of area.Example 2-BTable 2B.4 lists the physical and water retention data for the Otter soil(Dane County, Wisconsin). Estimate the total available water-holding capac-The AWC of the remaining horizons and the total profile appear in Table 2B.5.TABLE 2B.5 Available Water Content of the Entire Soil ProfileDepth, cm yV,AWC m3water m3dry soilh iAWC cmwater 050 0.24 12.050135 0.22 18.5135150 0.20 3.00150 33.5Chapter 2 Soil Moisture and Hydrology 75gravitational acceleration.Fgravitational mliquid g r V liquid g r pr2 l liquid gThe upward force results from the surface tension of the liquid g at the air-liquid interface. The surface tension g is a force that acts at an angle relativeto the vertical tube known as the contact angle y and is distributed along thecircumference of the capillary tube 2pr. The surface tension g is a property ofthe liquid, while the contact angle y depends on the adhesion between theliquid and the material from which the tube is composed.Fcapillary gliquid 2pr cosyAt equilibrium, the two forces are equal and opposite, enabling us to solvefor the capillary rise l in a round tube as a function of the radius of the tube r,A 12.0 cm rainfall would saturate the A-horizon AWC of this soil becausethe rainfall is expressed as a depth regardless of area.APPENDIX 2C. PREDICTING CAPILLARY RISELiquid in a capillary tube (Figure 2C.1) with radius r rises until the forcesacting on the liquid in the tube are balanced at height l. The downward forceis simply the gravitational force on the column of liquid: liquid mass timesthe density of the liquid r, the surface tension g, and the contact angle y.FIGURE 2C.1 The contact angle y ofwater in a capillary tube is related tothe meniscus radius R and diameter ofthe capillary tube r.Fgravitational Fcapillary rliquid pr2 l g gliquid 2pr cosyThe contact angle y for water and glass is approximately 0 and cos y 1.l 2 gwaterrwater g rFigure 2C.1 shows that the meniscus has a radius R that is greater than orequal to the radius of the capillary tube r. Simple geometry relates the radiusof the meniscus R and the capillary tube radius r to the contact angle y.APPENDIX 2D. SYMBOLS AND UNITS IN THE DERIVATIONOF THE RETARDATION COEFFICIENT MODEL OF SOLUTESoil and Environmental Chemistry76yV m3 m3 Volumetric water content of porous medium (yV f in thesaturated zone)rmineral Mg m3 Mineral density (2.65 Mg m3 )rB Mg m3 Bulk densityLw m Distance water travels in time tLS m Distance dissolved agent S travels in time tf m3 m3 PorosityTRANSPORTDerivation of the Retardation Coefficient Model relies on the followingexpressions. The bulk density rB is a function of the porosity f, which typi-cally assumes a mineral density rmineral equal to the density of quartz: 2.65Mg m3.rB 1 f rmineralAgent S distributes itself between the mobile water phase (dissolved state) andthe stationary solid phase (sorbed state) according to the following distribu-tion coefficient KD expression:KD qSCSTABLE 2D.1 Symbols and Units Used to Derive the Retardation CoefficientModelSymbol Units DefinitionCS Mg Mg1 Dissolved concentration of agent SPlate theory divides the flow cylinder into a series of identical cylindricalplates with a cross-sectional area A and length Lplate.vplate A LplateThe aquifer mass maquifer (stationary phase mass) in each plate is the productof the plate volume vplate and the bulk density of the aquifer rB.maquifer mplate A Lplate rBThe mobile phase volume vm in each plate along the flow cylinder is theproduct of the plate volume vplate and the volumetric water content of theaquifer yV .vm A Lplate yVThe following two expressions define the mass concentration of agent bound tothe stationary-phase aquifer qs and the volume concentration of agent dissolvedin mobile-phase water Cm. Plate theory adds two indices: the plate index (p)and the volume-transfer index (n). The latter tracks the advancement of agentdissolved in the mobile phase through the flow cylinder: 0 n p:qSnjp msSnjpmaquifermmSn pj coefficient KD expression used in the retardation coefficient model.KD qSCSDerivation of the plate theory model relies on the following expressions.Agent S distributes itself between the mobile water phase (dissolved state)and the immobile solid phase (sorbed state) according to the same distributionKD fOC KOCAPPENDIX 2E. SYMBOLS AND UNITS IN THEDERIVATION OF THE PLATE THEORY MODELOF SOLUTE TRANSPORTNeutral organic agents associate with a specific component of the solid phase:the organic matter coating the mineral grains (cf. Natural Organic Matter &Humic Colloids and Adsorption & Surface Chemistry). This specific interac-tion allows us to define the distribution coefficient KD in terms of the organiccarbon content of the soil or aquifer fOC and a universal distribution coeffi-cient for the sorption of neutral organic compounds by natural organic matterin the soil or aquifer KOC.Chapter 2 Soil Moisture and Hydrology 77CSn pj vmCombining the distribution coefficient expression with those defining the massand volume concentrations of the agent, we arrive at the following expressionthat relates the mass of agent S bound to the stationary phase msSn pj to theagent mass dissolved in water mmSn pj using the distribution coefficient KD:msSn pj KD maquifervm mmSn pj Plate theory partitions the chemical agent between mobile phase (water) andstationary phase (aquifer) in each plate using the dimensionless coefficient a.a mmSnjpmmSnjp msSn pj Plate theory coefficient a is related to the distribution coefficient commonlyencountered in environmental chemistry bym m KD maquifer m Soil and Environmental Chemistry78through n platesvplate m3 Plate volumevm m3 Water (mobile phase) volume per platemaquifer Mg Aquifer (stationary phase) mass per platerB Mg m3 Bulk density of aquifermmSn pj Mg Mass of mobile (dissolved) agent in plate p followingthe water advancement through n platesmSn pj a mS njp vm mS njp a 1 KD maquifervm 1The dimensionless plate theory distribution coefficient a is the inverse ofthe dimensionless retardation coefficient Rf (Eq. (2.42)). Recognizing thatplate volume is arbitrary leads us to replace maquifer with rB and vm with yVwith the result: Rf a1TABLE 2E.1 Symbols and Units Used to Derive the Plate Theory ModelSymbol Units Definitionp Plate index 1 p n 1n Volume transfer or agent advancement indexn Lplate m3 Distance water and agent S travels after advancingContinuedAPPENDIX 2F. EMPIRICAL WATER CHARACTERISTICFUNCTION AND UNSATURATED HYDRAULICTABLE 2E.1 Symbols and Units Used to Derive the Plate Theory ModelContdSymbol Units DefinitionmsSn pj Mg Mass of stationary (sorbed) agent in plate p followingthe water advancement through n platesa Dimensionless fractional distribution coefficientKD m3 Mg1 Distribution coefficientChapter 2 Soil Moisture and Hydrology 79soil texture classes. The key variable is the degree of saturation S.S yVf The two empirical functions estimate the absolute value of tension headhtension S j j and the unsaturated hydraulic conductivity Kh S .htension S j j hSj j Sb Kh S Kh sat Sc; c 2b 3TABLE 2F.1 Hydraulic Parameters Based on Soil (Soil and Environmental Chemistry80(225 g empty) with a tight-fitting lid. The can of soil is weighed (1209.0 g fieldmoist) and dried with the lid removed in an oven until it ceases to lose weight.The weight of the dried can with soil (including the lid) was 1005.0 g. Calculatethe gravimetric water content yM of the field moist soil.SolutionThe gravimetric water content yM of the field moist soil is the water loss ondrying divided by the mass of the dry soil. The mass of the dry soil mustaccount for the mass of the container.yM 1209 1005 moisture1005 225 dry soil 204 gmoisture780 gdry soil 0:26 gmoisture g1dry soilCalculate the bulk density rB of the oven-dried soil.SolutionThe bulk density rB of the oven-dried soil is the mass of dry soil divided by thesoil volume: the volume of the cylindrical sample container.Problems1. A cylindrical core (L 20 cm, r 3 cm) of the soil from problem 1 was recov-ered from the field site in Madison County, Iowa, and placed in a metal canSource: Data reproduced with permission from Clapp, R.B., and G.M. Hornberger, 1978. Empiricalequations for some soil hydraulic properties. Wat. Resour. Res. 14 (4), 601604.TABLE 2F.1 Hydraulic Parameters Based on Soil (tChapter 2 Soil Moisture and Hydrology 81Which way is the water flowingupward from the 30 cm depth to the15 cm depth or downward from the 15 cm depth to the 30 cm depthat eachmeasurement? Instead of using MSL as the elevation datum, set the datum atyV,AWC 48 cmsoil watercmsoil@ A 27 cmsoil watercmsoil@ AyV,AWC 15 cmwater3. Two tensiometers were inserted into the soil on the University of WisconsinMadison campus (elevation 281.9 m above MSL) to a depth of 15 cm and30 cm, and measurements of the tension head were recorded three times.the 30 cm depth: zelevation 30 0.Horizon rB Mgdry soil m3 10 kPa 100 kPa 1500 kPaA, 048 cm 1.49 0.29 0.22 0.14B, 48145 cm 1.38 0.31 0.25 0.19C, 145225 cm 1.33 0.32 0.25 0.16Determine the plant-available water-holding capacity of the vadose zone ofthis soil, reporting the water-holding capacity as centimeters of water per unitarea of soil.SolutionThe available water-holding capacity AWC is the difference between the watercontent at field capacity FC and the water content at the wilting point WP.ym,AWC ym, FC ym,WPym,AWC ym,10 kPa ym,1500 kPaConversion from gravimetric to volumetric water content requires multiplyingthe former by the ratio of bulk density to water density. Since the water table isin the B-horizon at a depth of 75 cm, there is no need to calculate the AWC forthe C-horizon.yAV ,AWC 1:49 Mg m3 0:29 0:14 1:00 Mg m3 0:22 m3waterm3soil 0:22 cmwatercmsoilyBV 1:38 Mg m3 0:31 0:19 1:00 Mg m3 0:17m3waterm3soil 0:17 cmwatercmsoilThe total AWC for the vadose zone accounts for the thickness of each horizonabove the water table.yV,AWC 48 cmsoil yAV ,AWC 75 cmsoil 48 cmsoil yBV,AWC 0:22 cm0 10:17 cm0 1divide. The soil has moderately low permeability and is considered poorlydrained. The water table is located at a depth of 75 cm.Mass Water Content ym at DifferenWater Tensions ptension.3822:65 Mg m Rf 1KD rBf0@1ARf 112 m3 Mg1 1:34 Mg m3 0@1A 33:50:49f 1 rBrS0@1Af 1 1:34 Mg m3 0@1A 0:494and a cyanazine sorption coefficient KD of 12m Mg . Cyanazine is aherbicide. Calculate the porosity f and cyanazine retardation coefficient Rffor this soil.SolutionThe soil has a porosity of 0.49.higher than the 15 cm depthbecause the soil is much drier at that depthand timeand water moves upward.4a. A soil from Johnson County, Illinois has a bulk density rB of 1:34Mg m33 1Sampling Depths1 htotal 15 > htotal 30 downward2 htotal 15 < htotal 30 upward3 htotal 15 > htotal 30 downwardWhen recording 2 is made, however, the total head at the 30 cm depth isRecording Relative Total Head Water Flow between1 13 cm 17 cm2 34 cm 18 cm3 5 cm 20 cmSolutionCalculate the total head at the three individual recordings by adding thetension and elevation heads.htotal htension zelevationRecording htension 15 htension zelevation htension 30 htension zelevation1 13 cm 2 cm 17 cm 17 cm2 34 cm 19 cm 18 cm 18 cm3 5 cm 10 cm 20 cm 20 cmWater flows in a direction that lowers the total head. When recordings 1 and 3are made, water flows downward from the 15 cm depth to the 30 cm depthbecause the total head is lower at the 30 cm depth at those two times.Depth 15 cm 30 cmElevation 15 cm 0 cmRecording htension 15 htension 30 Soil and Environmental ChemistryChapter 2 Soil Moisture and Hydrology 83htension, 1 hSj j Sb1 12:1 0:63 4:05htension, 1 77:2 cm 0:772 mhtension, 2 hSj j Sb2 12:1 0:38 4:05htension, 2 611 cm 6:11 m5b. Use the empirical hydraulic conductivity function Kh S of Clapp andHornberger (1978) to determine the hydraulic conductivity for water move-ment between these two points.Kh S Kh sat S 2b3 SolutionyV , 2 0:15m3water m3dry soil at an elevation z2 3:5 m above the water table.Use the empirical water characteristic function in Appendix 2F to determinethe tension head htension S at both points.S yVf0@1Ahtension S j j hSj j SbSolutionDetermine the degree of saturation S at each point using the empirical para-meters for fine-sand texture.S1 yV , 1f0@1A 0:250:3950@1A 0:63S2 yV , 2f0@1A 0:150:3950@1A 0:38Use the empirical water characteristic function to estimate the tension headhtension S at each point.4b. Calculate how deep cyanazine applied at the surface of this soil will migratein this soil after a 5 cm rainfall (assume no runoff or evaporation).SolutionSince the water content is not given, assume that the water-holding capacityof the soil is equal to the porosity f. This means 5 cm of water will penetrate5/0.49 10.1 cm.Lcyanazine LwaterRfLcyanazine Lwater33:5 10:1 cm33:5 0:30 cm5a. The volumetricmoisture content of a fine-sand soil is yV, 1 0:25 m3water m3dry soilat an elevation z1 3:0m above the water table andThe soil water contents is different at points 1 and 2. We can either computethe conductivity at the two points, using the water content at each point, andtake the mean, or use a mean water content to estimate the unsaturatedhydraulic conductivity. Using the latter: yV,mean 0:20m3water m3dry soil .Kh S Kh 0:200:3950@1A Kh 0:51 Kh 0:51 1:76 102 0:51 2 4:05 3 Kh 0:51 1:76 102 0:51 11:1 Kh 0:51 105 cm s1Soil and Environmental Chemistry84DhDz 0:5 htension, 2 0:0 htension, 1 0:5 0:0 DhDz 0:5 6:1 0:0 0:8 0:5 4:80:5DhDz 9:6The hydraulic gradient is higher at position 1 (0.8 cm) than at position2 (5.6 cm), so the water will flow upward from position 1 to position 2.Darcys Law yields a specific discharge qD for upward water flow.qD Kh 0:51 DhDz 105 9:6 104 cm s1specific discharge qD .SolutionPosition 1 has an elevation 3.0 m above the water table and position 2 has anelevation 3.5 m above the water table. The elevation heads arezdatum z1 0:0m and z2 0:5m, respectively.5c. Applying Darcys Law, estimate the direction of flow and magnitude of theOxidation Numbers 104 Pressure 1093.1Cl o uech c thspe C din ssurface, where the conditions favor the formation of the hydrous, fine-grainminerals. Clays, by virtue of their extremely small particle size and high sur-face-to-volume ratio, are one of the most chemically active components of--ject in and of itself, is generally not essential for environmental chemistry at thelevel of this book. Clay minerals, however, display physical and chemicalbehavior that simply cannot be appreciated without a grasp of their crystal struc-ture. This is our second task. With these basics in hand, we are prepared for ourfinal task: a description of clay mineral physical behaSoil and Environmental Chemistry.# 2012 Elsevier Inc. All rights reserved.soils and sediments.The chemical transformationweatheringof rock produces clays and clayminerals. Our first task is to identify the geological materials where clay minerals occur and where clay minerals appear in the geochemical weatheringsequence. Understanding mineral structures, while a worthy and interesting submost rocks because they are chemical alteration products formed at EarthAppendix 3B. The Geometryof Paulings Radius RatioRule 105. INTRODUCTIONay mineralogy is devoted to a gremical and physical properties. Thecific mineralogy and particle size.Appendix 3E. ExperimentalEstimates of InterlayerSwelling Pressure 111up of silicate minerals with uniqlay minerals connotation implies bolays differ from other minerals founChapter 3Clay Mineralogy and ClayChemistryChapter Outline3.1 Introduction 853.2 Mineral Weathering 863.3 The Structure of LayerSilicates 89Appendix 3A. FormalAppendix 3C. Braggs Law andX-Ray Diffraction in LayerSilicates 109Appendix 3D. Osmotic Modelof Interlayer Swellingvior and chemistry.853.2. MINERAL WEATHERING3.2.1. MineralogyTable 3.1 lists the major mineral classes. Silicate, phosphate, and sulfide miner-als occur in all types of rockigneous, sedimentary, and metamorphicandweathering products. Oxyhydroxide, hydroxide, and certain hydrous silicateminerals are stable only at temperatures where liquid water can exist. Carbonateand sulfate minerals are found only in chemically weathered materials such assaprolite, sediments, soils, and sedimentary rock formations.The Jackson Weathering SequencePhysical weathering and abrasion generate fine-grained particles that retainthe mineralogy of the rocks from which they form: sand (diameter range:0.052.0 mm) particle-size class. Soil is defined as any material that passesa 2.0 mm sieve. Chemical weathering transforms primary (rock-forming)Soil and Environmental Chemistry86minerals into secondary minerals that are stable under the moist, low-temperatureconditions existing at Earths surface. The clay particle-size class (diameterrange:Chapter 3 Clay Mineralogy and Clay Chemistry 87TABLE 3.2 Jackson Clay Mineral Weathering StagesWeathering Stage Clay Fraction1 Mineralogy1 Gypsum, halite2 Calcite, dolomite3 Olivine, pyroxene, amphibole4 Biotite, chlorite5 Feldspar (plagioclase and orthoclase)6 Quartz7 Muscovite, illite8 Vermiculite9 Smectite(25 mm) size fractions. The minerals that are most resistant to chemicalweathering, stages 813, occur predominantly in the clay fraction.Minerals in stages 12 and 812 are exclusively secondary minerals,while the minerals in stages 37 and 13 are exclusively primary minerals.Making sense of the mineral weathering sequence requires some explana-tion. The stages represent chemical weathering as seen from a particularperspective.Surficial depositssoil, sediment, or saprolitewhose clay size fractionscontain stage 1 or 2 minerals, may have undergone considerable chemicalweathering during their past history, but the presence of relatively solublechloride, sulfate, and carbonate minerals indicates that the recent chemicalweathering history has not been sufficiently intense to dissolve these particu-lar minerals. The absence of gypsum and halite in the fine-silt-size fractionmeans that the recent chemical weathering history has progressed beyondstage 1. Similarly, the absence of calcite or dolomite in the fine-silt- andcoarse-clay-size fractions means that the recent chemical weathering historyhas progressed beyond stage 2.10 Kaolinite11 Aluminum hydrous oxidesgibbsite12 Iron oxides and oxyhydroxideshematite, goethite13 Titanium oxidesrutile, anatase1Particle-size diameter 5 mm.Source: Jackson, Tyler et al., 1948.Muscovite, the last igneous silicate mineral to disappear from the fine-silt-Soil and Environmental Chemistry88size fraction, has been eliminated by stage 8, along with a closely related sec-ondary mineral: illite. The indicator minerals of stages 810 occur exclusivelyin the clay-size fraction. Vermiculite, smectite, and kaolinite, commonlyknown as clay minerals, are the major topic of this chapter.Chemical weathering of sufficient duration and intensity rarely results inthe loss of highly insoluble oxide minerals: aluminum hydrous oxides and ironoxides. Tropical soils with stage 11 clay mineralogy are often exploited asaluminum ores, while stage 12 soils are ideal iron ores.Chemical Weathering ReactionsMinerals such as gypsum, halite, and most carbonate minerals completelydissolve. Other minerals consist of both soluble and insoluble elements.Stages 310 minerals partially dissolve, leaving behind products that areeither highly insoluble or sufficiently reactive to form secondary mineralsthat persist throughout intermediate and advanced weathering stages. Givensufficient time, virtually all of the soluble Na, K, Mg, and Ca elements areleached from the vadose zone along with moderately soluble silica, leavinga highly insoluble residuum composed of aluminum, iron, and titanium oxideminerals.Appendix 3A describes a simplified method for calculating the formaloxidation numbers of elements in minerals. The formal oxidation numbersof iron in the minerals of the Jackson chemical weathering sequence clearlyindicate that primary (igneous) minerals undergo oxidation during chemicalweathering; iron typically occurs in a ferrous oxidation state in primaryminerals but occurs in the ferric oxidation state in secondary minerals.Deposits whose fine-silt- and coarse-clay-size fractions contain the pri-mary minerals of stage 3 have undergone primarily physical weathering andlittle chemical weathering. Stage 3 minerals are typical of igneous rocks con-sidered vulnerable to chemical weathering. The absence of stage 3 minerals inthe fine-silt-size fraction means that the recent chemical weathering historyhas progressed beyond stage 3. The chemical weathering of stage 3 mineralsproduces a variety of secondary minerals, but the key to advancing from stageto stage is the elimination of certain indicator minerals from the fine-silt- toclay-size fractions.Stage 46 minerals are found in igneous rocks but represent increasingresistance to chemical weathering. As chemical weathering dissolves andtransforms minerals in the fine silt to clay-size fractions, we witness the lossof biotite and chlorite (stage 5), feldspar minerals (stage 6), and, finally,quartz (stage 7). Regardless of whether these minerals occur in the coarser(>5 mm) size fractions, the chemical weathering stage is dependent on theirelimination from the fine (and other high-temperature rock-forming minerals. These added hydrogenChapter 3 Clay Mineralogy and Clay Chemistry 89of the link between silicate ions:Si O Si!H2O Si OH HO Si 3:2Secondary minerals fall into two broad groups: layer silicates (stages 710)and oxide minerals (stages 1113). The crystal structure of oxide mineralshas little direct bearing on their environmental chemistry. Oxide mineralchemistry arises from its solubilitywhich tends to be very lowand its sur-face propertieswhich is extremely important because oxide clays have avery high surface areatovolume ratio.3.3. THE STRUCTURE OF LAYER SILICATESThe three most abundant elements (oxygen, silicon, and aluminum) accountfor 83.3% of the total mass of Earths outer crust (Taylor, 1964). Silicateand aluminosilicate minerals differ from other mineral classes because siliconand aluminum combine with oxygen to form tetrahedral units that polymerizeinto complex networks. This tendency to polymerize, more than elementalabundance, accounts for silicate mineral diversityroughly 27% of the4000 or so known minerals.behind an oxygen ion:2 OH !heat O2 H2O 3:1Silicate minerals resist chemical weathering to different degrees, but, in gen-eral, resistance to chemical weathering is proportional to the amount of cross-linking of the silicate network. Basalt rocks contain easily weathered olivine,pyroxene, and amphibole minerals, while granite rocks contain a higher pro-portion of resistant minerals: muscovite, feldspar, and quartz. Cleavage ofthe silicate network involves the hydrolysis (addition of a water molecule)ions represent increased hydration of mineral compositions as a result ofchemical weathering. Hydration takes two forms: water molecules in themineral crystal structure and hydroxyl ions, the latter known as structuralhydration. The heating of minerals containing hydroxyl ions leads to weightloss: one water molecule vaporized for every two hydroxyl ions, leavingOxidation has several consequences: maintenance of charge neutralityrequires changes in chemical composition, and the reduction in the ionicradius of iron (rFe2 > rFe3 ) induces changes in crystal structure. Takentogether, these consequences promote the chemical transformation of primaryminerals containing ferrous ions.Inspection of the chemical composition of minerals in the Jackson chemi-cal weathering sequence reveals a second, profound transformation: second-ary minerals typically contain hydrogen ions that are absent from igneousbonded atoms. Pauling (1929) introduced an alternative model that becameSoil and Environmental Chemistry90very popular among mineralogists. Minerals are composed mainly of cationsand oxygen anions organized into coordination polyhedra. Oxygen anionsoccupy the vertices of these coordination polyhedra; lines drawn betweenthe vertices define the shape of the coordination polyhedron. Cations occupythe center of each coordination polyhedron and are usually not illustrated inthis convention (Appendix 3B).Figure 3.1 shows the equivalence between the two models. Ball-and-stickmodels of tetrahedral and octahedral coordination appear in the left column,and the same ball-and-stick models appear in the middle column, with linesdefining the vertices of the two polyhedra. Idealized symbols of a tetrahedronand an octahedron appear in the right column, similar to the illustrationsfound in Pauling (1929) and Bragg (1929).The idealized octahedron in the bottom right of Figure 3.1 is orientedwith its threefold rotation axis perpendicular to the pagenearly but notexactly the orientation of the ball-and-stick octahedron in the lower left.Two alternative orientations of idealized octahedra appear in Figure 3.2,where the orientation on the left is the same as in Figure 3.1, while the oneon the right has been rotated so the twofold rotation axis is perpendicular tothe page. You will often see both orientations in illustrations of layer silicateThe chemical structural diversity of silicate minerals parallels the diversityof carbon compounds and derives from similar chemical principles. Both car-bon and silicon atoms have four valence electrons and tend to form four bondswith other atoms to satisfy the octet rule. Carbon and silicon also favor tetra-hedral bond geometry, as rationalized by both the valence orbital hybridiza-tion and the valence shell electron-pair repulsion (VSPER; Gillespie andNyholm, 1957) chemical bonding models. The tetrahedral bond geometry ofcarbon-based compounds rests on direct carbon-carbon bonds, while oxy-gen-rich silicate minerals base their tetrahedral geometry on the silicate tetra-hedron SiO44 and its tendency to polymerize.General chemistry books discuss silicate minerals under a special categoryof network solids. Network solids favor crystal structures that are less densethan close-packed ionic solids because the dominant bonding in networksolids has a highly directional, covalent nature. Silicate minerals areorganized into classes, depending on the type of silicate network. As a generalrule, the melting point, mineral hardness, and resistance to chemicalweathering tends to increase as the dimensionality of the silicate networkincreases.3.3.1. Coordination PolyhedraChemists usually illustrate molecular structure using ball-and-stick models:atoms represented by balls and bonds represented by sticks drawn betweenmineral structures.Chapter 3 Clay Mineralogy and Clay Chemistry 91FIGURE 3.1 Ball-and-stick and polyhedral models for fourfold and sixfold coordination.3.3.2. The Phyllosilicate Tetrahedral SheetPhyllosilicatesrepresented by the mica group minerals muscoviteKAl2AlSi3O10OH2 and biotite K FexAl2x AlSi3O10OH2are com-mon in granite and the coarse (sand and silt) fraction of moderately weatheredsaprolite. Aluminosilicate tetrahedra polymerize to form a two-dimensionalnetwork that serves as a scaffold for crystal layers 0.701.00 nm thickseparated by cleavage planes (Pauling, 1930a, b).To visualize the aluminosilicate tetrahedral network, imagine placing a singletetrahedron with one trigonal face resting on a flat surface as if it were a trigonalpyramid. The upper right image in Figure 3.1 is a vertical view of this tetrahe-dron: three oxygen atoms forming the base and one the apex. Several space-filling networks are possible from joining the basal vertices, but the network withthe least bond strain consists of rings of six tetrahedra (Figure 3.3). The leftimage in Figure 3.3 is the aluminosilicate network found in phyllosilicatesalltetrahedra point in the same directionwhile the right image in Figure 3.3 isthe network found in tectosilicates such as quartz and feldspartetrahedraalternate pointing up and down around the sixfold ring. Figure 3.4 shows twounit cells for the two-dimensional aluminosilicate network.FIGURE 3.2 Two perspectives of anidealized octahedron: along sixfold screwsymmetry axis (left) and along twofoldrotation symmetry axis (right). The sixfoldscrew axis is perpendicular to the twofoldrotation axis.Soil and Environmental Chemistry92FIGURE 3.3 Aluminosilicatenetworks in phyllosilicates (left)and tectosilicates (right). Thephyllosilicate tetrahedra all pointup in the illustrated sheet. The tecto-silicate tetrahedra alternate up anddown in this sheet, with sheetsjointedby tetrahedrapointing towardeach other.FIGURE 3.4 Alternative unit cell settings for thephyllosilicate tetrahedral sheet: a trigonal unit cellwith composition Si2O25 denoted by open pointsand an orthogonal unit cell with compositionSi4O410 denoted by filled points. The orthogonalunit cell is commonly used for phyllosilicates.The phyllosilicate tetrahedral sheet is composed of three parallel atomicplanes: the basal oxygen plane, the silicon-aluminum plane above that, andthe apical oxygen plane. These atomic planes are crucial to understandingthe phyllosilicate layer structure.3.3.3. The Phyllosilicate Octahedral SheetThe lower right image of Figure 3.1 (left image of Figure 3.2) is an octahe-dron viewed along the threefold rotation axis perpendicular to one of the eighttriangular faces. Viewed from this perspective, the octahedron has a hexago-nal profile. A planar arrangement of octahedra in this orientation fills spacethe same way hexagonal cells of a honeycomb fill space (Figure 3.5). Similarillustrations appear in the original papers describing the structure of phyllosi-licates (Pauling 1930a, b).The octahedra in Figure 3.5 share edges, while the tetrahedra in Figure 3.3share corners (vertices). The symmetry and dimensions of these two sheetsmatch one another (Pauling, 1930a, b). The apical oxygen atoms of the tetra-hedral sheet align with vertices of the octahedral sheet to form the individualcrystal layers of all phyllosilicates (Figures 3.6a and 3.6b).Chapter 3 Clay Mineralogy and Clay Chemistry 93FIGURE 3.5 Octahedral sheets found in phyllosilicates: the trioctahedral Mg6 OH 12 sheet(left) and the dioctahedral Al4 OH 12 sheet (right).3.3.4. Kaolinite Layer StructureA common clay mineral with the simplest layer structure is kaoliniteAl4 OH 8Si4O10. Each kaolinite layer has the same composition and structure,consisting of one aluminosilicate tetrahedral sheet and one dioctahedralsheet (Figure 3.7), with a layer spacing of 0.70 nm. A less common mineral,lizardite Mg6 OH 8Si4O10, represents the trioctahedral end-member. Claymineralogists classify kaolinite and lizardite as 1:1 phyllosilicates.3.3.5. Talc Layer StructureThe mineral talc Mg6 OH 4 Si4O10 2 is a familiar phyllosilicate found inmetamorphic rocks, and its structure is similar to the mineral lizardite. Eachtalc layer consists of two aluminosilicate tetrahedral sheets and one triocta-hedral sheet (Figure 3.8), with a layer spacing of 0.94 nm. The mineral pyro-phyllite Al4 OH 4 Si4O10 2 represents the dioctahedral end-member. Claymineralogists classify pyrophyllite and talc as 2:1 phyllosilicates.FIGURE 3.6 The apical oxygen atoms of an aluminosilicate tetrahedral sheet also coordinate tri-valent ions of a dioctahedral Al4 OH 12 sheet. The illustrations offer two perspectives perpen-dicular to the sheets. The filled circles indicate OH ions that occupy the same atomic plane asthe apical oxygen atoms of the tetrahedral sheet.Soil and Environmental Chemistry943.3.6. Mica-Illite Layer StructureTwo types of mica are common in granite: the dioctahedral variant calledmuscovite and the trioctahedral variant called biotite. The layer structure(Figure 3.9) and composition of muscovite K2 : Al4 OH 4 AlSi3O10 2 and bio-tite K2 : Mg6xFex OH 4 AlSi3O10 2 closely resemble pyrophyllite and talc,respectively, except for two profound differences. Aluminum ions Al3FIGURE 3.8 A ball-and-stick model illustrates the talc layer structure (oxygenlarge open cir-cles, hydroxyllarge shaded circles, siliconsmall filled circles, aluminummedium filled cir-cles). The compositions of the tetrahedral sheet and trioctahedral sheet appear next to eachsheet. The overall composition Mg6 OH 4 Si4O10 2 avoids double counting apical oxygen atomsthat also coordinate magnesium in the octahedral sheet.FIGURE 3.7 A ball-and-stick model illustrates the kaolinite layer structure (oxygenlarge opencircles, hydroxyllarge shaded circles, siliconsmall filled circles, aluminummedium filledcircles). The compositions of the tetrahedral sheet and dioctahedral sheet appear next to eachsheet. The overall composition Al4 OH 8Si4O10 avoids double counting apical oxygen atoms thatalso coordinate aluminum in the octahedral sheet.Chapter 3 Clay Mineralogy and Clay Chemistry 95FIGURE 3.9 A ball-and-stick model illustrates the mica layer structure (oxygenlarge opencircles, hydroxyllarge shaded circles, siliconsmall filled circles, aluminummedium filledcircles, potassiumlarge shaded circles between the layers).replace one out of every four silicon ions Si4 in the tetrahedral sheet, and onepotassium ion K occupies the interlayer (the space between the crystallayers) for every Al3 substitution in the crystal layer. We know this becausethe molar content of potassium equals the molar aluminum content in mica(Pauling, 1930), and crystal structure refinements using x-ray diffractionlocate potassium ions between the mica layers.Cation substitution in micasthe replacement of Si4 by Al3 in the tetra-hedral sheetresults in negatively charged phyllosilicate layers whose chargeis balanced by interlayer cations. The combined effect of strong electrostaticforces binding the mica layers together, the low enthalpy of hydration for K,and the snug fit of the bare K cation into the sixfold rings of the aluminosili-cate network exclude water from the mica interlayer. The mica layer spacing is1.00 nm, significantly larger than in talc and pyrophyllite because interlayer Kions prop open the layers. The interlayer K ions also align the stacking of micalayers by occupying every hexagonal ring in the tetrahedral sheet. The coordi-nation number of interlayer K is 126 from each crystal layer.Illite closely resembles mica but is recognized as a distinct mineral by claymineralogists. The illite classification is based on layer charge, typicallyexpressed using O10 OH 2 units. A mineral is classified as mica if its layercharge is greater than 0.8 per O10 OH 2 and illite if its layer charge is inthe range of 0.70.8 per O10 OH 2. Layer charge in the illite range allowssome of the interlayer K to exchange with cations in solution.3.3.7. Chlorite and Hydroxy-Interlayered Smectite LayerStructureX-ray diffraction identifies two clay mineral groups with a characteristic1.4 nm layer spacing: the primary mineral group called chlorite and a modi-fied smectite variantcommonly known as hydroxy-interlayered smectite.Hydroxy-interlayered smectite is typically found in moderately weatheredacidic soils.The chlorite composition Mg4Al2 OH 12 : Mg6xFex OH 4 AlSi3O10 2 isreminiscent of trioctahedral biotite (to the right of the colon in the chloriteformula), with a layer charge arising from aluminum ions Al3 replacingone out of every four silicon ions Si4 in the tetrahedral sheet and an octa-hedral layer occupied by a blend of Mg2 and Fe2 cations. While the tetra-hedral layer charge in biotite is balanced by two nonexchangeable interlayerK cations per formula unit, in chlorite the interlayer is filled with a singleoctahedral sheet (Figure 3.10, left) resembling a layer from the mineralbrucite Mg6 OH 12 but with aluminum ions Al3 replacing one-third of themagnesium ions Mg2 in the interlayer octahedral sheet Mg4Al2 OH 12 (toSoil and Environmental Chemistry96the left of the colon in the chlorite formula). Many clay mineralogists desig-nate minerals of the chloride groups as 2:1:1 clay minerals (Figure 3.10, left)because a variant brucite octahedral layer lies between 2:1 biotite layers.The structure and layer spacing of hydroxy-interlayered smectite(Figure 3.10, right) resemble chlorite, but there are significant compositionaldifferences. First, the extent and location of cation substitution in the 2:1 pri-mary layers are characteristic of smectite clay minerals (Table 3.3). Second,FIGURE 3.10 A ball-and-stick model illustrates the layer structures of chlorite (left) and amodified smectite common in moderately weathered acidic soils generally known as hydroxy-interlayered smectite (right). The symbols used are oxygenlarge open circles, hydroxyllargecross-hatched circles, siliconsmall filled circles, aluminum or magnesiummedium filledcircles. Exchangeable interlayer cations (right): small filled circles, water hydrating interlayercationslarge gray circles with small filled circles representing protons.Chapter 3 Clay Mineralogy and Clay Chemistry 97the interlayer octahedral sheet is not continuous; instead, the interlayer isoccupied by a combination of hydrated exchangeable cations and pillars,whose structure and composition resemble gibbsite Al4 OH 12 instead of bru-cite. The gibbsitic interlayer of hydroxy-interlayered smectites results fromthe accumulation of aluminum ions Al3 released by chemical weatheringand their hydrolysis to form a product much like gibbsite between the smectitelayers.The interlayer octahedral sheet characteristic of both chlorite and hydroxy-interlayered smectites prevents a decrease in layer spacing as these mineralsare dried or subjected to mild heating to drive off interlayer water(Soil and Environmental Chemistry98The Swelling of Smectite and Vermiculite Clay MineralsA detailed picture of clay swelling began to emerge in the early 1950s, asillustrated by the x-ray diffraction results in Figures 3.12 and 3.13. (See Appen-dix 3C for an explanation of how the distance between crystal planes ismeasured using x-ray diffraction.) Increasing the relative humidity(Figure 3.12a) or decreasing the salt concentration in a clay suspension whenFIGURE 3.11 A ball-and-stick model illustratesinterlayer water molecules and the layer structure ofsmectite. This illustration is based on a moleculardynamics simulation. The interlayer cations are notshown in this illustration. Source: Reproduced withpermission from Chavez-Paez, M., Van Workum, K.,2001. Monte Carlo simulations of Wyoming sodiummontmorillonite hydrate. J. Phys. Chem. 114,14051413.salt concentrations are relatively high (Figure 3.12b) causes the layerspacingas indicated by d001to increase in a stepwise manner as waterenters the interlayer one layer of water molecules at a time. Crystalline clayswellingthe stepwise increases in layer spacing with the addition of 1, 2,and 3 water monolayers to the interlayerleads to abrupt jumps in d001 equalto the diameter of a water molecule: almost 0.25 nm. Notice that Ca2 saturatedsmectite jumps to a three-layer hydrate at a lower relative humidity than Nasaturated smectite (Figure 3.12a), demonstrating Ca2 hydrates more stronglythan Na, and draws water into the interlayer at a lower humidity.Low humidity or a high osmotic potential in concentrated salt solutions lim-its the amount of water available to hydrate interlayer cations. Clay swelling indilute salt solutions appears as a continuous increase in d001 as the salt concen-tration becomes increasingly more dilute (see Figure 3.13). Clay chemists referto this continuous swelling regime as osmotic clay swelling (see Appendix 3D).Structure of the Hydrated Clay Mineral InterlayerUnfortunately, no currently available experimental technique can reveal thedetailed structure of a hydrated smectite or vermiculite interlayer, leadingsome clay chemists to rely on molecular dynamic simulations. TheseChapter 3 Clay Mineralogy and Clay Chemistry 99simulations generate a host of predictions about the most probable structure ofthe interlayer: the positions and orientation of water molecules, cation posi-tions, interlayer spacing under specific conditions, and so on. To the extentsimulation predictions match measurable parameters (e.g., interlayer spacing),we can cautiously accept interlayer structure predictions that are currently notverifiable by experiment.Most simulations predict crystalline swelling behavior (see Figures 3.12and 3.13) quite well. Figure 3.14 displays probability distributions ofNa,Owater ,Hwater in the interlayer normal to the crystal layer for three crys-talline swelling states. Figure 3.15 displays probability distributions forK,Owater ,Hwater for three crystalline swelling states. Notice that Na ionsFIGURE 3.12 Crystalline swelling of smectite clays as influenced by (a) relative humidity(modified from Mooney, Keenan et al., 1952) and (b) ionic strength (modified from Norrish,1954).Soil and Environmental Chemistry100(see Figure 3.14) tend to move from the clay surface in the one-layer hydrateto the center of the interlayer in the two-layer hydrate, while K ions (see Fig-ure 3.15) remain near the clay surface as water enters the interlayer. Thisbehavior is consistent with the different swelling behavior of Na-saturatedand K-saturated smectite.FIGURE 3.13 Crystalline and osmotic swelling of smectite clays as influenced by ionic strength(modified from Norrish, 1954).Sodium ions promote continuous osmotic swelling of smectite (see Fig-ure 3.13), but potassium ions resist osmotic swelling because they lack suffi-cient hydration energy to swell the interlayer. Simulations such as this (Boek,Coveney et al., 1995; Tambach, Bolhuis et al., 2006) and the hydration prop-erties of these two ions are offered as an explanation for why potassium-saturated smectites resist swelling.In the osmotic swelling regime, interlayer cations shift away from the mid-plane, returning to positions near the clay layers (Figure 3.16). This configu-ration reduces electrostatic repulsion between interlayer cations (by increasingthe relative cation-cation distance) and increases the electrostatic attractionbetween the negatively charged clay layer and the interlayer cations (bydecreasing the relative cation-layer distance).The electrostatic force between the clay layer and the interlayer cationdepends on the hydrated radius of the cation and the location of the cation-substitution site in the clay layer. The strongest force exists when cation sub-stitution is in the tetrahedral sheet (Al3!Si4) and the cation hydrationenergy is relatively weak. In this configuration the cation comes into closecontact (see Figure 3.15) with the negative charge in the tetrahedral sheet.The weakest force exists when cation substitution is in the octahedral sheet(Mg2!Al3) and the hydration energy is strong. In this configuration waterChapter 3 Clay Mineralogy and Clay Chemistry 101HH HHHH HHONaOOOHH HHHH HHONaOOONaHOmolecules prevent interlayer cations from coming into close contact with theclay layer (see Figure 3.14), and the negative layer charge is in the centralatomic plane.Table 3.4 lists estimates of the hydrated radius and absolute enthalpy ofhydration DHabsolute for alkali and alkaline earth group cations. A decreasinghydrated radius correlates with a decreasing enthalpy of hydration in spiteof the trend for increasing ionic radius within each period.Smectite clay minerals exhibit crystalline swelling regardless of the typeof interlayer cation; differences arise from either the number of hydrationlayers that form during crystalline swelling or the conditions (humidity orionic strength) required to add a hydration layer. As a general rule, the greaterthe enthalpy of hydration, the lower the humidity or the higher the ionicstrength at which a crystalline swelling jump occurs. Smectites saturated withdivalent interlayer cations resist crystalline swelling relative to those saturatedHHHHH HHHH HHHH HOOO O ONaO O OFIGURE 3.14 Molecular dynamic simulations of the crystalline swelling of Na-saturatedsmectite clay representing d001 1.25 nm, one-layer hydrate (top); d001 1.35 nm, intermediatehydrate (middle); and d001 1.45 nm, two-layer hydrate (bottom). The probability distributionsnormal to the clay layer appear on the right. Source: Reproduced with permission from Tambach,T.J., Bolhuis, P.G., et al., 2006. Hysteresis in clay swelling induced by hydrogen bonding: Accu-rate prediction of swelling states. Langmuir 22, 12231234.HH HHHHHOKOOOHH HHHHHHKOHOKOOOHH HHHHOH HHHO O HHOK O OFIGURE 3.15 Molecular dynamic simulations of the crystalline swelling of K-saturated smectiteclay representing d001 1.25 nm, one-layer hydrate (top); d001 1.35 nm, intermediate hydrate (mid-dle); and d001 1.45 nm, two-layer hydrate (bottom). The probability distributions normal to the claylayer appear on the right. Source: Reproduced with permission from Tambach, T.J., Bolhuis, P.G.,et al., 2006. Hysteresis in clay swelling induced by hydrogen bonding: Accurate prediction of swellingstates. Langmuir 22, 12231234.NaO1.25 nm1.50 nmProbability Density1.80 nmz-coordinateHFIGURE 3.16 Molecular dynamic simulations of the crystalline swelling of Na-saturated smec-tite clay representing d001 1.25 nm, one-layer hydrate (upper right); d001 1.50 nm, two-layerhydrate (lower left); and d001 1.80 nm, three-layer hydrate (lower right). Source: Reproduced withpermission from Tambach, T.J., Hensen, E.J.M., et al., 2004. Molecular simulations of swelling clayminerals. J. Phys. Chem. B 108, 75867596.Chapter 3 Clay Mineralogy and Clay Chemistry 103with univalent interlayer cations. Of the ions listed in Table 3.4, only Li andTABLE 3.4 Hydrated Radius and Absolute Enthalpy of Hydration DHabsolutefor Alkali and Alkaline earth CationsIon Hydrated Radius1, pm DHabsolute2,kJ/molLi 405 531Na 348 416K 317 334Rb 300 308Cs 270 283Mg2 480 1949Ca2 440 1602Sr2 435 1470Ba2 430 13321Abbas, Gunnarsson et al., 2002.2Marcus, 1987.Na have the capacity to trigger osmotic swelling (see Figure 3.12) when theysaturate the interlayer of smectite clay minerals; the remaining cations resistosmotic swelling.Clay ColloidsColloid chemistry is a special branch of chemistry devoted to the study of sys-tems where surface properties have a measurable effect on physical and chem-ical behavior. Clay colloidal systems occur in the environment as a dispersionof ultra-fine clay particles in watereither a clay soil dispersed in the watercolumn of a river or lake, or a gel at low water contents. Particles qualifyas colloidal if at least one dimension is in the 11000 nm range. The upperlimit of the clay particle-size fraction (scheme adapted for mineralogy.1. The ox e t is always 0.2. The ox n sually 1.3. The ox in nerals is usually 2.4. The o ou A (alkali) element in mineralsis 1.5. The ox lkaline earth) element in mineralsis 2.Soil and Environmental Chemistry104OlivineThe formula notation places Mg and Fe in parentheses with a subscript of2: Mg,Fe 2SiO4. This notation is equivalent to Mg2xFexSiO4 and signifiesthat Mg and Fe are present in varying rather than fixed proportions. Theformal oxidation number for oxygen is 2. The formal oxidation numbersof Mg (Group IIA) and Si (Group IVA) are 2 and 4, respectively. The con-dition of charge neutrality requires assignment of formal oxidation number2 to Fe.Mg,Fe 2SiO4Formula Charge 0Formal Oxidation NumbersOMgSi224Fe 2Hedenbergite (Pyroxene)The formal oxidation number for oxygen is 2. The formal oxidation num-bers of Ca (Group IIA) and Si (Group IVA) are 2 and 4, respectively.6. The oxidation number of a Group IIIA element in minerals is 3.7. The oxidation number of a Group IVA element in minerals is usually4.8. The oxidation number of a Group VIIA element in minerals is 1.9. The sum of oxidation numbers for all the atoms in the formula unit of amineral is 0.10. The sum of oxidation numbers in a polyatomic ion is equal to the chargeof the ion.idation number of a Group IIA (axidation number of a Gridation number of hydrogeidation number of oxygenis umip Iidation number of a free el menAPPENDIX 3A. FORMAL OXIDATION NUMBERSMost general chemistry books introduce a scheme for calculating the formaloxidation number of elements in compounds. Following is an abbreviatedH 1APPENDI PAULINGS RADIUSRATIO RULinus Pauli es governing mineral structures;The Radius Ratio rule uses geometry to define the minimum radius ratio forstable coor . auling (1929) based this rule onthe notion o ancies created by the packingtogether of ved that cations preferentiallyoccupy tho o nic radius just matches the spaceavailable or a forcing the oxygen ions apart. Acation rarel re ionic radius is smaller than thespace availChapter 3 Clay Mineralogy and Clay Chemistry 105Geometry defining the minimum radius of a small spherethe cationthat can occupy the vacancy created by larger spheres is worked out in thisAppendix for three of the most common coordination types encountered inable.y occupies vacancies whe itswhen it is somewhat too l rge,that small cations fit intlarger oxygen ions. Hese vacancies where the cativacbelien iodination, listed in Table 3B 1. Phere we will consider only the Radius Ratio rule:Radius Ratio rule: A polyhedron of anions surrounds each cation. The cation-aniondistance is the sum of their respective radii, and the coordination number of the cationis determined by the radius ratio of cation to anion.ng (1929) proposed several rulLEX 3B. THE GEOMETRY OFFe 3The condition of charge neutrality requires assignment of formal oxidationnumber 2 to Fe.FeCaSi2O6Formula Charge 0Formal Oxidation NumbersOCaSi224Fe 2GoethiteThe formal oxidation number for oxygen is 2 and hydrogen is 1. The con-dition of charge neutrality requires assignment of formal oxidation number3 to Fe.FeOOHFormula Charge 0Formal Oxidation NumbersO 2TABLE 3B.1 Minimum Radius Ratios for Stable Coordination In MineralsCoordination Number Minimum Radius Ratio Formula3 0.15523p 3 3 4 0.2256p 2 2 6 0.4142p 1 8 0.7323p 1 12 1.000 1Soil and Environmental Chemistry106minerals: trigonal, tetrahedral, and octahedral. In each case we will assume aunit radius for the larger sphere and use geometry to determine the radius ofthe smaller sphere.TrigonalImagine three large spheres lying on a plane (Figure 3B.1). The large spheresdefine an equilateral triangle whose sides are each 2 times their radii. Assumethat the large spheres have a radius of 1. The distance from the center of theequilateral triangle to each of the vertices l is a function of the cosine of 30;the distance l is simply the radius of the small sphere plus the radius of the largesphere: 1 rc.FIGURE 3B.1 Trigonal close-packed spheres.cos 30 adjacenthypotenuse3p2 1l 1rc 1 rc 1 2p 2 3pChapter 3 Clay Mineralogy and Clay Chemistry 107vertex of the cube to the center is the sum of the radius of the anion and the radiusof the cation: l 1 rc. The distance from any vertex of the cube to the center isthe hypotenuse of a right triangle whose base is half of the diagonal distanceacross the face of the cube and whose height is half the edge length of the cube.l2 e20@1A2 120@1A 24 10@1Al rc 1 64s6p2rc 6p20@1A 10@1A 6p 220@1A 0:2247FIGURE 3B.2 Tetrahedron in a cube showing 2 times the anionradius along cube face diagonal.3 3rc 2 3p 330@1A 0:155TetrahedronThis geometry is best understood by visualizing a tetrahedron inside of a cube(Figure 3B.2). The diagonal distance across the face of the cube is the lengthof the edge of the embedded tetrahedron. If the cube-face diagonal equals 2,then edge of the cube is2pe2 e2 222 e2 4e 2pThe center of the cube is also the center of the tetrahedron. The distance from anyOctahedronOctahedral coordination is equivalent to four large spheres lying on a plane withtwo more spheres of the same radius placed above and below on the vertical axis.The geometry is completely defined by the four large spheres in the plane(Figure 3B.3). The spheres define a square whose sides are each 2 times the radii.Assume that each large sphere has a radius of 1. The distance from the center ofthe square to each of the vertices l is a function of the sine of 45; the distance l issimply the radius of the small sphere plus the radius of the large sphere: 1 rc.sin 45 oppositehypotenuse2p2 1l 1rc 1 rc 1 22p 2 2p2rc 2p 1 0:414The Radius Ratio rule allows us to estimate cation-anion bond lengths (Table 3B.2)for each coordination polyhedra in minerals given the radius of oxygen: 0.140 nm.Soil and Environmental Chemistry108TABLE 3B.2 Ideal Cation-Oxygen Distances Based on Coordination NumberCoordination Number Cation-Oxygen Distance, nm3 0.1624 0.1726 0.1988 0.242fourfold and sixfold coordination.FIGURE 3B.3 Square close-packed spheres for12 0.280distance dhklat an angle y. The difference in the distance traveled by twoCrystallographers identify x-ray reflections using hkl notation of specificatomic planes in crystals. The 001 x-ray reflection in phyllosilicate mineralsresults from Bragg diffraction by atomic planes parallel to the aluminosilicateFIGURE 3C.1 Braggs Law reflection of monochromatic x-rays from crystal planes. (imagesource: Chan, 2004)9tetrahedral sheet. The distance associated with each 001 x-ray reflection inphyllosilicates is denoted d001. The first-order 001 x-ray reflection (n 1)in a phyllosilicate is the repeat distance perpendicular to the crystal layers:d001 0.70 nm for kaolinite, d001 0.94 nm for talc, d001 1.00 nm for mica,and d001 > 12 nm for smectite.APPENDIX 3D. OSMOTIC MODEL OF INTERLAYER SWELLINGPRESSUREImagine a solution confined by a membrane that is permeable to water mole-cules but impermeable to solutes (e.g., the cytoplasm of a bacterium or a plantcell surrounded by a rigid cell wall). The equilibrium internal pressure actingagainst the confining membrane is given by the following expression forQreflected x-rays is an integral number times the x-ray wavelength n l,provided the reflection angle and distance between atomic planes satisfiesthe following conditionknown as Braggs Law (Figure 3C.1).n l 2 dhkl sinyAPPENDIX 3C. BRAGGS LAW AND X-RAY DIFFRACTION INLAYER SILICATESThe constructive interference of x-rays reflected by parallel atomic planewithin a crystal occurs when the difference in the distance traveled by tworeflected x-rays is an integral number times the x-ray wavelength: n l.Suppose x-ray beams reflect off parallel atomic planesseparated by aChapter 3 Clay Mineralogy and Clay Chemistry 10osmotic pressure (3D.1): R is the gas constant, T is the absolute tempera-ture, nsolute is the number of moles of solute, nsolvent is the number of moles11excluded, and water is free to enter or leave depending on the relative osmoticpotential Pswelling of the interlayer and the aqueous solution Psolution bathingthe clay particles (3D.5): i is the Vant Hoff factor for the solute, equal tothe number of moles of solute dissolved in solution per mole of solid added,and M is the concentration of the solute.Psolution i C R T of cmolc kg1and the interlayer spacing d001 in nanometers (3D.4).Pswelling 2 nNad001 R TA Pswelling 2 nNa cmolc kg1 d001 nm 33:05 kPa cmol1c kg nm 3D:4The osmotic model of clay swelling imagines the interlayer as a type of solu-tion where the interlayer cation concentration remains fixed, anions arewater per kilogram of clay (3D.3) based on the interlayer spacing d001 nm ,clay interlayer area (m2 kg1), and the molar volume V* of water at 25C(1:807 105 m3 mol1).nH2O d001 AV d001 nm 109 m nm1 7:5 105 m2 kg1 1:807 105 m3 mol1 3D:3The osmotic swelling pressure Pswelling becomes a simple function of thedegree of cation substitution in the claytypically nNa reported using unitsionic solutes dissociate, so a 1 M NaCl solution has the osmotic potential posmoticof a 2M sucrose solution. The smectite interlayer behaves like a solution, with theexception that one solute is the interlayer cation and the other is the negativelycharged site (which is also hydrated); dilution occurs by water entering the inter-layer and increasing the volume nH2O V as the layers are forced apart (3D.2).Pswelling 2 nNa R TnH2O V3D:2Using a surface area of 750,000 m2 kg1, which counts the interlayer area ofswelling clay minerals, we can calculate the number of moles of interlayerof solvent, V* is the molar volume of the solvent. Hydrologists use osmoticpotential interchangeably with osmotic pressure.P N m2 nsolute R Tnsolvent V posmotic Pa 3D:1Smectite clay minerals swell when interlayer cations hydrate, forcing the layers toexpand. The osmotic swelling pressure is given by Eq. (3D.2). Keep in mind thatSoil and Environmental Chemistry0Psolution i mol L1 2:479103 kPa L mol1 3D:5Chapter 3 Clay Mineralogy and Clay Chemistry 111The simplified osmotic model used by chemists does not precisely predict theexperimental water vapor pressure above real aqueous solutions because itassumes that the aqueous solution is ideal and the vapor pressure is a simplefunction of the mole fraction of the solvent. A more detailed model is requiredto accurately predict experimental vapor pressures, one that accounts for thenonideal behaviors of both the solute and the solvent. The similar shortcom-ings apply to the osmotic model of clay swelling; still, the simple osmoticmodel used here predicts the swelling tendency observed experimentally.Norrish (1954) used a clay product called Volclay (Volclay, AmericanColloid Co.) containing 89 cmolc kg1 interlayer cations. Norrish washedthe clay with concentrated NaCl to replace the interlayer cations in the natu-rally occurring clay to yield smectite containing 89 cmolc kg1 interlayerNa for the swelling experiment. Osmotic swelling begins with a d001 of4.0 nm (see Figure 3.12) at an ionic strength of:I 1=16 0:0625 mol L1:Pswelling 2 89 cmolc kg1 33:05 kPa cmol1c kg nm 4 nm 1455 kPa3D:6At equilibrium the osmotic swelling pressure of the interlayer water Pswelling(Eq. (3D.6)) equals the osmotic pressure of the aqueous solution Psolution(Eq. 3D.5)). Solving for CNaCl provides a surprisingly good estimate of theactual salt concentration in the clay suspensionabout fivefold larger thanmeasured experimentally by Norrish (1954):2 CNaCl 2:479103 kPa L mol1 1455 kPa 3D:7CNaCl 1455 kPa2 2:479103 kPa L mol1 0:294 mol L1 3D:8APPENDIX 3E. EXPERIMENTAL ESTIMATES OF INTERLAYERSWELLING PRESSUREImagine two chambers, one containing pure water and the other containing aclay gel, separated by a semipermeable membrane that allows water but not clayto pass. The glass columns allow each chamber to adjust its volume to remain atatmospheric pressure. The height of each column indicates the osmotic pressure(a milliliter of water contains 0.056 mole of H2O).Energy units [J mol1] can be converted into pressure units becauseenergy per unit volume [J m3 N m m3] has the same dimensions aspressure [N m2 Pa].11Question: What is the swelling pressure of the clay suspension (in atmo-sphere units) when the clay gel column attains a level 25 cm higher than thewater column?Solution: A pressure of 1 atm is equivalent to 1034 cm H2O l at 16C. If weassume the density of the clay gel is equal to water (i.e., the mass of the clayis negligible relative to the mass of water), 25 cm represents a pressure differ-2 2content is denoted by changesin the water column height.FIGURE 3E.1 Chambers con-taining pure water and a claygel connected by a rigid semi-permeable membrane. Anincrease in the clay gel waterSoil and Environmental Chemistry2ential of about 2:42 10 atm or p=p0 2:42 10DGswelling R T ln PP0DGswelling R T ln 2510340@1ADGswelling R T ln 0:0242 DGswelling R T 3:72 DGswelling 8:314 J mol1 K1 289K 3:72 DGswelling 8949 J mol1DGswelling 8949 N m mol1Converting energy units to pressure units, using 0.056 mole H2O per cubiccentimeter:Pswelling DGswelling VPswelling 8949 N m mol1 0:056 106 mol m3 Pswelling 4:962 108 N m2Pswelling 4898 atmP3ferred coordination of cation listed following using the ionic radius ofoxygen.Abundance Rank Element Ionic Radius, nm1 O2 0.1402 Si4 0.0343 Al3 0.0534 Fe2 0.0774 Fe3 0.0655 Ca2 0.1005 K 0.1386 Na 0.1027 Mg2 0.072P nBZRT 15101gNaClLh i103 Lm3 258:44moleionsgNaCl RT 5130 moleionsm3 RTP 5130 moleionsm3 8:314 298 1:23107 N mm3 P 1:23107 Nm2 11:013105atmN=m2 122 atm P 122 atm 11034cmH2Oatmh i 0:12 cmH2O Problems1. Discuss the physical processes and chemical reactions contributing to min-eral weathering.2. Apply Paulings Radius Ratio rule (see Appendix 3B) to determine the pre-Since we do not know the water content of the clay gel and already assumethat the density is unaffected by the gel, we will take this as the actualswelling pressure.Question: What would happen if 15 g of NaCl were added to the water (leftside)? The osmotic pressure p is related to the electrolyte valence Z and con-centration n by the following expression:P nRTZSolution: Adding NaCl to the pure water will lower the activity of water in thatcell, drawing water from the clay gel and increasing the height of the water col-umn relative to the clay gel column. Using the osmotic pressure equation:Chapter 3 Clay Mineralogy and Clay Chemistry 118 Ti4 0.0693. The following illustration shows the layer structure of four silicate minerals.Associate a specific mineral name with each structure, indicate which chem-ical weathering stage is dominated by the named mineral, and specifywhether the mineral is capable of crystalline swelling.Explain the relationship between layer charge and these physical properties.Soil and Environmental Chemistry114lected near the contact between saprolite and the granite bedrock clearlyshows the presence of fine-grained muscovite. The x-ray diffraction patternfrom the clay-size fraction of the saprolite collected from the soil profile atthe land surface lacks the characteristic diffraction lines of muscovite;instead, the dominant mineral is kaolinite. Explain the significance of thesefindings.6. Based on the Jackson chemical weathering sequence, what minerals wouldoccur in association with the following clay minerals: (a) kaolinite, (b) smec-tite, and (c) vermiculite?7. Explain why feldspar mineral grains tend to be larger than kaolinite mineral par-ticles and kaolinite particles tend to be larger than montmorillonite.8. What type of mineralsprimary or secondarydominates the sand- and silt-size fractions of soil or sediments?9. Layer charge of clay minerals influences a variety of physical properties:swelling behavior, surface area, and the exchangeability of interlayer ions.4. The surface area of a typical fine clay (0.2 mm) fraction of kaolinite is10m2 g-1,while smectite has a surface area of over 700 m2 g-1. Whataccounts for this dramatic difference in surface area?5. Consider a landscape underlain by granite that weathers in situ to saprolite.The x-ray diffraction pattern from the silt-size fraction of the saprolite col-10. Layer charge in clay minerals arises from ion substitution in the layer struc-ture. What determines whether a given ion can substitute for another in thelayer structure of a clay mineral?Chapter 3 Clay Mineralogy and Clay Chemistry 11511. A soil contains 30% clay by weight: 20% montmorillonite, 5% vermiculite,and 5% iron oxide. What is its approximate ion exchange capacity?12. Estimate the swelling pressure Pswelling kPa of a sodium-saturated smectite(SAz-1, Cheto, Arizona) with a cation exchange capacity of 97 cmolc kg1and a layer spacing d001 of 5.0 nm. Assume the surface area of thissmectite is 750 m2 kg1. The molar volume of water at 25C (298.13 K)is 1:807 105 m3 mol1.13. Following are three illustrations of layer silicate structures. The repeat dis-tance is shown for the 1:1 mineral kaolinite (0.70 nm) and the 2:1:1 mineralchlorite (1.40 nm). Based on these repeat distances and layer structure, esti-mate the repeat distance of 2:1 mica.SolutionThe 1.40 nm repeats after six planes of oxygen atoms, while the 0.70 nm claymineral consists of three planes, so a clay mineral that repeats after four oxygenplanes would have an approximate thickness of 93 nm. Since there are interlayercations but no water, we can add a bit more to the repeat distance and concludeSoil and Environmental Chemistry116it would be more than 0.93 nm.4.5 Summary 140 Vermiculite 1444.1W u l-tur g x-pe u vean t ofsci ina r ntchemical reaction with applications in nearly all chemistry fields.This chapter begins with a brief account of the discovery and the implica-tions of ion exchange for environmental chemistry. The next topic is a com-developed several ways of writing the equilibrium quotient, and, not surpris-ingly, the different formulations are equivalent to each other. The most impor-tant topic is a discussion of the physical parameters that determine ionexchange equilibrium.Soil and Environmental Chemistry.# 2012 Elsevier Inc. All rights reserved.plete description of an ion exchange experiment itself and the data collectedfrom such an experiment. Scientists studying ion exchange reactions haveentists worked out the broad outlines of the ion exchange reaction withemarkably short time. Ion exchange is now recognized as a very importaAppendix 4A. Thermodynamicand Conditional SelectivityCoefficients 142. INTRODUCTIONhile studying the chemistry of manal chemists discovered ion exchancted and all the more puzzling becaaccurate understanding of electrolyre in soil, nineteenth-century agricue. This discovery was wholly unese chemists at that time did not hae solutions. Regardless, a handfulChapter 4Ion ExchangeChapter Outline4.1 Introduction 1174.2 The Discovery of IonExchange 1184.3 Ion ExchangeExperiments 1194.4 Interpreting the IonExchange Isotherm 125Appendix 4B. Nonlinear LeastSquare Fitting of ExchangeIsotherms 143Appendix 4C. Equivalent Fraction-Dependent SelectivityCoefficient for (Mg2, Ca2)Exchange on the Libby117Soil and Environmental Chemistry1184.2. THE DISCOVERY OF ION EXCHANGEA chief concern of agriculturalists has been soil fertilitythe capacity of soilto supply essential nutrients to crops. Nitrogen is one of the most importantplant nutrients, and maintenance of soil nitrogen fertility is critical to cropyield. Manure is a rich and readily accessible nitrogen source, with the nitro-gen in manure being released largely as ammonia through the microbial deg-radation process known generally as mineralization.Much of the strong odor from animal manure comes from ammonia gas,and nineteenth-century agricultural chemists understood that ammonia lossfrom manure meant that there was less nitrogen for crop uptake. H. S. Thomp-son (1850) began studying methods to prevent ammonia loss from storedmanure in 1845, including sulfuric acid additions that produced large amountsof ammonia sulfate. In a report to the Royal Agricultural Society, Thompsonmentions an interesting property of soil: the power of retaining ammonia.Thompson designed experiments to measure the extent of this power andto ascertain whether it also extended to the [sulfate] by mixing ammoniumsulfate with soil, filling a glass column with the soil, washing the soil columnwith water to simulate rainfall, and analyzing the drainage solution. Thomp-son was certainly aware of an observation made by Mr. Huxtable when liquidmanure drained through a soil bed: it went in manure and came out water(Way, 1850). Thompson found that the salt remaining after he evaporatedthe drainage solution proved to be chiefly gypsum.This was a complete surprise. The large portion of gypsum . . . [in the drainage solution]. . . showed that a considerable portion of the sulphate of ammonia mixed with the soilhad been decomposed and that this process was in some way connected with the pres-ence of lime in the soil, as the sulphuric acid was washed out in combination with lime.Thompson performed an experiment to observe the result when theabsorptive powers of the soil were fully called into play by passing the filteredliquid repeatedly through the [soil column]. He found that the whole of theammonia was retained by the soil, whether applied in the form of sulphate orsesquicarbonate.J. T. Way (1850) published a report in the same publication of the RoyalAgricultural Society, discussing possible explanations for the absorptivepower of soil and describing numerous experiments that extended those per-formed by Thompson. Way found that after adding ammonia sulfate solutionto a soil column, the drainage solution was entirely free of the pungent smellof ammonia. Way also noticed that the soil had a fixed capacity to retainammonia; after continued washing of the soil column, the ammonia wouldshortly have passed through, the soil being saturated with it.Way (1850, 1852) traced the absorbing power of soil to the clay frac-tion, but how clays retain cations would remain a mystery until Linus Pauling(1930) solved the crystal structure of mica. The most abundant material innature with significant ion exchange capacity is smectite. A number of otherminerals have measurable ion exchange capacityfor example, oxide clays,natural organic matter, zeolite mineralsbut the overwhelming number ofion exchange studies involved smectite.4.3. ION EXCHANGE EXPERIMENTSChapter 4 Ion Exchange 119The surface of all solids has some capacity to retain cations and anions, butunless the surface-to-mass ratio is extremely high, it is impossible to reliablymeasure the ion exchange capacity. If the ion exchange capacity of the mate-rial is very low, ion exchange reactions will have a negligible effect on thecomposition of the solution. The coarse clay particle-size fraction2.0 mmspherical diameterhas a surface area of about 2 m2 g1. Particles muchlarger than this, with surface areas less than 1 m2 g1, have negligible ionexchange capacity. The mineral kaolinite has a cation exchange capacity of5 cmolc kg1 and a surface area of about 10 m2 g1, one of the lowest ionexchange capacities of any naturally occurring ion exchanger and amongthe lowest surface areas of any clay mineral.4.3.1. Preparing Clay Saturated with a Single CationNaturally occurring ion exchanges found in the soils, sediments and aquifersare cation exchangers, with the notable exception of oxide clays under acidicconditions (more on this in Chapter 9). The first step when measuring cationexchange capacity is saturating the cation exchanger with a single cation,preferably a cation that is easy to chemically analyze. Suspend the clay in acentrifuge bottle or tube containing a concentrated (e.g., 1 M) solution of ahighly soluble salt (Figure 4.1a). Agitate or shake for an hour or so to allowsufficient time for cation exchange (Figure 4.1b). Centrifuge until the super-natant solution contains no clay particles (Figure 4.1c). Discard the superna-tant solution (Figure 4.1d) and repeat (suspend, agitate, centrifuge, discard)several times. Wash the clay repeatedly with pure water (suspend, agitate,centrifuge, discard). The clay is now saturated by a single cation and washedfree of excess salts. All that remains is to suspend the clay in salt-free waterand accurately determine the mass concentration of suspended clay. This isnecessary because the ion exchange capacity is reported on a mass basis.FIGURE 4.1 Preparing clay saturated by cation A. (a)Suspend clay in centrifuge tube containing a concentratedsolution of a highly soluble salt AX-. (b) Agitate to allowsufficient time for cation exchange. (c) Centrifuge untilthe supernatant solution contains no clay particles. (d)Discard the supernatant solution and repeat.FIGURE 4.2 Measuring cation exchange capacity(CEC) by quantitatively replacing all of the exchangeableA from A-saturated clay with a new cation B. (a) Sus-pend A-saturated clay in centrifuge tube containing anew salt BX. (b) Agitate. (c) Separate the supernatantsolution from the clay, and (d) reserve the supernatantsolution.Soil and Environmental Chemistry1204.3.2. Measuring Cation Exchange CapacityBegin with a known volume of a well-mixed clay suspension whose massconcentration of clay has been measured. The next series of steps are a repe-tition of the cation saturation process just described, except this time using anew salt to displace the cation presently saturating the clay. Transfer clay sus-pension to a centrifuge bottle or tube containing a concentrated solution of thenew salt (Figure 4.2a). Agitate or shake for an hour or so to allow sufficienttime for cation exchange (Figure 4.2b). Centrifuge until the supernatant solu-tion contains no clay particles (Figure 4.2c). Reserve the supernatant solutionin another bottle (Figure 4.2d) and repeat (suspend, agitate, centrifuge,reserve) three or four times. The reserved supernatant solutions are combinedin a volumetric flask, diluted to the volume mark on the flask, and analyzedfor the concentration of the original saturating cation. The cation exchangecapacity is the number of moles of original saturating cation divided by thedry mass of clay in the suspension aliquot; the units are centimoles ofchargecmolcper kilogram of clay.4.3.3. Measuring the Cation Exchange IsothermThe simplest experiment begins with a known volume of a well-mixed clay sus-pension containing negligible soluble electrolyte. The mass concentration ofclay is known, and the clay is saturated with one or the other of the two cationsundergoing exchange. In the example shown in Figure 4.3a, the clay is initiallyA-saturated. Solution aliquots from two stock solutionsAX andBXareFIGURE 4.3 Measuring the cation exchange isotherm by allow-ing a series of solutions containing varying concentrations (a) oftwo saltsAX and BXto exchange with A-saturatedclay, agitation (b), and separation of clay from solution (c).1added to the clay suspension, yielding initial concentrations A initial andB initial (Figure 4.3a). It is important that the ionic strength of the initial solu-tions remains constant with only the concentration ratio of the two cations Aand B being varied.The exchange reaction is generally quite rapid at ionic strengths greaterthan 0.01 M, but it can take weeks in more dilute solutions. It is best to con-tinually agitate the clay suspension until equilibrium is reached(Figure 4.3b). Analysis of the equilibrium solution to determine A finaland B final usually requires centrifugation to remove clay from suspension(Figure 4.3c).Analysis of the equilibrium solution becomes difficult under certain condi-tions: the clay particles are less than 0.2 mm, the exchanger is a smectite, andthe saturating cation is either Li or Na. Chapter 3 discusses both crystallineand osmotic swelling of clay minerals. Vermiculite exhibits crystalline swellingbut not osmotic swelling, regardless of the saturating cation. Smectite exhibitsboth crystalline swelling and osmotic swelling; the latter with saturating cationis either Li or Na, and the ionic strength (or osmotic potential) is low. A lowionic strength suspension of either Li- orNa-saturated smectite may form a sta-ble colloidal dispersion that resists sedimentation in the operating range of con-ventional centrifuges. Under these circumstances, clay chemists resort todialysis to analyze the concentrations of soluble cations.Table 4.1 illustrates the experimental design of a typical exchange isotherm(Vanselow, 1932). The exchanger that Vanselow used for this experiment was amontmorillonite with a cation exchange capacity of 104.1 cmolc kg1. Half ofthe suspensions used Na-saturated montmorillonite, and the other half usedK-saturated montmorillonite. Vanselow based the clay content on the volumeconcentration of the exchangeable cation24.0 g L1 ofK-saturated montmo-rillonite, yielding a K concentration of 25.0 mmolc L1 as exchangeable K.For his experiment, he used different amounts of montmorillonite: 24.0 g L-1(25.0 mmolc L1) and 41.2 g L-1 (42.9 mmolc L1).Table 4.2 lists the equilibrium composition of the montmorillonite suspen-sion, and Figure 4.4 plots the exchange isotherm. Vanselow did not have tomeasure the amounts of Na and K bound to the montmorillonite becausehe could determine those quantities by mass balance. The total Na concen-tration is the sum of the soluble concentration Na and the amount ofclay-bound Na expressed in volume concentration units qNa . The initialand final total Na concentration remains unchanged; only the relative solubleand clay-bound concentrations change.Na qNa initial Na qNa finalqNa final Na qNa initial Na finalA comparison of Tables 4.1 and 4.2 clearly shows that cation exchange hasChapter 4 Ion Exchange 12altered the solution concentration of both cations and the quantities of bothcations bound to the clay.TABLE 4.1 Initial Conditions of a Symmetric Cation Exchange ExperimentNa mmolc L1 K mmolc L1 qNammolc L1 qKmmolc L1 Soil and Environmental Chemistry122100.0 0.0 0.0 25.0100.0 0.0 0.0 42.985.7 14.3 0.0 42.971.4 28.6 0.0 42.957.1 42.9 0.0 42.942.9 57.1 0.0 42.925.0 75.0 0.0 25.075.0 25.0 25.0 0.0Row 5 in Table 4.2where Na K also shows that the fraction ofclay-bound Na is significantly less than the Na fraction in solution.4.3.4. Selectivity Coefficients and the Exchange IsothermTable 4.3 lists the most frequently encountered ion exchange expressions,commonly known as selectivity coefficients.1 All of the expressions are basedon specific exchange reactions, both symmetric and asymmetric. Some exam-ples involving abundant ions are presented following.57.1 42.9 42.9 0.042.9 57.1 42.9 0.028.6 71.4 42.9 0.014.3 85.7 42.9 0.00.0 100.0 42.9 0.00.0 100.0 25.0 25.0Source: Data reproduced with permission from Vanselow, A.P., 1932. Equilibria of the base-exchange reactions of bentonites, permutites, soil colloids, and zeolites. Soil Sci. 33, 95113.1. Usage of selectivity coefficient can be confusing because it may refer to both the coefficient(e.g., KGT) and the quotient. The superscript c (Table 4.3) indicates a conditional coefficient(see the discussion of activity in Chapter 5). Appendix 4A lists thermodynamic selectivity coeffi-cient expressions corresponding to those listed in Table 4.3.TABLE 4.2 Equilibrium Conditions of a Symmetric Cation ExchangeExperimentNa mmolc L1 K mmolc L1 qNammolc L1 qKmmolc L1 86.3 14.9 13.70 10.1081.1 20.6 18.90 22.3071.9 29.3 13.80 27.9061.8 39.5 9.60 32.0050.5 50.6 6.60 35.2038.7 62.2 4.20 37.8023.7 76.9 1.30 23.1085.3 15.6 14.70 9.4079.8 22.3 20.20 20.6070.4 31.5 15.40 25.6060.0 42.1 11.50 29.3048.4 53.1 8.80 32.6037.0 64.7 5.90 35.3022.7 78.3 2.30 46.70Source: Data reproduced with permission from Vanselow, A.P., 1932. Equilibria of the base-exchange reactions of bentonites, permutites, soil colloids, and zeolites. Soil Sci. 33, 95113.FIGURE 4.4 The cation exchange isotherm for Na,K exchange on a montmorillonite(Vanselow, 1932).solution exchanger exchanger solutionCommon Asymmetric Exchange Reactions2 Naaqsolution Ca2exchanger$ 2 NaexchangerCa2aqsolution2 Kaqsolution Mg2exchanger$ 2 KexchangerMg2aqsolutionThe Kerr selectivity quotient (Kerr, 1928) employs solution concentrations(mol L1) and solid concentrations (mol kg1). The Vanselow selectivityquotient (Vanselow, 1932) expresses exchanger-bound ions using molefractions ~NAu (mol mol1). The Vanselow formalism treats the exchanger-bound ions (commonly referred to as the exchange complex) as a mixture:~NAu ~mAu~mAu ~mBv 4:1~NAu 1 ~NBv 4:2The Gaines-Thomas selectivity quotient (Gaines and Thomas, 1953) expresses12~EAu u ~mAuu ~mAu v ~mBv 4:3~EAu 1 ~EBv 4:4KV ~NK Na KV ~NCa2 Na 2Gaines-ThomasKcGT K ~ENa~EK Na KcV KcGT Ca2 ~E2Na~ECa2 Na 2GaponKcG K ~ENa~EK Na KcV KcG Ca2 1=2 ~ENa~ECa2 Na the concentration of ion A bound to the ion exchanger:TABLE 4.3 Frequently Encountered Ion Exchange Selectivity Coefficientsand QuotientsDesignation Symmetric Exchange Asymmetric ExchangeKerrKcK K qNaqK Na KcK Ca2 q2NaqCa2 Na 2Vanselowc K ~NNa c Ca2 ~N2Naexchanger-bound ions using equivalent fractions ~EAu (molc mol1c ) to quantifyuCommon Symmetric Exchange ReactionsNaaqsolution Kexchanger$ NaexchangerKaqsolutionCa2aq Mg2 $ Ca2 Mg2aqSoil and Environmental Chemistry4ultimately yield the same Gibbs free energy for an ion exchange reaction.Chapter 4 Ion Exchange 125ion exchanger, yields an expression in which the equivalent fraction ~EAsbecame the master variable. An equivalent integral expression can be derivedusing the Gaines-Thomas selectivity quotient; the equivalent fraction ~EAsremains the master variable:~NAu ~mAu~mAu ~mBv~mAu ~NAu1 ~NAu0@1A ~mBv~EAu u ~mAuu ~mAu v ~mBv u ~NAu1 ~NAu0@1A ~mBv0@1Au ~NAu1 ~NAu0@1A ~mBv0@1A v ~mBv~EAu u ~NAuu ~NAu v 1 ~NAu u ~NAuv u ~NAu v ~NAu ~EAu u ~NAuv u v ~NAu4:5The exchange isotherm (Figure 4.4) plots the equivalent fraction of one cation,Nain this case, bound to the exchanger ~ENa as a function of the equivalent fractionENa of the same cation in solution. This cation exchange experiment (Table 4.2and Figure 4.4) clearly demonstrates the montmorillonite selectively binds Kfrom solution, yielding a higher clay-bound equivalent fraction: ~EK> EK .4.4. INTERPRETING THE ION EXCHANGE ISOTHERMThe example in Table 4.2 and Figure 4.4 is from a classic paper by Vanselowon ion exchange phenomena. The purpose of that and other studies was anattempt to understand the quantitative details of the ion exchange reactionArgersinger and colleagues (1950) developed an integral method for deter-mining the thermodynamic equilibrium constant based on the Vanselowselectivity quotient. Their result, though derived from a selectivity quotientusing mole fraction ~NAu to quantify the concentration of ions bound to theThe Gapon selectivity quotient (Gapon, 1933) employs a much different con-vention than the other expressions (cf. Appendix 4A) and is widely used byscientists studying salinity and sodicity problems (see Chapter 7). The two con-tenders for a thermodynamic formulationthe Vanselow selectivity quotientand coefficient and the Gaines-Thomas selectivity quotient and coefficientand the selective adsorption of certain ions, resulting in a different proportionof .Sc rto aco .Soil and Environmental Chemistry126Chemists commonly plot experimental data using an exchange isotherm ratherthan plotting the selectivity quotient. The exchange isotherm for symmetricexchange is derived from the selectivity quotient as follows:General Symmetric Exchange ReactionAuaqsolution Buexchanger$ AuexchangerBuaqsolutionKcGT Bu ~EAuAu ~EBu4:6KcGT Bu Au Bu ~EAuAu Au Bu ~EBu EBu ~EAuEAu ~EBuKcGT 1 EAu ~EAuEAu 1 ~EAu 4:7The conditional Gaines-Thomas selectivity coefficient KcGT includes activitycoefficients for the exchanger equivalent fractions (Table 4A.1). Equation(4.7), which contains one parameter and two variables is readily rearrangedto yield the symmetric exchange isotherm:Symmetric Exchange Isotherm~EAu KcGT EAu1 EAu KcGT EAu4:8Example 4.1 Estimate the conditional selectivity coefficient KcGT for the symmet-ric Na,K exchange results in Table 4.2.Figure 4.4 is a plot of the exchange isotherm derived from the data listed inTable 4.2. An estimate of the selectivity coefficient KcGT can be made using anydata point plotted in Figure 4.4, but the most reliable values will be those whereMuch of the scientific research devoted to ion exchange seeks to properlyformulate the equilibrium quotient for the ion exchange reaction. Thehistorical developments in ion exchange research are beyond the scope of thisbook, but a summary of the most prominent ion exchange expressions is inorder.4.4.1. The Ion Exchange Isotherm for Symmetric Exchangeions bound to the exchanger than the proportion dissolved in solutionientists studying ion exchange anticipated an equilibrium expression similaother chemical reactions in which the equilibrium quotient equalsnstant determined by the Gibbs free energy of the ion exchange reactionthe equivalent fraction of either cation in solution is about 0.5.Na 0:0505mol L1 and K 0:0506 mol L1. Entering these values in74.4.2. The Ion Exchange Isotherm for Asymmetric ExchangeThe exchange isotherm for asymmetric exchange is more complex than thesymmetric exchange isotherm because the stoichiometric coefficients do notcancel. Rather than tackle the general asymmetric exchange isotherm, thefollowing derivation is for the specific case of asymmetric Na,Ca2 exchange:2 Naaqsolution Ca2exchanger$ 2 NaexchangerCa2aqsolutionKcGT Ca2 ~E2Na~ 24:9KcGT 0:0506mol L1 0:160:84 0:0505mol L1 KcGT 0:160:84 0:19This selectivity coefficient KcGT 0:19 is for the ion exchange reaction as itis written above. Notice that the solution concentrations of the two cations atequilibrium are essentially equal for the selected data (Table 4.2, row 5). If theexchange were nonselective, then the equivalent fractions of the two cationswould be equal KcGT 1 . The exchange results appearing in Table 4.2 andFigure 4.4, however, clearly indicate an enrichment of K in the exchangecomplex ~EK 0:84 and a depletion of Na in the exchange complex~ENa 0:16 .for the following ion exchange reaction:Naaqsolution Kexchanger$ NaexchangerKaqsolutionKcGT K ~ENa~EK Na Eq. (4.6) yields a single-point estimate of Gaines-Thomas selectivity coefficientTaking the experimental results from row 5 of Table 4.2, first determine each termin the symmetric Gaines-Thomas selectivity coefficient expression (Eq. (4.6)). Theequivalent fractions of Na and K on the exchanger (Eq. (4.3)) are determinedfollowing:~ENa ~mNa~mNa ~mK~ENa 6:606:60 35:20 0:16~EK 1 ~ENa 1 0:16 0:84The corresponding equilibrium solution composition (Table 4.2, row 5) isChapter 4 Ion Exchange 12ECa2 Na Soil and Environmental Chemistry128Equation (4.10) reduces the univalent-divalent asymmetric exchange isothermto a quadratic equation (Eq. (4.11)) whose solution is given by Equation(4.12), where the term b is defined in Eq. (4.13):2 C0 KcGT 1 ENa ~E2NaE2Na 1 ~ENa 2 C0 KcGT E2Na 1 ~ENa 1 ENa ~E2Na~E2Na 2 C0 KcGT E2Na1 ENa ~ENa 2 C0 KcGT E2Na1 ENa 0 4:11~ENa bb2 4 bp24:12b 2 C0 KcGT E2Na1 ENa4:13Example 4.2 Estimate the conditional selectivity coefficient KcGT for the asymmet-ric K,Ca2 exchange reaction on a smectite from Crook County, Wyoming.The Twotop soil series from Crook County, Wyoming, whose clay fraction isThe solution charge concentration C0 allows us to convert solution concentra-tions to solution equivalent fractions, but we must recognize a factor of 2 inthe numerator for the equivalent fraction of the divalent ion:Define : C0 Na 2 Ca2 ECa2 2 Ca2 Na 2 Ca2 2 Ca2 C0KcGT C0 ECa220@1A ~E2NaC0 ENa 2 ~ECa2KcGT 12 C0 1 ENa ~E2NaE2Na 1 ~ENa !4:10Replacing solution activities with solution equivalent fractions leads to a newsolution parameter C0 absent from the symmetric exchange isotherm.Solution parameter C0 is the solution charge concentration summed over allions involved in the exchange C0 Na 2 Ca2 Units : molc L1 .predominantly smectite, has a CEC of 76.4 cmolc kg1. The asymmetricK on the exchanger (Eq. (4.3)) is the simplest term because the denominator isChapter 4 Ion Exchange 1294.4.3. Effect of Ionic Strength on the Ion Exchange IsothermThe symmetric exchange isotherm does not contain any terms explicitly influ-enced by ionic strength. The exchange isotherm contains a conditional selec-tivity coefficient KcGT , but that term adds ionic strength dependence indirectly(see Chapter 5). Figure 4.5 is a plot of exchange isotherms for a symmetriccation exchange at two different ionic strengths. The effect of ionic strengthis clearly negligible relative to experimental error.The asymmetric exchange isotherm (Eq. (4.12)) does contain a term explic-itly influenced by solution composition: solution parameter C0. Figure 4.6 is aplot of experimental exchange isotherms for an asymmetric cation exchangeat ionic strength 0.01 M and 0.001 M. Figure 4.7 plots asymmetric A-B2exchange isotherms in solutions, where the ionic strengths are 0.1 M, 0.01 M,Eq. (4.9) yields a single-point estimate of Gaines-Thomas selectivity coefficientfor the asymmetric exchange reaction:KcGT 0:50 1:017 102 20:50 2 5:65 104 KcGT 5:17 1051:41 104 0:37the cation exchange capacity CEC:~EK ~mK~mK 2 ~mCa2 ~mKCEC~EK 38:276:4 0:50~ECa2 1 ~EK 0:50Entering the exchange equivalent fractions and cation concentrations inanK,Ca2 exchange experiment reports the following results: K 10:17mM,Ca 0:565 mM, exchangeable K equals 38.2 cmolc kg1, and exchange-able Ca2 equals 38.2 cmolc kg1. What is the value of the Gaines-Thomas con-ditional selectivity coefficient KcGT for K,Ca2 exchange in this soil?The asymmetric ion exchange reaction and corresponding Gaines-Thomasselectivity quotient (Eq. (4.9)) follow:2 K ex Ca2aq $ 2 Kaq Ca2 ex KcGT K 2 ~ECa2~E2K Ca2 As in Example 4.1, determine each term in the asymmetric Gaines-Thomasselectivity coefficient expression. The equivalent fraction of the univalent cationd 0.001 M using the Gaines-Thomas exchange isotherm (Eq. (4.12)).FIGURE 4.5 Experimental cation exchange isotherms for symmetric K,Na exchange(Jensen and Babcock, 1973), where the ionic strengths are 0.1 M (open circles) and 0.01 M (filledcircles).FIGURE 4.6 The cation exchange isotherm for asymmetric K,Ca2 exchange (Jensen andBabcock, 1973) at two ionic strengths: 0.1 M (open circles) and 0.01 M (filled circles).Soil and Environmental Chemistry130Chapter 4 Ion Exchange 1314.4.4. Effect of Ion Selectivity on the Ion Exchange IsothermFigures 4.4 and 4.5 illustrate the second major influence on the exchangeisotherm: ion selectivity. In both of these experiments, the exchanger, mont-morillonite in the first case and a soil containing 18% clay dominated bymontmorillonite and vermiculite in the second, exhibits exchange selectivityfavoring K over Na. Quantifying this selectivity and interpreting the basisfor ion selectivity are the topics of this section. The approach presented herediffers from the conventional approach described in the published ionexchange literature. The approach used here is based on a least sum-squareregression of the exchange isotherm (Appendix 4B).Example 4.3 Determine which cationKor Ca2is selectively enrichedduring the ion exchange reaction described in Example 4.2.The Gaines-Thomas conditional selectivity coefficient for the exchange reac-tion in Example 4.2 is KcGT 0:37. Selectivity in an asymmetric exchange reac-tion can be determined only by comparing the experimental equivalentFIGURE 4.7 The asymmetric A,B2 cation exchange isotherms in three solutions, where theionic strengths are 0.1 M, 0.01 M, and 0.001 M. The isotherm plots are for a Gaines-Thomasselectivity coefficient KGT 14 ~ ~2 4 ~Soil and Environmental Chemistry132exchange is predicted to be 0.65 for the solution composition as specified inExample 4.2 K 10:17mM and Ca 0:565 mM. The experimentalequivalent fraction ~ECa2 is 0.50, clearly demonstrating that selective exchangedepletes Ca (and enriches K).A least sum-square regression of symmetric Mg2,Ca2 exchange fromJensen and Babcock (1973) appears in Figure 4.8. The symmetric exchangeisotherm model (Eq. (4.8)) estimates of the Gaines-Thomas selectivity coeffi-cients KGT for these data are 0.616 (I 0.001 M) and 0.602 (I 0.01 M).A single-value Gaines-Thomas selectivity coefficient KGT appears to be anacceptable model for the data in Figure 4.8.Figure 4.9 is a symmetric exchange isotherm with a nonselective isotherm(i.e., KGT 1) extending from the lower left corner to the upper right corner.If data are plotted on the nonselective isotherm, the ion ratios in solution andexchange is found by solving the preceding quadratic equation.~ECa2 x b b2 4 a cp2 a~ECa2 1:233 103 1:233 103 2 4 5:650 104 5:650 104 q2 5:65 104 ~ECa2 1:233 103 2:444 107p1:130 103 ~ECa2 1:233 103 4:944 104 1:130 103 ~ECa2 7:390 1041:130 103 0:65The exchanger-bound equivalent fraction ~ECa2 for nonselective asymmetric5:65 10 1 2 ECa2 ECa2 1:034 10 ECa25:65 104 ~E2Ca2 2 5:65 104 1:034 104 ~ECa2 5:65 104 0The exchanger-bound equivalent fraction ~ECa2 for nonselective asymmetricfractionfor example, ~ECa2with the equivalent fraction of that same ion withthe selectivity coefficient KGT set equal to 1. (NOTE: The solution composition inboth cases must be identical; only the equivalent fractions on the exchanger willdiffer.)Define : KGT ~ECa2 K 2~E2K Ca2 1~E2K Ca2 1 ~ECa2 K 2 1 ~ECa2 2 5:65 104 ~ECa2 1:017 102 2in the exchange complex are identical for all compositions EA ~EA .FIGURE 4.8 The experimental cation exchange isotherm for symmetric Mg2,Ca2 exchange (Jensen and Babcock, 1973) at two ionic strengths and sum-square regression estimatesof single-value Gaines-Thomas selectivity coefficients KGT.FIGURE 4.9 The exchange isotherm for nonselective symmetric A,B exchange (i.e.,KGT 1) appears as a straight line.Chapter 4 Ion Exchange 133Experimental symmetric exchange data rarely exhibit nonselective exchange;the results in Figures 4.4, 4.5, and 4.7 are more typical.The asymmetric exchange isotherm (Eq. (4.9)) also permits estimates ofKGT through the least sum-square regression of the experimental exchangeisotherm. A least sum-square regression of the asymmetric K,Ca2 exchange from Jensen and Babcock appears in Figure 4.10. The model esti-mates of the Gaines-Thomas selectivity coefficients KGT for these data are0.0463 (I 0.001 M) and 0.0931 (I 0.01 M).Physical Basis for Ion SelectivityIon selectivity appears to arise from differences in the Coulomb interactionbetween ions of the exchange complex and charged sites of the exchanger. Thehydration of ions in the exchange complex determines how close they canapproach surface-charge sites, which determines the energy that binds the ionsin the exchange complex. Ions that can approach the surface more closelyionssurrounded by fewer water moleculesare selectively adsorbed relative toions whose hydrated radius keeps them further from the surface-charge site.Argersinger and colleagues (1950) and Gaines and Thomas (1953) showedthat the Gibbs free energy DGexchange of ion exchange is related to the sel-ectivity coefficient KGT. In those cases where a single-value selectivitySoil and Environmental Chemistry134FIGURE 4.10 The cation exchange isotherm for asymmetric K,Ca2 exchange (Jensen andBabcock, 1973) at two ionic strengths and the sum-square regression estimates of single-valueGaines-Thomas selectivity coefficients.coefficient KGT yields a good fit of the exchange isotherm, the single-valueselectivity coefficient KGT is a good estimate of the thermodynamic Gibbsfree energy of exchange constant DGexchange:DGexchange RT lnKGT 4:13Gast (1969) proposed a Coulomb expression for the Gibbs free energy ofexchange using the Debye-Huckel radius ri of closed approach for ions Aand B (e: charge of an electron; e0: permittivity of free space; e: dielectricconstant of water):Aaqsolution Bexchanger$ AexchangerBaqsolutionDGion exchange e24pe0e 1rA 1rB 4:14The radius ri of the closed approach for the exchangeable interlayer cationsK and Na is illustrated in Figure 4.11 based on molecular dynamic simula-tions of interlayer cations and water in a smectite (Tambach, Bolhuis et al.,Chapter 4 Ion Exchange 135FIGURE 4.11 Molecular dynamic simulations of the crystalline swelling of K- (top) and Na-saturated (bottom) smectite clay representing the two-layer hydrate. The probability distributionsnormal to the clay layers appear on the right. Source: Reproduced with permission from Tambach,T.J., Hensen, E.J.M., et al., 2004. Molecular simulations of swelling clay minerals. J. Phys. Chem.B 108, 75867596.2006). The position of interlayer K is relatively closer to the clay layer (andthe layer charge) than interlayer Na, meaning that K cations are held by astronger electrostatic force than Na cations.The Gibbs free energy DGexchange values listed in Tables 4.4 and 4.5 arefrom Gast (1969) and Krishnamoorthy and Overstreet (1950). Recent researchshows that the Debye-Huckel radii used by Gast lack a firm physical basis(Marcus, 1988; Ohtaki and Radnai, 1993; Abbas, Gunnarsson et al., 2002).A more reliable indication of ion hydration is the enthalpy of hydration(Marcus, 1987) listed in Table 4.4.Figure 4.12 plots the standard Gibbs free energy of symmetric univalentexchange DGexchangekJ mol1 as a function of the Debye-Huckel radius riTABLE 4.4 Standard Gibbs free energies of exchange DGexchange (kJ mol-1)and absolute standard enthalpy of hydration DHabsolute (kJ mol-1) for alkalimetal cations on Wyoming montmorillonite.Exchange Reaction DGexchange DHabsolute,kJ mol-1Na ! Cs 4.52 4.96Na ! Rb 2.65 2.85Na ! K 1.28 1.36Na ! Li 0.20 0.12Source: Data reproduced with permission from Gast, R.G., 1969. Standard free energies of exchangefor alkali metal cations on Wyoming bentonite. Soil Sci. 69, 4155.; Marcus, Y., 1987. Thethermodynamics of solvation of ions. Part 2. The enthalpy of hydration at 298.15 K. J. Chem. Soc.,Faraday Trans. I 83. 339349.TABLE 4.5 Standard Gibbs free energies of exchange DGexchange (kJ mol-1)and absolute standard enthalpy of hydration DHabsolute (kJ mol-1) fordivalent metal cations on Utah montmorillonite.Soil and Environmental Chemistry136Exchange Reaction DGexchange DHabsoluteCa2 ! Mg2 207 1949Ca2 ! Sr2 236 1470Ca2 ! Ba2 473 1332Ca2 ! Cu2 317 2123Ca2 ! Pb2 834 1572Source: Data reproduced with permission from Krishnamoorthy, C. and Overstreet, R., 1950.An experimental evaluation of ion-exchange relationships. Soil Sci. 69, 4155; Marcus, Y., 1987.The thermodynamics of solvation of ions. Part 2. The enthalpy of hydration at 298.15 K. J. Chem.Soc., Faraday Trans. I 83. 339349.Chapter 4 Ion Exchange 137and the absolute standard enthalpy of hydration DHabsolutekJ mol1 for alkalications. Figure 4.13 plots the standard Gibbs free energy of symmetric univalentexchangeDGexchangekJ mol1 as a function of the absolute standard enthalpy ofhydration DHabsolutekJ mol1 for selected divalent cations using selectivitycoefficients from Krishnamoorthy and Overstreet (1950).FIGURE 4.12 Ion exchange selectivity for Na exchange with Li, K, Rb, and Cs usingdata listed in Table 4.4 based on the correlation between the Gibbs free energy of exchangeDGexchange and (a) Debye-Huckel radii rA (modified from (Gast (1969)) and (b) absolute standardenthalpy of hydration DHabsolute of the ions.Soil and Environmental Chemistry138FIGURE 4.13 Ion exchange selectivity for Ca2 exchange with Mg2, Sr2, Ba2, Cu2, andPb2 (data listed in Table 4.5) based on the correlation between the Gibbs free energy ofexchange DGexchange and the absolute standard enthalpy of hydration of the ions (modified fromKrishnamoorthy and Overstreet (1950)).The correlation between the Gibbs free energy of exchange DGexchange andeither the Debye-Huckel radii (Gast, 1969, Figure 4.12a) or the absolute stan-dard enthalpy of hydration DHabsolute (Figures 4.12b and 4.13) is not withoutuncertainty. Gast noted the anomalous behavior of the Na, Li exchange.Figures 4.12 and 4.13 demonstrate that ion selectivity is correlated withion hydration, which affects the distance between ion and surface-charge siteand, thus, the strength of the Coulomb interaction between ion and site. Simi-lar results for symmetric alkaline earth cation exchange appear in the study byWild and Keay (1964).4.4.5. Other Influences on the Ion Exchange IsothermA single-value selectivity coefficient often yields a reasonable fit of theexchange isotherm, but there are numerous cases where experimentalexchange isotherm data deviate from a single-value selectivity coefficient.One way to evaluate the relative importance of deviations from a single-valueselectivity coefficient is to compare the deviation of data from a sum-squareregression using a single-value selectivity coefficient to displacement of theselectivity isotherm caused by ion selectivity.Two high-quality studies of symmetric exchange report sufficient data toplot the exchange isotherms: Na,K exchange (Jensen and Babcock,1973) and Ca2,Fe2 exchange (Saeki, Wada et al., 2004). The exchangeisotherms appear in Figure 4.14. Displacement of the exchange isotherm inboth cases indicates ion selectivity in the two exchange reactions (seeFigure 4.9). Notice that deviations of the data from the sum-square regressionon a single-value selectivity coefficient in the Na,K exchange example(Jensen and Babcock, 1973) are much smaller than the displacement causedChapter 4 Ion Exchange 139FIGURE 4.14 Ion exchange isotherm for symmetric exchange: (a) of Na,K (Jensen andBabcock, 1973) and (b) Ca2,Fe2 (Saeki, Wada et al., 2004). The experimental data are plot-ted as filled circles and the sum-square regression estimate of a single-value Gaines-Thomasselectivity coefficients KGT is plotted as a smooth line.strength (asymmetric exchange only) and ion selectivity.Soil and Environmental Chemistry140Do the deviations plotted in Figures 4.14 and 4.15 have thermodynamic sig-nificance? Systematic deviations of the type shown in Figures 4.14 and 4.15have little effect on the Gibbs free energy of exchange. Ruvarac and Vesely(1970) found that the value of the selectivity coefficient determined when theequivalent fraction of either ion is 0.5 is a good estimate of the selectivity coef-ficient determined by the integral method of Argersinger and colleagues (1950).A notable exception to the deviations from a single-value selectivity coefficientthat is shown in Figures 4.4, 4.5, 4.6, 4.8, 4.10, 4.14, and 4.15 is the symmetricMg2,Ca2 cation exchange on the Libby vermiculite (Petersen, Rhoadeset al., 1965; Rhoades, 1967), which is discussed in Appendix 4C.4.5. SUMMARYIon exchange is an extremely important chemical reaction in soils, sediments,and aquifers, a process that has profound effects on the solution concentrationof many ions. The ion exchange isotherm that describes the relation betweensolution composition and the ion exchange complex is influenced by twomajor factors: ionic strength and ion selectivity.Ionic strength affects the exchange isotherm only for asymmetricexchange reactions, the effect being proportional to the equivalent concentra-tion of the solution C0. Ion selectivity influences symmetric and asymmetricexchange reactions and arises from Coulomb interactions between the ionand the exchange site (see Figure 4.11).The strength of the Coulomb interaction between ion and site relate to ionhydration because the hydration shell determines how closely each ion canapproach the exchange site. Weakly hydrated ions that are able to shed theirhydration shell can bind more strongly to the exchange site than stronglyby ion selectivity. Deviations in the Ca2,Fe2 exchange example (Saeki,Wada et al., 2004) are comparable to the displacement caused by ion selectivitybecause, in this case, the selectivity coefficient is rather small (1.2).Two high-quality studies of asymmetric exchange report sufficient data toplot the exchange isotherms at two different ionic strengths: K,Ca2 exchange (Jensen and Babcock, 1973; Udo, 1978). The exchange isothermsappear in Figure 4.15. Displacement of the exchange isotherm in both cases indi-cates the effects of ionic strength (dashed line) and ion selectivity (solid line) onthe exchange isotherm (see Figure 4.10). Notice that deviations of the data fromthe sum-square regression on a single-value selectivity coefficient in theK,Ca2 exchange example (Jensen and Babcock, 1973; Udo, 1978) aremuchsmaller than the displacement caused by both ionic strength and ion selectivity.Deviations of the exchange isotherm data in all of these cases from asingle-value selectivity coefficient are significant, but the magnitude of thesedeviations is small relative to the major influences we have identified: ionichydrated ions. As a general rule, a single-value selectivity coefficient is aChapter 4 Ion Exchange 141good model of the exchange isotherm. In certain cases (Appendix 4C) theselectivity coefficient adopts two limiting values representing preferred inter-layer hydration states and undergoes an abrupt transition between the two lim-iting values when the exchange complex reaches a critical value.FIGURE 4.15 Ion exchange isotherm for asymmetric K,Ca2 exchange: (a) I 0.001(Jensen and Babcock, 1973) and (b) I 0.012 (Udo, 1978). The experimental data are plottedas filled circles and the sum-square regression estimate of a single-value Gaines-Thomas selectiv-ity coefficients KGT is plotted as a smooth line. The nonselectivity isotherm is plotted as a dashedline in both cases.APPENDIX 4A. THERMODYNAMIC AND CONDITIONALSELECTIVITY COEFFICIENTSTable 4A.1 lists the most commonly encountered ion exchange selectivity quo-tients and coefficients. Each solution concentration term in Table 4.3 is replacedby the corresponding solution activity (see Chapter 5), and each exchangeablemole fraction or equivalent fraction is multiplied by the corresponding exchangeactivity coefficient. All of the expressions are based on specific exchange reac-tions, symmetric and asymmetric, and some examples involving abundant ionsappear following.The Gapon quotient for asymmetric exchange demands further explana-tion because Gapon (1933) employed a convention quite different from otherscientists. The term designating an exchanger-bound cation Au is the equiv-alent fraction ~EAu , but it represents a single negatively charged site plus oneSoil and Environmental Chemistry142reaction, meaning that the stoichiometric coefficient for solution cationAu aq is 1=u .The Gapon activity coefficient f 00Au is different from the Gaines-Thomasactivity coefficient f 0Au even though both use equivalent fraction ~EAu to quan-tify exchanger-bound species. The numerical value of ~EAu is identical regard-less of convention; both count one unit of charge. The activity coefficients, onTABLE 4A.1 Thermodynamic Ion Exchange Selectivity Coefficients andQuotientsDesignation Symmetric Exchange Asymmetric ExchangeVanselowKV aK fNa ~NNa fK ~NK aNa KV aCa2 fNa ~NNa 2fCa2 ~NCa2 a2NaGaines-ThomasKGT aK f 0Na ~ENa f 0K ~EK aNa KV KGT aCa2 f 0Na ~ENa 2f 0Ca2 ~ECa2 a2NaGaponKG aK f 00Na ~ENa f 00K ~EK aNa KV KG a1=2Ca2 f 00Na ~ENa f 00Ca2 ~ECa2 aNaunit of charge of the exchanger cation. The Gapon exchanger-bound speciesare charge neutral:Na aq solution SCa2exchanger$ SNaexchanger 12Ca2 aq solutionThe stoichiometric coefficient for exchange specie SAu is always 1 because itconsists of one negative charge (representing one unit of charge from the site)and one positive charge (representing one unit of charge from the exchange-able cation). Gapon (1933) counts one unit of charge throughout the exchangesolution exchanger exchanger solutionChapter 4 Ion Exchange 143The K equivalent fraction on the exchanger ~EK varies as a function of thecorresponding equivalent fraction in solution EK . The single-value selectivitythe other hand, are different because the two conventions apply different stoi-chiometric coefficients to the exchanging cations.APPENDIX 4B. NONLINEAR LEAST SQUARE FITTINGOF EXCHANGE ISOTHERMSSymmetric Exchange: The symmetric exchange isotherm (Eq. (4.8)) is thebasis for the nonlinear least sum-square regression estimate of selectivitycoefficient KGT. The simplest regression model uses a single value of theselectivity coefficient KGT, which is tantamount to assuming that the exchangecomplex behaves as an ideal mixture. Section 4.4.5 discusses the relativeimportance of nonideal behavior of the exchange complex.Consider the symmetric Ca2 Mg2 exchange reaction:Ca2aqsolution Mg2exchanger$ Ca2exchangerMg2aqsolutionThe Ca2 equivalent fraction on the exchanger ~ECa2 varies as a function ofthe corresponding equivalent fraction in solution ECa2 . The single-valueselectivity coefficient model for this exchange reaction ~ECa2 is a functionof a single parameter KGT and a single solution composition variabletheCa2 equivalent fraction in solution ECa2 :~ECa2 KGT ECa21 ECa2 KGT ECa24B:1The optimal single-value selectivity coefficient parameter KGT is found byminimizing the sum-square error for all data points in the exchange isotherm.A least sum-square regression of symmetric Ca2 Mg2 exchange fromJensen and Babcock (1973) appears in Figure 4.8:S Xi~ECa2 ~ECa2 2 4B:2Asymmetric Exchange: The asymmetric exchange isotherm (Eq. (4.9)) alsopermits estimates of KGT through the least sum-square regression of the exper-imental exchange isotherm. The simplest model, once again, uses a singlevalue of the selectivity coefficient KGT.Consider the asymmetric K Ca2 exchange reaction:2 Kaq Ca2 $ 2 K Ca2aqcoefficient model (Eq. (4B.3)) for this exchange reaction ~EK is a quadraticSoil and Environmental Chemistry144CaexchangerMg aq $ Ca aq MgexchangerKcGT ~EMg2 Ca2 ~ECa2 Mg2 The exchange isotherm (Figure 4C.1) strongly deviates from a single-valueselectivity coefficient, jumping from KcGT 0:6 in the range ~EMg2 < 0:40to KcGT 10 as ~EMg2 > 0:70.The explanation for this dramatic change in cation selectivity appears to berelated to the effect of interlayer composition on the crystalline swelling state(see Chapter 3). Petersen and colleagues (1965) suggest the exceedinglystructured (i.e., crystal-like) hydrated interlayer for Mg2-saturated vermiculiteapparently accounts for KcGT 10 when the exchange complex is dominated byMg2,Ca2 exchange reaction on vermiculite from Libby, Montana. Simi-lar results were found for Mg2,Ba2 exchange reaction involving vermic-ulite (identified as the World vermiculite) from Transvaal, South Africa (Wildand Keay, 1964):2 2 2 2Petersen and colleagues (1965) and Rhoades (1967) reported the symmetric b 2 C0 KcGT E2K1 EK 4B:4The optimal single-value selectivity coefficient parameter KGT is found byminimizing the sum-square error for all data points in the exchange isotherm:S Xi~EK ~EK 2 4B:5A least sum-square regression of asymmetric K,Ca2 exchange fromJensen and Babcock (1973) appears in Figure 4.15.APPENDIX 4C. EQUIVALENT FRACTION-DEPENDENTSELECTIVITY COEFFICIENT FOR (Mg2, Ca2) EXCHANGEON THE LIBBY VERMICULITEfunction of a single parameter KGT and two solution composition variablessolution normality C0 and the K equivalent fraction in solution EK(Eq. (4B.4)):~EK bb2 4 bp24B:3Mg2 i:e:, ~EMg2 > 0:60. In contrast, the interlayer for Ca2-saturatedChapter 4 Ion Exchange 145vermiculite i:e:, ~EMg2 < 0:40 may be less structured (i.e., fluid-like), allow-ing differences in cation hydration to determine the position of interlayercations and, therefore, selectivity (see Figure 4.13).Picture the evolution of the hydrated interlayer of the Libby vermiculiteas the interlayer Mg2 equivalent fraction ~EMg2 decreases from 1.0 (i.e.,Mg2-saturated interlayer). Initially, the interlayer behaves as if it is a solidsolutionthe position of the interlayer cations fixednegating any differ-ences in the hydration shell surrounding the cations. In this state, selectivityfavors Mg2 relative to Ca2. When the interlayer equivalent fraction ~EMg2decreases below 0.6, the interlayer begins to melt, allowing interlayer cationsto adopt positions relative to the clay layer that are consistent with the dimen-sions of their respective hydration shells. Interlayer melting is complete oncethe equivalent fraction ~EMg2 decreases below 0.4. At this interlayer composi-tion, the lower hydration energy of Ca2 ions (see Figure 4.13) allows themto reside closer to the clay layer, and the higher hydration energy of Mg2ions forces them to reside further from the clay layer. As a consequence,exchange selectivity favors Ca2 relative to Mg2 for compositions where~EMg2 < 0:40.FIGURE 4C.1 The ion exchange isotherms for symmetric Mg2,Ca2 exchange on a vermic-ulite sample from Libby, Montana (Petersen, Rhoades et al., 1965), exhibit a dramatic change inselectivity.alay sos tin swh yco -goPro1.2. Determine which cationK or Ca is selectively enriched during ionexchange reaction from Problem 1. This requires analysis of the exchange iso-Soil and Environmental Chemistry146therm for this reaction. Please show results to support your answer. (HINT:You may wish to use the quadratic relation from the exchange isotherm forasymmetric univalent-divalent exchange.)SolutionSelectivity in an asymmetric exchange reaction can be determined only bycomparing the experimental equivalent fraction on the exchanger of an ioninvolved in the exchangefor example, ~ECa2with the equivalent fractionKGT 0:88 0:40 1030:12 2 0:20 103 1:41 1072:80 106 5:04 1022~EK 2:218:6 0:12~ECa2 1 ~EK 0:88 2SolutionDetermine the equivalent fraction of each exchangeable cation before enter-ing each value into the Gaines-Thomas selectivity expression.~EK mKmK 2 mCa2 mKCECKGT Ca~E2K Ca2 ~ECa2 ~EK 1What is the value of the Gaines-Thomas selectivity coefficient KGT forK,Ca2 exchange in this soil?~E 2 K 2blemsThe CEC of a soil whose clay fraction is predominantly smectite is 18.6cmolc kg1. An asymmetric K,Ca2 exchange experiment reportsthe following results for a solution containing 0.40 mM K aq and0.20 mM Ca2 aq : exchangeable K equals 2.2 cmolc kg1, exchangeableCa2 equals 16.4 cmolc kg1.2 K ex Ca2aq $ Ca2 ex 2 KaqThe behavior seen in Figure 4C.1 appears to be unique to vermiculite,er silicate whose layer charge permits crystalline swelling but preventmotic swelling. Furthermore, the cation exchange reaction apparently musvolve Mg2. Symmetric and asymmetric exchange isotherms for reactionere Mg2 is not involved appear to conform to a single-value selectivitefficient that is appropriate to the hydration energy of the cations undering exchange.of that same ion with the selectivity coefficient KGT set equal to 1.3.Chapter 4 Ion Exchange 147ing each value into the Gaines-Thomas selectivity expression.and 0.04 M, respectively. We will neglect activity coefficients for ions dis-solved in solution.2 Na ex Ca2aq $ Ca2 ex 2 NaaqKGT ~ECa2 Na 2~E2Na Ca2 ~ECa2 ~ENa 1What is the value of the Gaines-Thomas selectivity coefficient KGT forNa,Ca2 exchange in this soil?SolutionDetermine the equivalent fraction of each exchangeable cation before enter-in the soil solution, which occupies 30% of the soil volume, are 0.025 Mmol kg of exchangeable Na . Measured concentrations of Ca and Na~ECa2 4:0016 104 1:6013 107 1:6000 107p4:0000 104 ~ECa2 4:0016 104 1:13 105 4:0000 104 ~ECa2 3:89 1044:00 104 0:97The Ca2 equivalent fraction on the exchanger for nonselective exchangewould be 0.97, while the experimental equivalent fraction is 0.88. The soilclay favors K over Ca2.A soil whose clay fraction is predominantly smectite has a CEC of 26cmolc kg1 balanced by 0.117 mol kg1 of exchangeable Ca2 and 0.0261 2 2:0 104 ~E2Ca2 4:0 104 ~ECa2 2:0 104 0Solve the quadratic equation for the Ca2 equivalent fraction on theexchanger.~ECa2 x b b2 4 a cp2 a~ECa2 4:0016 104 4:0016 104 2 4 2:0 104 2:0 104 q2 2:0 104 Define : KGT 1~E2K Ca2 1 ~ECa2 K 2 1 ~ECa2 2 0:2 103 ~ECa2 0:4 103 22:0 104 1 2 ~ECa2 ~E2Ca2 1:6 107 ~ECa2KGT ~ECa2 K 2~E2K Ca2 4.y148~ECa2 5:16 102 5:16 102 2 4 2:50 102 2:50 102 q2 2:50 102 ~ECa2 5:16 102 1:63 104p5:00 102 ~ECa2 5:16 102 1:28 102 5:00 102 ~ECa2 3:88 1075:00 102 0:776~E2Na Ca2 1 ~ECa2 Na 21 ~ECa2 2 0:025 ~ECa2 0:04 20:025 1 2 ~ECa2 ~E2Ca2 1:60 103 ~ECa20:025 ~E2Ca2 2 0:025 1:60 103 ~ECa2 0:025 0Solve the quadratic equation for the Ca2 equivalent fraction on theexchanger.~ECa2 x b b2 4 a cp2 aisotherm for asymmetric univalent-divalent exchange.)Solution 1Selectivity in an asymmetric exchange reaction can be determined only bycomparing the experimental equivalent fraction on the exchanger of an ioninvolved in the exchangefor example, ~ECa2with the equivalent fractionof that same ion with the selectivity coefficient KGT set equal to 1.KGT ~ECa2 Na 2~E2Na Ca2 Define : KGT 1 answer. (HINT: You may wish to use the quadratic relation from the exchange~ENa mNamNa 2 mCa2 mNaCEC~ENa 2:626 0:10~ECa2 1 ~ENa 0:90KGT 0:90 0:04 20:10 2 0:025 1:44 1032:50 104 5:76Determine which cationCa2 or Nais selectively enriched during theion exchange reaction described in Problem 3. This requires analysis of theexchange isotherm for this reaction. Please show results to support yourSoil and Environmental ChemistrThe Ca2 equivalent fraction on the exchanger for nonselective exchangewould be 0.776, while the experimental equivalent fraction is 0.90. The soilclay favors Ca2 over Na.5.Chapter 4 Ion Exchange 149clay favors Ca2 over Na.What determines the relative selectivity of two ions in an ion exchangereaction?would be 0.22, while the experimental equivalent fraction is 0.10. The soil~ENa 0:22The Na equivalent fraction on the exchanger for nonselective exchange~ENa 6:4 102 6:4 102 2 4 6:4 102 q21 ENa 1 0:44 b 2 C0 KGT ENa 2 9:0 10 1 0:44 6:4 102Selectivity in an asymmetric exchange reaction can be determined only bycomparing the experimental equivalent fraction on the exchanger of an ioninvolved in the exchangefor example, ~ECa2with the equivalent fractionof that same ion with the selectivity coefficient KGT set equal to 1.C0 Na 2 Ca2 4:0 102 2 2:5 102 ENa 4:0 1029:0 102 0:442 2 2b 2 C0 KcGT E2Na1 ENaNa 22 Naaqsolution Ca2exchanger$ 2 NaexchangerCa2aqsolutionKcGT Ca2 ~E2Na~ECa2 Na 2The univalent-divalent asymmetric exchange isotherm as a function of theunivalent cation equivalent fractions follows:~E2Na 2 C0 KcGT E2Na1 ENa0@1A ~ENa 2 C0 KcGT E2Na1 ENa0@1A 0~E bb2 4 bpSolution 2An alternative solution adapts the expression for asymmetric Na,Ca2 exchange isotherm.5.2 Activity and the Equilibrium Calcite-Apatite-PyromorphiteSolubility 1995.15.1.1. Thermodynamic Functions for Chemical ReactionsYou first encountered thermodynamics and the equilibrium concept in general--ant energy, kinetic energy, or heat in chemical bonds or transforming the energystored in chemical bonds into heat, kinetic energy, and radiant energy. This energyconversion is quantified in various ways: the enthalpy of reaction DHrxn, theentropy of reaction DSrxn, and the Gibbs energy of reaction DGrxn. Each of theseenergy variables changes with absolute temperatureSoil and Environmental Chemistry.# 2012 Elsevier Inc. All rights reserved.chemistry. This initial encounter covered several important ideas while passingover other ideas that, in the context of environmental chemistry, we must confront. Every chemical reaction involves the conversion of energy: capturing radi. THE EQUILIBRIUM CONSTANTConstant 1535.3 Modeling WaterChemistry 1565.4 Summary 187Appendix 5A. ChemEQL ResultData File Format 187Appendix 5B. Validating WaterChemistry Simulations 188Appendix 5C. ValidationAssessment for Examples5.13 and 5.16 193Appendix 5D. Cinnabar Solubilityin an Open System Containingthe Gas DihydrogenSulfide 196Appendix 5F. SimultaneousGibbsite-VarisciteSolubility 200Appendix 5G. Apatite Solubility asa Function of pH 200Appendix 5H. Effect of theCitrate on the Solubility of theCalcium Phosphate MineralApatite 201Appendix 5I. Effect of the BacterialSiderophore DesferrioxamineB on the Solubility of the IronOxyhydroxide Goethite 203Chapter 5Water ChemistryChapter Outline5.1 The Equilibrium Constant 151 Appendix 5E. SimultaneousT and pressure P. The15115side of Eq. (5.3) is the product of a constant and two parameters: the universalgas constant R (8.314 472 J K1 mol1), the absolute temperature T (K), andthe natural logarithm of the reaction quotient Q (Eq. (5.4)). We will symbolizethe concentration of component (i) as Ci rather than the more familiar squarebrackets:DGrxn DGrxn RT ln Q 5:3Q M nM N nN . . . CnMM CnNN . . . 5:4i products j reactants5.1.2. Gibbs Energy of Reaction and the Equilibrium ConstantThe standard state, of course, is not representative of prevailing conditions inthe environment. Remarkably enough, a simple function relates the Gibbsenergy of reaction under prevailing conditions DGrxn to the Gibbs energy ofreaction under standard conditions DGrxn. The second term on the right-handDGf ,CaCO3 s DHf ,CaCO3 s T DSf ,CaCO3 s Chemists have adopted a standard state conventionthe chemical state ofevery element and compound at 298.15 K (25C) and 1 atmosphere. Bythis convention, the enthalpy, entropy, and Gibbs energy of formation ofany compound from its constituent elements are the standard enthalpyDHf , standard entropy DSf , and standard Gibbs energy DGf of formation,respectively. The standard Gibbs energy of any reaction DGrxn is a func-tion of the standard Gibbs energy of formation DGf for the educts and pro-ducts involved:DGrxn Xni DGf , i !Xnj DGf , j !5:2symbols ni represent the stoichiometric coefficients for each educt (A, B, . . .) andproduct (M, N, . . .) involved in the reaction in the hypothetical chemical reaction:nA A nB B . . .educts$ nM M nN N . . .productsDGrxn DHrxn T DSrxn 5:1A chemical reaction exists for every compound, quantifying the energy con-version upon formation of the compound from its constituent elements:enthalpy of formation DHf , entropy of formation DSf , and Gibbs energy offormation DGf . The formation of one mole of the mineral calcite CaCO3 s from its constituent elements follows:Ca s C s 32O2 g elements$ CaCO3 s compoundSoil and Environmental Chemistry2A nA B nB . . . CnAA CnBB . . .Chapter 5 Water Chemistry 153The reaction quotient Q (Eq. (5.4)) is written as a product of concentrations,just as it would appear in any general chemistry textbook. Equation (5.4)relating the Gibbs energy of reaction under prevailing conditions DGrxn tothe Gibbs energy of reaction under standard conditions DGrxn and the reactionquotient Q, however, is an approximate equality (more on that in the follow-ing section).Figure 5.1 demonstrates graphically that the Gibbs energy of reactionDGrxn under prevailing conditions is a linear function of the natural logarithmof Q with a temperature-dependent slope: RT. Two significant interceptsoccur in the linear relation between the Gibbs energy of reaction under pre-vailing conditions DGrxn and the natural logarithm of Q (Figure 5.1, right):when ln Q 0 (standard conditions: DGrxn DGrxn) and when ln Q 1(equilibrium: DGrxn 0 and DGrxn RT ln K ). At equilibrium the reactionquotient Qeq attains an invariant value known as the thermodynamic equilibriumconstant K:ln K DGrxnRT5:5AK eDGrxn=RT 5:5BFIGURE 5.1 The transformation of eductsinto productsregardless of prevailing condi-tions (horizontal axis)yields a Gibbs energyof reaction DGrxn (vertical axis) dependent onthe reaction quotient Q and absolute tempera-ture T.5.2. ACTIVITY AND THE EQUILIBRIUM CONSTANT5.2.1. Concentrations and ActivityIf we write the reaction quotient Q or the equilibrium constant K using con-centrations (Eq. (5.4))the way it is written in most general chemistrybooksthen Eq. (5.3) must include an approximate equality. The need forthis became apparent when component concentrations are used to calculatethe equilibrium constant K under what appear to be equilibrium conditions.It soon became evident that the apparent equilibrium coefficient forreactions usually encountered in environmental chemistryaqueouselectrolyte solutionsclearly varied as a function of the electrolytePeter Debye and Erich Huckel (1923), to seek an explanation. Debye andSoil and Environmental Chemistry154ai gi Ci 5:85.2.2. Ionic Strength IIn their theory of electrolyte solutions, Debye and Huckel derived an expressionknown as the ionic strength Ithat was the natural measure of electrolyteconcentration accounting for variability in the conditional equilibrium coef-ficient Kc (Eq. (5.6)). The ionic strength I is a sum over the concentration ofeach ionic solute Ci multiplied by the square of the ion charge ziI 12Xiz2i Ci 5:9Ions with a larger valence have a disproportionate influence on ionic interac-tions in electrolyte solutions.5.2.3. Empirical Ion Activity Coefficient ExpressionsDebye and Huckel derived a simple expression for ion activity coefficientscentration into parametersion activity coefficients githat adjusted theconcentration of each ion involved in the reactioneduct or product. Theconditional equilibrium coefficientthe equilibrium coefficient that varieswith electrolyte concentrationis typically assigned the symbol Kc:K gM CM nM gN CN nN . . .gA CA nA gB CB nB . . .K gnMM g nNN . . .g nAA g nBB . . .0@1A C nMM C nNN . . .C nAA C nBB . . .0@1AK gnMM g nNN . . .g nAA g nBB . . . Kc 5:6Both the reaction quotient Q and the equilibrium constant K are the product ofion activities (Eq. (5.7)). Each ion activity ai is the product of the concentra-tion Ci and an ion activity coefficient gi that depends on electrolyte concentra-tion (Eq. (5.8)):K anMM a nNN . . .a nAA a nBB . . . 5:7Huckel collected all of the variability caused by changes in electrolyte con-concentrationeven if some of the ions dissolved in the solution were noteducts or products in the chemical reaction. This prompted two chemists,based on fundamental physical principles. The Debye-Huckel limiting law(Eq. (5.10)) is a single-parameter expression (A 0.5109 at 25C) that is ade-quate for most freshwater environments where ionic strength I tends to be 0.01 M. Guntelberg (1926) developed an empirical single-parameterexpression (Eq. (5.11)) based on the Debye and Huckel limiting law, extend-ing the ionic strength I range to 0.1 M:log gi A z2i Ip5:10log gi A z2i Ip1 Ip 5:11Davies (1938) developed a two-parameter empirical expression that extendsthe ionic strength range to 0.5 M. None of these expressions is adequatefor seawater or extremely saline lake or groundwater:log gi A z2i Ip1 Ip 0:2 I 5:12How significant are ion activity coefficients under prevailing environmentalconditions? Were Debye and Huckel, Guntelberg, and Davies engaged in min-utiae, or would the use of concentration rather than activity yield significantChapter 5 Water Chemistry 155FIGURE 5.2 The effect of increasing electrolyte concentration C on the Davies activity coeffi-error when applying equilibrium principles to environmental chemistry?Figure 5.2 illustrates the magnitude of the error.In Chapter 7 we estimate the ionic strength I of calcareous water in contactwith the atmosphere, an electrolyte solution whose major constituent iscients for univalent, divalent, and trivalent symmetric electrolytes.Soil and Environmental Chemistry156calcium carbonate dissolved from the mineral calcite CaCO3 s and aqueouscarbon dioxide from the atmosphere. The ionic strength I of this representa-tive environmental electrolyte solution is about 1 millimolar.This ionic strength I representative of natural waters is indicated inFigure 5.2 by a dashed line. The error is roughly 48% for trivalent ions androughly 18% for divalent ions in 103 M solutions, significantly greater thanexperimental error that tends to be on the order of 1%. Based on a reasonableestimate of the ionic strength, we are likely to find that the error introducedfrom reliance on concentrations rather than activities in the environmentalcontext is much too great to neglect.5.3. MODELING WATER CHEMISTRY5.3.1. Simple Equilibrium SystemsGeneral chemistry demonstrates the properties of simple equilibrium systemssuch as the hydrolysis of weak monoprotic acids, the formation of soluble ionpairs, or the solubility of systems containing a single ionic compound. Some-what more complicated equilibrium systemsrequiring either simplifyingassumptions or complex algebraic manipulationsinclude the hydrolysis ofweak diprotic acids, the effect of ion-pair formation on the solubility of a singleionic compound, or the simultaneous solubility of two ionic compounds with asingle common ion. None of these simple systems approach the complicatedaqueous solutions commonly encountered by environmental chemists.In this section we briefly consider simple equilibrium systems of the type youwould have encountered in general chemistry, pausing to consider the simplifyingassumptions used in general chemistry to solve what soon become very compli-cated problems. This review serves two purposes: it reminds us of familiar meth-ods for solving equilibrium problems, and it will demonstrate the need for activitycorrections and computer models to solve realistic water chemistry problems.Hydrolysis of a Weak Monoprotic AcidGeneral chemistry usually examines two problems involving the hydrolysis ofweak monoprotic acids (and bases): calculating the hydrolysis constant for asolution containing a weak acid (or base) when the pH is known or calculatingthe pH of a solution where the hydrolysis constant is known.An important problem-solving method employs an equilibrium tablelisting the initial concentration of the weak acid (or base) and a variable xrepresenting the moles of weak acid or base converted into conjugate base(or conjugate acid). The equilibrium table assigns concentration values toeach component in the equilibrium expression, creating an algebraic expres-sion that is either solved directly or is simplified before attempting a solution.One thing you would not have noticed from the examples appearing ingeneral chemistry is a tendency to use weak acid concentrations that are farriu c hefolChapter 5 Water Chemistry 157Ka CA CHCHA x x0:10 x We know x from the pH: x CH 10pH 102:94 1:15 103. Sincex An equilibrium table assigns values to each component in the equilibriumA second si ibriu enyi h athe t aSoil and Environmental Chemistry158x x2The m x 0 e esti-mate x of e weakacid on. 10 mil-Chapter 5 Water Chemistry 159The equilibrium expression using concentrations from the preceding tablefollows.Ka CA CHCHAKa x x1:50 104 x In this example we solve the quadratic equation rather than using the simpli-fying assumption made in Example 5.3.limolar in the environment, but typical weak acid concentrations tend to belower by one to four orders of magnitude. Concentrations encountered inthe environment require solving the quadratic equation, as illustrated inExample 5.4.Example 5.4 Calculate the pH of a weak acid solution when given the hydro-lysis constant of the acid.The typical acetic acid concentration in soil pore water rarely exceeds 150mM. Calculate the pH of a 150 mM aqueous solution of acetic acid(Ka 1:86 105).The solution uses an equilibrium table to assign values to each component inthe equilibrium expression.Stage acetic acid aq $ acetate aq H aq Initial 1:50 104 0 0Reaction x x xEquilibrium 1:50 104 x x xconcentrati Some weak acids reach concentrations as high asd value for almost two order magnitud smaller than theassumption ade in Example 5.3is sa bility constant Ks0.Soil and Environmental Chemistry160solubility constant Ks0 of the solid.Gypsum is a relatively soluble soil mineral found in arid and semiarid cli-mates, where chemical weathering is slowed by the scarcity of rainfall. Calculatethe solubility of gypsum in aqueous solution (Ks0 2:63 105; logKs0 4:58).Use an equilibrium table to assign values to each component in the equilib-rium expression. All of the Ca2 and SO24 dissolved in solution at equilibriumcome from the mineral gypsum.Stage CaSO4 2H2O s $ Ca2 aq SO24 aq Initial 1 0 0Reaction 1 x xExample 5.5 Calculate the solubility of a sparingly soluble ionic solid given theAqueous Solubility of an Ionic CompoundThe solubility of ionic solids is another simple chemical equilibrium process dis-cussed in general chemistry. Solubility is a key water chemistry process involvingboth the dissolution and precipitation of sparingly soluble minerals during thechemical weathering stage of the rock cycle and soil formation. The chemistryof many inorganic pollutants, as it pertains to both biological availability to livingorganisms and remediation treatment, involves solubility reactions.Consider the solubility reaction of the mineral gypsum CaSO4 2H2O s and the equilibrium solubility expression. The conditional solubility coeffi-cient Kcs0 is the product of ion concentrations in solution, while the thermody-namic solubility constant Ks0 is the product of ion activities in solution. Thesymbol Ks0 indicates an equilibrium expression in which the solute ions areidentical to the ions in the ionic solid:CaSO4 2H2O s $ Ca2 aq SO24 aq Kcs0 CCa2 CSO24Ks0 aCa2 aSO24Example 5.5 demonstrates how solubility is determined when given the solu-x 1:86 105 1:86 105 2 4 1:50 104 1:86 105 2x 4:44 105 CHpH 4:35The simplifying assumption made in Example 5.3 would definitely not work ina more dilute acetic acid solution. Dilute solutions require application of the qua-dratic equation.Equilibrium2qx K1K2a 4 CT Kaxpxriu si o lefolKs0 CCa2 CSO2which the solute ions are identical to the ions in the ionic solid:Chapter 5 Water Chemistry 161Al OH 3 s $ Al3 aq 3 OH aq Kcs0 CAl3 C3OHKs0 aAl3 a3OHExample 5.6 Calculate the solubility of a sparingly soluble ionic solid given thesolubility constant Ks0 of the solid.Gibbsite is a soil mineral found in humid climates, where chemicalweathering is quite advanced. Calculate the solubility of gibbsite in aqueoussolution (Ks0 1:29 1034; logKs0 33:89).Use an equilibrium table to assign values to each component in the equilib-rium expression. We will assume no further reactions occur; all of the Al3 andOH dissolved in solution at equilibrium come from the mineral gibbsite.Stage Al OH 3 s $ Al3 aq 3 OH aq Initial 1 0 0Reaction 1 x 3 xCCa2 10 MCSO24 102:29MDividing logKs0 by 2 is equivalent to taking the square root. Aqueous solutionis saturated by (i.e., in solubility equilibrium with) gypsum when 102.29 molesdissolve per liter.Example 5.6 represents a more complicated solubility reaction because thedissolution of each mole of the aluminum hydroxide mineral gibbsiteAl OH 3 s releases four moles of ions into solution: one mole of the ionAl3 and three moles of the hydroxide ion OH. As in the solubility reactionof the mineral gypsum, the symbol Ks0 indicates an equilibrium expression in4Ks0 x xSince the right side of the expression is a product of ion concentrationsrather than activitiesit does not exactly equal the thermodynamic solubilityconstant.x Ks0p 2:63 105p 104:58 1=2x 102:29 5:13 1032:29lows.EquilibriumThe equilib m expression u1ng concentrations frxm the preceding tab3 x16environment appear in Table 5.1. Some of these gasesdioxygen, dinitrogen,and methanedo not react with water other than hydrating. Othersnitrogenmonoxide, nitrogen dioxide, sulfur dioxide, sulfur trioxide, and carbon dioxide,to name a fewreact with water to form acids. Hydrogen sulfide dissolvedin water undergoes hydrolysis without combining with water.The Henrys Law constant kH is a good predictor of solubility for nonreactivegases. The solubility of reactive gases depends on acid-base reactions occurringin solution in addition to the partial pressure of the gas in the atmosphere inA system common in water chemistry is liquid water in contact with an atmo-sphere containing several gases. Each gas in the atmosphere will dissolve to somedegree in water. Henrys Law states that the amount of a gas dissolved in a liquidX aq is proportional to the partial pressure of the gasPX in the atmosphere in con-tact with the liquid. The proportionality constant is the Henrys Law constant kHand is characteristic of both the gas and the liquid:X g $ X aq CX aq def kH PXHenrys Law constants for several gases commonly dissolved in water in the27 x4 Ks0x Ks0270@1A1=4 1:29 1034270@1A1=4x 108:83 1:48 109CAl3 x 1:48 109MCOH 3 x 4:44 109MAqueous solution is saturated by (i.e., in solubility equilibrium with) gibbsitewhen 108.83 moles dissolve per liter.The solubility of gibbsite Al OH 3 s is more complicated than represented inExample 5.6 because the aluminum ion Al3 forms a complex with watermolecules, and this complex cation, the hydrated aluminum ion Al H2O 3n ,is a polyprotic acid that undergoes several hydrolysis steps. We will returnto the gibbsite solubility problem in a later section, taking into full accountthe hydrolysis of the hydrated aluminum ion Al H2O 3n .Henrys Law: Aqueous Solubility of GasesThree moles of OH dissolve for each mole of Al3, and the OH concentra-tion at equilibrium is 3 x. The exponent 3 results from the way the stoichiometriccoefficient appears in the equilibrium expression (Eq. (5.4)).Ks0 CAl3 C3OHKs0 x 3 x 3 27 x4Since the right side of the expression is a product of ion concentrationsratherthan activitiesit does not exactly equal the thermodynamic solubility constant.Soil and Environmental Chemistry2contact with the solution. This becomes apparent in the following section.3Hydrolysis of a Weak Diprotic BaseThe hydrolysis of a weak acid produces a conjugate base:propionic acid aq weak acidH2O l $ propionate aq conjugate baseH3O aq benzoic acid aq weak acidH2O l $ benzoateconjugate baseaq H3O aq The weak acid hydrolysis constant Ka is related to the hydrolysis constant ofSO2 1:2 105CO2 3:6 107H2S 8:6 107TABLE 5.1 Henrys Law ConstantsGas Henrys Law Constant kH mol L1 Pa1 O2 1:3 108N2 6:0 109CH4 1:3 108NO 1:9 108NO2 1:2 107Chapter 5 Water Chemistry 16the conjugate base Kb (Eq. (5.13)) through the water ionization constant Kw(Eq. (5.14)):Ka Kb Kw 5:13Kw 1:0 1014 aH3O aq aHO aq 5:14Consider the weak acid propionic acid with acid dissociation constantKa 1:32 105. The base association constant for the conjugate base propi-onate is Kb 7:58 1010:propionic acid aq weak acidH2O l !Ka propionate aq conjugate baseH3O aq acidpropionate aq conjugate baseH2O l !Kb propionic acid aq weak acidHO aq Kb Kw K1aKb 1:0 1014 1:32 105 1Kb 7:58 1010Soil and Environmental Chemistry164HS aq conjugate baseH2O l ! H2S aq weak acidOHbaseaq Kb2 1:05 107The sulfide ion S2 aq is an important solute in water chemistry. The mostcommon source in soil pore water, surface water, and many unconfined aqui-fers is the anaerobic respiration of bacteria. In Chapter 8 we examine anaero-bic respiration, but for now it is enough to know that sulfate-reducing bacteria(SRB) respire in the absence of molecular oxygen by reducing sulfate to sul-fide. Sulfide production by SRB, because it is linked to respiration, requiresa carbon source. Substantial dissolved sulfide in groundwater aquifersthat contain negligible dissolved organic or organic carbon coating mineralsurfaces probably results from sulfide leached from organic rich sedimentsand soil.Examples 5.7 and 5.8 examine a sulfide solution produced by an SRB ofgenus Clostridium (Cunningham and Lundie, 1993). Cunningham and Lundiewere studying the precipitation of greenockite CdS(s) by sulfide evolved dur-ing the anaerobic respiration of the Clostridium bacteria. Cadmium is toxic tobacteria, and the precipitation of greenockite substantially lowers the solubil-ity and, thus, the biological availability of Cd to the organism. If sulfide pro-duction were linked to Cd detoxification, Cunningham and Lundie reasoned,then this Clostridium bacteria would overproduce sulfide, possibly throughthe overproduction of cysteine and its subsequent transformation to hydrogensulfide by the enzyme cysteine desulfhydrase to lower Cd biological availabil-ity. Clostridium thernoaceticum produces 0.38 mM of sulfide in the absenceof dissolved Cd:L cysteine aq H2O l !cysteine desulfhydrase HS aq NH4 aq pyruvic acid aq Example 5.7 Calculate the pH of a polyprotic base solution given hydrolysisconstants for the base. What is the pH of a solution containing 0.38 mM of totaldissolved sulfide?First approximating assumption: The second base association constant Kb2 ismuch smaller than the first base association constant Kb1, so the hydroxide ionOH aq concentration results almost entirely from the first ionization step.Sulfide S2 aq and hydrogen sulfide HS aq function as conjugate bases ofthe weak acid H2S aq in water chemistry. The hydrolysis reactions for thesetwo bases follow:S2 aq conjugate baseH2O l ! HS aq weak acidOHbaseaq Kb1 7:94 101Assume, as a first approximation, that only the first step occurs.using a sec ying trateExample e th solutionChapter 5 Water Chemistry 165given the hydrolysis constants of dihydrogen sulfide and hydrogen sulfide.Suppose we estimate the concentration of dihydrogen sulfide H2S(aq),the product of the second hydrolysis step, from Example 5.7. To do this wewill cons5.8 Calculattruct an equilibe dihydrogen sulfide concentration in sulfiderium table for the hydrolysis of hond simplif assumption, illus d in Example 5.8.pOH 3:42pH 14 pOH 10:58We estimated the pH of a 0.38 mM sulfide solution by assuming that the sec-ond hydrolysis step, the hydrolysis reaction that produces dihydrogen sulfidefrom the hydrolysis of hydrogen sulfide, is negligible relative to the firsthydrolysis step. The result confirms the validity of the simplifying assumptionsubject to a 10% error. Suppose we wish to estimate the concentration ofdihydrogen sulfide in a 0.38 mM sulfide solution. This estimate can be madeKb1 CT x x2x2 Kb1 x Kb1 CT 0The solution is found by solving the quadratic equation.x Kb1 K2b1 4 CT Kb1q2x 7:94 101 7:94 101 2 4 3:8 104 7:94 101 q2x 3:78 104 COHUse an equilibrium table to assign values to each component in the equilib-rium expression.Stage S2 aq $ HS aq OH aq Initial 3:8 104 0 0Reaction x x xEquilibrium 3:8 104 x x xThe equilibrium expression using concentrations from the preceding tablefollows.Kb1 7:94 101 CHS COHCS27:94 101 x xCT x ydrogen sulfideb2occurs to a much smaller extent than the first. This means that the amount ofpyrom a r using afluor t e ral fromhydroA involvesad d(II teSoil and Environmental Chemistry166ding soluble phosphate salts, with the intention of converting all of the lea) compounds into pyromorphite. By virtue of its insolubility, pyromorphixy-apatite ifavored rento the more insolubleand harderfluoro-apatite.mediation technology for lead(II) contaminated soilide dental w sh is to conve he surfac layer of dental mineorphite occur in nature. The ra rttionale fo fluoridating water and5 4 3 5 4 3Simultaneous Equilibrium: Aqueous Solubility of Two Ionic SolidsSimultaneous equilibrium of numerous minerals is common in water chemis-try problems. General chemistry introduces the concept of simultaneousequilibrium involving two ionic solids to illustrate the behavior of thesesystems. The example we will use involves two insoluble phosphate minerals:apatite Ca5 PO4 3OH and pyromorphite Pb5 PO4 3OH.These two minerals are believed to be the most stable (i.e., the most insoluble)calcium and lead phosphate minerals in the environment. Other, more solublemineralsmay precipitate and persist for a time, but eventually thesemetastable cal-cium and lead phosphate minerals convert to apatite and pyromorphite. The com-position of either mineral can, and most probably will, vary in nature. The fluorideand chloride variants of both apatiteCa PO F and Ca PO ClandH2S aq and OH aq produced in the second step (y) is much smaller than3:78 104 M. It is therefore reasonable that both CHS and COH are very closeto 3:78 104 M.HS(aq) to assign values to each component in the equilibrium expressionas before.Stage HS aq $ H2S aq OH aq Initial 3:78 104 0 3:78 104Reaction y y yEquilibrium 3:78 104 y y 3:78 104 yThe equilibrium expression using concentrations from the preceding tablefollows.Kb2 COH CH2SCHSKb2 3:78 104 y y3:78 104 y 1:05 107 3:78 104 y3:78 104 y 1:05 107Because the second hydrolysis constant K is relatively small, the second stepChapter 5 Water Chemistry 167Ks0APATITE CCa2 CPO34 COH g5Ca2 g3PO34 gOH 10Pb5 PO4 3OH s PYROMORPHITE$ 5 Pb2 aq 3 PO34 aq OH aq Kcs0PYROMORPHITE C5Pb2 C3PO34 COH 1048:8g5Pb2 g3PO34 gOH 1048:8Combining the two solubility expressions, after inverting the apatite expres-sion, yields the net conditional coefficient Kcnet for the simultaneous equilibrium.The greater insolubility of pyromorphite relative to apatite is revealed in the con-centration ratio of the two ions.Pb5 PO4 3OH s PYROMORPHITE5 Ca2 aq $ Ca5 PO4 3OH s APATITE5 Pb2 aq Kcs0PYROMORPHITEKcs0APATITEC5Pb2 C3PO34 COHC5Ca2 C3PO34 COH 1048:81030:2Kcnet 1018:6 C5Pb2C5Ca2CPb2CCa2 103:72A typical concentration of Ca2 aq in natural water is about 103:3 M. Thepreceding concentration ratio suggests a probable Pb2 aq concentration (notto be confused with a total soluble lead(II) concentration) when both apatiteand pyromorphite are present of about 107M.Example 5.9 Estimate the soluble Pb2 concentration in soil pore water whenthere is simultaneous equilibrium between aqueous solution and the two phos-phate minerals apatite Ca5 PO4 3OH s and pyromorphite Pb5 PO4 3OH s .The solubility equilibrium expression for the minerals apatiteCa5 PO4 3OH s and pyromorphite Pb5 PO4 3OH s follows. The thermody-namic solubility constants Ks0 are the product of ion activities in solution, whilethe conditional solubility coefficients Kcs0 are the product of ion concentrationsand, as such, are subject to the ionic strength of the solution. For this example,since the ionic strength is not specified, we will neglect activity coefficients,recognizing Kcs0APATITE 1030:2 and Kcs0PYROMORPHITE 1048:8 are both approximate.Ca5 PO4 3OH s APATITE$ 5 Ca2 aq 3 PO34 aq OH aq c 5 3 1030:2 30:2is less biologically available to organisms than the more soluble lead(II)minerals that precipitate in the absence of sufficient phosphate.16Example 5.10 Determine the effect of pH on the solubility of troilite FeS s .The pH effect involves the simultaneous equilibrium between sulfide ion hydro-lysis in aqueous solution and solubility of the mineral troilite FeS s .The solubility equilibrium expression for the mineral troilite FeS s appearsfollowing. The thermodynamic solubility constant Ks0 is the product of ion activ-ities in solution, while the conditional solubility coefficient Kcs0 is the product ofion concentrations and, as such, is subject to the ionic strength of the solution.For this example we will neglect activity coefficients, recognizing thatKcs0 1019:15 is approximate.FeS s TROILITE$ Fe2 aq S2 aq Kcs0TROILITE CFe2 CS2 1019:15gFe2 gS2 1019:15The sulfide ion S2 aq is a weak conjugate base that reacts with water toform the hydrogen sulfide ion HS aq .HS aq $ S2 aq H aq Kca2 CS2 CHCHS 1013:90Multiplying the troilite FeS s solubility expression by the inverse of thehydrogen sulfide hydrolysis expression yields a pH-dependent troilite FeS s sol-ubility expression.FeS s TROILITEH aq $ Fe2 aq HS aq Kcs0TROILITEKca20@1A CFe2 CS2 CHSCS2 CH0@1A 1019:151013:90c CFe2 CHS 5:25known quantity that controls the solubility of most minerals in the system.The treatment of simultaneous equilibrium in general chemistry usuallyincludes several examples of how pH influences the solubility of insolubleionic solids. Example 5.10 examines the effect of pH on the solubility ofthe ferrous sulfide mineral troilite FeS s .Simultaneous Equilibrium: The Effect of pH on the Solubilityof a MineralAcidity is such an important issue in environmental chemistry that we devotean entire chapter to the topic. Since many processes ultimately determinewater pH in the environment, a simple cause and effect are usually impossibleto discern. For this reason, and because pH is so easy to measure, water pH isusually treated as an independent variable in water chemistry problemsaSoil and Environmental Chemistry8Knet CH 10Kc CCa Citrate CHCO3 106:55Chapter 5 Water Chemistry 169net CCitrate3 CHIn calcareous water, the pH is 10, and the HCO3 aq concentration is104 M. The ratio of Ca Citrate aq to Citrate3 aq under these conditionsis 100:6 4. The citrate mass balance is solved following, assuming all of theexamines the solubility of calcite CaCO3 s in a solution containing 1 mM ofcitric acid.Example 5.11 What is the solubility of calcite CaCO3 s in a 1mM citric acidsolution?The solubility equilibrium expression for the mineral calcite appearsfollowing.CaCO3 s CALCITEH aq $ Ca2 aq HCO3 aq KcsCALCITE 101:85KcsCALCITE CCa2 CHCO3CHNotice that the Ca Citrate aq formation constant Kf (below) is rather large,indicating that equilibrium favors the product Ca Citrate aq over the educts.Citrate3 aq Ca2 aq $ Ca Citrate aq Kf 104:70Multiplying the calcite solubility expression by the Ca Citrate aq formationexpression yields a solubility expression showing the effect of complex formation.CaCO3 s CALCITECitrate3 aq H aq $ Ca Citrate aq HCO3 aq H2O l KcsCALCITEKcf CCa2 CHCO3CH0@1A CCa Citrate CCa2 CCitrate30@1A 101:85 104:70 Lupine (Lupinus spp.) is a legume genus known for its ability to thrive insoils with low soluble phosphate, an essential nutrient. Lupines will excreteprodigious amounts of citrate in phosphate-limiting conditions. Example 5.11teliers Principle to the preceding pH-dependent solubility expression. IncreasingpH (i.e., lowering the H aq concentration) causes the equilibrium to shift to theleft, decreasing troilite FeS s solubility.Simultaneous Equilibrium: The Effect of Ion Complexes on theSolubility of a MineralBacteria, fungi, and plants secrete a host of organic acids, some of whichare by-products of respiration and other physiological processes, but someare excreted specifically to increase the solubility of essential nutrients.To understand the effect of pH on troilite FeS s solubility, we apply Le Cha-dissolved citrate is Citrate3 aq at pH 10.Soil and Environmental Chemistry170for the computer operating system that you prefer or at your disposal. This bookuses ChemEQL (Muller, 2005) in all of the examples and problems. ChemEQLoffers an opportunity to learn the basics of water chemistry modelingsettingup a problem for simulation and result validation (Table 5.2)and illustratesimportant water chemistry principles.Computer-based numerical models designed to solve practical waterchemistry problems relieve you of an enormous computational burden, butdoes not mean you can check your knowledge of equilibrium chemistry atCCitrate 103 CCa Citrate CCitrate3CCa Citrate 100:6 CCitrate3 4 CCitrate3103 4 CCitrate3 CCitrate3CCitrate3 0:2 103 M 2:0 10 4 MCCa Citrate 8:0 104 MCalcite solubility in the presence of 1 mM of citric acid is 8:0 104 M com-pared to 104 M in its absence.Another example of the effect that complexes have on mineral solubilityappears in Appendix 5I. This example describes a very important chemicalreaction in which a siderophore (a bioorganic compound) forms a complexwith ferric iron to increase its solubility. Bacteria, fungi, and grass plantsexcrete siderophores to meet their iron nutritional requirements.5.3.2. Water Chemistry SimulationsThe Importance of Validating Water Chemistry SimulationsExamples 5.1 through 5.11 serve several purposes. First, they review the equi-librium principles and problem-solving methods from general chemistry. Sec-ond, several of the examples illustrate limitations in applying simplifyingassumptions to aid problem solving. As a general rule, the simplifying assump-tions introduced in general chemistry tend to fail when solute concentrationsbecome more dilute, which is typical for solutes in most practical water chem-istry problems. Third, these examples demonstrate the challenges a water chem-ist faces when simple equilibrium systems become more complexinvolvingnumerous minerals, soluble complexes, and hydrolysis reactions where two ormore protons or hydroxyl ions dissociate from weak acids and bases. Compli-cated water chemistry systems demand an entirely different numerical strategyto solve the numerous reactions in simultaneous equilibrium.Environmental chemists can choose from several applications designed tosimulate chemical equilibrium in water. They differ in the computationaloptions, the output options, and the reactions and equilibrium constantsincluded in their basic database; the fundamental numerical method used tosimulate the equilibrium reactions, however, is essentially the same. The deter-mining issue, besides ease of use, is whether a version of the model is availableTABLE 5.2 C fo s ChemistryModels1. Valida an2. Valida c h poChapter 5 Water Chemistry 171Modeling the Hydrolysis of Weak Monoprotic Acids or BasesThe first modeling exerciseExample 5.12revisits the simple equilibriumproblem discussed in Example 5.3, calculating solution pH given the hydroly-sis constant and weak-acid concentration. The ChemEQL website offers anelectronic users guide, ChemEQL Manual, and you are encouraged to referto it for detailed instructions. Example 5.12 is very similar to the first exampleon page 8 (ChemEQL Manual, version 3.0).the door. Computer-based numerical models do not understand chemistry.Your task, besides generating the input data necessary to solve the problemand interpreting the results, is to use your chemistry knowledge to assessthe validity of each simulation.Validity assessment requires an understanding of equilibrium chemistryand a handful of simple calculations that reveal whether the numerical resultsare consistent with basic equilibrium principles. We will refer to the valida-tion checklist in Table 5.2 repeatedly throughout the remainder of thischapter.3. Validate the ionic strength estimate.4. Validate ion activity coefficients.5. Validate the ion activity products for important reactions match thermodynamicequilibrium constants listed in the model database.6. Validate the thermodynamic equilibrium constants used in the model database,especially the most critical reactions in the simulation, against published values.Example 5hydrolysisThe Chand 1.0E-7therefore,radio buttby ChemEequation (te charge balte mass balan.12 Calculatconstant Ka emEQL simulM H (total)any input valuon is selectedQL. Select Actp. 21, ChemESpeciesAcetic AcidAcetate-OHHce.e for eace the pH o1:86 10ation has. Solutione is acce. The resuivity fromQL ManuaLog K0.004.7314.000.00constrained comf a 20mM acetic5.two components:pH is a dependeptable for componlts were copiedthe Options menl, version 3.0), AConc. [mol/L]1.94E-026.09E-041.69E-116.09E-04nent.Validation hecklist r Computer-Ba edWateracid solution when given the2.0E-2 M Acetic Acid (total)nt variable in this simulation;ent H as long as the Totalfrom the data file generatedu, and then select the Davies 0.5109 at 25C.Activity1.94E-025.92E-041.64E-116.09E-04of i dm d sEx w e c g -ity ts a lha 1 -lat(p eef r-re yth -iosth tsfoSoil and Environmental Chemistry172ion in Example 5.12 yields identical results: aH 6:09 104 MH 3:21). Under these conditions the simplifying assumptions had littlfect on the accuracy of the results, and ignoring the activity coefficient coctions had a negligible effect on the estimated pH. Dividing the activities be concentrations in the first table in Example 5.12 reveals that the Acetaten activity coefficient is 0.972.To reinforce the importance of validation assessment, Example 5.12 appliee entire validation checklist (see Table 5.2). Complete validation assessmenr examples 5.13 and 5.16 appear in Appendix 5C.ve CH 6:10 10 M (pH 3:2 ) at equilibrium. The ChemEQL simucoefficien . Example 5.34estimates that a 20 mM cetic acid solution wilample 5.3, e can evaluat the effe t of simplifyin assumptions and activSince Exa ple 5.12 uses the same weak acid an acid concentration aaddresses file format isseach assessment appearses specin Appenic to ChemEQix 5B.. A detailed discussionValidate by opening the data file using the spreadsheet application Excel(Appendix 5A).Charge Balance and Ionic Strength. The following table lists the chargebalance (1.00E-07 molc L-1) and ionic strength I (6.09E-04 mol L-1) calculatedfrom the concentrations listed above. The charge balance is validatedbecause it is much smaller than the most concentrated ion concentrations.The ionic strength I reported by ChemEQL is also validated because itmatches the ionic strength calculated from the concentrations listed in theresults table.Species Conc. [mol/L] Charge Conc. [molc/L] Ionic Strength. [mol/L]Acetic Acid 1.94E-02 0 0.00E00 0.00E00Acetate- 6.09E-04 1 6.09E-04 3.05E-04OH- 1.69E-11 1 1.69E-11 8.44E-12H 6.09E-04 1 6.09E-04 3.05E-04Sum 1.00E-07 6.09E-04Mass Balances. The acetic acid/acetate mass balance is validated becausethe concentration, calculated from the preceding table, matches the input value2.0E-2 M Acetic Acid (total).Database Equilibrium Constants. The logarithm of thermodynamic equilib-rium constant in the ChemEQL database is 4.73. This compares with 4.74listed in a popular general chemistry book. The logarithm of the reaction quotientlog Q for acetic acid hydrolysis, computed using activities listed in the preced-ing table, is LOG(1.862E-05) 4.73, validating agreement between the data-base constant and solute activities generated by the simulation.Most computer-based water chemistry models generate a file containingthe results of each simulation. Transferring data from the results file to aspreadsheet application will greatly simplify the validation process. Appendix5A u f Land solut b v n refore,any input c p l radiobutton is h co ted byChemEQLChapter 5 Water Chemistry 173CaSO4(aq) 5.37E-03 5.37E-03 1.000SO4 1.11E-02 5.12E-03 0.461HSO4 5.50E-08 4.53E-08 0.824OH 1.34E-07 1.11E-07 0.824H 9.05E-08 9.05E-08 1.000Solubility. ChemEQL estimates a solubility of 1.648E-02 M (101.78 M) com-pared to results from Example 5.5 when 102.29 moles dissolve per liter. SeeAppendix 5C for a validation assessment.We can anticipate a significant deviation between concentration and activ-ity, especially because the two dominant ions are both divalent and the con-centration is relatively high (see Figure 5.2). Example 5.13 is very similarto the example of calcite CaCO3 s solubility that appears on page 9 (Chem-EQL Manual, version 3.0).Example 5.5 underestimates gypsum solubility by 69%. This error hasseveral sources: neglecting formation of the specie CaSO4(aq) represents33% of the error, while the remainder arises from the lower activity ofthe two major cations Ca and SO4. Monovalent ions require activitycoefficients of 0.824, while divalent ions require activity coefficientsof 0.461.CaCaOH1.11E-021.14E-085.12E-039.41E-090.4610.824Species Conc. [mol/L] Activity Activity Coefficient.selected. T e results were pied from the data file generavalue is ac eptable for com onent H as long as the Totaion pH are oth dependent ariables i this simulation; the1, ChemEQ Manual, versio 3.0), A 0.5109 at 25 C. SolModeling Mineral SolubilityExample 5.13 revisits the equilibrium problem discussed in Example 5.5,calculating the solubility of the mineral gypsum.Example 5.13 Calculate the solubility of the mineral gypsum given the miner-als solubility constant Ks0 2:63 105; logKs0 4:58.The ChemEQL simulation has three components: 0 M Ca (total), 0 M SO4(total), and 1.0E-7 M H (total). After compiling and saving the input matrix, selectInsert Solid Phase... from the Matrix menu, following the directions in the Chem-EQL Manual. You can replace either Ca or SO4 with CaSO4:2H2O(gypsum).Unlike Example 5.5, the ChemEQL matrix lists several ion species neglectedin the typical general chemistry treatment of gypsum solubility: CaOH,CaSO4(aq), and HSO4.Select Activity from the Options menu, and then select the Davies equa-tion (p. 2 L n ubilityCH aH : This is not as arbitrary as it might appear; H aq concentrationered concenHenrys L e it seDissolved g e im m most waterchemistry s C is aj geochem-istry and many environmental problems, is deferred to Chapter 7.S 1.90E-07 1.74E-07 0.915OH 3.81E-04 3.72E-04 0.978Soil and Environmental Chemistry174H 2.69E-11 2.69E-11 1.000The approximate solution in Example 5.7 made estimates quite similar to thissimulation. The greatest difference is found in the predicted S concentration:1.05E-07 M and 1.90E-07 M, respectively. The simulation also estimates the par-tial pressure of H2S(g): 1.02E-06 atm.Bacteria and other organisms produce a variety of gases during respiration.As a consequence, the partial pressure of these gases in soil pores is oftenorders of magnitude higher than in the aboveground atmosphere. BacteriaExample 5.14 Calculate the pH of a solution containing 0.38 mM total sulfide.Cunningham and Lundie (1993) found that C. thernoaceticum produced a0.38 mM sulfide solution under normal culture conditions.A ChemEQL simulation uses two components in the input matrix: the totalS concentration is 3.80E-04 M, while the H concentration is allowed tovary, select Total radio button. The results in the following table are copied fromthe output data file. The activity coefficients were computed using the Daviesequation (Eq. (5.12)).Species Conc. [mol/L] Activity Activity CoefficientH2S(g) 1.02E-06 1.02E-06H2S(aq) 1.04E-07 1.04E-07 1.000HS 3.79E-04 3.70E-04 0.978produce diystems.hydrogenarbonate chemsulfide by thetry, a menzyme cor topic in aqueousases hav an important pact on ineral solubility inaw: Aqu ous Solubil y of Ga strations.is generally measured using a pH glass electrode, which is a type of ion-selec-tive electrode. It is possible to directly measure the activity of certain ions(cyanide, nitrate, nitrite, most halides, most alkaline cations, Ag, NH4 , anda few divalent cations) using ion-selective electrodes; otherwise, analyticalresults from all methods other than ion-specific electrodes should be consid-ChemEQL Treatment of Hydrogen Ion ActivityThe results in Examples 5.12 and 5.13 reveal an important attribute of Chem-EQL: the model treats the H aq concentration CH as an activity aH :defysteine desulfhydrase. Somem rth e.ddihydrogen s y de dix5D. The re ix e at gensulfide from e y aModeling s : s oIonic SoliExample 5. am is lta-neous equil aq n m onion in the m h n les5.9 and 5.1Example s nc in nsimultane x o te dpyromorpThe res Q p ta ycoefficien u s (E nestimated 2Chapter 5 Water Chemistry 175Pb2OH 3.72E-16 3.53E-16 0.949Pb3(OH)4 2.45E-16 2.39E-16 0.977Pb4(OH)4 3.32E-22 3.03E-22 0.912Pb6(OH)8 9.93E-28 9.05E-28 0.912PbHPO4 6.19E-12 6.19E-12 1.000PbH2PO4 4.48E-15 4.46E-15 0.994PO4 1.01E-09 9.57E-10 0.950HPO4 3.97E-06 3.88E-06 0.977H2PO4 1.12E-07 1.11E-07 0.994H3PO4 2.84E-14 2.84E-14 1.000OH 5.56E-06 5.53E-06 0.994H 1.81E-09 1.81E-09 1.000The total calcium concentration in equilibrium with apatite is 105:2 M, andthe total lead concentration in equilibrium with pyromorphite is 107:7 M.The way ChemEQL handles this process is discussed in the ChemEQL Manualunder the topic Several Solid Phases (p. 13, ChemEQL Manual version 3.0).CaOH 6.14E-10 6.10E-10 0.994CaPO4 1.85E-08 1.84E-08 0.994CaHPO4(aq) 1.42E-08 1.42E-08 1.000CaH2PO4 1.87E-11 1.86E-11 0.994Pb 1.30E-09 1.27E-09 0.977PbOH 1.41E-08 1.40E-08 0.994Pb(OH)2 3.08E-09 3.08E-09 1.000Pb(OH)3 1.71E-11 1.70E-11 0.994SpeciesCaConc. [mol/l]6.81E-06Activity6.65E-06Activity Coefficient0.977ionic strength I .441E-05 M.ts were computed sing the Davie equation q. (5.12)) based on aults of the ChemE L simulation ap ear in the ble following. Activithite.ous equilibrium e ists with the tw phospha minerals apatite an5.15 Estimate the oluble Pb2 co entration soil pore water whe5 is PO4 aq .ineral solubility3expressions. T e commo ion in both Exampibrium between ueous solutio and two inerals with a comm15 revisits the s e problem d cussed in Example 5.9: simudsSimultaneou Equilibrium Aqueou Solubility of TwSRB has on m rcury solubilit under an erobic conditions.sults in Append 5D show th effect th dissolved dihydrosulfide gas with oluble mercur and sulfi s appears in Appenicrobiologists believe the production of dihydrogen sulfide is essential foe optimal functioning of the respiratory system located in the cell envelopThe simulation of equilibrium involving the mineral cinnabar HgS(s) anSoil and Environmental Chemistry176occur in the environment because calcite CaCO3 s is probably present wher-ever apatite is found (see Appendix 5E). Constraining phosphate solubilitywith apatite and carbonate solubility with calcite yields the following solutioncomposition: Ca (total) 1.22E-04 M, Pb (total) 1.34E-05 M, and PO4(total) 2.70E-09 M, and pH 9.86. The inclusion of calcite in the equilib-rium system results in a 100-fold increase in lead solubility accompanied by a100-fold decrease in phosphate solubilityan example of the common-ioneffect in nature.Appendix 5F illustrates another example of simultaneous equilibriuminvolving aqueous solution and minerals sharing a common component. Thesimultaneous equilibrium in Appendix 5F is representative of phosphate solu-bility in acidic soils, where the aluminum phosphate mineral varisciteAlPO4 2H2O s controls phosphate solubility, and aluminum solubility mustsatisfy the coexistence of both variscite and gibbsite Al OH 3 s .Modeling Simultaneous Equilibrium: the Effect of pHon the Solubility of a MineralExample 5.6 calculates the solubility of the soil mineral gibbsite using afamiliar general chemistry method: the equilibrium table. The example didnot explicitly examine the pH effect, but the equilibrium solubility expressionAfter compiling the input matrix, the user replaces solution components byselecting Insert Solid Phase... from the Matrix menu. Components are replacedin a specific order; each replacement removes a component and the ChemEQLdatabase; equilibrium expressions of subsequent replacements must match theremaining components. The ChemEQL simulation in Example 5.15 has four com-ponents: 0 M Ca (total), 0 M Pb (total), 0 M PO4(total), and 1.0E-7 MH (total). After compiling the input matrix, select Insert Solid Phase... from theMatrixmenu, replacing components Ca and PO4 with Ca10(OH)2(PO4)6(hydroxyapatite) and Pb5(PO4)3OH (hydroxypyromorphite). Replacement in thatorder eliminates Ca as a component first and PO4 as a componentsecond, leaving Pb and H as the two remaining variables.The solubility equilibrium expressions used in Example 5.15 are from theChemEQL database:10 Ca2 aq 6 PO34 aq $ 2 H aq Ca10 PO4 6OH2 s K 1088:405 Pb2 aq 3 PO34 aq $H aq Pb5 PO4 3OH s K 1062:40Dividing the apatite stoichiometric coefficients by 2 (and taking the squareroot of the solubility constant) would make the two expressions easier to com-pare but has no effect on the simulation results.Adding another component CO3 generates a system more likely toimplies pH-dependent solubility:s0 O et 1aaTaking t s e g aHyields on y andsolutioChapter 5 Water Chemistry 177Al 6.52E-13 6.50E-13 0.996AlOH 3.80E-11 3.79E-11 0.998Al(OH)2 1.76E-09 1.76E-09 0.999Al(OH)3(aq) 1.62E-09 1.62E-09 1.000Al(OH)4- 1.50E-08 1.50E-08 1.000Al2(OH)2 2.88E-19 2.86E-19 0.993Al3(OH)4 4.03E-24 3.99E-24 0.990OH- 5.83E-08 5.83E-08 1.000H 1.72E-07 1.72E-07 1.000Aqueous solution is saturated by (i.e., in solubility equilibriumwith) gibbsitewhen107:73 moles dissolve per liter. Validation assessment appears in Appendix 5C.Example 5.16 Calculate the solubility of a sparingly soluble ionic solid giventhe solubility constant Ks0 of the solid.Gibbsite is an insoluble soil mineral found in humid climates, where chemicalweathering is quite advanced. Calculate the solubility of gibbsite in aqueoussolution (Ks0 1:29 1034; logKs0 33:89).The simulation results appear following.Species Conc. [mol/L] Activity Activity Coefficientlog Knet 8:11 log aAl3 3 log aH 8:11 log aAl3 3 pHlog aAl3 3 pH 8:11Example 5.16 is a ChemEQL simulation illustrating the equilibrium principlesdiscussed earlier in Examples 5.6 (mineral solubility), 5.10 (pH-dependentmineral solubility), and 5.11 (the effect of ion complexes on mineralsolubility).The solubility of gibbsite Al OH 3 s is more complicated than repre-sented in Example 5.6 because the aluminum ion Al3 forms a complex withwater molecules, and this complex cation, the hydrated aluminum ionAl H2O 3n , is a polyprotic acid that undergoes several hydrolysis steps. Wewill return to the gibbsite solubility problem in Chapter 7, taking into fullaccount the hydrolysis of the hydrated aluminum ion Al H2O 3n . The hydro-lysis species should be considered ion complexes (see Example 5.11) whenapplying the equilibrium gibbsite solubility expression.n pH.a linear expressi between the logarithm of Al3 aq activitthe logarithm of he equilibrium olubility xpression containinw 3HKn Ks0 K3 08:11 Al3Al OH 3 s 3 H aq Al aq 3 H2O l 3Al HK3 1:29 1034 a 3 aAl OH s $ Al3 aq 3 OH aq 3ChemEQL allows the user to vary a single component as an independentvariable, which is discussed in the ChemEQL Manual under the topics Arrayof Concentrations and Graphic Representation (pp. 2425, ChemEQLManual version 3.0).The logarithm of the equilibrium expressiona linear activity functionfor gibbsite is plotted as the Al3 aq line in Figure 5.3, which is a completerepresentation of pH-dependent gibbsite solubility with minimum solubility105:6 M occurring near pH 6.3.Another example of pH-dependent solubility appears in Appendix 5G, wherethe mineral is the calcium phosphate mineral apatite Ca5 PO4 3OH s . Appen-dices 5H and 5I give examples of the effect that soluble complexes haveon mineral solubility. The example in Appendix 5H is another facet of apatitesolubility, this time showing the effect of complexes formed when the citricacid is present. Certain plants secrete citric acid from their roots to increasephosphate solubility in the surrounding soil. Bacteria, fungi, and certain plantssecrete compounds that have a highly specific capacity to complex and dis-solve ferric iron from insoluble iron minerals. This process is discussed inAppendix 5I.Soil and Environmental Chemistry178FIGURE 5.3 This graph plots the logarithm of ion activity for the five most abundant aluminumsolution species as a function of pH as simulated using ChemEQL. The solubility of Al3 aq isconstrained by gibbsite solubility as discussed in Example 5.16, except here H aq is treated asan independent variable covering the range depicted in the graph.95.3.3. Modeling the Chemistry of Environmental Samples:Groundwater, Soil Pore Water, and Surface WaterThe Gibbs Phase RuleEnvironmental chemists simulate the chemistry of water samples for manyreasons, the most important being the identification of minerals that controlthe chemistry in water samples. The minerals that control solution concentra-tions are the minerals in solubility equilibrium with the solution. The controlof solution chemistry implies a very specific and concrete concept: the activ-ities of two or more solutes are constrained by equilibrium solubility and,therefore, are not independent of each other.Some of the minerals in contact with waterminerals in the aquifer for-mation if the sample is groundwater, soil minerals if the sample is soil porewater, or minerals suspended in the water column or sediments if the sampleis lake or river waterwill not or cannot attain solubility equilibrium. Manyprimary rock-forming minerals that crystallize from magma (igneous rockminerals) or sinter at high temperatures (metamorphic rock minerals) arenot stable in the presence of liquid water. Some sedimentary minerals precip-itate from water whose composition is very different from prevailing condi-tions (May et al., 1986). Solubility equilibrium can exist only if bothdissolution and precipitation reactions are possible.Another important instance when a mineral cannot control solution chem-istry occurs when the residence time of the water is less than the time neces-sary for the mineral to dissolve sufficiently to saturate the solution. This isillustrated by the effect of groundwater discharge on lake water alkalinity(Figure 2.1, Soil Moisture and Hydrology). Lake water alkalinity increasesproportionately with the mean residence time of groundwater discharged intothe lake (Wolock et al., 1989).Environmental chemists rely on the principle of chemical equilibrium toidentify minerals that control water chemistry. If the chemistry of a watersample is controlled by the equilibrium solubility of a suite of minerals, itshould be possible to identify the mineral by calculating the ion activity prod-uct for mineral solubility (see Table 5.2 and Appendix 5B). The application ofequilibrium methods requires water chemistry analyses that report solution pHand the concentration of one or more elements or compounds.Each element or compound in the analysis, including solution pH, is con-sidered a component. Chemical reactions distribute each solution componentover a constellation of solution species (see Appendix 5B). The number ofminerals that control water chemistry is subject to the Gibbs Phase Rule, aphysical rule defining the degrees of freedom F in a system containing Ccomponents and P phases. The Gibbs Phase Rule for a system at fixed pres-sure and temperature is a very simple expression:Chapter 5 Water Chemistry 17F C P 0 5:15A more general expression for the Gibbs Phase Rule adds an additional twodegrees of freedom if temperature and pressure are allowed to vary, but mostenvironmental chemistry models assume constant temperature and pressure.The phase rule, as we will see, provides much needed guidance when modelingSoil and Environmental Chemistry180equilibrium in environmental water samples because the number of phases Pmust be less than or equal to the number of components C.Phase Rule ExamplesSuppose the system consists of two phasesaqueous solution and a gaseousphaseand two components: H aq 1 and carbon dioxide CO2: F 2 2 0. The CO2 g partial pressure PCO2 fixes the activity of dissolved carbondioxide CO2 aq and solution pH or, conversely, there are no degrees of free-dom F. Solution pH is a direct consequence of PCO2 .Suppose the system consists of three components C: liquid water H2O l ,Mg2 aq , and carbon dioxide CO2 aq . The number of phases can rangefrom 1 to 3, and, consequently, the degrees of freedom F can range from2 to 0: F 3 P 0. A single-phase system (F 3 1 2) would be anaqueous solution of Mg2 aq and carbon dioxide CO2 aq . These two com-ponents would react to form numerous solute species by hydrolysis and theformation of ion complexes. The two degrees of freedom allow two indepen-dent variables: aMg2 and aCO2 aq determine pH (or permutations thereof).Two 2-phase systems (F 3 2 1) are possible: an aqueous solution andgaseous carbon dioxide CO2 g , or an aqueous solution saturated by a singlemagnesium mineral (e.g., magnesite MgCO3 s or brucite Mg OH 2 s ). Thesingle degrees of freedom allow one independent variable: aMg2 determinesaCO2 aq and pH (or permutations thereof). The composition of the aqueous solu-tion will determine which of the two magnesium minerals is the solid phase.Two 3-phase systems (F 3 3 0) are possible: an aqueous solutionsaturated by a single magnesium mineral (e.g., magnesite MgCO3 s or bru-cite Mg OH 2 s ) and gaseous carbon dioxide CO2 g , or an aqueous solutionsimultaneously saturated by magnesite MgCO3 s and brucite Mg OH 2 s .Zero degrees of freedom allow no independent variables: aMg2 , aCO2 aq ,and pH are fixed, depending on the nature of the three-phase system.Saturated zone water encompasses systems where the only allowed phasesare the aqueous solution and minerals. Since pH is always a component, thepotential number of mineral phases P in equilibrium with the solution cannotexceed the number of components (elements or compounds other than pH). Itis unlikely that some components (e.g., sodium, potassium, or other alkaline1. Molecular watera component and phase in all water chemistry problemshas no impact onthe degrees of freedom F. A component in every water chemistry problem, however, is the hydro-gen ion H aq . If we identify H aq as a component, then OH aq must be regarded a solu-tion species, related to component H aq through water hydrolysis equilibrium (Eq. (5.14)).Chapter 5 Water Chemistry 181elements) will be constrained by mineral solubility. Some components areconstrained by mineral solubility within a given pH range and by some otherprocess not included in equilibrium water chemistry models (ion exchange oradsorption) in another pH range. The bottom line is that the number of min-eral phases P that can saturate solution cannot exceed the number of compo-nents C. The following two sections describe methods for identifying theminerals that control water chemistry (i.e., solubility) in environmental watersamples.Reaction Quotients and Saturation IndicesThe dissolution reaction for Al OH 3 s and its associated reaction quotient Qappear following. Remember that the reaction quotient Q is computed fromthe activities of specific solutes in the reaction expression and can assumeany numerical value (see Figure 5.1):Al OH 3 s 3 H aq ! Al3 aq 3 H2O l Q aAl3 a3HWhen the solid phase Al OH 3 s is in solubility equilibrium with aqueoussolution, the reaction quotient Q is numerically equal to the thermodynamicequilibrium constant K:Al OH 3 s 3 H aq Al3 aq 3 H2O l K 108:11 aAl3 a3HSolubility equilibrium may be approached as the mineral dissolves, risingtoward saturation Q Ks from a state of undersaturation Q < Ks . A min-eral may also approach solubility equilibrium by precipitating, drifting down-ward toward saturation Q Ks from a state of oversaturation Q > Ks . Thesaturation index SI reveals whether solubility equilibrium exists between amineral and the surrounding aqueous solution. The saturation index SI(Eq. (5.16)) is defined as the ratio of the reaction quotient Q to the thermody-namic solubility constant Ks. Some environmental chemists use the expressionion activity product IAP rather than reaction quotient Q:SI QKs5:16In some instances the reaction quotient Q may have to exceed a thresholdoversaturation (SI > 1) before a mineral will begin to precipitate. Under thesecircumstances the SI tends to decrease with time. A precipitate consisting ofextremely small particles will also yield SI > 1. Precipitate ripening occurswhen small particles dissolve at the expense of large particles, leadingeven u ti V in l on,crys , c a u ralsin th t lSoil and Environmental Chemistry182Environmental chemists can identify minerals in solubility equilibriumwith aqueous solution by performing a water chemistry simulation whereprecipitation is suppressed. This would mean not employing the InsertSolid Phase.. . command under the ChemEQL Matrix menu after compilingthe input matrix, applying the Activity command under the ChemEQL Optionmenu, and running the simulation to generate an output data file listing speciesactivities. If you open the output data file as an Excel document, you can gen-erate SI values for likely mineral candidates. Your final list of minerals will beless than or equal to the number of components other than pH.Example 5.17 illustrates the use of saturation indexes SI for the identifica-tion of minerals that control water chemistry. The water chemistry analysescome from a study of calcareous river and groundwater by Crandall and col-leagues (1999).ChemEQL provides another method for assessing whether the saturationindex SI of a particular mineral indicates undersaturation, saturation (solu-bility equilibrium), or oversaturation. This is described under the headingCheck for Precipitation (p. 12). First, identify a candidate mineral and usethe Insert Solid Phase... command to replace one of the solution componentswith the candidate mineral. The mineral component is placed insolidPhase mode (the solid phase activity is 1.0) after performing the InsertSolid Phase... command. Change the mode from solidPhase to checkPrecipmode, following the instructions in the ChemEQL Manual. Finally, enter thetotal concentration of the original solution component below the checkPrecipmode listing (hit the tab key to write the concentration in the input matrix datafile). Select Activity from the Options menu and run the simulation. Theresulting output data file will indicate whether the chemical analysis concen-tration of the solution component is oversaturated or undersaturated by theresults reported under In or Out of System.Example 5.17The following data are from water samples drawn from Wingate Sink, located5.2 km west of OBrien, Suwannee County, Florida (Crandall et al., 1999). TheChemEQL simulation does not replace any solution component with mineralphases. The reported pH values are much lower than expected for calcareousgroundwater (pH 9.91). We can conclude that the water at Wingate Sink is inequilibrium with atmospheric carbon dioxide.Date pH Ca, mol/L Mg, mol/L Na, mol/L K, mol/L Fe, mol/L2/11/95 7.55 1.62E-03 2.35E-04 1.17E-04 6.39E-054/8/95 7.31 1.50E-03 2.30E-04 1.17E-04 2.30E-05 1.43E-077/2/96 7.33 1.47E-03 2.43E-04 1.13E-04 1.28E-05e enviro11/4/96nmen7.39(May et a9.98E-04., 1986).2.14E-04 1.44E-04 2.30E-05tallinity and particle size ommonly lter the sol bility of actual minetually to a sat rated solu on SI 1. ariations chemica compositi2.69E-064/8/95 7.31 0.8898 0.1648 0.9999 3.80E5itate po o heLogari A ty sFigure s a in ic o hat isco din isco iceq ese fa Malso teactiviti m a ic nction(typica t - f d bility-control .Wa y le l t. Themodel l s is m ation)to predChapter 5 Water Chemistry 183ter chemistrsimulates soict the activimodels play aution reactionty of specificcritical ro(hydrolyssolutes usein graphicaand ion-cod as variablesassessmenplex formling minerallly a straigh line in a log log plot) or each can idate solues in environ ental water s mples typ ally plot one activity fummonly called an activity diagram. The use of activity diagrams is illustrateLindsay (1979) and Schwab (2004). The equilibrium solubility expressionnverted into a linear expression by taking the logarithm of the thermodynamuilibrium constant and the activity quotient in the matter demonstrated in thction Modeling Simultaneous Equilibrium: Effect of pH on the Solubility oineral for the solubility expression for gibbsite Al OH 3 s .The log-log plot in Figure 5.3 shows the pH-dependent activity of severlutes, but the activity diagrams used to identify minerals controlling soluthmic5.3 plotsctivioluteDiagramctivities us g a logarithm scale on b th axes in wwhen ex sed t oxygen in t sink.7/2/96 7.33 0.8043 0.1451 1.066711/4/96 7.39 0.5092 0.0753 0.9999 7.51E6The saturation indexes SI for every water sample clearly indicate that calciteand quartz control the solubility of two components: Ca and SiO2(aq). Themineral dolomite is significantly undersaturated and probably does not controlthe solubility of Mg. The solid phase amorphous FeOOH s is significantlyoversaturated, indicating that Fe is probably actively precipitating. Oversat-uration by ferric iron suggests that the groundwater feeding Wingate Sink likelycontains high concentrations of ferrous iron that oxidize to ferric iron and precip-SO4, mol/L HCO3, mol/L SiO2(aq) NO3, mol/L Cl, mol/L1.04E-04 3.11E-03 1.12E-04 1.21E-04 1.41E-041.04E-04 3.56E-03 1.05E-04 1.36E-04 1.55E-049.47E-05 3.08E-03 1.12E-04 1.07E-04 1.38E-048.43E-05 2.34E-03 1.05E-04 4.85E-05 1.66E-04It is unlikely that the following components are controlled by mineral solubil-ity: Na, K, NO3-, and Cl. It is possible, however, the following componentsare controlled by mineral solubility: Ca, Mg, Fe, SO4 , HCO3,and SiO2(aq). A completely thorough analysis would calculate the saturationindexes SI for every mineral in the ChemEQL Solid Phase Library containing thesecomponents in their composition. The following table, however, lists the satura-tion indexes SI for the most likely candidate minerals: calcite, dolomiteCaMg CO3 2 s , quartz SiO2 s , and amorphous FeOOH s .Date pH Calcite SI Dolomite SI Quartz SI FeOOH SI2/11/95 7.55 1.5096 0.4485 1.0648in the activitydiagram. If data points representing solute species in the water sample plot onor near the activity function representing a particular mineral, it is likely thatthis mineral is controlling solute activities in the water sample.Figures 5.4 to 5.7 illustrate the use of activity diagrams to identify poten-tial mineral phases constraining the chemistry of water samples. Figure 5.4plots Ca2 aq activities from simulations of Wingate Sink water samples(Crandall et al., 1999), along with solubility lines for two systems: one thatincludes a gas phase (PCO2 3:47 104 atm) and one that lacks a gas phase.The groundwater seeping into Wingate Sink would come from the latter typeof system but potentially come into equilibrium with the atmosphere while inthe Sink. The simulation suggests that the water is in equilibrium with calciteand shows little effect of dissolved carbon dioxide from the atmosphere.Figure 5.5 plots Mg2 aq activities from simulations of Wingate Sinkwater samples (Crandall et al., 1999), along with the solubility line for atwo-phase system: dolomite-controlling Mg2 aq activity and calcite-controlling Ca2 aq activity. The groundwater seeping into Wingate Sinkis nearly 100-fold undersaturated relative to dolomite solubility and relativelyinsensitive to pH. The Mg2 aq activity is apparently unconstrained by min-eral solubility in these water samples.Figure 5.6 plots H4SiO04 aq activities from simulations of Wingate Sinkwater samples (Crandall et al., 1999), along with the solubility line for threeSoil and Environmental Chemistry184FIGURE 5.4 This graph plots the logarithm of Ca2 aq activity as a function of pH. The opensquare symbols represent Wingate Sink water samples (Crandall et al., 1999) as simulated usingChemEQL. The solid line plots Ca2 aq activity constrained by calcite solubility and atmo-spheric CO2 g . The dashed line plots Ca2 aq activity constrained by calcite solubility for aclosed system without atmospheric CO2 g .FIGURE 5.5 This graph plots the logarithm of Mg2 aq activity as a function of pH. The opensquare symbols represent Wingate Sink water samples (Crandall et al., 1999) as simulated usingChemEQL. The dashed line plots Mg2 aq activity constrained by simultaneous equilibrium ofdolomite and calcite solubility (constraining Ca2 aq activity) in this pH range.FIGURE 5.6 This graph plots the logarithm of H4SiO04 aq activity as a function of pH. Theopen square symbols represent Wingate Sink water samples (Crandall et al., 1999) as simulatedusing ChemEQL. The solid line plots H4SiO04 aq activity constrained by quartz solubility, thedot-dashed line indicates chalcedony solubility, and the dashed line indicates opal solubility.Chapter 5 Water Chemistry 185Soil and Environmental Chemistry186FIGURE 5.7 This graph plots the logarithm of Fe3 aq activity as a function of pH. The opensquare symbols represent Wingate Sink water samples (Crandall et al., 1999) as simulated usingChemEQL. The solid line plots Fe3 aq activity constrained by ferrihydrite Fe OH 3 s solubil-ity, and the dashed line indicates goethite FeOOH s solubility.SiO2 s minerals of increasing solubility and decreasing crystallinity: quartz,chalcedony and opal. The groundwater seeping into Wingate Sink is saturatedrelative to quartz, the most insoluble SiO2 s mineral.Figure 5.7 plots Fe3 aq activities from simulations of Wingate Sinkwater samples (Crandall et al., 1999), along with the solubility line for twoferric oxyhydroxide minerals of increasing solubility and decreasing crystal-linity: goethite and ferrihydrite. The groundwater seeping into Wingate Sinkis clearly oversaturated relative to ferrihydrite, the most soluble ferric oxy-hydroxide mineral. This result is intriguing but easy to explain.The groundwater before entering the Sink is probably anaerobic, character-ized by high dissolved ferrous iron concentrations. Upon entering Wingate Sink,the water exposure to oxygen in the atmosphere causes the oxidation of ferrousiron to ferric iron. This oxidation process causes ferric oxyhydroxide mineralsto precipitate. The chemistry clearly indicates that the precipitation of ferricoxyhydroxide minerals is underway. A more careful chemical analysis of thewater that measures both total soluble iron and soluble ferrous iron would prob-ably result in a significant reduction in the estimate of oversaturation.Perhaps you may recall fresh well water with a distinct metallic taste.The metallic taste is almost entirely the result of dissolved ferrous iron. Theferrous iron originates from water percolating from a vadose zone whoseporosity is nearly saturated with water, rich in organic matter, and relativelywarm. These circumstances produce reducing conditions characterized by anChapter 5 Water Chemistry 187APPENDIX 5A. CHEMEQL RESULT DATA FILE FORMATAn important attribute of ChemEQL is the format of the output data file.When the simulation is complete, a window appears displaying the results.You save the output data file by selecting Save Data.. . from the File menu(Figure 5A.1). The data file is saved in text format regardless of the defaultsuffix (Figure 5A.2). Get into the habit of saving the file in an appropriateExcel workbook format: (Figure 5A.3). This is an important step because5.4. SUMMARYIn this chapter we discussed the thermodynamic basis for chemical equilib-rium and the equilibrium constant. In most water chemistry problems we needto adjust concentrations using activity coefficients; otherwise, the apparentequilibrium coefficient will depend on the concentration of dissolved ions insolutionthe ionic strength I. Chemists have proposed several different equa-tions for calculating ion activity coefficients (all of the examples used in thechapter are based on the Davies equation).General chemistry introduced you to several methods for solving simpleequilibrium problems. Few of these methods are practical when faced withactual water chemistry problems. The same basic principles apply, butcomputer-based numerical methods are required to solve the numerous simul-taneous equilibrium relations. Your knowledge of chemistry and chemicalequilibrium comes into play whenever you assess the validity of any waterchemistry simulation. We covered the basic steps of a validity assessment,and you are strongly encouraged to develop the habit of validating any com-puter simulation.The final topic we covered addresses a central issue in any simulation ofenvironmental water samples: the identification of minerals that control waterchemistry. A simple rulethe Gibbs Phase Ruleplaces an upper limit onthe number of mineral phases that can actively control water chemistry. Withthis limit in hand, you can use water chemistry simulations to compute the sat-uration index SI for each candidate mineral, or you can plot data from yoursimulation in activity diagrams. Either method is a suitable strategy for iden-tifying minerals controlling the chemistry of the water samples.active anaerobic bacteria community. The ferrous iron is a by-product of theanaerobic respiration of iron-reducing bacteria.If you let a glass of this metallic-tasting water sit out, exposed to the air, afterseveral hours the water will be cloudy and a yellow precipitate will cover the bot-tom of the glass. This yellow precipitate is the ferric mineral ferrihydrite. If youtaste the water, you will find that it has lost its metallic taste because you can onlytaste dissolved iron. Much the same process is occurring in Wingate Sink.results validation becomes quite simple using spreadsheet functions.Soil and Environmental Chemistry188APPENDIX 5B. VALIDATING WATER CHEMISTRYSIMULATIONSTable 5.2 contains a checklist for validating computer-based water chemistrysimulations. The list is not intended to be comprehensive. Consider it a frame-work that you can add to as your experience increases and you become morefamiliar with water chemistry modeling. Any user of computer-based modelsshould develop the habit of routinely validating the data used to simulate theprocess being studied and specific simulation results.Charge Balance Validation: This assessment evaluates the condition ofcharge neutrality in solution. It determines whether the charge sum over allFIGURE 5A.1 Save the ChemEQL results data file by selecting Save Data... from the Filemenu. You will be prompted to name the file (default: z.xls). This naming convention allowsyou to open the file using the spreadsheet application Excel.FIGURE 5A.2 The ChemEQL results data file default format is text.Chapter 5 Water Chemistry 189cation species equals the charge sum over all anion species in solution. Com-puting this sum requires multiplying the concentration of each ionCi mol L1 times its valence zi to convert molar concentration to moles ofcharge concentration (formerly called normality): zi Ci molc L1 . If thissum is performed using a spreadsheet, then sum over all cations (using molesof charge units) plus the sum over all anions (using moles of charge units)should equal zero to within rounding error:Xizi Ci Xjzj Cj FIGURE 5A.3 Save the ChemEQL data files after opening in Excel by selecting an appropriateworkbook format.The followiulation. Theproduct ofSupposetable. The(Eq. 5B.1)Mass Beach compoXng table liststhird columcharge and cSpeciesAcetic AcidAcetate-OHHthe columnsformula inis a sum ovealance Validnent (e.g., Ecationsizi Ci cationsXjthe species andn lists the chargoncentration.Conc. [mol/L]1.939E-026.093E-041.687E-116.094E-04are labeled Acell D2 is r terms in columation: There iq. (5B.2A), Eq.anionszj Cj anionsconcentrae of eachCharge0111D and theB2*C2. Tn D: SUs a separ(5B.2B)). 0 5B:1tion from a ChemEQL sim-species, and the fourth theCharge Conc. [molc/L]0.000E006.093E-041.687E-116.094E-04rows are labeled 15 in thehe charge neutrality sumM(D2:D5).ate mass balance sum forThe sum is over all speciescontaining the component s mplex species) and mustequal the total concentrati c is sum requires multiply-Soil and Environmental Chemistry190Mass Balance Expression: Component BCM XjnM, j CM, j 5B:2BCM CM HA CM HA 02 CM HA 3 CM A 0 CM A 22 The following table lists the species and concentration from a ChemEQL sim-ulation involving two components: Ca and SO4 . Suppose the columnsare labeled A and B and the rows are labeled 18 in the following table. Themass balance formula for component Ca is (B2B3B4). The massbalance formula for component SO4 is (B4B5B6).Species Conc. [mol/L]Ca 1.11E-02CaOH 1.14E-08Mass Balance Expression: Component ACA XinA, i CA, i 5B:2ACA CH2A CHA CA2 CM HA 2 CM HA 02 3 CM HA 3 CM A 0 2 CM A 22 Complexation ReactionsM2 aq HA aq $ M HA aq M2 aq 2 HA aq $ M HA 02 aq M2 aq 3 HA aq $ M HA 3 aq M2 aq A2 aq $ M A 0 aq M2 aq 2 A2 aq $ M A 22 aq tion, then a sum over the concentrations of all species containing each compo-nent in the results of the simulation should equal the initial input values.Hydrolysis ReactionsH2A aq $ HA aq H aq HA aq $ A2 aq H aq ing the concentration of every species Ci mol L times the stoichiometriccoefficient ni to account for every molecule: ni Ci mol L1 . Rather than relyon a general definition, the following example should make the mass balanceexplicit. If known concentrations of components M and A are added to a solu-on of thatCaSO4(aq)omponent. Th1(hydrolysi species and co5.37E-03from the ChemEQL simula d in columns C and D. Theactivity coefficients in colu co iding the activity of eachspecies (column D) by its c on he activity coefficient incell E2 is calculated by the 2 strength terms in columnF are identical to the termsChapter 5 Water Chemistry 191oncentratiterms (Din column D(column C). T/C2). The ionicmn E are mputed by divtion result ata file appearto select the equation and parameters used to calculate activity coefficients oractivities in the simulation results (see Eqs. (5.10), (5.11), and (5.12)). If themodel reports both concentrations and activities, you can determine the activitycoefficient for each ion by dividing the reported activity by the concentration(see Eq. (5.8)). Your validation of reported activities should use the concentra-tions in the output data file and the ionic strength I computed from those results.The validation results should agree with the values listed in the output data file.The following table is from the same ChemEQL simulation used to illustratethe preceding ionic strength validation. Suppose the columns are labeled AGand the rows are labeled 19 in the following table. Concentrations and activitiesThe ionic strength I from the model simulation is validated when the valuereported in the results matches the value based on the preceding calculation.Activity Coefficient Validation: Water chemistry models usually allow youH 9.05E-08 1of the pre4.52E-084.44E-02OH 1.34E-07 1 6.71E-08HSO4 5.50E-08 1 2.75E-08SO4 1.11E-02 2 2.22E-02CaSO4(aq) 5.37E-03 0 0.00E00CaOH 1.14E-08 1 5.71E-09Ca 1.11E-02 2 2.22E-02Species Conc. [mol/L] Charge Ionic Strength [mol/L]SO4 1.11E-02HSO4 5.50E-08OH 1.34E-07H 9.05E-08Ionic Strength Validation: The simulation may or may not report the ionicstrength I in the results, but ionic strength I, which also depends on an accu-rate charge balance, affects the estimate of each ion activity coefficient. If theionic strength I sum is calculated using a spreadsheet, the sum is best per-formed using Eq. (5B.3) rather than Eq. (5.9):I Xiz2i Ci2 5B:3The following table lists the species and concentration from a ChemEQL sim-ulation involving two components: Ca and SO4. Suppose the columnsare labeled AD and the rows are labeled 19 in the following table. The for-mula in cell D2 is (C2^2)*(B2/2). The ionic strength I, computed usingEq. (5B.3), is the sum in cell D9: SUM(D2:D8).vious table.ic u vi c n na o ( E ac ffar tey V : ct t ea m s t. r tp e (E e ofn n .4 ea n lito the product of educ duct activit .4 thSoil and Environmental Chemistry192metric quotient ni is positive for all products and negative for educts.Q anMM anNN . . .anAA anBB . . . Yianii Yigi Ci ni 5B:4The activity product is equal to the thermodynamic equilibrium constant K(Eq. (5B.4)) when the reaction is at equilibrium (Figure 5.1).K anMM anNN . . .anAA anBB . . . equilibriumYianii Yigi Ci ni 5B:5ChemEQL lists the logarithm of the thermodynamic solubility constant forgypsum: 4.58. This is found in the Solid Phase Library Species under theLibrarymenu. The activity product (Eq. (5B.5)) for this simulation is computedfrom the preceding tabt and prole used to validate aies (Eq. (5Bctivity coeffict Q, in rea)), whereients. The ce stoichio-quotient Qproduct coas an apcentratioroximates (Eq. (5quality)). The rq. (5.4)), thction quotieproduct educt andty, is equaltion under ny circu stances i a produc Earlier we epresented he reactionActivit Product alidation The rea ion quotien Q for a ch mical reac-activities e valida d.simulated ctivity c efficients column ), then the tivity coe icients andIf the expl itly calc lated acti ty coeffi ients (colum G) are ide tical to thecell address $F$9. 10 ^0:5109 B2^ 2 SQRT$F$9=1 SQRT$F$9 0:2 $F$9Species Charge Conc.[mol/L]Activity ActivityCoefficientIonicStrength[mol/L]ActivityCoefficientCa 2 1.11E-02 5.12E-3 0.461 2.22E-02 0.461CaOH 1 1.14E-08 9.40E-9 0.824 5.71E-09 0.824CaSO4(aq) 0 5.37E-03 5.37E-3 1.000 0.00E00 1.000SO4 2 1.11E-02 5.12E-3 0.461 2.22E-02 0.461HSO4 1 5.50E-08 4.54E-8 0.824 2.75E-08 0.824OH 1 1.34E-07 1.11E-7 0.824 6.71E-08 0.824H 1 9.05E-08 9.05E-8 1.000 4.52E-08 1.0004.44E-02activity coefficient expression used by the model and the ionic strength I com-puted from the simulation (cell F9). In the following example, all activitycoefficients are calculated using the Davies equation (Eq. (5.12))withtemperature-dependent parameter A 0.5109 for 25Cand the ionicstrength from the simulation in cell F9: 4.44E-02 [mol/L]. The formula in cellG2 is given following, where the ionic strength I is indicated by its absoluteThe validated activity coefficients listed in column F are computed fromell formulas v r c l u -se c od ac cs, o er i -i u ins s ti it st b d p -d ng d erChapter 5 Water Chemistry 193than the most concentrated ion. The ionic strength I reported by ChemEQL isalso validated because it matches the ionic strength calculated from the con-centrations listed in the results table.Species Conc. [mol/L] Charge Conc. [molc/L] Ionic Strength. [mol/L]Ca 1.11E-02 2 2.22E-02 2.22E-02CaOH 1.14E-08 1 1.14E-08 5.71E-09CaSO4(aq) 5.37E-03 0 0.00E00 0.00E00SO4 1.11E-02 2 2.22E-02 2.22E-02HSO4 5.50E-08 1 5.50E-08 2.75E-08OH 1.34E-07 1 1.34E-07 6.71E-08H 9.05E-08 1 9.05E-08 4.52E-088.72E-08 4.44E-02Mass Balances: This example simulates the dissolution of a mineral intopure water. The mass balance for the two components Ca and SO4 isvalidated against the solubility predicted by the simulation (1.648E-02 molL1). The data file does not list Ca as a component (Ca was replacedby CaSO4:2H2O (gypsum) when executing Insert Solid... after compilingconstant in the database. It is also wise to check the thermodynamic equilibriumconstants in the database, especially for the reactions most critical for the chemis-try you are modeling, against published values.APPENDIX 5C. VALIDATION ASSESSMENT FOR EXAMPLES 5.13AND 5.16Example 5.13: Gypsum SolubilityCharge Balance and Ionic Strength: The following table lists the charge bal-ance (8.72E-08 molc L1) and ionic strength I (4.44E-02 mol L1) calculatedfrom the concentrations generated by ChemEQL and listed in Example 5.13.The charge balance is validated because error is six orders of magnitude lessficients, anthe input mthen compariatrix and beforethe prorunninguct with the ththe simulation).modynamic equilibriumfrom the da a file generated y the mo el and the appro riate stoichiometric coefexpression from the databa e, compu ng the ion activ y product using activitietion of the on activity prod cts IAP volves selecting one or more equilibriumcoefficient and the corresp nding th modynamic equ librium constant. Validation databa listing the edu ts and pr ucts for each re tion, their stoichiometriDataba e Validation: E ery wate hemistry mode ses an equilibrium reacmineral.is (D2*D5), equal to the value 2.626E-05. The base-10 logarithm of 2.626E-05is LOG(2.626E-05), which equals 4.58, validating the ion activity productIAP for gypsum. Stated another way, the IAP computed from the activities ofthe two species Ca and SO4 equals the gypsum solubility product, mean-ing these activities are consistent with an aqueous solution saturated by theThe concentration sumi er asd l c Lti ne i n n0 r to en b E al ils00 1 n n u-on st e ol r,e b on olL ). If we add the 1.000-07 molc L req e tya ic h E orSoil and Environmental Chemistry1942.234E-07 mol L if added as a divalent anion). The ionic-strength errorranges from 29% to 45%.Species Conc. [mol/l] Charge Charge Conc.[molc/L]Ionic Strength[mol/L]Al 6.52E-13 3 1.957E-12 2.935E-12AlOH 3.80E-11 2 7.590E-11 7.590E-11Al(OH)2 1.76E-09 1 1.756E-09 8.780E-10Al(OH)3(aq) 1.62E-09 0 0.000E00 0.000E00Al(OH)4- 1.50E-08 1 1.499E-08 7.495E-09Al2(OH)2 2.88E-19 4 1.153E-18 2.306E-18Al3(OH)4 4.03E-24 5 2.017E-23 5.043E-23OH 5.83E-08 1 5.833E-08 2.917E-08H 1.72E-07 1 1.715E-07 8.575E-081.000E-07 1.234E-07Mass Balances: This example simulates the dissolution of a mineral intopure water. The mass balance for component Al is validated against thesolubility predicted by the simulation (1.841E-08 mol L1). The data file doesnot list Al as a component (Al was replaced by Al(OH)3 (Gibbsite,crist) when Insert Solid... was executed after the input matrix was compiledand before the simulation was run). The solid phase specie Al(OH)3 (Gibbsite,crist) represents crystalline gibbsite, whose solubility differs from other solidphase species in the database for the same chemical composition: microcrystal-line gibbsite, bayerite, and the amorphous solid Al OH 3 s .as a monovalent nion, the ion1strengtuired to achievbecomes 1.734charge neutrali-07 mol L1 (is identical to th1ionic strength reported1y the simulati (1.234E-07 mlated from the c centrations li ed in th results table f lowing, howeveto account for 1. 0-07 molc L of anio charge. The io ic strength calcThe ionic stre gth I reportedy Chem QL is also inv id because it facadditional 1.000- 7 mol L1 is equired achieve charg neutrality.model: the condi on of charge utrality s not imposed o the solution. Amost concentrate ion. This example revea s a characteristi of the ChemEQThe charge bala e is invalid b cause it s the same ord of magnitudenc eEQL and liste in Example 5.1over all species containing component Ca (Ca, CaOH, CaSO4(aq))and the concentration sum over all species containing component SO4 (SO4 , HSO4-, CaSO4(aq)) both equal the predicted solubility (1.648E-02mol L1), validating the two mass balance equations.Example 5.16: Gibbsite SolubilityCharge Balance and Ionic Strength: The following table lists the charge bal-ance (1.000-07 molc L1) and ionic strength I (1.243E-07 mol L1) calculatedfrom the concentrations generated by Chem d 4.If w it e io xplic-itly sat al 4 l L 4E 1 (seeionic-s o e e . emon-strates p ge ty ig ect onChemE esThe r i riu f phasespecie it n m s or thefollow x T uc al usingthe activities in the preceding table. AYS IT3Chapter 5 Water Chemistry 195K 108:11 aHaAl37:76 108 1:72 107 36:50 1013The logarithm of thermodynamic equilibrium constant for the solution specieAl(OH)4- in the ChemEQL database is 22.70 for the following equilibriumexpression. This product is identical to the IAP using the activities in the pre-ceding table.Al3 aq $ 3 H aq CRl OH 3 s TALLINE GIBBS Eing equilibrium e pression. his prod t is identic to the IAPAl(OH)3 (Gibbs e, crist) i the Che EQL databa e is 8.11 flogarithm of the modynam c equilib m constant or the solidQL simulation r ults.that failing to im ose char neutrali has an ins nificant efftrength errors ab ve)the rror nev r exceeds 0 4%. This disfy charge neutr ity1.73 E-07 mo 1 or 2.23 -07 mol Le calculate activ y coeffici nts using nic strength values that e(1.841E-08 mol L ), validating the mass balance equation.Activities and Activity Product: The following table lists the results fromthe ChemEQL simulation of Al(OH)3 (Gibbsite, crist) dissolution in col-umns 2 and 3 and the activity coefficients generated by the simulation incolumn 4 (activity divided by concentration). The validated activity coeffi-cients appear in column 5 calculated using the invalid ionic strength fromthe simulation.Species Conc.[mol/L]Activity SimulatedActivityCoefficientValidatedActivityCoefficientAl 6.52E-13 6.50E-13 0.996 0.996AlOH 3.80E-11 3.79E-11 0.998 0.998Al(OH)2 1.76E-09 1.76E-09 0.999 1.000Al(OH)3(aq) 1.62E-09 1.62E-09 1.000 1.000Al(OH)4- 1.50E-08 1.50E-08 1.000 1.000Al2(OH)2 2.88E-19 2.86E-19 0.993 0.993Al3(OH)4 4.03E-24 3.99E-24 0.990 0.990OH 5.83E-08 5.83E-08 1.000 1.000H 1.72E-07 1.72E-07 1.000 1.000The concentration sum over all species containing the component Al(first seven species in the preceding table) is equal to the predicted solubility1Soil and Environmental Chemistry196taining gases that are free to dissolve into the solution. The preceding expres-sion is not appropriate for a system whose components include, for example,dihydrogen sulfide gas H2S g , the mineral phase cinnabar HgS s , and anaqueous solution containing H2S aq , Hg2 aq , H aq , and other speciesproduced by hydrolysis and the formation of soluble complexes. The follow-ing solubility reaction and equilibrium expression are appropriate for an open,3-phase system consisting of an atmosphere with dihydrogen sulfide gasH2S g , the mineral cinnabar HgS s , and an aqueous solution. The numericalvalue for the following net solubility equilibrium expression depends on thepressure units. ChemEQL designates the partial pressure of gas using the pres-sure unit atmosphere (atm) rather than Pascal (Pa).Hg2 aq H2S g $ 2 H aq HgS s CINNABARK 1030:09 a2HaHg2 PH2SGenerating New Equilibrium Expressions for a Water Chemistry Model: Eachwater chemistry model has its own protocol for modifying its equilibrium data-base, but all permit the user to tailor the database to suit their specific modelingrequirements by adding equilibrium expressions for components, solution spe-cies, and mineral phases that do not already appear in the database.2:00 1023 1:72 107 4 1:50 1086:50 1013APPENDIX 5D. CINNABAR SOLUBILITY IN AN OPEN SYSTEMCONTAINING THE GAS DIHYDROGEN SULFIDEThe solubility equilibrium expression for the mineral cinnabar HgS s asit appears in the ChemEQL library for Solid Phase Speciesis appropriatefor closed systems where equilibrium is confined to the solution and mineralphases.Hg2 aq S2 aq $ HgS s CINNABARK 1052:00 1aHg2 aS2An open system adds another phase: an atmosphere in contact with and con-Al3 aq 4 H2O l $ 4 H aq Al OH 4 aq K 1022:70 a4H aAl OH 4aAl3 solution spe s t containall of the s o tallic ele-ments. A c ra d requiremany more ngChapter 5 Water Chemistry 197Hg S HgS(aq) 7.90Hg 2.S HgS2 14.30Hg S H Hg(OH)S- 4.50Hg 2.S 2.H Hg(HS)2(aq) 65.51Hg 2.S H Hg(HS)S- 59.32Hg S HgS (Cinnabar) 52.00Next, we generate nine new equilibrium expressions and constants whereH2S g is a component. The following examples illustrate how this is done.Invert the first expression, placing H2S(g) on the left and changing its rolefrom product to educt.H2Sg 2:H S; logK 21:91Adding the second expression to the preceding one generates a second expres-sion, defining the specie H2S(aq) in terms of the new component H2S(g).H2Sg H2Saq; logK 21:91 20:92 0:99Adding the third expression to the inverse of the first expression generates a thirdexpression, defining the specie HS- in terms of the new component H2S(g).H2Sg H HS; logK 21:91 13:90 8:01S H HS- 13.90S 2.H H2S(aq) 20.92S 2.H H2S(g) 21.91Equilibrium Expression Based on Component: S log(K)expressions than the ones listed in the followi table.omprehensive modification of the Regular Lib ry woulolution species that contain sulfide involving ther mecies that contain both sulfide and Hg(II). This li t does notion species database lists nine equilibrium exp ssions thdatabase (i.e., the Regular Library) and the mineral species database (i.e., theSolid Phase Library) do not contain H2S g as a component. Most of the solu-tion and mineral species containing sulfide, and the associated equilibriumexpressions and constants that define these sulfide-containing solution andmineral species are based on the component S2 aq . Hydrogen sulfideHS aq is a component in the standard Regular and Solid Phase libraries.A few solution and mineral species are defined by equilibrium expressionsbased on hydrogen sulfide HS aq .The solu re at defineunder the heading Access the Libraries (p. 15). The first step is to identifyentries in the existing database that can be modified or combined to generateequilibrium expressions that are appropriate for an open system where H2S g is a component rather than a species. The standard ChemEQL solution speciesChemEQL uses two databases, one for solution species and one for solid-phase (mineral) species. The ChemEQL Manual gives detailed instructionsHg 14.01Hg 29.52Hg 17.41Hg 21.69Hg 15.50Hg r) 30.09Since the stan d b not contain H2S g as a component, de a re adding the newequilibrium expr n e sion is consideredas adding a newThe ChemEQ f b three components:0 M Hg (tota d H (total). Des-ignating H2S(g) a t (g) partial pressureremains fixed at r ti r compiling, selectInsert Solid Pha M a e component H2S(g) with HgS (CiThe not v gSoil and Environmental Chemistry198(3.23E-38 M) and S (3.10E-15). When cinnabar dissolves to saturate theaqueous solution in a closed system without an atmosphere and no other sulfideminerals, thable result from this simulation is the relative actie activity of the two ions would be Hg (3.21ity of HH 1.99E-07 1.99E-07OH 5.02E-08 5.02E-08S 3.10E-15 3.10E-15HS 4.91E-08 4.90E-08HgS2 6.19E-53 6.18E-53HgS(aq) 7.94E-45 7.94E-45Simulation results for cinnabar solubility in an open system containing1.0E-6 atm H2S(g) partial pressure appear following, using Davies activitycoefficients and I 1.49E-7 M.Species Conc. [mol/L] ActivityH2S(aq) 1.02E-07 1.02E-07H2S(g) 1.00E-06 1.00E-06Hg(HS)2(aq) 3.98E-15 3.98E-15Hg(HS)S 1.29E-14 1.29E-14Hg(OH)S 1.59E-41 1.59E-41Hg 3.23E-38 3.23E-38HgOH 6.45E-35 6.45E-35Hg(OH)2 5.13E-31 5.13E-31Hg(OH)3 3.24E-39 3.24E-39Hg2OH 2.63E-72 2.62E-72Hg3(OH)3 1.70E-99 1.69E-99se.. . from thennabar).atrix menu nd replac1.0E-6 atm du ing the simula on. Afteas a free vari ble ensures tha the H2Sl), 1.0E-6 atm H2S(g) (free), an 1.0E-7 ML simulation o cinnabar solu ility hasspecies.essions and co stants. Each n w expresit must be ad d to both libr ries befodard Regular an Solid Phase li raries do H2S(g) 2.H HgS (Cinnaba 2.H2S(g) 3.H Hg(HS)S- 2.H2S(g) 2.H Hg(HS)2(aq) H2S(g) 3.H Hg(OH)S- 2.H2S(g) 4.H HgS2 H2S(g) 2.H HgS(aq)The remaining expressions listed following were generated in the same way.Equilibrium Expression Based on Component: H2S(g) log(K)E-26 M) andS (3.12E tm al i tiv-ity by 12 or e t s ofmagnitude s 5APPENDI A L PPYROMO BThis Chem po M MPb (tota C t H(total). Afte e d f enuand replace o O4)3OH (hydro ) w (O xy-apatite), an w (C T asesequence c ts ,CO3 , an co s andH), and C m entlist. Simula a i s .CaHPO4(aq) 7.32E-11 7.32E-11 1.000CO3 3.40E-05 3.10E-05 0.914Chapter 5 Water Chemistry 199PO4 4.89E-12 3.99E-12 0.817HPO4 1.37E-09 1.25E-09 0.914H2PO4 2.83E-12 2.76E-12 0.978H3PO4 5.45E-20 5.45E-20 1.000OH 7.32E-05 7.16E-05 0.978CaH2PO4 7.57E-15 7.41E-15 0.978Pb 2.22E-08 2.03E-08 0.914PbOH 2.97E-06 2.91E-06 0.978Pb(OH)2 8.28E-06 8.28E-06 1.000Pb(OH)3- 6.07E-07 5.93E-07 0.978Pb2OH 1.44E-12 1.18E-12 0.816Pb3(OH)4 3.05E-08 2.78E-08 0.914Pb4(OH)4 8.11E-13 5.66E-13 0.697Pb6(OH)8 1.76E-11 1.23E-11 0.698PbHCO3 2.85E-09 2.79E-09 0.978PbCO3 1.35E-06 1.35E-06 1.000Pb(CO3)2 9.79E-08 8.95E-08 0.914PbHPO4 3.20E-14 3.20E-14 1.000PbH2PO4 1.82E-18 1.78E-18 0.977H2CO3 2.90E-08 2.90E-08 1.000HCO3 9.48E-05 9.27E-05 0.978CaHCO3CaPO4H1.30E-071.26E-091.40E-101.27E-071.23E-091.40E-100.9780.978CaCO3(aq) 5.50E-06 5.50E-06 1.000CaOH 1.30E-07 1.27E-07 0.978Ca 1.17E-04 1.07E-04 0.914Species Conc. [mol/l] Activity Activity Coefficienttion results appe r following us ng Davie activity coefficientsO3 (final co ponents: Ca and H ) from the compond H), PO4 (remaining mponent : Ca, CO3 ,removes Pb (remaining omponen : Ca, PO4d (3) CO3 ith Ca(CO3) alcite). his insert solid phxypyromorphite , (2) PO4 ith Ca10 H)2(PO4)6 (hydrocomponents in the following rder: (1) Pb with Pb5(Pr compiling, sel ct Insert Soli Phase... rom the Matrix ml), 0 M PO4 (total), 0 M O3 (to al), and 1.0E-7 MEQL simulation has five com nents: 0 Ca (total), 0RPHITE SOLU ILITYX 5E. SIMULT NEOUS CA CITE-A ATITE-o as to maintain the IAP 10 . 2.00ders of magnitud , driving down he Hg activity by 12 order-27). A 1.0E-6 a H2S(g) parti pressure ncreases the S ac1.000The IAP ra (a s) 4(H2O)2(variscite) K C L Library.At equilibrium, with the solution saturated by both mine a total of5.88E-06 M or 2 of O)2 (var-Soil and Environmental Chemistry200(see p. 24 of ChemEQL Manual). Simulation results appear following, usingDavies activity coefficients. The graph uses a logarithmic scale for the activ-ity of each species (only the most abundant are plotted) and resembles the pH-iscite) have dissolved into solution. The total soluble aluminum 5.99E-06 M isthe sum of the solubility of both minerals.APPENDIX 5G. APATITE SOLUBILITY AS A FUNCTION OF pHThis ChemEQL simulation has three components: 0 M Ca (total), 0 MPO4 (total), and 0 M H (free). After compiling, select Insert SolidPhase.. . from the Matrix menu and replace component PO4 withCa10(OH)2(PO4)6 (hydroxyapatite). The simulation treats H as a freeor independent variable that can be assigned values within a specified rangedependent gof Al(OH)3 (amibbsite solubility pphous) and 1.1lot in Figure 5.E-07 M3.ral phases,AlPO4(H2match the LOG( ) values in the hemEQ Solid Phasefor both mine lsAl(OH)3 morphou and AlPOH 4.55E-07 4.55E-07 1.000OH 2.20E-08 2.20E-08 0.998H3PO4 6.31E-12 6.31E-12 1.000H2PO4 9.84E-08 9.82E-08 0.998HPO4 1.37E-08 1.36E-08 0.992PO4 1.36E-14 1.34E-14 0.982Al3(OH)4 6.49E-14 6.16E-14 0.950Al2(OH)2 3.52E-12 3.40E-12 0.968Al(OH)4 2.77E-06 2.77E-06 0.998Al(OH)3(aq) 7.94E-07 7.94E-07 1.000Final Solution Concentrations Ca (total) 1.22E-04 M, Pb (total) 1.34E-05 M, and PO4 (total) 2.70E-09 M, and pH 9.86.APPENDIX 5F. SIMULTANEOUS GIBBSITE-VARISCITESOLUBILITYThis ChemEQL simulation has three components: 0 M Al (total), 0 MPO4 (total), and 1.0E-7 M H (total). After compiling, select Insert SolidPhase.. . from the Matrix menu and replace components in the followingorder: (1) PO4 with AlPO4(H2O)2 (variscite) and (2) Al with Al(OH)3 (amorphous). Simulation results appear following, using Davies activitycoefficients (I 3.14E-6 M).Species Conc. [mol/L] Activity DaviesCoefficientAl 6.05E-09 5.94E-09 0.982AlOH 1.32E-07 1.31E-07 0.992Al(OH)2 2.29E-06 2.28E-06 0.998Chapter 5 Water Chemistry 201APPENDIX 5H. EFFECT OF THE CITRATE ON THE SOLUBILITYFIGURE 5G.1 The graph plots pH-dependent activities for the four most abundant phosphatespecies and the total phosphate concentration in a two-phase system: aqueous solution and themineral apatite Ca10 PO4 6 OH 2 s .OF THE CALCIUM PHOSPHATE MINERAL APATITEPhosphorus nutrition is problematic for plants in both acidic and alkaline soils.Low phosphorus availability in acid soil results from low strengiteFePO4 2H2O s or variscite AlPO4 2H2O s solubility. Phosphorus deficiencyin alkaline soil arises from low apatite Ca10 PO4 6 OH 2 s solubility. Legumesof the lupine genus (Lupinus spp.) secrete citrate and other weak organic acids tosolubilize phosphate and enhance uptake. The present water chemistry simula-tion illustrates the effect of citrate complexes on the solubility of apatite.The solubility equilibrium expression for the mineral apatiteCa10 PO4 6 OH 2 s as written in the ChemEQL database appears following.10 Ca2 aq 6 PO34 aq $ 2 H aq Ca10 PO4 6 OH 2 s APATITEK 1088:40 a2Ha10Ca2 a6PO34The ChemEQL simulation of apatite solubility has three components: 0 MCa (total), 0 M PO4 (total), and 1.0E-7 M H (total). After compil-ing, select Insert Solid Phase.. . from the Matrix menu and replace compo-nent PO4 with Ca10(OH)2(PO4)6 (hydroxyapatite). Simulation resultsfor apatite solubility in the absence of citrate appear following, using Daviesactivity coefficients and I 2.45E-5 M.6 6 06 6 01 1 01 1 11 1 01 9 03 3 01 1 02 2 15 5 01 1 1Apatite n o a 88E-7moles of C 4 he Q addedcitrate has ne ), total),1.0E-3 M C to - ( SolidPhase . . . to 0 O ite) aspreviously. es e itrate,using Davi ef ollow-Finally, e e o fficients(fourth colucitrate has20compare thmn, both tabla substantial eeffect of addes). The changeffect on activitd citratein ionic sy correction the activity coeH 4.40E-10 4.40E-10 1.000OH 2.44E-05 2.27E-05 0.930HCitrate 7.41E-07 5.56E-07 0.750Citrate 9.71E-04 5.08E-04 0.523H3PO4 5.70E-15 5.70E-15 1.000H2PO4 9.87E-08 9.18E-08 0.930HPO4 1.76E-05 1.32E-05 0.750PO4 2.56E-08 1.34E-08 0.523H3Citrate 8.23E-18 8.23E-18 1.000H2Citrate 1.33E-11 1.24E-11 0.930CaH2Citrate 2.17E-16 2.02E-16 0.930ing table.The presence of 1.0E-3 M citrate increases ionic strength 100-fold andapatite solubility from 6.88E-7 moles of Ca10(OH)2(PO4)6 per liter in theabsence of citrate to 2.96E-5 moles per liter. Although all calcium citrate spe-cies represent a mere 2.8% of the total added citrate, these species represent95% of the total dissolved calcium.Species Conc. [mol/L] Activity Davies CoefficientCa 1.37E-06 1.03E-06 0.750CaOH 4.18E-10 3.89E-10 0.931CaPO4 4.27E-08 3.98E-08 0.930CaHPO4(aq) 7.46E-09 7.46E-09 1.000CaH2PO4 2.55E-12 2.37E-12 0.930CaCitrate 2.82E-05 2.62E-05 0.930CaHCitrate 7.27E-10 7.27E-10 1.000Simulation res activity coults for apatitficients and Isolubility4.44E-3trnsin the absence of cM, appear in the freplace PO4 with Ca1 (OH)2(P 4)6 (hydroxyapatitrate ( tal), and 1.0E 7 M H total). Use Insertfour compo nts: 0 M Ca (total 0 M PO4 (a10(OH)2(PO )6 per liter. T ChemE L simulation withsolubility (i the absence f citrate) t saturation is 6.H .83E-09 .83E-09 .000OH .50E-06 .47E-06 .994H3PO4 .91E-14 .91E-14 .000H2PO4 .13E-07 .13E-07 .995HPO4 .98E-06 .89E-06 .977PO4 .00E-09 .50E-10 .949CaH2PO4 .91E-11 .90E-11 .994CaHPO4(aq) .43E-08 .43E-08 .000CaPO4 .85E-08 .84E-08 .995CaOH .11E-10 .07E-10 .994Ca .85E-06 .69E-06 .977Species Conc. [mol/l] Activity Davies CoefficientSoil and Environmental Chemistry2ength induced by addingin this example.3appears following. This solubility expression takes into account goethite pH-dependent solubility in much the same way as in Example 5.10.FeOOH s GOETHITE3 H aq $ Fe3 aq 2 H2O l KsGOETHITE aFe3a3H 101:00The bacterial siderophore ferrioxamine B is trivalent when fully dissociated:FOB3 aq . The pH-dependent formation expression follows (Smith and Mar-tell, 2001) and was added to the ChemEQL database for this simulation (seeAppendix 5D). Notice that the formation constant Kf 1041:39 is very large,indicating equilibrium favors the product Fe FOB aq over the educts.Fe3 aq FOB3 aq H aq $ Fe FOB aq Kf aFe FOB aFe3 aFOB3 aH 1041:39Multiplying the goethite solubility expression by the siderophore formationexpression yields a solubility expression showing the effect of complexformation.FeOOH s GOETHITEFOB3 aq 4 H aq $ Fe FOB aq 2 H2O l KsGOETHITEKf aFe3a3H0@1A aFe FOB aFe3 aFOB3 aH0@1A 101:00 1041:39 q requirements. Siderophores are organic compounds that form highly specific,extremely stable complexes with the Fe3 aq ion in solution. The ferric-sidero-phore complex binds to a receptor on the cell surface of bacteria and fungi spe-cifically designed to transport the complex across the cell membrane into thecytoplasm, where enzymes reduce Fe3 to Fe2. The ferrous-siderphore com-plex, being relatively weak, releases Fe2 following reduction to cytoplasmicchaperone complexes that specifically bind and transport ferrous iron. The fol-lowing example illustrates the effect of siderophore complexes on the solubilityof the ferric oxyhydroxide mineral goethite FeOOH s .The solubility equilibrium expression for the mineral goethite FeOOH s APPENDIX 5I. EFFECT OF THE BACTERIAL SIDEROPHOREDESFERRIOXAMINE B ON THE SOLUBILITY OF THE IRONOXYHYDROXIDE GOETHITEIron nutrition is problematic for plants and soil microbes because ferric iron sol-ubility is extremely low. Grass species, bacteria, and fungi secrete compoundscalled siderophores to dissolve ferric iron in order to meet their nutritionalChapter 5 Water Chemistry 20Knet Fe FOB aFOB3 a4H 1040:39At neutral pH the ratio of Fe FOB aq to FOB3 aq is 1012.39.Adding 1 mmole of ferrioxamine B per liter will dissolve 106 moles of goethite.A ChemEQL simulation of ferrihydrite Fe OH 3 solubility has threecomponents: 0 M Fe (total), 1.0E-4 M FOB (total), and 0 MH (free). Ferrihydrite is a poorly crystalline hydrous ferric oxide mineralof indeterminate structure and composition; its mineralogy is defined by acharacteristic x-ray diffraction pattern. Typical siderophore concentrationsin soil pore water are on the order of 100 mM.After compiling, select Insert Solid Phase.. . from the Matrix menu andreplace component Fe with Fe(OH)3 (s), making the initial Feirrelevant. The simulation treats H as a free or independent variableforced to assume values within a specified range (see p. 24 of the ChemEQLManual). Simulation results for ferrihydrite solubility in a solution contain-ing 100 mM ferrioxamine B appear graphically following. The graph uses alogarithmic scale for the activity of each solution species (only the mostabundant are plotted), which resembles the pH-dependent gibbsite solubilityplot in Figure 5I.1.Soil and Environmental Chemistry204FIGURE 5I.1 The graph plots pH-dependent activities for the five most abundant ferricspecies in a two-phase system: aqueous solution containing 100 mM ferrioxamine B andthe mineral ferrihydrite Fe OH 3. The activity and concentration of Fe FOB aq arevirtually independent of pH and represent 96% of the total dissolved ferric iron and ferriox-amine B.Pro1.2.Chapter 5 Water Chemistry 205FERRIHYDRITEFe3 aq $ FeOOH s GOETHITE3 H aq K 101:00The chemical composition and crystal structure of goethite are known.Ferrihydrite is identified by its x-ray diffraction pattern, but its chemical com-position and crystal structure remain undetermined. Figure 5.7 plots Fe3 aq aH4SiO4 K 103:98log1aH4SiO40@1A log K log 103:98 QUARTZ : log aH4SiO4 3:98The logarithmic activity expressions for chalcedony and opal are similarexcept for the values for log K .CHALCEDONY : log aH4SiO4 3:55OPAL : log aH4SiO4 2:71The ChemEQL equilibrium database for minerals (Solid Phase Library) con-tains the following entry for ferric oxyhydroxide minerals goethite and ferrihy-drite (amorphous ferric hydroxide).Fe3 aq $ Fe OH 3 s 3 H aq K 103:201activity as a line on a logarithmic activity diagram. Using the preceding equi-librium expressions and constants, give the equations for the three solubilitylines plotted in Figure 5.6.SolutionFollow the gibbsite solubility example discussed prior to Example 5.16. Writeeach equilibrium expression as an activity quotient, and then take the loga-rithm of both sides of the expression. The logarithmic activity expression forquartz follows.the sequence just listed, water content increases. Figure 5.6 plots H4SiO4 aq QUARTZH4SiO4 aq $ SiO2 s CHALCADONYK 103:55H4SiO4 aq $ SiO2 s OPALK 102:71These minerals are nominally silicon dioxide, but as crystallinity decreases, inThe ChemEQL equilibrium database for minerals (Solid Phase Library) con-tains the following entry for silicon dioxide minerals quartz, chalcedony,and opal (amorphous silica).H4SiO4 aq $ SiO2 s K 103:98blemsactivity as a line on a logarithmic activity diagram. Using the preceding4.Soil and Environmental Chemistry206The standard free energies of formationDGf for each component in the struvitesolubility reaction appear in the following table (Smith and Martell, 2001).Mg NH4 PO4 6H2O s STRUVITE$Mg2 aq NH4 aq PO34 aq 6 H2O l Component DGf kJ mol1 Mg2 aq 456.405.acid solution at pH 4.)l 1 mM tartaric acid at pH 4.l 1 mM tartaric acid at pH 5.Please save your output file and perform a charge balance calculation todetermine whether this restriction is satisfied.Using your results from Problem 3, specifically the charge balance calcula-tion, add a suitable total concentration of a strong-acid anion (chloride,nitrate, etc.) and repeat the calculation.Please save your output file and perform a charge balance calculation todetermine whether this restriction is satisfied after adding sufficient strong-acid anion to satisfy the solution charge balance.the example appearing on pages 89 of the ChemEQL Manual: 1 mM aceticlog K value.FERRIHYDRITE : log aFe3 3 pH 3:20The Fe3 aq activity at pH 7.25 for solutions in equilibrium with thesetwo minerals are 22.75 and 18.55, respectively.3. Install ChemEQL on a computer you have access to, and simulate the follow-ing two solutions. Remember: the weak acid is entered as total, while theproton concentration is entered as free (meaning fixed). (NOTE: ReviewFollow thegibbsite solubility example discussedprior to Example 5.16.Write eachequilibrium expression as an activity quotient, and then take the logarithm of bothsides of the expression. The logarithmic activity expression for goethite follows.a3HaFe3 K 101:00loga3HaFe30@1A log K log 101:00 3 log aH log aFe3 1:00GOETHITE : log aFe3 3 pH 1:00The logarithmic activity expression for ferrihydrite is similar except for theequilibrium expressions and constants, give the equations for the two solubil-ity lines plotted in Figure 5.7.SolutionNH4 aq 79.51Chapter 5 Water Chemistry 207PO4 6.3E-3pH 7.537. The ChemEQL equilibrium database for minerals (Solid Phase Library) con-tains the following entry for ferric oxyhydro6.09E-2sin (data provided by Prof. Phillip Barak, Soil Science Department, Universityof Wisconsin-Madison).Component Concentration [mol L-1]Ca 5.0E-4Mg 3.0E-4NH4saturation indexes for a water sample from a second-stage thermophilicdigester at the Madison Metropolitan Sewerage District in Madison, Wiscon-the pipes carrying digested sewage from the second-stage digester, and thecomponents of the dewatering unit that receive the digested sludge from thesecond digester. Use ChemEQL to estimate the struvite and hydroxyapatitedeposits accumulate on the inner wall of the second-stage digester,H2O l 237.34Mg NH4 PO4 6H2O s STRUVITE3061.6Calculate the standard Gibbs energy and the thermodynamic equilibriumconstant for the solubility reaction at 298.15 K (25C). The appropriate idealgas constant R has units kJ mol1 K1 .SolutionApply Eqs. (5.2) and (5B.5) to calculate DGrxn and K, respectively.DGrxn 456:40 79:51 1026:6 6 237:34 products 3061:6 reactants 75:05 kJ mol1 K exp DGrxnR T0@1A exp 75:05 kJ mol1 8:3145 103 kJ mol1 K1 298:15 K 0B@1CAK 7:110 10146. Sewage treatment facilities rely on anaerobic digesters to eliminate patho-gens and reduce waste volume. A typical two-stage anaerobic digester hasan initial acid stage where anaerobic bacteria ferment organic solids intoorganic acids, followed by a second stage where methane-producing bac-teria consume the organic acids from the first stage. Metabolic heatingraises the temperature in the acid-stage to about 40C, while the secondstage is typically heated to about 50C to promote the activity of thermo-philic bacteria essential for rapid second-stage digestion. Not surprisingly,the pH of the sewage increases sharply as acid-stage sewage is pumpedinto the second-stage digesters.Coincidental with the second-stage digestion is the prodigious precipi-tation of the mineral struvite Mg NH4 PO4 6H2O s . Thick struvitePO34 aq 1026.6xide mineral goethite.Fe3 aq $ FeOOH s GOETHITE3 H aq K 101:00Calculate the conditional equilibrium coefficient Kc for this reaction usingEq. (5.6) and one of the empirical activity coefficient expressions (5.105.12) when the ionic strength I 0.001 M.SolutionApply Eq. (5.6) to the equilibrium solubility expression for goethite to yield anSoil and Environmental Chemistry208I 0.001.g3HCalculate the activity coefficients gFe3 and gH , using the Davies expression(5.12).log gH 0:5085 1 2 0:001p1 0:001p 0:2 0:001 0@1AgH 100:015 0:965log gFe3 0:5085 3 2 0:001p1 0:001p 0:2 0:001 0@1AgH 100:139 0:725The conditional equilibrium coefficient Kc 100:91 at an ionic strengthKc gFe3@ A KK a3HaFe3 101:00a3HaFe3 g3H C3HgFe3 CFe3 g3HgFe30@1A C3HCFe30@1AK g3HgFe30@1A Kc0 1activity coefficients for Fe aq and H aq .expression for the conditional equilibrium constant Kc as a function of the3 6.4 DissolvedOrganic Carbon 2236.5 Humic Substances 229Content and TitratableWeak Acids 252Appendix 6D. Hydrophobicand Hydrophilic Colloids 2526.1Th b den rypa aldecomposition. The path leading from biomass to the stable natural organicmatter fraction takes hundreds to thousands of years, a path subject to consid--r-fmicrobial decomposition.6.2. SOIL CARBON CYCLEThe global carbon cycle (Figure 6.1) encompasses both marine andterrestrial environments, but here we focus on a key coSoil and Environmental Chemistry.# 2012 Elsevier Inc. All rights reserved.erable speculation but little verification. Our focus will be the chemical properties of natural organic matter that are, in turn, intimately linked to theicolloidal properties. The chemically active components lie at the extremeends of the carbon transformation trajectory: identifiable biomolecules in dissolved organic carbon and colloidal humic substancesthe end product ods with a discussion of naturally occurring organic colloids. This trajectorallels the path taken by carbon fixed as biomass as it undergoes microbi6.6 Humic Colloids 2456.7 Summary 246Appendix 6A. Hydroxamateand CatecholamideSiderophore Moieties 247. INTRODUCTIONis chapter follows a trajectory that egins with the soil carbon cycle anChapter 6Natural Organic Matterand Humic ColloidsChapter Outline6.1 Introduction 2096.2 Soil Carbon Cycle 2096.3 Soil Carbon 217Appendix 6B. SurfaceMicrolayers 250Appendix 6C. Humic Oxygenmponent of the terrestrial209Soil and Environmental Chemistry210carbon cycle:1 the soil (or belowground) carbon cycle. The cycle begins withbiological carbon fixation: the conversion of carbon dioxide to biomass carbonby photolithotrophic (i.e., photosynthetic eukaryotes and prokaryots) and, to amuch lesser degree, chemolithotrophic microorganisms. The cycle ends withthe mineralization of organic carbon into carbon dioxide through a processcalled oxidative metabolism. Oxidative metabolism releases the chemicalenergy stored during carbon fixation.6.2.1. Carbon FixationPhotosynthetic carbon fixation converts light energy into chemical energy.Photosynthesis reduces C(4) in carbon dioxide to C(1) in the terminalcarbon in glyceraldehyde-3-phosphate, the feedstock for simple sugars, aminoacids, and lipids. The process involves four steps in the Calvin cycle, which isshown in Figures 6.2 to 6.5.In the first step (Figure 6.2), a single CO2 molecule attaches to carbon-2of ribulose 1,5-bisphosphate. The product2-carboxy-3-keto-arabinitol-1,5-bisphosphateis an extremely unstable compound. The second step (Figure 6.3)FIGURE 6.1 Simplified representation of the global carbon cycle (Genomics:GTL, 2005).1. The freshwater and marine carbon cycles involve similar carbon transformations and yieldorganic matter products with chemical properties similar to soil organic matter.FIGURE 6.2 Ribulose 1,5-bisphosphate and carbon dioxide combine to form 2-carboxy-3-keto-arabinitol-1,5-bisphosphate.FIGURE 6.3 The unstable molecule 2-carboxy-3-keto-arabinitol-1,5-bisphosphate undergoeshydrolysis to yield two molecules of 3-phosphoglycerate.FIGURE 6.4 ATP phosphorylateseach 3-phosphoglycerate molecule,forming 1,3-bisphosphoglycerate.Chapter 6 Natural Organic Matter and Humic Colloids 211Soil and Environmental Chemistry212is the hydrolysis of the bond between carbons 2 and 3 in 2-carboxy-3-keto-arabinitol-1,5-bisphosphate, the product of the reaction in Figure 6.2, toyield two molecules of 3-phosphoglycerate.The third step (Figure 6.4) is the phosphorylation of 3-phosphoglycerateby adenosine-5-triphosphate ATP to yield 1,3-bisphosphoglycerate andadenosine-5-diphosphate ADP. The fourth step (Figure 6.5) is the reductionof 1,3-bisphosphoglycerate to glyceraldehyde 3-phosphate by nicotinamideadenine dinucleotide phosophate NADPH.The nicotinamide adenine dinucleotide phosophate NADPH that reduces1,3bisphosphoglycerate in step 4 (Figure 6.5) is generated by the absorptionof light. The reduction (Figure 6.5) is a two-electron transfer to carbon 1 thatreduces it from a formal oxidation state of (3) to a formal oxidation state of(1). Glyceraldehyde 3-phosphate, also known as triose phosphate, is a simple3-carbon sugar that serves as the fundamental feedstock for biosynthesis of allbioorganic compounds. The net chemical reaction (Eq. (6.1)) fixes 6 moleculesof CO2 to 6 molecules of ribulose 1,5-bisphosphate; the absorption of light(Eq. (6.2)) generates the ATP and NADPH required by reaction (Eq. (6.1)).6 CO2 6 ribulose 1, 5 bisphosphate 12 ATP 12 NADPH! 12 glyceraldehyde 3-phosphate 6:1FIGURE 6.5 NADPH reduces 1,3-bisphosphoglycerate to glyceraldehyde 3-phosphate.12 H2O 12 NADP 18 ADP3 18 H2PO4! 6 O2 12 NADPH 12 H 18 ATP4 6:26.2.2. Carbon MineralizationThe mineralization of reduced carbon in biomass and biological residue toCO2 releases chemical energy for the growth and maintenance of soil organ-isms. The plants that fix virtually all carbon end up mineralizing a consider-able fraction for their growth and maintenance. A fraction of standing plantbiomass is consumed directly by herbivores, while the remainder becomesbiological residue supporting a diverse community of decomposing chemoor-ganotrophic organisms ranging from arthropods to bacteria and fungi.electrons from the carbon atom, form four bonding molecular orbitals csg inChapter 6 Natural Organic Matter and Humic Colloids 213the methane CH4 molecule (one electron spin in each pair is spin-up, and theother is spin-down). The hydrogen atomic orbitals in methane are groupedinto four linear combinations that are determined by the tetrahedral symmetryof methane: combination (6.4) has the symmetry of the central carbon 2sorbital, while combinations (6.5), (6.6), and (6.7) have the symmetry of thecentral carbon 2p orbitals: 2px, 2py, and 2pz. All of the combinations appearin Figure 6.7.s1a1 12 fA fB fC fD 6:4s1t2 x 12 fA fB fC fD 6:5s1t2 y 12 fA fB fC fD 6:616.2.3. Oxidation of Organic Compounds by DioxygenYou were introduced to molecular orbital theory in general chemistry. Thistheory represents the chemical bonds in any molecule as molecular orbitalsci, each consisting of a sum of the atomic orbitals fj from the constituentatoms (Eq. (6.3)). The coefficients cij weight the relative contribution of eachatomic orbital fj with the sign denoting the phase along the bonding axis. Iftwo atomic orbitals are in phase along the bond axis, then orbital overlapincreases electron density in the bond; if they are out of phase, the overlapdecreases electron density. The magnitude of the electron density along thebond axis determines the strength of each chemical bond.ci Xjcij fj 6:3Figure 6.6 is the molecular orbital diagram for methane CH4. The singleelectron (depicted as arrows) in each hydrogen atom pair, along with the fourIn Chapter 8 we examine mineralization in greater detail. Catabolismdeconstructs large organic molecules into smaller molecules. The chemicalenergy released during catabolism is accumulated in the same compoundfound in Eq. (6.1)nicotinamide adenine dinucleotide phosphate NADPHnow serving as the electron donor for the electron transport chain. Aerobicrespiration is the reverse of the net reaction shown in Eq. (6.2).An often overlooked characteristic of the carbon cycle is the chemical sta-bility of biomass and biological residue in the presence of dioxygen O2. Thecarbon in biomass and biological residue is thermodynamically unstable whenin the presence of dioxygen in the aboveground and soil atmosphere. The per-sistence of biomass and biological residue has more to do with the properties ofthe dioxygen molecule than the chemical bonding in bioorganic compounds.s1t2 z 2 fA fB fC fD 6:7Soil and Environmental Chemistry214The electronic structure of methane is representative of most bioorganiccompounds; all of the electrons in the highest occupied molecular orbital(HOMO) are paired. The pairing of all electrons in the HOMO makes themclosed-shell compounds.Atomic oxygen has 6 electrons in its valence atomic shell; when two oxy-gen atoms combine to form a molecule of dioxygen O2, a total of 12 electronsFIGURE 6.6 The molecular orbital diagram for methane CH4 illustrates how valence hydrogenand carbon atomic orbitals combine to form an equal number of molecular orbitals.FIGURE 6.7 The four linear combinations of hydrogen 1s atomic orbitals represented byexpressions (6.4) through (6.7) that match the tetrahedral symmetry of the carbon 2s and 2patomic orbitals in CH4. Shading denotes phasethat is, the sign of the coefficient cij.Chapter 6 Natural Organic Matter and Humic Colloids 215are available to fill the molecular orbitals. The molecular orbital diagramFIGURE 6.8 The molecular orbital diagram for ground state (triplet) dioxygen 3O2 uses arrowsto denote the electron spin state. The 6 electrons in each oxygen atom, a total of 12 electrons, donot completely fill the seven occupied molecular orbitals in dioxygen O2.for dioxygen O2 appears in Figure 6.8. The two HOMOs have the sameenergy and are half filled with one electron in each; this is the lowest energyor ground state electron configuration. The two unpaired electrons in triplet2dioxygen 3O2 make it an open-shell compound. Its electron configurationis fundamentally different from that of methane and other closed-shellcompounds.Molecular orbital theory forbids closed-shell compounds from reactingwith open-shell compounds. The reaction is allowed if the closed-shell com-pound (e.g., methane) enters an excited state with an open-shell electron con-figuration. A molecule enters an excited state by absorbing sufficient energyto promote a single electron from the HOMO to the LUMO, changing its elec-tron configuration. Groundstate triplet dioxygen can enter an excited singletstate by absorbing sufficient energy to promote one of its unpaired electronsto pair with the other electron (Figure 6.9), changing it to a closed-shell elec-tron configuration.The energy required to excite either the closed-shell organic compound(to an excited-state open-shell configuration) or open-shell dioxygen (to an2. A triplet electron configuration has three possible orientations of the unpaired electrons in amagnetic field H: both unpaired electron spins aligned in the same direction as the field H, onespin aligned with and one aligned against the field H and both unpaired spins aligned in the oppo-site direction of the magnetic field H.excited-state closed-shell configuration) is the activation energy needed toovercome the energy barrier that prevents organic compounds from beingoxidized by dioxygen (Figure 6.10).FIGURE 6.9 The molecular orbital diagrams showing excitation of ground state triplet 3O2 tothe lowest energy singlet 1O2* excited state. The unpaired electrons in triplet 3O2 become paired(i.e., a closed-shell configuration) in the excited state singlet 1O2*.Soil and Environmental Chemistry216The rationale behind Figures 6.8 to 6.10 may seem difficult to grasp, butconsider what it takes to start a fire where dioxygen is the oxidizer and woodtinder is the propellant. A magnifying glass can focus sufficient sunlightto heat wood tinder to its auto-ignition temperature. The auto-ignition temper-ature (or kindling point) is the temperature required to heat the propellant toFIGURE 6.10 The ground state energy barrier Ea(1CH4 3O2) prevents oxidation of closed-shell (singlet) 1CH4 by open-shell (triplet)3O2. The excited state energy barrier Ea(1CH4 1O2*)is lower, allowing a reaction between closed-shell (singlet) 1O2* and closed-shell (singlet) 1CH4.biomass accumulates at the surface and may, especially in forest ecosystems,mass. Biological residue, the third component, is the second stage of theChapter 6 Natural Organic Matter and Humic Colloids 217soil carbon trajectory.Ecologists have developed models to describe the turnover of biologicalresidueits mineralization to carbon dioxide, assimilation into decomposerbiomass, and sequestration as belowground soil organic carbon. Hans Jenny(1941) proposed one of the simplest models (Eq. (6.8)) of organic carbon Csoilturnover in soils. Jenny originally applied his turnover model to soil organicnitrogen Nsoil dynamics (Figure 6.11).The Jenny soil organic carbon (or nitrogen) turnover model is a rate lawform an organic soil horizon (>18% organic carbon by weight). Belowgroundnet primary production comes from the root system that supports a diversedecomposer community that, along with root biomass, represents total below-ground biomass.One technical criterion of soil includes all mineral grains, organic residueand biomass that pass through a 2 mm sieve. This definition excludes manyarthropods, earthworms, and larger plant rootsto name a fewbut doesinclude much of the decomposer community. Soil biomass, regardless ofwhether it is from the plant community or the soil decomposer supported bynet primary production, is the starting point of the carbon trajectory that ulti-mately leads to the humic colloids mentioned in the introduction.6.3.1. Carbon Turnover ModelsNet primary productionthe total carbon fixed by photosynthesis during thegrowing seasonends up in one of three forms: carbon dioxide, biomass, andbiological residue. Respiration of and biosynthesis derived from photosyn-thetic carbon represent investments in building and maintaining plant bio-the open-shell excited state, removing the energy barrier blocking combustionby ground state (triplet 3O2) dioxygen.Bacteria, fungi, and other decomposers use enzyme catalysis to bypass theenergy barrier blocking oxidation. Most of the chemical energy stored in bio-sphere organic compounds is released by enzyme-catalyzed biological oxida-tion reactions. Organic compounds represent kinetically stable chemicalenergy that organisms release at a rate matched to their metabolic needs.6.3. SOIL CARBONBelowground carbon decreases with increasing depth within the soil profile;relatively little carbon is found below the plant root zone in the intermediatevadose and saturated zones. This distribution reflects the source: photosyn-thetic carbon fixation by the plant community. Litter fall from standing plant(or rate equation) that combines a zero-order termthe annual addition of100.0%Soil and Environmental Chemistry21850.0%0.0 10.0 20.0 30.0 40.0Years of Cultivation50.0 60.0 70.0FIGURE 6.11 The accelerated mineralization of soil organic nitrogen during 60 years of agri-cultural cultivation resulted in a net 35% loss of soil nitrogen in midwestern U.S. soils. Source:Reproduced with permission from Jenny, H., 1941. Factors of Soil Formation: A System of Quan-titative Pedology. New York, McGraw Hill.85.0%80.0%75.0%70.0%65.0%60.0%55.0%Relative Soil Nitrogen Co95.0%90.0%ntentplant residue A from net primary productionand a first-order term thatdescribes the mineralization of soil organic carbon kM Csoil3:DCsoilDt A kM Csoil 6:8The units for each of the terms in Eq. (6.8) are A kgOC m2 y1 ,Csoil kgOC m2 and kM y1 .Henin and Dupuis (Henin, 1945) proposed a slightly different model(Eq. (6.9)) that adds the isohumic coefficient kic, a first-order rate constantfor the conversion of net primary production CNPP into soil organic carbonCsoil. The Jenny model (Eq. (6.8)) assumes that all of the residue input A willtransform into soil organic carbon Csoil:DCsoilDt kic CNPP kM Csoil 6:9Turnover rate laws (Eqs. (6.8) and (6.9)) appear in differential form. The inte-gral forms (Eqs. (6.10) and (6.11)) are better suited to fitting measuredchanges in soil organic carbon content Csoil t as a function of time. The soilorganic carbon content at the beginning of the turnover experiment is Csoil 0 :3. The constant kM is the first-order rate constant for mineralization.Jenny 1941 : Csoil t AkM kM Csoil 0 AkM ekM t 6:10Henin & Dupuis 1945 :Csoil t kic CNPPkM kM Csoil 0 kic CNPPkM ekM t 6:11The soil organic carbon content will converge on a steady-state contentCsoil 1 after a time interval that is long relative to the mineralization rateconstant kM:Steady-State :DCsoilDt 0Chapter 6 Natural Organic Matter and Humic Colloids 219Mineralization RateConstant kM y1 Half-Life t1=2 years Location Reference0.0608 11 Ohio (USA) (Jenny, 1941)0.052 13 Ohio (USA) (Salter, 1933)0.072 10 Ohio (USA) (Haynes, 1955)0.07 10 Kansas (USA) (Myers, 1943)1933; Jenny, 1941; Myers, 1943; Haynes, 1955).The soil organic carbon mineralization rate constant kM and half-life t1/2 forsoil organic carbon for these midwestern U.S. agricultural soils (see Table 6.1)TABLE 6.1 Rate Constant and Half-Life for Soil Organic Carbon inAgricultural Soilchanges in soil organic carbon as it converges on its steady-state content:Csoil t Csoil 1 Csoil 0 Csoil 1 ekM tlnCsoil 0 Csoil 1 Csoil t Csoil 1 kM tlog10Csoil 0 Csoil 1 Csoil t Csoil 1 kMln 10 t kM2:303 t 6:13Table 6.1 lists data from four soil organic carbon turnover studies (Salter,Csoil 1 AkM kic CNPPkM6:12Substituting Eq. (6.12) into Eq. (6.10) results in a linearized expression forare very similar. Both turnover models (Eqs. (6.10) and (6.11)) recognize twocarbon pools: plant residue and soil organic carbon.Woodruff (1949) proposed a model that subdivided soil organic carboninto several fractions j, each with a characteristic mineralization rate constantkMj. This representation of soil organic carbon is embodied in the mathemati-cally complex Rothamsted carbon turnover model (Jenkinson, 1977, 1990).Plant material is subdivided into two formsdecomposable plant materialDPM and resistant plant material RPMand each type of plant residue hasa characteristic rate constant for its conversion into soil organic carbon:Jenkinson and Rayner 1977 : Csoil t CDPM ekDPM t CRPM ekRPM t6:14Data from a relatively short-term experiment measuring the mineralization ofa one-time addition of 14C labeled ryegrass appear in Figure 6.12, clearlyshowing the precipitous loss of decomposable plant material DPM duringthe first year followed by a more gradual loss of resistant plant materialRPM over the remainder of the study.The Rothamsted model divides soil organic carbon into two sub-pools:microbial biomass BIO and humus HUM. All biologically fixed carbon(net primary production NPP) flows through three pathways (Figure 6.13):Soil and Environmental Chemistry2200.600.500.400.300.200.100.000.0 2.0 4.0 6.0YearsRelative Soil C-14 Co8.0 10.0FIGURE 6.12 Decomposition of 14C-labeled ryegrass under field conditions (Jenkinson, 1990)1.000.900.800.70ntentis fitted to Eq. (6.14).FIGURE 6.13 The carbon transformation pathways and carbon pools of the Rothamsted soilorganic carbon turnover model: net primary production NPP, decomposable DPM, and resistantRPM, mineralization CO2, assimilation BIO, and transformation into soil humusHUM. Each pathwayhas its characteristic transformation rate constant. Source: Reproducedwith permission fromJenkinson,D.S., Andrew, S.P.S., et al., 1990. The turnover of organic carbon and nitrogen in soil. PhilosophicalTransactions of the Royal Society of London Series B Biological Sciences 329 (1255), 361368.Chapter 6 Natural Organic Matter and Humic Colloids 221mineralization into CO2, assimilation into chemoorganotrophic biomass BIO,or transformation into soil humus HUM. Plant material initially partitions(Eq. (6.14)) between rapidly decomposing and slowly decomposing fractions;thereafter the carbon either is mineralized or partitions between the biomassof the soil decomposer community and soil humus.6.3.2. Soil Carbon PoolsScientists recognizing multiple soil carbon pools have developed methodsdesigned to quantify the carbon in each pool. The scheme illustrated inFigure 6.14, which Zimmermann and colleagues (2007) used, is representa-tive. Dissolved organic carbon DOC is defined operationally: any dissolvedcarbon passing a 0.45 mm filter membrane. Zimmermann and colleagues sep-arate the particulate material into a coarse and fine fraction using a 63 mmFIGURE 6.14 A representative fractionation procedure separates soil organic carbon into threepools: labile, stabilized, and resistant. Source: Reproduced with permission from Zimmermann,M., Leifeld, J., et al., 2007. Quantifying soil organic carbon fractions by infrared-spectroscopy.Soil Biol. Biochem. 39, 224231.sieve. The coarse (>63 mm) fraction consists of particulate organic matterPOM, and organic carbon associated with stable soil aggregates (A) and sand(S) particles. The coarse fraction is separated into low (1.8 Mg m3) density fractions. You may recall (from Chapter 2) thatthe mineral fraction is defined using the density of quartz (2.65 Mg m3).The low-density fraction is designated particulate organic matter POM, whilethe high-density fraction is stabilized through its association with mineralparticles.The fine particulate (6.4. DISSOLVED ORGANIC CARBONThe labile carbon pool consists of two fractions according to the fractionationscheme in Figure 6.14: dissolved organic carbon (DOC) and particulateorganic carbon (POM). These soil carbon fractions represent organic materialisolated without the use of chemical treatment.7 This section identifies someof the bioorganic compounds dissolved in soil pore water. The bioorganiccompounds dissolved in soil pore water are extremely labile, characterizedby soil half-lives on the order of hours to days. Their short half-life doesnot diminish their importance because they are extremely reactive and contin-ually replenished by soil organisms.6.4.1. Organic AcidsSoil pore water, particularly in the rhizosphere,8 contains a large variety of lowmolecular weight organic acids. Certain plant species actively secrete weakacids from their roots to increase nutrient availability (e.g., citric acid (Gardner,1982), malic acid, fumaric acid, and oxalic acid). Other weak acids (e.g., thelignin precursors, Figure 6.15) leak from plant roots during cell wall biosynthe-sis. Bacteria and fungi release a variety of organic acids as fermentationby-products: succinic acid, butanoic acid, propionic acid, and lactic acid.Chapter 6 Natural Organic Matter and Humic Colloids 223FIGURE 6.15 Lignin precursor molecules: ferulic acid, courmaric acid, gallic acid, and syringicacid.7. Some authors use the term water extractable organic carbon (WEOM) interchangeably withDOM (Chantigny, 2003). Dissolved organic matter (DOM) encompasses all major elements (car-bon, oxygen, nitrogen, etc.), while dissolved organic carbon (DOC) or dissolved organic nitrogen(DON) is based solely on carbon (or nitrogen) analysis.8. The rhizosphere is the narrow region of soil directly around roots. It is teeming with bacteriathat feed on sloughed-off plant cells and the proteins and sugars released by roots (Ingham,1999).Soil and Environmental Chemistry224Organic acids dissolved in soil pore water are on the order of 10100mmolc L1 (Quideau, 1997). Proton dissociation constants and formationconstants for metal-weak acid complexes for many of the common organicacids are included in the popular computer-based water chemistry models(see Chapter 5, Water Chemistry) or can be found in comprehensive chemis-try databases (e.g., Critically Selected Stability Constants of Metal Com-plexes; U.S. National Institute of Standards & Technology).6.4.2. Amino AcidsFree amino acids in soil pore water are on the order of 105 mol L1 (Jones,2002; Jones, 2004; Hannam, 2003) and represent about 1 to 10% of the dis-solved organic nitrogen (DON). The remaining DON is unidentifiable and pre-sumably derived from soluble humic compounds (see following). The solutionchemistry of free amino acids is best understood in the context of computer-based water chemistry models (see Chapter 5, Water Chemistry).6.4.3. Extracellular EnzymesSome enzymes remain active after the death of plant and microbial cells,associated with ruptured (lysed) cell debris or adsorbed to soil particles. Soilbiochemists refer to these as extracellular enzymes. Many endocellularenzymes require cofactors, but active extracellular enzymes cannot be cofac-tor dependent (Pietramellara, 2002). Enzymes, regardless of whether they areendo- or extracellular, tend to lose activity outside a relatively narrow pHrange because tertiary enzyme structure is pH sensitive. Apparently theadsorption of extracellular enzymes to soil particles stabilizes tertiary struc-ture, at least active-site tertiary structure, extending both the active pH rangeand the lifetime in soil.A recent review assayed extracellular enzyme activity in soil samples collectedat 40 U.S. sites (Sinsabaugh, 2008). The assays evaluated the activity of sevenenzyme classes (Table 6.2). The activity of glucosidase and cellobiohydrolaseshows no apparent change between pH 4.0 and 8.5. The activity of N-acetylgluco-saminidase and phosphatase decreases in the same pH range, while the activity ofthe remaining extracellular soil enzymes increases throughout the range.Soil biochemists believe that extracellular enzymes explain soil organic mat-ter turnover rates exceeding predictions based strictly on soil microbial biomassand respiration. There is no question that extracellular phosphatase enzymes areessential for phosphate release in soils (see Chemical Composition following).6.4.4. SiderophoresPlants, fungi, and bacteria face identical challenges to meet their iron nutri-tional requirements. Kosman (2003) provides an excellent summary of thesechemical challenges in the typical pH range of aerated soils: (1) Fe2Chapter 6 Natural Organic Matter and Humic Colloids 225TABLE 6.2 Soil Extracellular EnzymesExtracellular Enzyme Reaction Classificationb-1, 4-glucosidase Hydrolysis of terminal b-1, 4-glucosylresidues, releasing b-D-glucose.EC 3.2.1.21cellobiohydrolase Hydrolysis of 1,4-b-D-glucosidiclinkages in cellulose, releasingcellobiose.EC 3.2.1.91b-N-acetylglucosaminidase Random hydrolysis of N-acetyl-b-D-glucosaminide (1!4)-b-linkages inchitin.EC 3.2.1.14aminopeptidase Hydrolysis of N-terminal amidelinkages, releasing amino acid.EC 3.4.11.1acid (or alkaline)phosphataseHydrolysis of phosphate monoester,releasing phosphate.EC 3.1.3.1phenol oxidase Hydroxylation of diphenols tosemiquinones, releasing water.EC 1.10.3.2peroxidase Oxidation (wide specificity) using EC 1.11.1.7spontaneously oxidizes to Fe3; (2) Fe3 undergoes hydrolysis to form insolu-ble ferric oxyhydroxide minerals (Fe2 has little tendency to hydrolyze, therebyexplaining its higher inherent solubility); and (3) Fe3 forms extremely stablecomplexes that are kinetically inert (Fe2 forms weak complexes that are verylabile to ligand exchange). Kosman places particular emphasis on the finalchemical property; even if Fe3 were not susceptible to hydrolysis (i.e., insolu-ble), the kinetic stability of its complexes would render them biologically inert.Plants, bacteria, and fungi rely on elaborate biological systems to solubilize,transport, and absorb ferric iron from soil pore water; central to this system isa family of compounds known as siderophores.The list of siderophores in Table 6.3 is not comprehensive but is representa-tive of the siderophores secreted by soil fungi and bacteria. Microbiologistsreport numerous siderophores in addition to those listed in Table 6.3; manyremain uncharacterized, their structures unknown, and their detailed iron chem-istry uncertain. Structures 1 and 2 illustrate the two major classes, respectively:hydroxamate and catecholamide (see Appendix 6A). Rhizoferrin (Structure 3)is representative of the siderophore class known as carboxylates. Species ofthe Poaceae (or Gramineae) family are the only plants known to secrete phyto-siderophores: mugineic acid (Structure 4) and related compounds (nicotiana-mine, avenic acid, 2-dehyxroxymugenic acid, 3-hydroxymugenic acid, etc.).H2O2.Source: Sinsabaugh, 2008.Soil and Environmental Chemistry226TABLE 6.3 Representative Fungal and Bacterial SiderophoresSiderophore Class OrganismCoprogen Hydroxamate FungiFerrichrome Hydroxamate FungiFerrioxamine Hydroxamate BacteriaFerrichrysin Hydroxamate FungiFerrirubin Hydroxamate FungiFerrirhodin Hydroxamate FungiRhodotorulic acid Hydroxamate FungiStructure 1Structure 2Fusigen Hydroxamate FungiPutrebactin Hydroxamate BacteriaRhizoferrin Carboxylate FungiAminochelin Catecholamide BacteriaProtochelin Catecholamide BacteriaAzotochelin Catecholamide BacteriaPyoverdine Hydroxamate-catecholamide BacteriaEnterobactin Hydroxamate-catecholamide BacteriaSalmochelin Hydroxamate-catecholamide BacteriaAzotobactin Hydroxamate-catecholamide BacteriaAerobactin Carboxylate-hydroxamate Bacteria7direct ferrous uptake pathway. The direct ferrous uptake pathways (plants, fungi,bacteria)which are not operative under aerobic conditions when iron solubilityis at its lowestemploy low-affinity transmembrane ion channels (or porins).Poaceae use phytosiderophores to transport Fe3 ions to root surfaces, whereferric reductase enzymes reduce Fe3 to Fe2 (Chaney, Brown, et al., 1972;Romheld, 1981). The labile ferrous complex releases Fe2 to ion channelsthat transport it into the cytoplasm. The fungal reductive iron uptake pathwayis functionally equivalent to the plant reductive iron uptake pathway.The nonreductive siderophore uptake pathways in both bacteria and fungi relyon outer membrane receptors that bind the ferri-siderophore complex (Ferguson,2002; Kosman, 2003; Philpott, 2006). Once the ferri-siderophore reachesthe cytoplasm, it is reduced, and the labile ferrous complex releases Fe2 to acytoplasmic chaperone. As noted by Kosman (2003), Fe2 is cytotoxic, makingStructure 3Structure 4Fungi (Kosman, 2003; Philpott, 2006) rely on three uptake pathways tobalance their iron nutritional requirements against iron cytotoxicity: a nonreduc-tive siderophore uptake pathway, a reductive iron uptake pathway, and a directferrous uptake pathway. Plants, regardless of whether they secrete siderophores,employ two of these pathways: a reductive iron uptake pathway and a directferrous uptake pathway. Bacteria, regardless of whether they secrete sidero-phores, employ two of these pathways: a nonreductive siderophore uptake and aChapter 6 Natural Organic Matter and Humic Colloids 22iron uptake and homeostasis a tightly regulated process in all living organisms.The dissolved iron concentration in the pore water of neutral aerated soilsconsistently falls in the 110 mm range (Fuller, 1988; Grieve, 1990; Ammari,2006), well above the saturation concentration of even the most solublesecondary ferric oxide minerals but within the range required to meet thenutritional requirements of plants, fungi, and bacteria. Weak organic acidsdo not form complexes sufficiently stable to account for the observed ironsolubility, providing solid evidence that siderophore soil pore water con-centrations typically fall in the 110 mm range.6.4.5. BiosurfactantsMicrobial biosurfactants in soil pore water and surface water are secreted aseither extracellular agents (Table 6.4) with specific functions (Desai, 1997;Lang, 2002; Wosten, 1999; Wosten, 2001) or cell envelope constituentsreleased by the autolysis of dying cells. Cell envelope biosurfactants arebelieved to influence cell attachment to environmental surfaces by alteringthe surface properties of individual cells.The molecular properties of microbial biosurfactants arise from theiramphiphilic9 nature (Figure 6.16): limited water solubility (a result of theirTABLE 6.4 Extracellular Bacterial BiosurfactantsBiosurfactant ExamplesGlycolipids Rhamnolipids, mycolic acidsLipoproteins Surfactin, visconsin, putisolvinProteins HydrophobinsSoil and Environmental Chemistry228FIGURE 6.16 Surfactant molecules self-organize, forming films at the air-water interface andcolloidal molecular aggregates (micelles) dispersed in water. Illustration adapted from Wikipedia.9. Amphiphilic molecules have a primary structure that contains at least one significant segmentthat is strongly hydrophilic or polar and at least one significant segment that is strongly hydropho-bic or nonpolar.hydrophobic molecular segment) and a tendency to form micelles above acharacteristic critical micelle concentration (CMC).An intriguing consequence of extracellular biosurfactants is the enhancedChapter 6 Natural Organic Matter and Humic Colloids 229solubility and bioavailability of hydrophobic or sparingly soluble organic con-taminants in soil pore water (Cameotra, 2003; Mulligan, 2005). This behavioris intimately dependent on self-organization (see Figure 6.16) andat least inthe surface microlayer (see Appendix 6B)does not require biosurfactantconcentrations exceeding a CMC.6.5. HUMIC SUBSTANCESThe elemental and chemical composition of soil organic matter and itschemical properties are virtually impossible to determine in situ becausehumic substances10 are intimately associated with soil mineral colloids(Mikutta, 2006). This section describes a typical method for extracting soilorganic matter with minimal chemical alteration and a fractionation schemebased on pH-dependent solubility and concludes with a summary of the ele-mental and chemical composition of soil organic matter extracts and theirmost salient chemical properties.6.5.1. Extraction and FractionationThe International Humic Substance Society (IHSS) maintains a collection ofsoil, aquatic, and peat humic substances extracted by a standard protocol.The protocol begins with an initial 1-hour extraction with 0.1 M HCl to dis-solve an acid-soluble fulvic acid fraction. The second step employs 4-hourextraction 0.1 M NaOH to dissolve base-soluble humic substances, taking careto exclude dioxygen to minimize oxidation at high pH. The humic extract typ-ically contains a considerable quantity of suspended minerals. The humicextract is acidified by adding 6 M HCl and allowed to stand for 1216hours.11 The supernatant is the second acid-soluble fulvic acid fractionwhich is combined with the first acid-soluble extractwhile the precipitateis the humic acid fraction.The humic acid fraction is dissolved a second time using 0.1 M KOH andsufficient KCl to make the final K aq concentration 0.2 M (this step isdesigned to coagulate much of the entrained mineral colloids). The humicacid fraction is precipitated a second time using a combination of 0.1 MHCl and 0.3 M HF for 12 hours (this step is designed to dissolve any remain-ing silicate clays associated with the humic acids). The final cleanup involves10. Soil and environmental chemists commonly designate natural organic matter suspended infresh or marine water, associated with mineral particles in soils and sediments or preserved in peatas humic substances.11. The standard method for protein hydrolysis refluxing 24 hours at 110C in 6 M HCl.adjusting to pH 7 and dialyzing to remove excess salts. The organic carbonthat cannot be dissolved by this treatment protocol is designated humin.Efforts to maximize the yield of organic carbon in the extract or to mini-mize chemical alteration by oxidation and hydrolysis have led to alternativeextraction methods, some using organic solvents rather than aqueous solution,but the IHSS protocol is the most widely adopted and represents an acceptablecompromise between yield and alteration. The fractionshumic acids, fulvicacids, and huminare operationally defined: humic acids are soluble in basicsolutions but precipitate at pH 1, fulvic acids are soluble at and above pH 1,and humin is the insoluble organic carbon residue (Rice, 1990).6.5.2. Elemental CompositionThe most comprehensive study of the elemental composition of humic sub-stances is the report by Rice and MacCarthy (1991). They report compositionprobability distributions for five elements (C, H, O, N, and S) for a populationof 215 soil humic acid samples, 127 soil fulvic acid samples, and 26 humin sam-ples (soil, peat, aquatic, and marine sources pooled). Rice and MacCarthy alsolist statistics for humic and fulvic acids from peat, aquatic, and marine sources.Most of the composition probability distributions appear to be symmetricSoil and Environmental Chemistry230or normal distributions, and the exceptions are indicated in Table 6.5. As aconsequence, the arithmetic mean and standard deviation are suitable distribu-tion statistics for most sample populations.TABLE 6.5 Mean and Standard Deviation of Soil Humic Acids (N 215),Soil Fulvic Acids (N 127), and Humin (N 26)Soil Humic Acids C,gC g1OMH,gH g1OMO,gO g1OMN,gN g1OMS,gS g1OMMean 0.554 0.048 0.360 0.036 0.008{Standard Deviation 0.038 0.010 0.037 0.013 0.006{Soil Fulvic Acids C, gC g1OM H, gH g1OM O, gO g1OM N, gN g1OM S, gS g1OMMean 0.453 0.050 0.462 0.026 0.013Standard Deviation 0.054 0.010 0.052 0.013 0.011Humin C, gC g1OM H, gH g1OM O, gO g1OM N, gN g1OM S, gS g1OMMean 0.561 0.055 0.347 0.037 0.004{Standard Deviation 0.026 0.010 0.034 0.013 0.003{Note: The statistics for sulfur ({) are geometric; all others are arithmetic. The sample populations forthe sulfur analyses are consistently smaller because the sulfur content is rather low: humic acids (N 67), soil fulvic acids (N 45), and humin (N 16).Source: Rice, 1991.Soil Fulvic Acids 0.318 0.419 0.244 0.016 0.003 0.364Chapter 6 Natural Organic Matter and Humic Colloids 231Rice and MacCarthy found remarkably low variation in elemental compo-sition within each population and no significant difference between humicacid and humin fractions. The only statistically significant composition differ-ence between populations was the composition of the fulvic acid fractionrelative to humic acid and humin fractions.Most scientists reporting elemental composition quote mass fractions.The mole fractions in Table 6.6, computed from the data in Table 6.5, aremore compelling because elements combine on a molar basis. The oxygen-to-nitrogen mole ratio in fulvic acids (16) is twice the ratio in humic acidsand humin (8). The oxygen-to-carbon mole ratio in fulvic acids (0.8) isnearly twice the ratio in humic acids and humin (0.5). These results clearlyindicate that the fulvic acid fraction has significantly higher oxygen contentthan the humic acid and humin fractions.Using the results from Table 6.6, we can estimate the mean formal oxi-dation number (Example 6.1) of carbon NC in each humic fraction. Chemi-Humin 0.371 0.434 0.172 0.021 0.001 0.070Note: The last column is the mean formal oxidation number of carbon NC .Source: Rice, 1991.TABLE 6.6 The Mean Mole Fraction X for Each of the Most AbundantElements in Humic Acid, Fulvic Acid, and HuminXC XH XO XN XS NCSoil Humic Acids 0.387 0.400 0.189 0.022 0.002 0.111cal bonding details are irrelevant provided that nitrogen is assigned a formaloxidation number of (3). It makes no difference whether hydrogen isassigned to H-O bonds or H-C bonds because, ultimately, the formal oxida-tion number of oxygen is (2). The median formal oxidation number for car-bon NC in each of the three humic fractions is listed in the last column ofTable 6.3.6.5.3. Chemical CompositionBiochemists employ a hierarchy to describe the structure of complexbiological molecules. The primary structure of a peptide is the amino acidsequence, while the primary structure of a glycan (or polysaccharide) is thesaccharide sequence. Secondary structure refers to three-dimensional geome-try of a particular segment of a biomolecule, while tertiary structure refersto the three-dimensional geometry of the entire biomolecule.Soil and Environmental Chemistry232XC 0:0461 molC g1OM0:0461 molC g1OM 1:000 molC mol1CXH 0:0476molH g1OM0:0461 molC g1OM 1:032molH mol1CXO 0:0225 molO g1OM0:0461 molC g1OM 0:488 molO mol1CXN 0:0026 molO g1OM0:0461molC g1OM 0:056molO mol1CStep 3: Assign valence hydrogen electrons 1 XH to H-O bonds, followed byH-N bonds, ending with H-C bonds. Assume all nitrogen is amide-N, assigningonly one H-N bond per nitrogen. Oxygen has two valence electrons but remainsattached to the humic molecules only if half of the oxygen electrons are assignedto H-O bonds.n H O XO 0:488 molHO mol1Cn H N XN 0:056 molHN mol1Cn H C 1 XH n H O n H N 0:488molHC mol1CStep 4: Assign valence carbon electrons 4 XC to C-O bonds, followed by0:554 gC g1OM12:0107 gC mol1 0:0461 molC g1OM0:048 gH g1OM1:0079 gH mol1 0:0476 molH g1OM0:360 gO g1OM15:9994 gO mol1 0:0225 molO g1OM0:036 gN g1OM14:0067 gN mol1 0:0026 molN g1OMStep 2: Normalize the moles per gram of each element by the moles of carbonper gram from Step 1.Example 6.1Estimating the mean formal oxidation number of carbon NC is one way to applythe elemental composition data of humic substances. In this example we use themean composition of soil humic acids (Table 6.5), applying rules #3 and #4 fromthe protocol used in this book (Clay Mineralogy & Clay Chemistry, Appendix 3A):NH 1 , NN 3 and NO 2 . The estimate requires five steps toassign valence electrons to chemical bonds before estimating the formal oxida-tion number using the electronegativity principle.Step 1: Divide the mass fraction of each element in soil humic acid fraction(Table 6.5) by the atomic mass of the element.C-N bonds, ending with C-C bonds. Because most organic nitrogen is amide-N(see Figure 6.18), assign two C-N bonds per nitrogen.1elements listed in Ta and 6 hemical moieties12in humic substances. o evid cules are polymersin the sense that pept ns, an polymers. Further-more, we have no und g of p molecular structurein humic substances. standi ic molecular struc-tu c.de rChapter 6 Natural Organic Matter and Humic Colloids 233infrared spectroscopy (IR), nuclear magnetic resonance spectroscopy (NMR),photoelectron absorption spectroscopy covering the spectrum from visible tox-ray, and mass spectrometry. The physical details of how these methods iden-tify specific chemical moieties and quantify their abundance are beyond thescope of this book, but we will summarize the most reliable results.12re is limited but probably more reliable than any other structural characteristiOur knowledge of chemical moietiesthat is, local molecular structurerives from a variety of chemical and instrumental methods: vibrational o. Chemical moiety is gerstandinOur underenerally used to sigrimary and secondaryng of the tertiary humides, glyca d polynucleotides areThere is n ence that humic molebles 6.5 .6 combine to form cNC 0:488molCO mol1C 0:111molCN mol1C 0:488molHC mol1C NC 0:111The key implication is this: assigning hydrogen to H-O bonds is equivalent toassigning carbon to C-O bonds. Assigning hydrogen to H-O bonds reduces thenumber of C-O bond required to satisfy the requirement: NO 2 . Alterna-tively, assigning hydrogen to H-C bonds increases the number of C-O bondrequired to satisfy the requirement: NO 2 .Despite considerable research, we still have limited understanding of how then C O XO 0:488 molCO molCn C N 2 XN 0:111 molCN mol1Cn C C 4 XC n H C n C O n C N 2:913molCC mol1CStep 5: The formal oxidation number of carbon NC in soil humic acid (Table6.5) is found by accounting for electron loss in C-O and C-N bonds and the elec-tron gain from H-C bonds. There is no need to count CC bonds because theyhave no effect on NC .BondNet Electron TransferRelative to Carbonn C O 0.488n C N 0.111n H C +0.488NC +0.111Atomic carbon has four valence electrons 4 XC balanced by four protons inthe nucleus. The net electron transfer relative to carbon means each carbon loses0.111 electrons resulting in a net effective charge of +0.111 because nuclearcharge remains unaffected by bonding.NC n C O n C N electron loss n HC electron gainnify part of a molecule (Muller, 1994).Acidometric TitrationAcidometric titration is the most common method for quantifying the weakacid content of humic samples. Acidometric titration curves for two humicsamples appear in Figure 6.17: Suwannee River (Georgia, USA) aquatic ful-vic acid and Summit Hill (New Zealand) soil humic acid. The amount of baseadded during the titration QTOT mmolc g1C is normalized by the mass ofdissolved humic carbon.The displacement of the fulvic acid titration curve in Figure 6.17 revealsthe higher weak acid content of the fulvic acid sample relative to the humicacid sample, consistent with the significantly higher oxygen content of fulvicacid fractions relative to humic acid fractions.The hydrolysis constants Ka1, Ka2 determine the pH of the equivalencepoints, as indicated in Figure 6.17. The amount of each weak acidQ1 mmolc g1C and Q2 mmolc g1C , respectivelydetermines the positionof the respective equivalence points along the QTOT-axis.QTOT Q11 Ka1 aH 1=n1 ! Q21 Ka2 aH 1=n2 !6:15Titration curves of dissolved humic molecules are significantly broadenedcompared to the titration curve typical of a weak acid with a single functionalSoil and Environmental Chemistry23418Summit Hill soil humic acid16141210864202 3 4 5pHKa1Ka1Ka2Ka2Q TOT (mmol c gC1)6 7 8 9 10 11 12Suwannee River fulvic acidFIGURE 6.17 The acidometric titration curve of a fulvic acid and a humic acid sample from theInternational Humic Substance Society collection identifies two weak acid populations: a weakacid population with mean hydrolysis constant Ka1 and a very weak acid population with meanhydrolysis constant Ka2. Source: Reproduced with permission from Ritchie, J.D., Perdue, E.M.,2003. Proton-binding study of standard and reference fulvic acids, humic acids, and naturalorganic matter. Geo. Cosmo. Acta 67 (1), 8596.13Chapter 6 Natural Organic Matter and Humic Colloids 235group. The two remaining parameters n1, n2 express this broadening effect(see Figure 5 in (Katchalsky, 1947)). Katchalsky and Spitnik (Katchalsky,1947) attribute a diffuse equivalence point to electrostatic interactions betweenclosely spaced weak acid groups. Some humic chemists interpret equivalencepoint broadening to chemical heterogeneity of the weak and very weak acids.The electrostatic effect, in its simplest terms, reduces the tendency of pro-tons to dissociate from weak acid moieties when surrounded by chemicallyidentical moieties that have already dissociated. In essence, the proximity ofnegatively charged (i.e., dissociated weak acid) sites exerts a collective attrac-tive electrostatic force on protons, lowering the tendency of remaining weakacid moieties to release their protons.Structure 5Structure 6The smooth line through each titration curve in Figure 6.17 is the best fit by asix-parameter model (6.15) proposed by Katchalsky and Spitnik (1947). Model(6.15) represents the total acidity of a humic sample as the sum of a weak acidnominally a carboxylmoiety (Structure 5)with hydrolysis constantKa1and a veryweak acidnominally a phenol moiety (Structure 6) with hydrolysis constant Ka2.Appendix 6C illustrates how the elemental composition of a humic sampleand the quantification of weak acid content by acidometric titration can be usedto assess the chemical forms of oxygen in a humic sample. Regardless ofwhether the sample is a fulvic acid or a humic acid, a considerable fractionof the oxygen in humic samples cannot be assigned to weak acid moieties.Nitrogen-15 Nuclear Magnetic Resonance SpectroscopyWhat little we know about nitrogen in humic substances comes from N-15(157N) NMR. Nuclear magnetic resonance spectroscopy is an isotope-specificmethod. Although both stable nitrogen isotopes have a nuclear magneticmoment, and both absorb microwave radiation in an NMR experiment, eachisotope presents distinct challenges when studying humic substances.Nitrogen isotope 147N is very abundant (99.63%), but the large electricquadrupole moment of its nucleus causes profound signal broadening, render-ing 147N of little practical use (Lambert, 1964). Nitrogen isotope157N, thoughnot susceptible to electric-quadrupole signal broadening, produces a relatively13. Katchalsky and Spitnik (Katchalsky, 1947) report this behavior for polymeric acids.Thorn and Cox (Thorn, 2009) recorded the natural abundance N-15 NMRspectra of fulvic and humic acids, shown in Figure 6.18. The recording ofthese spectra required 56560 hours, reflecting the low relative sensitivity ofnatural abundance N-15 NMR. Thorn and Cox (Thorn, 2009) assign the119120 ppm resonance peak to amide nitrogen typical of peptides (Structure7) and N-acetylated amino-polysaccharides (Structures 8 and 9) and the 3136ppm to amine nitrogen found in amino sugars and terminal amino acidsAmide nitrogen typically accounts for 75 to 85% of the total organic nitrogenterminal amine 6 to 8%, and unidentified nitrogen accounts for the remainderTABLE 6.7 Nuclear magnetic properties of the most abundant elements inhumic and fulvic acidsIsotope NaturalAbundanceNuclearSpinNuclear GyromagneticRatio g MHz T1 RelativeSensitivity{11H 99.985% 1/2 267.513 1.000021H 0.015% 1 41.065 5:43 107137C 1.10% 1/2 67.262 1:69 104147N 99.63% 1 19.331 2:05 105600 500 400 300 200 100 0ppm100 20600 500 400 300 200 100 0ppm100 200600 500 400 300 200 100 0ppmELLIOT SOILFulvic Acid Std.(1S102F)2.72% Nct = 2 msecELLIOT SOILHumic Acid Std.(1S102H)4.14% Nct = 2 msecSUMMIT HILL SOILHumic Acid Ref..(1R106H)5.13% Nct = 2 msec120 120 119323334100 200FIGURE 6.18 Nitrogen-15 nuclear magnetic resonance spectra of soil fulvic and humic acidsamples from the IHSS collection. Chemical shifts are relative to the single N-15 resonance inthe amino acid glycine. Source: Reproduced with permission from Thorn, K.A., Cox, L.G., 2009N-15 NMR spectra of naturally abundant nitrogen in soil and aquatic natural organic mattersamples of the International Humic Substances Society. Org. Geochem. 40, 484499.Soil and Environmental Chemistry236weak signal2:11 107 relative to 11Hin natural humic samples becauseboth its low natural abundance (0.37%) (Lambert, 1964) and small gyromag-netic ratio g (Table 6.7).157N 0.37% 1/2 27.116 2:11 107178O 0.038% 5/2 36.264 4:48 1073115P 100% 1/2 108.291 1:39 1043316S 0.75% 3/2 20.534 1:43 108{Relative sensitivity is the product of the mean element abundance of soil humic acid (Rice, 1991),isotope abundance, and the cube of the gyromagnetic ratio gi=g1H 3, where i indicates isotope..,.0.The survival of amide nitrogen in humic substances extracted by the IHSSChapter 6 Natural Organic Matter and Humic Colloids 237method is significant. The acid phase of the IHSS extraction protocol repre-sents conditions suitable for the acid-hydrolysis of labile amide linkages. Alu-wihare and colleagues (2005) found that mild acid14 hydrolysis (1 M HCl,10-hour reflux at 90C) converted about 24% of amide-N into amine-N viade-acetylation hydrolysis. They suggest that most of the amide in marineorganic nitrogen is acetylated amino sugars (Structures 8 and 9).Structure 7. Source: Reproduced with permission from Aluwihare, L.I., Repeta, D.J., et al., 2005.Two chemically distinct pools of organic nitrogen accumulate in the ocean. Science 308, 10071010.Structure 8. Source: Reproduced with permission from Aluwihare, L.I., Repeta, D.J., et al., 2005.Two chemically distinct pools of organic nitrogen accumulate in the ocean. Science 308, 10071010.Peptidoglycan (Structure 9)the primary cell wall polymer in bacteriais cross-linked by tetrapeptide segments besides containing acetylated aminosugars. Peptide hydrolysis releases free amino acids, while de-acetylationreleases acetic acid from chitin and lactic acid from peptidoglycan; bothhydrolysis reactions convert amide-N to amine-N.Structure 914. Strong acid hydrolysis (6 M HCl, 12-hour reflux at 110C) released hydrolyzes 21% ofamideN into free amino acids (Henrichs, 1985).p8:0@ 1 1 8Soil and Environmental Chemistry238kgC 1molcarboxyl molCu kg1S102H 0:306 kgCukg1S102H0@1Acarboxylicphenol groups1:87molphenolickgC0@1A 1molCu1molcarboxyl0@1A 63:546 103 kgCumolCu0@1A 0:5813 kgCkg1S102H0@1A 0:069 kgCukg1S102H0@1AphenolicThe Elliot Soil Standard Humic Acid (IHSS sample 1S102H) containssufficient amine, carboxylic, and phenolic groups to bind 28 mg, 306 mg, and69 mg Cu per gram, respectively, of humic acid, for a total binding capacity of403 mg Cu per gram of humic acid.amine28molcarboxylic1A0@carboxyl groumolCu1A 63:5460@s03 kgCu1A 0:50@ 13 kgC1Akg1S102HAlthough the significance of amide-N as the major form of humic nitrogenremains a topic of scientific discussion, it strongly suggests that microbial cellwall residue is a prominent secondary source of humic substances. The assim-ilation of plant carbon (and nitrogen) as a soil microbial biomass is consistentwith the Rothamsted turnover model (see Figure 6.13) and represents an evol-ving understanding of the respective roles of plant and microbial biomass inthe formation of humic substances.Example 6.2The Elliott Soil Standard Humic Acid (IHSS sample 1S102H) has the followingcarbon and nitrogen content. Assuming 15% of the total nitrogen is amine andthe remaining 85% is amide, what percentage of the total Cu2 binding capacitycan be assigned to amine complexes? Assume that the total binding capacity isthe sum of amine, carboxyl, and phenol.Carbon,kgcarbon kg11S102HNitrogen,kgnitrogen kg11S102HCarboxyl,molc kg1carbonPhenol,molc kg1carbon0.5813 0.0414 8.28 1.87amine groups6:21 103 kgamineNkg1S102H0@1A molN14:0067 103 kgN0@1A 1molCu1molN0@1A 63:546 103 kgCumolCu0@1A 0:028 kgCu0@1ANitrogen-Containing Chemical Moieties in Humic SubstancesNatural abundance nitrogen-15 NMR clearly identifies two nitrogen-containing chemical moieties in humic substances: amine and amide. Thechemical significance is twofold. First, amide moieties have low affinityfor bonding to trace metals, making amine moieties the only significantnitrogen-containing trace-metal bonding site in humic substances (Example6.2). Second, amide moieties occur in peptides (Structure 7) and amino sugars(Structures 8 and 9). Peptide amides are labile to both extracellular soil pro-tease enzymes and the IHSS extraction protocol, suggesting acetylated aminosugars may explain the slow rate of organic nitrogen turnover: soil organicnitrogen half-life on the order of 100 years (see Figure 6.11).Phosphorus-31 Nuclear Magnetic Resonance SpectroscopyPhosphorus-31 NMR results indicate that humic-associated phosphorus takesthe form of phosphate mono- and diesters (Figure 6.19 and Structure 10).The cluster of resonance peaks in the range 3.5 ppm to 5.2 ppm isassigned to monoesters, while the broad peak in the range 0.5 ppm to 0.9ppm is assigned to diesters. The resonance at 5.6 ppm is orthophosphateChapter 6 Natural Organic Matter and Humic Colloids 239FIGURE 6.19 Phosphorus-31 nuclear magnetic resonance spectra of soil humic acidsamples collected from the Bankhead National Forest (Alabama), courtesy of R. W. Taylor andT. Ranatunga. Chemical shifts are relative to the single P-31 resonance in phosphoric acid, anPO34 that would be absent if the sample were thoroughly dialyzed to removeall small ions. The resonance peak at 5.0 ppm is pyrophosphate that oftenappears in P-31 NMR spectra of humic extracts.external reference.Soil and Environmental Chemistry240Structure 10The final step in the alkaline IHSS humic extraction protocol removes bydialysis the excess salt that accumulates during the various extraction treatments.Dialysis traps humic molecules while allowing small ions to diffuse through thepores of the dialysis membrane. An indeterminate amount of the phosphorus inthe initial extract is lost during dialysis as orthophosphate ion PO34 aq . Someof orthophosphate in the dialysate derives from mineral colloids dispersed andultimately dissolved during the extraction procedure; the remaining orthophos-phate derives from the hydrolysis of phosphate mono- and diesters. Some humicchemists studying humic-associated phosphorus modify their extraction protocolto specifically minimize phosphate ester hydrolysis.It is unclear whether the phosphate esters detected by P-31 NMR (Fig-ure 6.19) derive from the labile soil carbon pool (i.e., microbial biomassand decomposable plant residue) or from esters that form during humification.Phosphorus-Containing Chemical Moieties in Humic SubstancesNatural abundance phosphorus-31 NMR identifies phosphate mono- and diestersas the dominant phosphorus chemical moieties in humic substances. Phosphateesters (Structure 10) represent a significant source of phosphorus fertility in nat-ural ecosystems. Extracellular phosphatase enzymes secreted by plant roots, soilbacteria, and soil fungi (Dodd, 1987;Kim, 1998) hydrolyze phosphate ester bonds,releasing orthophosphate ions into soil solution for plant and microbial uptake.Sulfur K-edge X-Ray Absorption SpectroscopyOur understanding of organosulfur in humic substances draws heavily on x-ray absorption spectroscopy. In many respects the level of our understandingof organosulfur is comparable to our understanding of organonitrogen, despitedifferences in chemistry and spectroscopic method.Sulfur absorbs x-ray photons in a relatively narrow energy range above2472.0 eVthe sulfur K x-ray absorption edge (or K-edge). X-ray absorptionby sulfur at the K-edge excites an electron in the lowest energy atomicorbitalan electron in a 1s atomic orbitalto one of the lowest unoccupiedmolecular orbitals (LUMOs). The LUMO energy distribution mirrors thebonding interactions that determine the energy of each occupied molecularorbital (see Figures 6.6, 6.8, and 6.9).Figure 6.20 displays the normalized x-ray absorption spectrum for thiol(SH) sulfur in the amino acid L-cysteine. Peaks and oscillations near theChapter 6 Natural Organic Matter and Humic Colloids 241edgethe x-ray absorption near-edge structure (XANES) or near-edge x-rayabsorption fine structure (NEXAFS)obscure the precise position of thex-ray absorption edge. Two key components of the sulfur K-edge XANESspectrum in Figure 6.20 are the absorption edge (an arctangent step functionplotted as a solid line) and the white-line peak (a Gaussian function plottedas a dashed line) centered on the absorption edge.FIGURE 6.20 Normalized sulfur K-edge x-ray absorption spectrum of the thiol (-SH) sulfur inLcysteine shows negligible x-ray absorption below the absorption edge (2472.5 eV) but consid-erable absorption above the edge.The position of the edge step and both the position and intensity of thewhite-line peak are sensitive to the effective sulfur oxidation number. Formaloxidation numbers are useful when balancing electron transfer reactions becausethe reaction involves the transfer of an integral number of electrons from onemolecule to another. Formal oxidation numbers are less reliable when interpret-ing XANES spectra because chemical bonding generally does not transfer awhole number of electrons between two atoms in the same compound.By comparing the sulfur K-edge XANES spectra of natural samples withthe XANES spectra of known organosulfur compounds, we can infer the pres-ence of different sulfur oxidation states and their relative abundance in thehumic sample. The peat fulvic acid fraction shown in Figure 6.21 contains whatappear to be 6 distinct sulfur oxidation states. The estimated relative abundanceof each sulfur oxidation state and its chemical name appear in Table 6.8.Structure 11Structure 12Soil and Environmental Chemistry242The effective sulfur oxidation numbers listed in Figure 6.19 do not allmatch the formal oxidation numbers of representative organosulfur specieslisted in Table 6.9. The sulfur in disulfide (Structure 11), thioester (Structure12), and thioether moieties all have a formal oxidation number of S(0), assum-ing that the difference in Pauling electronegativity for carbon wC 3:55 andsulfur wS 3:58 is negligible.FIGURE 6.21 Normalized sulfur K-edge x-ray absorption spectra of sulfur in peat fulvic acidfraction (Loxely peat, Marcell Experimental Forest, Grand Rapids, MN; sample courtesy ofP. R. Bloom).TABLE 6.8 Formal Oxidation Numbers of Organosulfur Species and TheirRelative Abundance in the Peat Fulvic Acid Fraction Shown in Figure 6.21Sulfur Formal OxidationNumberRelative Position ofAbsorption EdgeRelativeAbundance0.0 0.4 eV 24%0.5 1.0 eV 27%2 3.5 eV 5%4 5.5 eV 3%5 8.5 eV 20%6 10.0 eV 22%Chapter 6 Natural Organic Matter and Humic Colloids 243Thiol (-SH) would have a formal oxidation number of S(1), a result of thedifference in Pauling electronegativity for hydrogen wH 2:20 and sulfurwS 3:58. The formal oxidation number assigned to thiosulfate (Structure 13)is the average S(2) of the two sulfur atoms: S(1) and S(5). The sulfone sul-fur (Structure 14) is bonded to two oxygen atoms and two carbon atoms, result-ing in a formal oxidation number of S(4). Sulfonate sulfur (Structure 15) isidentical to the S(5) sulfur in thiosulfate, while sulfate esters (Structure 16)register a formal oxidation number of S(6).Structure 13, 14Oxidation Number Absorption Edge0.5 Disulfide 0.4 eV0.5 Thiols and thiol esters 1.0 eV2 Thiosulfate 3.5 eV4 Sulfone 5.5 eV5 Sulfonate 8.5 eV6 Sulfate esters 10.0 eVTABLE 6.9 Formal Oxidation Numbers of Representative OrganosulfurSpeciesSulfur Formal Chemical Name Relative Position ofStructure 15, 16Chemical heterogeneity prevents scientists from distinguishing subtle var-iations in the chemical bonding of each sulfur oxidation state in humic sub-stances. Sulfur K-edge XANES distinguishes little difference between thiol(-SH), disulfide (-SS-), and thioether (-S-) when all are present in a complex nat-ural sample. Sulfur K-edge XANES allows humic chemists to quantify theeffective oxidation states of sulfur in humic substances and to infer the identityof organosulfur moieties. What little we know about the chemical bonding ofhumic organosulfur moieties requires supplemental chemical information.Spectroscopy24The assignment of proton or H-1 (11H ) NMR spectra derives largely from thecarbon to which the protons are bonded, providing essentially the same chem-ical information found in C-13 (136 C ) NMR spectra. The most practical dis-tinction between H-1 NMR spectra and C-13 NMR spectra of humicsubstances is found in Table 6.4; natural abundance C-13 NMR spectroscopyis roughly 10,000-fold less sensitive than H-1 NMR.The sensitivity advantage enjoyed by H-1 NMR enhances a particularC-13 NMR experiment: cross-polarization 1H ! 13C solid-state NMR (Pines,1973; Schaefer, 1976). Hydrogen-1 nucleirather than carbon-13 nucleiabsorb radiation in a cross-polarization 1H ! 13C solid-state NMR experi-ment and are then coaxed to transfer their magnetic alignment to a dilutepopulation of C-13 nuclei before the spectrum is recorded. Technical issuesbeyond the scope of this book make H-1 NMR the method of choice if thehumic sample is dissolved, while cross-polarization 1H ! 13C solid-stateNMR is the method of choice for solid humic samples.Regardless of the method, H-1 and C-13 NMR spectra of humic substancescontain resonance peaks assigned to the following carbon moieties: aromatic, ali-phatic, enols (alcohols or polysaccharides), and ketones (including carboxylicgroups). Keeping in mind that these assignments pertain to the primary structureof humic molecules, NMR spectroscopy has yielded little reliable information onSulfur-Containing Chemical Moieties in Humic SubstancesNatural abundance sulfur K-edge XANES identifies multiple sulfur chemicalmoieties in humic substances representing a considerable range of formal oxi-dation numbers (see Figure 6.21). Extracellular soil sulfatase enzymes hydro-lyze sulfate esters in a process resembling phosphate release by phosphataseenzymes in soil. Humic chemists have no explanation for the occurrence ofsulfur moieties registering oxidation numbers greater than S(2) and less thanS(6) because these intermediate forms do not correspond to the acceptedmechanism for dissimilatory sulfate reduction (see Chapter 8).Reduced organosulfur moieties have twofold importance: reducing agentsand binding moieties for chalcophilic (sulfur-loving) trace metals. Szulczewskiand colleagues (Szulczewski, 2001) found that reduced sulfur species inhumic substances could reduce chromate CrO24 to Cr3. Several scientistsstudying the binding of methylmercuryCH3Hg by humic substances observedthe formation of Hg-S bonds that originate from humic thiol ligands (Amirbah-man, 2002; Qian, 2002; Yoon, 2005). Roughly one-third of the reduced sulfurin the humic samples appears to be capable of binding methylmercury CH3Hgcations. The unreactive reduced sulfur could be thio ether, disulfide, andthioester moieties.Hydrogen-1 and Carbon-13 Nuclear Magnetic ResonanceSoil and Environmental Chemistry4humic secondary molecular structure. In simple terms, we know the type of car-bon moieties found in humic substances but are uncertain of their precise relativeabundance or how these simple structures combine to form an entire molecule.Since humic substances are a mixture of humic molecules, each with a differentsecondary structure, it is unlikely we will ever be able to draw the structure of ahumic molecule whose tertiary structure and molecular properties match the col-lective properties of a natural humic substance sample.Quantifying Carboxyl Moieties in Humic SubstancesAcidometric titration typically identifies two weak organic acid classes in humicextracts based on two equivalence points in the titration curves (see Figure 6.17).Carboxyl moieties estimated using NMR (Ritchie, 2008) overestimate titratablecarboxyl acidity by roughly 40 to 50%. Nuclear magnetic resonance spectros-copy fails to distinguish carboxyl moieties from carboxyl ester and amidemoieties, accounting for this overestimate. Phenol moieties cannot be reliablyresolved using either H-1 or C-13 NMR. As in previous cases (N-15 NMRestimates of amine moieties and sulfur K-edge XANES estimates of thiol moi-eties), the NMR spectroscopic measurement overestimates chemically reactivemoieties capable of binding metal ions or dissociating as a weak acid.Chapter 6 Natural Organic Matter and Humic Colloids 2456.6. HUMIC COLLOIDSHumic molecules dissolved in water exhibit properties similar to simple amphi-philes such as phospholipids. The formation of molecular-aggregate colloidsabove the critical micelle concentration (CMC) lowers the average diffusion rateof charge carriers in the electrical conductivity results plotted in Figure 6.22.FIGURE 6.22 The critical micelle concentration of a humic acid solution (0.16%(w/v))appears as an inflection point (marked by an arrow) in a plot of the electrical conductivity ofthe molecular solution as a function of concentration.24The adsorption of amphiphilic molecules at the air-water interface (seeFigure 6.16) lowers the surface tension of water until a monolayer is formed,forcing molecules to aggregate as micelles in solution. Surface tension measure-ments of humic extract solutions consistently detect a CMC (Chen, 1978;Tschapek, 1978; Tschapek,Wasocusk, et al., 1981; Hayase, 1983; Yonebayashia,1987; Kile, 1989; Shinozuka, 1991; Guetzloff, 1994; Wershaw, 1999).It is unlikely, though not impossible, that humic molecules have a single polarend and a single nonpolar end (see Figure 6.16 and Appendix 6D). A more prob-able model for humic molecules would be a segmented amphiphile, a flexiblemolecule with alternating polar and nonpolar segments. Such molecules wouldfold and aggregate in water by presenting their polar segments at the aqueouscontact and burying their nonpolar segments within their interior (Figure 6.23a).Humic molecules have little tendency to form aggregates of the type seen inFigure 6.23a in the natural state because they adsorb strongly to soil mineralparticles. Humic molecules self-organize on mineral surfaces in the naturalstate, folding in such a manner as to present their polar segments to either liquidwater or the solid mineral surface, withdrawing their nonpolar segments into theaggregate interior to create nonpolar domains (Figure 6.23b) much like the inte-FIGURE 6.23 The molecular aggregates formed by segmented amphiphiles in aqueous solution(a) and at the mineral-water interface (b). Polar segments are white circles, and nonpolar segmentsare gray lines.Soil and Environmental Chemistry6rior of the lipid bilayer (see Appendix 6D, Figure 6D.1).Evidence for the existence of hydrophobic domains capable of adsorbingnonpolar organic compounds (e.g., pesticides and industrial organic chemi-cals) appears in Chapter 9. The unique capacity of soil to adsorb nonpolarorganic compounds is also displayed by humic extractsprovided that thehumic solution is more concentrated than its CMC. This behavior is a directresult of amphiphilic molecular properties and gives rise to the colloidalbehavior of humic molecules: their tendency to form colloidal aggregates thatdisperse in water or organized colloidal films at the mineral-water interface.6.7. SUMMARYNatural organic matter is a component of the terrestrial carbon cycle, repre-senting both an important environmental substance and a vital component ofthe biological energy cycle. Photolithotrophs convert light energy into7chemical energy during photosynthesis, storing this chemical energy in a hostof bioorganic compounds comprising living biomass. The reduced carbon inbioorganic compounds is kinetically stable in the presence of ground state(triplet) dioxygen, a consequence of the peculiar electron configuration ofthe dioxygen molecule. The release of the chemical energy stored in naturalorganic matter requires enzymatic catalysis, firmly placing carbon turnoverin the hands of a complex community of soil organisms.The mathematical models quantifying organic carbon (and organic nitro-gen) turnover have changed little in the past 70 years. The decomposition ofsoil organic carbon appears to follow a first-order rate lawa rate law famil-iar from general chemistry. Ecologists studying carbon turnover distinguishtwo or three carbon pools that turn over at different rates.The labile carbon pool has a residence time of less than a year but containsmany chemically and biologically active compounds. Though much of thedissolved organic carbon in pore water cannot be identified, environmentalchemists have identified organic acids, free amino acids, active extracellularenzymes, siderophores, and biosurfactants (to say nothing of vitamins, growthfactors, DNA fragments, etc.).Chemically unidentifiable natural organic matter is collectively designated:humic substances. With the exception of the dissolved organic matter men-tioned in the previous paragraph, humic substances occur largely as a colloidalfilm coating mineral particles. Environmental chemists routinely extract humicsubstances for chemical analysis and characterization. The elemental composi-tion of humic extracts is remarkably invariant. Unfortunately, we know littleabout the primary or secondary structure of humic molecules beyond the iden-tity of chemical moieties formed by the principle elements: carbon, oxygen,nitrogen, phosphorus, and sulfur. Our most comprehensive knowledge relatesto humic molecular and colloidal properties rather than molecular structure.Humic substances have a substantial capacity to adsorb ionic speciesfrom solution by ion exchange and complexation of metal ions to specific chemicalmoieties, a chemical property similar to mineral colloids in its effect on solu-tion chemistry but arising from profoundly different chemical mechanisms. Theaffinity of humic substances for nonpolar organic compounds is a colloidal propertythat has no parallel in mineral colloids. Humic substances in situ are, in fact, hydro-philic colloids (see Appendix 6D) whose self-organized molecular arrangementresults from the inherent amphiphilic properties of individual humic molecules.APPENDIX 6A. HYDROXAMATE AND CATECHOLAMIDESIDEROPHORE MOIETIESIron chemistry in the vadose zone and the water column of most freshwaterand marine environments dramatically lowers iron biological availability.Bacteria and fungi have evolved complex systems to meet their iron nutri-Chapter 6 Natural Organic Matter and Humic Colloids 24tional requirements, including the secretion of siderophorescompounds thatform extremely stable, water-soluble ferric iron complexes.Soil and Environmental Chemistry248Biological activity is most intense under aerated conditionsthroughoutthe water column in most freshwater and marine environments and above thesaturated zone in terrestrial environments, precisely the conditions that favorferric iron as the most stable oxidation state. Ferric iron solubility limits bacteriaand fungal growth above pH 5, where total iron concentrations drop below107108 M. The extremely low ferric iron solubility is a consequence ofthe Lewis acidity of hexaquoiron(3), leading to its hydrolysis at low pH.The Lewis acidity of FeH2O63aq arises from the small ionic radiusand large charge of the Fe3 ion, the same physical characteristics that lowerthe ligand exchange rate of aqueous Fe3 (Kosman, 2003). The slow rate ofligand exchange accounts for the high kinetic stability of Fe3 complexes.Ligand moieties that form two (or more) simultaneous bonds to Fe3chelate complexesfurther lower the ligand exchange rate because ligandexchange requires the simultaneous detachment of two (or more) ligand moi-eties. All natural siderophores contain bidentate ligand moieties; the entireferrisiderophore complex is often hexa-dentate.Structure A1Structure A2The two most common ligand moieties in natural siderophores are the hydro-xamate moiety (Structure A1) and the catecholate moiety (Structure A2). Thesetwo ligand moieties have several features in common: their bidentate geometryclosely matches the preferred nonbonded O O distance of the Fe3 centerby the relative length and bond angles in the ligand moiety, and both ligand moi-eties have bonding properties that permit fine-tuning of an already favorablegeometry.Structure A39Structure A5Structure A6Structure A7bidentate moiety to fit the preferred geometry of the Fe3 center. The two mostimportant hydroxamate resonance structures (Shanzer, 2009) are Structures A3and A4. Structure A4 evenly distributes oxygen charge over the asymmetrichydroxamate ligand moiety, lengthens the C O bond, shortens the N C bond, and restricts free rotation by a partial N C double bond.Siderophores based on bidentate catecholate moieties, with few exceptions,should be classified as catecholamide (Structure 2). Intermolecular hydrogenbonding, common in catecholamide siderophores (Structures A5A7), may per-mit fine-tuning of the bidentate geometry (Structure A7) (Hay, 2001).Structure A4Bond resonance provides a mechanism for fine-tuning the geometry of theChapter 6 Natural Organic Matter and Humic Colloids 24The bidentate ligand moieties are coupled together through the sidero-phore molecular backbone, containing structural moieties that increase watersolubility. The siderophore molecular backbone also includes several hydro-gen-bonding moieties for attaching the siderophore to outer membrane recep-tors that transport the intact ferri-siderophore complex into the cytoplasm.APPENDIX 6B. SURFACE MICROLAYERSChemical studies of freshwater and marine air-water interface date from theearly 1970s (Duce, 1972; Andren, 1975; Liss, 1975; Mackin, 1980; Maguire,Soil and Environmental Chemistry2501983; Meyers, 1983; Knulst, 1997; Knulst, 1998; Calace, 2007; Gasparovic,2007; Wurl, 2008). These studies describe a surface microlayera chemicallyand biologically distinct layer ranging in thickness from a few tens to a fewhundreds of nanometerscontaining surface-active compounds (as evidencedby lower surface tension relative to pure water and compounds identified asfatty acids and fatty acid esters) and enriched in hydrophobic compoundsrelative to subsurface water (Duce, 1972; Andren, 1975; Maguire, 1983;Meyers, 1983; Knulst, 1997; Knulst, 1998).Microbes living in the water column are one source of surface microlayersurfactants; soil humic substances eroded from surrounding land surfaces areanother in freshwater bodies (Hunter, 1986). Andren and colleagues (1975)found that dissolved and particulate organic matter in the surface microlayerof Lake Mendota (Madison, Wisconsin) had ultraviolet-visible spectra indis-tinguishable from humic substances of terrestrial origin.The organisms and conditions that generate the surface microlayer infreshwater and marine systems also exist in soils, as well as the humic colloi-dal film at the mineral-water interface (Figure 6B.1). The autolysis of dyingbacteria and fungal cells releases cell membrane biosurfactants into soil porewater. Numerous bacteria and some fungi secrete exocellular biosurfactants asantibiotic or pathogenic agents and in response to the presence of hydrocarbonsubstrates. The microbial biosurfactants need not remain dissolved in poreFIGURE 6B.1 The air-water interface insoils at water contents less than fieldcapacity will be nearly equal to the totalsurface area of the soil. The water filmthickness will be at most a couple ofmicrometers thick in coarse sand and lessthan a micrometer in finer-textured soils.Chapter 6 Natural Organic Matter and Humic Colloids 251water but can adsorbalong with dissolved humic substances (Herbert,1995)at the soil air-water interface. The following two examples provideestimates of the magnitude of the soil air-water interface and the water filmthickness in gravity-drained soils.Nam and colleagues (Nam, 1998) conducted a study of the relationshipbetween soil organic matter content and the adsorption of phenanthrene.The organic carbon content and surface area of the soil are as reported byNam and colleagues, but the remaining soil properties listed in Table 6B.1are from the official soil series description.Using soil bulk density rB, we can estimate the surface area of each soilbased on soil volume. The volume-based surface area of the Savannah soilseries is given by expression (6B.1), which is an estimate of the total air-waterinterface in the Savannah soil series at field capacity.Savannah Sand 1.15 0.89 1.51 0.133{Field capacity: pFC 10 kPa or hFC 1:0m.Source: Nam, 1998.York) and Savannah Soil Series (Clarke County, Mississippi)SoilSeriesTexture OrganicCarbon(wt%)SurfaceArea,m2 g1Bulk DensityrB, Mg m3Water Content{yV FC , m3 m3Lima Siltloam2.99 6.04 1.10 0.14TABLE 6B.1 Select Properties of Lima Soil Series (Cayuga County, NewSavannah Series :0:89 m2106 Mg 1:51Mgm3 1:34 106 m2 m3 6B:1The volumetric water content at field capacity yV FC is a thin water filmspread over the total soil surface area found by dividing the volumetric watercontent by the volume-based surface area (6B.2). The water film thickness atfield capacity is remarkably thin.Savannah Series :0:13m3 m31:34 106 m2 m3 9:90 108 m 0:10 mm 6B:2Lenhart and Saiers (2004) studied the adsorption of natural organic matter atthe air-water interface using a column packed with fine sand (300355 nm).The volumetric water content yV was 0.12 m3 m3 at a constant tension-headof htension 0:298 m. Given the uniform particle diameter of the sand(Accusand 40/60) and the precise water content measurements, we can easily1S102H) re % o t. ng contentmust be ass e caSoil and Environmental Chemistry252APPENDIX 6D. HYDROPHOBIC AND HYDROPHILICCOLLOIDSA liquid dispersion of colloidal particles is stablemeaning that the particleswill not settle outif the constant thermal motion of molecules in the liquidphase is sufficient to overcome the effects of gravity on the particles (seeChapter 9, Appendix 9A). Colloid chemists distinguish two different typesof colloidal particles that disperse in liquids: hydrophobic and hydrophilic col-loids. Hydrophobic colloids are solidsultrafine mineral particles or claysand hydrophilic colloids are molecular aggregatescomposed of either humicsubstancespresents 50.3igned to somor biosurfactanof the totalother chemits secreted byxygen contenl form.microbes.The remainile acidity of he Elliot Soi Standard Hu ic Acid (IHS0.5813 0.3408 8.28 1.87carboxyl groups8:28molcarboxylickgC0@1A 2molO1molc0@1A 15:9994 103 kgOmolO0@1A 0:5813 kgCkg1S102H0@1A 0:154 kgcarboxylicOkg1S102Hphenol groups1:87molphenolickgC0@1A 1molO1molc0@1A 15:9994 103 kgOmolO0@1A 0:5813 kgCkg1S102H0@1A 0:017 kgphenolicOkg1S102H0:154 kgcarboxylicOkg1S102H0@1A 0:017 kgphenolicOkg1S102H0@1A0@1A kg1S102H0:3408 kgO0@1A0:171 kgweak acidOkg1S102H0@1A kg1S102H0:3408 kgO0@1A 0:503 kgweak acidOkgOThe titratab t l m S sampleCarbon,kgcarbon kg1Oxygen,kgoxygen kg1Carboxyl,molc kg1carbonPhenol,molc kg1carbonestimate the mean volume-based area of the sand 5 104 m2 m3 and waterfilm thickness 2 mm.APPENDIX 6C. HUMIC OXYGEN CONTENT AND TITRATABLEWEAK ACIDSThe Elliott Soil Standard Humic Acid (IHSS sample 1S102H) has the follow-ing composition: carbon and oxygen content, and carboxylic and phenolicacid content. What fraction of the total oxygen content cannot be assignedas weak acids?FIGURE 6D.1 Aqueous solution structures of amphiphilic molecular aggregates: micelle andlipid bilayer. Modified from (Villarreal, 2007).Chapter 6 Natural Organic Matter and Humic Colloids 253Hydrophobic Mineral Colloids. Chapter 3 provides an adequate descriptionof mineral (hydrophobic) colloids. It may seem trivial, but hydrophobic colloidshave a well-defined surface that forms an interface between solid particles andthe surrounding liquid (see Chapter 9, Figure 9.1); the surface is a barrier separ-ating the interior of the hydrophobic colloid from the liquid. Adsorbate mole-cules attach to the surface but cannot penetrate the surface because theinterior of a hydrophobic colloid does not behave like a fluid.15Hydrophilic Organic Colloids. Organic (hydrophilic) colloids aremolecular aggregates, not solid particles. Unlike hydrophobic colloids,molecular-aggregate colloids have a penetrable surface separating the inte-rior of the colloid particle from the liquid. Adsorbates either attach to theparticle surface or penetrate the liquid-colloid interface, entering the interiorof molecular-aggregate colloid. The interior of molecular-aggregate colloidsbehaves much like a fluid.The cell membrane of all living organisms is an aggregation of amphiphilicmolecules called a lipid bilayer (Figure 6D.1). An amphiphilealso known asa surfactant or detergentis a molecule that has both polar16 and nonpolar17structures. The most abundant amphiphiles in cell membranes are phospholi-pids, the phosphate head is the polar structure, and the lipid tail is the nonpo-lar structure. The amphiphiles in a lipid bilayer aggregate to form two sheets,hence the term bilayer; the nonpolar tails oriented toward the center or inte-rior of the bilayer; and the polar heads form the surface in contact with theliquid water. The bilayer is actually a liposome with a very large radius.Micelles are the smallest amphiphile aggregates, consisting of a fluid-likecore formed by the nonpolar portion of the amphiphiles encased in a shell15. The interlayer of swelling phyllosilicates is considered an extension of the surrounding solu-tion. Solution cations exchange with interlayer cations and water molecules enter the interlayer tohydrate interlayer cations but the crystalline phyllosilicate layers do not imbibe interlayer cationsand water molecules.16. Polar in this context refers to the following molecular structures: weak inorganic acids (e.g.,organosulfate esters), weak organic acids (e.g., carboxylic acid or phenolic acid groups), weakorganic bases (e.g., primary amines), hydrogen-bond donors (e.g., alcohol groups, secondaryamines), or hydrogen-bond acceptors (e.g., carbonyl groups). Polar structures usually involveextremely electropositive or electronegative elements bonded to carbon.17. Nonpolar in this context refers to molecular structures in which carbon is bonded to carbon orhydrogen. Aliphatic structures are extremely nonpolar.forme .The t -trationDe -lar or -tition .The a dwater -gates -vent ry254c Coxygen content kgO kg1HA .Summit Hill Soil Reference Humic Acid (1R106H)Carbon,kgC kg1HAOxygen,kgO kg1HACarboxyl,molc kg1CPhenol,molc kg1C0.5400 0.3790 7.14 2.42carboxyl groups7:14 molcarboxylickgC0@1A 2 molO1 molc0@1A 15:9994 103 kgOmolO0@1A 0:5400 kgCkgHA0@1A 0:123 kgcarboxylicOkgHAphenol groups2:42 molphenolickgC0@1A 1 molO1 molc0@1A 15:9994 103 kgOmolO0@1A 0:5400 kgCkgHA0@1A 0:021 kgphenolicOkgHAand Acidic Functional Groups links.Using the oxygen content from the Elemental Composition page and thecombined carboxyl and phenol content from the Acidic Functional Groupspage, determine the oxygen percentage in the Summit Hill Soil ReferenceHumic Acid (IHSS sample 1R106H) attributable to carboxyl and phenolgroups. What might be the chemical nature of the remaining oxygen?SolutionConvert the carboxylic and phenol contents mol kg1 to the equivalentProblems1. The International Humic Substances Society supplies reference samples toresearchers (IHSS Products link at the website www.ihss.gatech.edu/). TheChemical Properties link leads you to data under the Elemental Compositioninterior of the aggregate or from the aggregate interior into aqueous solution.d by the polar portion of the amphiphiles in contact with fluid waterype of aggregate structure depends on the solution amphiphile concenand the molecular characteristics of the amphiphile itself.tergents aggregate to form micelles that solubilize oils and other nonpoganic liquids in water. Molecules of the nonpolar liquid dissolve or parinto the nonpolar interior of the micelle, causing it to swellggregate structure accommodates both the nonpolar compound anin a stable colloidal system. The nonpolar interior of all of these aggremicelles and bilayersbehaves like a fluid. The surface does not prethe movement of molecules from aqueous solution into the nonpolaSoil and Environmental ChemistrcChapter 6 Natural Organic Matter and Humic Colloids 255The Summit Hill Soil Reference Humic Acid (IHSS sample 1R106H) containssufficient carboxylic and phenolic groups to bind 329 mg Cu per gram ofhumic acid.7:14molcarboxylickgC0@1A 1molCu1molcarboxylic0@1A 0:5400 kgCkg1R106H0@1A 3:86molCukg1R106H0@1Acarboxyli2:42molphenolickgC0@1A 1molCu1molphenolic0@1A 0:5400 kgCkg1R106H0@1A 1:31molCukg1R106H0@1AphenolicThe titratable acidity of Summit Hill Soil Reference Humic Acid (IHSS sample1R106H) represents 38% of the total oxygen content. The remaining contentis probably alcohol oxygen from polysaccharides and acetal ether from theb(1-4) condensation of pentose and hexose sugar monomers into polysacchar-ides. Schnitzer also recognizes small quantities of carbonyl oxygen CO.2. The International Humic Substances Society supplies reference samples toresearchers (IHSS Products link at the website www.ihss.gatech.edu/). TheChemical Properties link leads you to data on the Elemental Compositionand Acidic Functional Groups.Using the oxygen content from the Elemental Composition page and thecombined carboxyl and phenol content from the Acidic Functional Groupspage, determine the percentage of oxygen content in the Pahokee ReferenceHumic Acid (IHSS sample 1R103H) attributable to carboxyl and phenolgroups.3. Table 1.2 in The Chemical Composition of Soils (Helmke, 2000) lists thegeometric mean Cu content of world soils: 20 mgCu g1soil . The soil organiccarbon content of the Summit Hill (Christchurch, New Zealand) A-horizonis 4.3% (0.043 mgOC g1soil ). Assume the metal binding capacity is the weakacid content of the Summit Hill Soil Reference Humic Acid. Compare themetal binding capacity of the A-horizon with the Cu content of the soil,assuming one Cu2 per metal binding group. Is the metal binding capacitygreater or less than the mean soil Cu content?SolutionConvert the carboxylic and phenol contents molc kg1C to the equivalentcopper content kgCu kg1HA , using the weak acid content, the carbon con-tent, and the atomic mass of copper.Add the oxygen content of the two weak acid moieties and divide by the totaloxygen content of the sample.0:123 kgcarboxylicOkg1R106H0@1A 0:021 kgphenolicOkg1R106H0@1A0@1A kg1R106H0:3790 kgO0@1A 0:144 kgweak acidOkg1R106H0@1A kg1R106H0:3790 kgO0@1A 0:381 kgweak acidOkgO 5.6.Soil and Environmental Chemistry256The International Humic Substances Society supplies reference samples toresearchers (IHSS Products link at the website www.ihss.gatech.edu/). TheChemical Properties link leads you to data on the Elemental Composition.Using the oxygen content from the Elemental Composition page for the Wask-ish Peat Reference Humic Acid (IHSS sample 1R107H), estimate the meanformal oxidation number of carbon NC . Assume the following formal oxida-tion states: NH 1 , NO 2 , and NN 3 .of the total Cu2 binding capacity may be attributed to amine complexes.(IHSS sample 1R103H). Compare the metal binding capacity of this peat withthe Cu content of U.S. peat soils, assuming one Cu2 per metal binding group.Is the metal binding capacity greater or less than the mean soil Cu content?The International Humic Substances Society supplies reference samples toresearchers (IHSS Products link at the website www.ihss.gatech.edu/). TheChemical Properties link leads you to data on the Elemental Compositionand Acidic Functional Groups.Using the oxygen content from the Elemental Composition page for theSuwannee River Standard Fulvic Acid (IHSS sample 1S101F), and assuming10% of the total nitrogen is free amine (90% being amide), what percentage3:86molcarboxylicCukg1R106H 1:31molphenolicCukg1R106H 0:063546 kgCumolCu 0:329 kgCukg1R106H This represents a binding capacity of 26.2 mg Cu per gram of soil (for a soilwith 4.3% organic matter). The potential Cu binding capacity of the organicmatter in this soil is nearly 1000-fold higher than the geometric mean Cu con-tent of world soils.0:329 kgCukg1R106H0@1A kg1R106H0:5400 kgOC0@1A 0:043 kgOCkgsoil0@1A 2:62 102 kgCukgsoil2:62 102 kgCukgsoil 2:62 102 gCugsoil2:89 102 gCugsoil0@1A 103 mgCugCu0@1A 28:9mgCugsoil4. Table 1.4 in The Chemical Composition of Soils (Helmke, 2000) lists the geo-metric mean Cu content of U.S. peat soils (Histosols): 193 mgCu g1soil . Theorganic matter content of peat soils is essentially 100%. Assume the metalbinding capacity is identical with the Pahokee Peat Reference Humic AcidAcid-Base ChemistryAtmospheric Conversion ofSulfur Trioxide to SulfuricAcid 305Simulation 3167.1. INTRODUCTIONEnvironmental chemistry has a much different perspective on acid-base chemis-try than the one you encountered in general chemistry. The most important dif-ference is the reference point used to define acidity. Gacidity and basicity relative to aH 107 or pH Soil and Environmental Chemistry.# 2012 Elsevier Inc. All rights reserved.Composition 305Appendix 7C. Saturation Effect:Changes in SAR byWater ChemistryChapter Outline7.1 Introduction 2577.2 Principles of Acid-BaseChemistry 2587.3 Sources of EnvironmentalAcidity and Basicity 2637.4 Atmospheric Gases 2697.5 Ammonia-Based Fertilizersand Biomass Harvesting 2767.6 Charge Balancing in PlantTissue and theRhizosphere 2787.7 Mechanical Propertiesof Clay Colloids andSoil Sodicity 2837.8 Exchangeable Acidity 2987.9 Summary 302Appendix 7A. Buffer Index 303Appendix 7B. Converting MassFraction to Sum-of-OxidesAppendix 7D. Bicarbonate andCarbonate ReferenceLevels 306Appendix 7E. Calculating the pHof a Sodium CarbonateSolution 308Appendix 7F. Calculating theAqueous Carbon DioxideConcentration in a WeakBase Solution 309Appendix 7G. Ion ExchangeIsotherm for Asymmetric(Ca2+, Al3+) Exchange 310Appendix 7H. The Effect of(Na+, Ca2+) Exchange onthe Critical CoagulationConcentration ofMontmorillonite 313Appendix 7I. PredictingChapter 7eneral chemistry defines7, the pH of pure water.25725of anthropogenic acidity determines the viability of natural ecosystems andalters human exposure to inorganic toxicants.7.2. PRINCIPLES OF ACID-BASE CHEMISTRY7.2.1. Dissociation: The Arrhenius Model of Acid-Base ReactionsAcid-base chemistry is fundamentally based on our understanding of acid-base reactions that, it turns out, can be understood in different ways. The mostfamiliar is the Arrhenius concept that defines an acid as any chemical sub-stance that dissociates to release hydrogen ions H aq or more accuratelyhydronium ions H3O aq into aqueous solution:HA aq H2O l $ A aq H3O aq 7:1A base is any chemical substance that dissociates to release hydroxide ionsOH aq into aqueous solution:BOH aq $ B aq HO aq 7:2The formation of water molecules when hydrogen ions H aq andhydroxide ions OH aq combine in solution is an acid-base reaction:H aq HO aq $ H2O l orH3O aq HO aq $ 2 H2O l 7:3The Arrhenius concept has an acid and a base reacting to form a salt andwater:HNO3acidNaOHbase! NaNO3saltH2Ooracid base7:4in water and chemical reactions on the surfaces of mineral colloids bufferthe pH of natural water, yet this buffer capacity (Appendix 7A) is finite andcan be overwhelmed by acidity released by human activity. The magnitudeand rate at which the pH of natural water decreases in response to the releaseenvironmental reference point acknowledges the ubiquity and importance ofaqueous CO2 aq in atmospheric, surface and soil pore water.The environmental perspective on acid-base chemistry is also stronglyinfluenced by two seemingly conflicting features of environmental acidityand alkalinity: the capacity of natural waters to resist changes in pH yetremain susceptible to shifts resulting from human activity ranging from landuse and waste management to atmospheric emissions. Compounds dissolvedEnvironmental chemists define acidity and alkalinity relative to aH 105:5 orpH 5.5, the pH of pure water in equilibrium with an atmosphere containingcarbon dioxide gas CO2 g at a partial pressure of pCO2 103:41 atm. TheSoil and Environmental Chemistry8HNO3NaOH ! Na aq NO3 aq H2O l 97.2.3. Conjugate Acids and BasesThe hydrolysis reaction of a base is rarely written as a hydronium-ion dissocia-tion reaction (Eq. (7.7)) with acid dissociation constant Ka (Eq. (7.8)) but as thedissociation of the base to release a hydroxyl ion into solution (Eq. (7.9)) withbase association constant Kb (Eq. (7.10)).BH aq conjugateacidH2O l $ B aq weakbaseH3O aq 7:7Ka aB aH3OaBH7:8B aq H2O l weakbase$ BH aq conjugateacidHO aq 7:9Kb aBH aHO 7:107.2.2. Hydrogen Ion Transfer: the Brnsted-Lowery Modelof Acid-Base ReactionsThe Brnsted-Lowery concept defines an acid as any chemical substance thatcan donate hydrogen ions H and defines a base as any chemical substancethat can accept hydrogen ions. The Brnsted-Lowery concept has an acidand a base reacting to form conjugate bases (Eq. (7.5A)) and conjugate acids(Eq. (7.5B)) through hydrogen ion transfer reactions. The concept of acid-conjugate base and base-conjugate acid pairs appears in the following section.HA aq weakacidH2O l weakbase$ A aq conjugatebaseH3O aq conjugateacidKa aA aH3OaHA7:5AH2O l weakacidB aq weakbase$ OH aq conjugatebaseBH aq conjugateacidK0a aBH aOHaB7:5BAcids HA aq and conjugate acids BH aq are both H donors, while basesB aq and conjugate bases A aq are H acceptors. The Brnsted-Loweryacid-base concept is more general than the Arrhenius concept because saltand water formation are not required.The most important benefit of the Brnsted-Lowery acid-base concept isthat it explains the dissociation of water in dilute solutions in the absence ofeither acids or bases:H2O l weakacidH2O l weakbase$ OH aq conjugatebaseH3O aq conjugateacidKw 1014:00 7:6Chapter 7 Acid-Base Chemistry 25aBSoil and Environmental Chemistry260Ka Kb Kw 7:137.2.4. Defining Acid and Base StrengthThe criteria that chemists use to distinguish strong acids from weak acids orstrong bases from weak bases should be considered qualitative. Acid strengthis generally quantified by the thermodynamic acid dissociation constant Ka foran acid-base reaction (Eq. (7.11)):Ka aA aH3OaHA7:14Strong acids are identified by pKa 1:0, while weak acids are identified by1 < pKa < 7. Base strength is quantified on the same scale using the thermody-namic acid dissociation constant Ka for acid-base reaction (7.7). Strong baseslowing two expressions use Eq. (7.6) to convert the hydronium iondissociation constant of the conjugate acid BH aq (Eq. (7.8)) into ahydroxyl ion dissociation constant of the base B aq (Eq. (7.9)).KaKw aB aH3OaBH0@1A 1aOH aH3O0@1AKaKw aBaBH aOH0@1A K1bExpression (7.13) relates the acid dissociation constant Ka to its correspondingbase association constant Kb using the hydrolysis constant of water Kw:sociation reaction of an acid (or conjugate acid) (Eq. (7.7) or Eq. (7.11))whoseequilibrium constant is an acid dissociation constant Kaor a hydroxyl-ion dis-sociation reaction of a conjugate base (Eq. (7.9) or Eq. (7.12))whose equilib-rium constant is a base association constant Kb.HA aq weakacidH2O l $ A aq conjugatebaseH3O aq 7:11A aq conjugatebaseH2O l $ HA aq weakacidHO aq 7:12Hydronium-ion dissociation expressions are related to a hydroxyl-ion dissoci-ation reaction through the hydrolysis expression for water (Eq. (7.6)). The fol-In fact, every acid-base reaction can be written as either a hydronium-ion dis-are characterized by 13 pKa, and weak bases by 7 < pKa < 13.Acidity and BasicityAqueous acid-base reactionsaccording to the Brnsted-Lowery acid-baseconceptinvolve ions formed by the transfer of protons to or from water(Eq. (7.6)): H3O aq and OH aq . The participation of H3O aq andOH aq in all aqueous acid-base reactions introduces an equilibrium con-straint known as the proton balance. In Chapter 5 we introduced several equi-librium constraints to validate water chemistry simulations:1 charge balance(electroneutrality condition), mass balances of all solutes other than water (massconservation), and equilibrium activity products involving all solutes.7.2.5. Water Reference LevelChapter 7 Acid-Base Chemistry 261CH3O COH Kw 10 10 7:16The water reference level (Eq. (7.16)) is the appropriate proton reference levelfor solutions where the only weak acid or base is water itself (Eq. (7.6)), and itremains the appropriate proton reference level even if the solution containsstrong acids, strong bases, and neutral salts. Table 7.1 lists the conjugateacid-base pairs in solutions whose solutes are completely dissociated: strongacids, strong bases, or neutral salts formed by the acid-base neutralizationof strong acids with strong bases. For example, the charge balance in solutionscontaining nitric acid HNO3 and sodium hydroxide NaOH is given byEq. (7.17), regardless of the relative concentration of strong acid and base.TABLE 7.1 Conjugate Acid-Base Pairs in Aqueous Solutions of StrongAcids, Strong Bases, and Neutral SaltsWeak Acid Conjugate BaseH3O+ H2OH2O OHGeneral chemistry defines acidity and basicity relative to a reference pointdetermined by the proton balance of pure water (Eq. (7.15)). Subject to theequilibrium constant Kw for the spontaneous dissociation of water(Eq. (7.6)), the proton balance of pure water occurs at pH 7 (Eq. (7.16)),which we designate the water reference level:Proton Balance of Pure Water : CH3O COH 7:15 1=2 14:00 1=2 7:001. See Chapter 5, Appendixes 5B and 5C for details.Rearranging charge balance expression (7.17) to yield (7.18) allows us toassociate pH > 7 with CNa > CNO3and pH < 7 with CNa < CNO3.CH3O CNa COH CNO3 7:17CNa CNO3 COH CH3O 7:187.2.6. The Aqueous Carbon Dioxide Reference LevelSoil and Environmental Chemistry262Environmental chemistryrecognizing the presence of aqueous carbon diox-ide CO2 aq in all natural waters in contact with Earths atmosphere and itseffect on the pHdefines acidity and alkalinity relative to a reference pointdetermined by the proton balance of water in equilibrium with carbon dioxideCO2 g . This reference point is the aqueous carbon dioxide CO2 aq refer-ence level.Table 7.2 lists the conjugate acid-base pairs in solutions containing car-bonate solutions. Four species in Table 7.2 are boldface. Unlike solutionswhose only conjugate acid-base pairs derive from water (see Table 7.1), car-bonate solutions (see Table 7.2) encompass three proton reference levels:aqueous carbon dioxide CO2 aq , bicarbonate HCO3 aq , and carbonateCO23 aq . The boldface solute species are those defining the aqueous carbondioxide CO2 aq reference level. Appendix 7D discusses the remaining twoproton reference levels defined in carbonate solutions but not used by envi-ronmental chemists: the bicarbonate HCO3 aq and carbonate CO23 aq ref-erence levels.All of the remaining solutes in solutions containing the weak acidsdepicted in Table 7.2 are completely dissociated: strong acids, strong bases,or neutral salts. For example, the charge balance in a solution containing nitricacid HNO3, sodium hydroxide NaOH, and aqueous carbon dioxide CO2 aq isgiven by the following expression, regardless of the relative concentration ofstrong acid and base:CH3O CNa COH CNO3 CHCO3 2 CCO23 7:19TABLE 7.2 Conjugate Acid-Base Pairs in Aqueous Carbonate SolutionsWeak Acid Conjugate BaseH3O+ H2OCO2 aq HCO3HCO3 CO23H2O OHConsider a carbonate solution in equilibrium with CO2 g at a partial pres-sure of 3:87 104 atm. The proton balance (expression (7.20)) for the aque-ous carbon dioxide CO2 aq reference level2 at this specific CO2 g partialhand side of the expression, yields the following:Chapter 7 Acid-Base Chemistry 2637.3. SOURCES OF ENVIRONMENTAL ACIDITY AND BASICITYSurface and pore water chemistry is dynamic, a result of atmospheric deposi-tion, biological activity, and the chemical weathering of minerals. In this sec-tion we examine examples of each source and the associated chemicalprocesses.2. The proton balance defined for the aqueous carbon dioxide CO2 aq reference levelreference level and the bicarbonate proton reference level but shifts the carbondioxide proton reference level to lower pH values and the carbonate protonreference level to higher pH values. Figure 7.2 illustrates the effect of increas-ing CO2 aq partial pressure 100-fold pCO2 3:87 102 atm relative to thepartial pressure used in Figure 7.1.CNa CNO3 COH CHCO3 2 CCO23 CH3O 7:21Expression (7.21) associates pH > 5.5 with CNa > CNO3and pH < 5.5 withCNa < CNO3. Remember: The explicit reference pH for expression (7.20)depends on the CO2 g partial pressure.Figure 7.1 plots the conjugate acid-base species listed in Table 7.2 for acarbonate solution in equilibrium with CO2 g at a partial pressure of3:87 104 atm. The concentration of carbonic acid H2CO3 aq is also plottedto emphasize its status as a minor solution species in carbonate solutions re-lative to aqueous carbon dioxide CO2 aq . Four proton reference levels aredesignated in Figure 7.1: water, aqueous carbon dioxide CO2 aq , bicarbonateHCO3 aq , and carbonate CO23 aq .Increasing the CO2 g partial pressure has no effect on the water protonpressure (using boldface species in Table 7.2) is satisfied at pH 5.5:COH CHCO3 2 CCO23 CH3O 0 7:20Rearranging the charge balance expression (7.19), moving the proton balance(7.20) for the aqueous carbon dioxide CO2 aq reference level to the right-excludesby definitionCO2 aq .FIGURE 7.1 All concentrations are plotted as the negative logarithm of their concentrations pC.The CO2 aq partial pressure: pCO2 3:87 104 atm.FIGURE 7.2 Increasing the CO2 g partial pressure (pCO2 3:87 102 atm) alters the pH ofthe aqueous carbon dioxide and carbonate proton reference levels (see Figure 7.1).Soil and Environmental Chemistry2647.3.1. Chemical Weathering of Rocks and MineralsGeologists classify rocks according to the geological process that led to their for-mationigneous, sedimentary, and metamorphic. The major rock classes arefurther subdivided by texture and mineralogy. Sedimentary rocks are subdividedinto two major subclasses: clastic and chemical. Clastic sedimentary rocks formby the cementation of rock fragments: conglomerates, sandstones, and shales.Chemical sedimentary rocks result from either evaporation or biogenic precipita-tion from solution. The mineralogy of evaporite sedimentary rocks is predomi-nantly chloride and sulfate minerals. Precipitate sedimentary rocks consist ofbiogenic carbonate and silicate mineralscalcite, aragonite, dolomite, and diat-omitederived from the exoskeleton of aquatic and marine organisms.In the context of acid-base chemistry, geochemists group all igneous,metamorphic, and clastic sedimentary rocks into a single broad group: silicateChapter 7 Acid-Base Chemistry 265rocks. Of the chemical sedimentary rocks, only the carbonates influence acid-base chemistry, and they represent the second broad group. As we will see fol-lowing, environmental acid-base chemistry is indifferent to evaporite anddiatomite rock mineralogy.7.3.2. Silicate RocksThe chemical weathering of silicate rocks is most easily understood if wedenote rock composition as a sum of oxides. This representation neglects crys-tal structure distinctions, since crystal structure has a relatively minor effectwhen considering the global impact of chemical weathering on acid-basechemistry. Table 7.3 lists the oxide mole-per-mass fraction composition ofEarths crust. A detailed discussion of how the composition of rocks or miner-als is converted from a mass fraction representation to a sum of oxides repre-sentation appears in Appendix 7B.TABLE 7.3 Oxide Mole-per-Mass Composition of Earths CrustOxide Mole-per-Mass Fraction, mol kg1SiO2 s 9.68Al2O3 s 1.54FeO s 1.11CaO s 1.16Na2O s 0.49MgO s 1.14K2O s 0.24Source: Greenwood and Earnshaw, 1997.Soil and Environmental Chemistry266CaO s and MgO s are considered weak bases, but recognizing the qualita-tive nature of this distinction, we consider all alkali and alkaline earth oxidesin the chemical weathering reaction (7.23) and Table 7.3 as strong bases.Clearly, the chemical weathering of silicate rocks (7.23) is a source of strongbases in natural waters.Natural waters at the Earth surface absorb carbon dioxide from the atmo-sphere. Two processes cause CO2 aq to dissolve in natural waters: the inherentwater solubility ofCO2 aq (Eq. (7.25)) and the acid-base neutralization reaction(Eq. (7.26)) involving aqueous carbon dioxide and hydroxyl ions, the latter4 4 2Adding two moles of water to the left-hand side of Eq. (7.23) for each mole ofSiO2 s and replacing SiO2 aq with H4SiO4 aq on the right-hand side, whilemore accurate chemically, has essentially no impact on environmental acid-base chemistry.The acid-base significance of the chemical weathering of Earths silicatecrust (7.23) is the dissolution of the alkali and alkaline earth oxides. Chargeneutrality demands one mole of HO aq on the right-hand side ofEq. (7.23)and one-half mole of H2O l on the left-hand sidefor everymole of solute charge:CaO s H2O l !dissolution Ca2 aq 2 HO aq 7:24Based on the criteria chemists use to distinguish strong and weak bases, bothnum, iron, and titanium oxides in the final stages of the mineral weatheringsequence. The oxides Al2O3 s and Fe2O3 s behave as inert substances in thereaction depicting the chemical weathering of Earths silicate crust. The onlyreactive substances in the reaction depicting the chemical weathering of Earthssilicate crust (expression (7.23)) are the alkali and alkaline earth oxides andSiO2 s :9:68 SiO2 s 1:54 Al2O3 s 0:56 Fe2O3 s 1:16 CaO s 1:14 MgO s 0:49 Na2O s 0:24 K2O s 6:06 H2O l !dissolution 9:68 SiO2 aq 1:54 Al2O3 s 0:56 Fe2O3 s 1:16 Ca2 aq 1:14 Mg2 aq 0:99 Na aq 0:47 K aq 6:06 HO aq 7:23Geochemists typically represent aqueous silicic acid H SiO aq as SiO aq .The formal oxidation state of iron in the crust is Fe II , but chemicalweathering occurs under oxidizing conditions, favoring the oxidation ofFe II to Fe III . Environmental acid-base chemistry is indifferent to this oxi-dation reaction:2 FeO s 12O2 g ! Fe2O3 s 7:22The Jackson clay mineral weathering sequence (see Table 3.2) lists alumi-resulting from the chemical weathering of silicate minerals (Eq. (7.23)).7CO2 aq H2O l ! H2CO3 aq 7:30Because carbonic acid H2CO3 aq is a weak acid, carbonate CO23 aq and bicarbonate HCO3 aq are soluble conjugate bases:CO23 aq conjugate base2 H aq ! H2CO3 aq weak acid7:31environmental acid-base chemistry. The chemical formula for calciteCaCO3 s the principle mineral in limestonecan be reformulated ascomponent oxides: CaO CO2 s . Calcite dissolution (Eq. (7.29)) releasesboth strong base and aqueous carbon dioxide. The aqueous carbon dioxideCO2 aq combines with water (Eq. (7.30)) to form carbonic acid H2CO3 aq :CaO CO2 s calcite H2O l ! Ca2 aq 2 HO aq strong baseCO2 aq 7:29weak acidThe Garrels-Mackenzie estimate of bicarbonate resulting from the chemicalweathering of silicate minerals derives from the composition of Earths crust(see Table 7.3) and the chemical weathering of silicate minerals (Eq. (7.27)).7.3.3. Carbonate RocksThe chemical weathering of carbonate rocks is another major factor insilicate rocks : CHCO3 CSiO2 aq 27:28CO2 aq weak acidHO aq strong base!neutralization HCO3 aq conjugate base7:26Taking into account acid-base reaction (7.26), the chemical weathering ofsilicate minerals (7.23) can be reformulated as the followingneglecting theinert oxides Al2O3 s and Fe2O3 s :9:68 SiO2 s 3:03 H2O l 6:06 CO2 g 1:16 CaO s 1:14 MgO s 0:49 Na2O s 0:24 K2O s !dissolution 9:68 SiO2 aq 6:06 HCO3 aq 1:16 Ca2 aq 1:14 Mg2 aq 0:99 Na aq 0:47 K aq 7:27Garrels and Mackenzie (1971) observe that an estimate of solution bicarbon-ate derived from the chemical weathering of silicate rocks can be achieved ifit is assumed that, on the average, silicate minerals produce one bicarbonateion and two silica ions for each molecule of carbon dioxide:CO2 g !dissolution CO2 aq 7:25Chapter 7 Acid-Base Chemistry 26The dissolution of calcite written as an acid-base reaction identifies calcite asSoil and Environmental Chemistry2684 FeSferroussulfides 9 O2g 4 H2Ol ! 2 Fe2O3ferricoxides 4 H2SO4sulfuricacid7:36a mineral conjugate base:CaCO3 s calciteconjugate base2 H aq ! Ca2 aq H2CO3 aq weak acid7:32Garrels and Mackenzie (1971) proposed an estimate of solution bicarbon-ate derived from carbonate rock dissolution (Eq. (7.33)). The total solutionbicarbonate estimate (Eq. (7.34)) is the sum of estimates (7.28) and (7.33):carbonate rocks : CHCO3 2 CCa2 CMg2 CSO24 7:33total bicarbonate : CHCO3 2 CCa2 CMg2 CSO24 carbonates CSiO2 aq 2 silicates7:347.3.4. Sulfide MineralsThe sulfate dissolved in natural waters (Eq. (7.33)) comes from two sources:the dissolution of gypsum CaSO4 2H2O s in evaporite sedimentary rocksand the oxidation of sulfide minerals. Sulfide oxidation is a natural sourceof sulfuric acid. The atmospheric chemistry of sulfur oxides and the resultingatmospheric deposition of sulfuric acid are deferred to a later section; here, wefocus on the reaction between molecular dioxygen and sulfide ions.The formal oxidation state3 of sulfur in the disulfide ion S22 found in theferrous disulfide FeS2 s minerals pyrite and marcasite is (1). The sulfide ionS2 found in troilite FeS s has a sulfur formal oxidation state of (2). Otherelements form sulfide and disulfide minerals, but their relative abundance ismuch lower than iron, making them relatively insignificant contributors tothe acid-base chemistry of natural waters.The complete oxidation of both ferrous disulfide (Eq. (7.35)) and ferroussulfide (Eq. (7.36)) minerals yields insoluble ferric oxide Fe2O3 s and sulfu-ric acid H2SO4:4 FeS2ferrousdisulfides 15 O2g 8 H2Ol ! 2 Fe2O3ferricoxides 8 H2SO4sulfuricacid7:353. See Chapter 3, Appendix 3A for details.We examined in this section the chemical weathering reactions and the acid-Chapter 7 Acid-Base Chemistry 269equilibrium with natural waters (Garrels and Mackenzie, 1971). The carbondioxide dissolution reaction in water is given as follows with a Henrys Lawconstant KH 3:31 102 mol L1 atm1 (Zheng, Guo et al., 1997):CO2 g $ CO2 aq 7:38The hydration of aqueous carbon dioxide CO2 aq (Pietramellara, Ascheret al., 2002) yields carbonic acid H2CO3 aq in reaction (7.39), but the equi-librium constant Khydration 1:18 103 favors aqueous carbon dioxidebase implications of four types of rocks or minerals: silicates, sulfides, carbo-nates, and evaporite minerals. Chemical weathering of silicate rocks(Eq. (7.23)) and carbonate rocks (Eq. (7.29)) is the primary source of environ-mental basicity. Chemical weathering involving disulfide (or sulfide) oxidationand ferric iron oxide precipitation produces soluble sulfate ions and acidity(Eq. (7.35) and Eq. (7.36)). Congruent dissolution of evaporite rock minerals(Eq. (7.37)) is a source of soluble sulfate ions but has little impact on acid-basechemistry in natural waters. The acidity associated with the complete oxidationof ferrous sulfide minerals (Eq. (7.35) and Eq. (7.36)) results 1627% from thehydrolysis of the weak acid hexaquairon(3) during the precipitation of ferriciron oxides and 7384% from the oxidation of sulfide itself.7.4. ATMOSPHERIC GASES7.4.1. Carbon Dioxide: Above GroundThe carbon dioxide content of Earths atmosphere (Table 7.4) is 3:87 104 or103:41 atmospheres (atm). Of the ten most abundant gases in Earths atmo-sphere, carbon dioxide CO2 g is the most soluble in water (Table 7.4). Regard-less of its water solubility, gaseous carbon dioxide CO2 g is not necessarily inThe congruent dissolution of gypsum CaSO4 2H2O s in sedimentary rocksgenerates a neutral salt solution:CaSO4 2H2O s gypsum! Ca2 aq SO24 aq 2 H2O l 7:37Congruent dissolution reactions produce solutions where the mole ratio ofthe ions in solution is identical to their mole ratio in the solid (Eq. (7.37)). Thehighly soluble minerals typical of evaporite sedimentary rockshaliteNaCl s , sylvite KCl s , fluorite CaF2 s , and a host of borate mineralspre-cipitate from concentrated salt solutions or brines and dissolve congruently.The reaction depicting the chemical weathering of Earths silicate crust(7.23) is an incongruent dissolution reaction because two of the constituentoxidesAl2O3 s and Fe2O3 s behave as inert substances and do not sus-tain a solute mole ratio identical to the composition of the solid.7.3.5. Evaporite RocksCO2 aq over carbonic acid H2CO3 aq by a ratio of 555-to-1:27Source: Sander, 2009.Argon Ar 0.934 1:4 103Carbon dioxide CO2 0.0387 3:3 102Neon Ne 0.001818 4:5 104Helium He 0.000524 3:8 104Methane CH4 0.000179 1:4 103Krypton Kr 0.000114 2:5 103Hydrogen H2 0.000055 7:8 104Nitrous oxide N2O 0.00003 2:5 102TABLE 7.4 Composition and Henrys Law Constants of the Most AbundantGases in Earths AtmosphereGas Volume % KH mol L1 atm1 Nitrogen N2 78.084 6:1 104Oxygen O2 20.946 1:3 103Soil and Environmental Chemistry0CO2 aq H2O l $ H2CO3 aq 7:39Though many books identify carbonic acid H2CO3 aq as the weak acid inacid dissociation reactions (7.40), and others symbolize aqueous carbon diox-ide CO2 aq as the effective carbonic acid H2CO3 aq , the most chemicallyaccurate reaction is (7.41). The second acid dissociation step is given by reac-tion (7.42).H2CO3 aq $ H aq HCO3 aq Ka1,H2CO3 aq 3:64 104 7:40CO2 aq H2O l $H aq HCO3 aq Ka1,CO2 aq 4:30 107 7:41HCO3 aq $H aq CO23 aq Ka2,CO2 aq 4:68 1011 7:42Ifwe combine the hydration reaction (7.39)with the carbonic acidH2CO3 aq hydrolysis reaction (7.40), we obtain the aqueous carbon dioxide CO2 aq aciddissociation constant Ka1,CO2 aq for reaction (7.41). Carbonic acid H2CO3 aq is a significantly stronger acidKa1,H2CO3 aq 3:64 104than aqueouscarbon dioxide CO2 aq Ka1,CO2 aq 4:30 107.Khydration Ka1,H2CO3 aq aH2CO3 aq aCO2 aq aH aHCO3aH2CO3 aq Ka1,CO2 aq 1:18 103 3:64 104 4:30 107 7.4.2. Carbon Dioxide: Below GroundRespiration by soil organismsplant roots and soil microbescombined withsluggish gas exchange between soil pores and the aboveground atmosphereresult in CO2 g partial pressures 10 to 100 times higher in soil pores relativeto the aboveground atmosphere. The significance of variations in CO2 g partial pressure is illustrated in Box 7.1. Aqueous carbon dioxide CO2 aq is classified as a weak acid, but it remains an important geochemicalweathering agent.7.4.3. Sulfur OxidesThe two most important sulfur oxides in Earths atmospheresulfur dioxideSO2 g and sulfur trioxide SO3 g enter the atmosphere through both naturaland anthropogenic processes, the former being emissions originating in volca-nate theH activity to be a simulation variable (select totalwhen generating the inputmatrix)4 and enter any concentration; designate CO2 g pressure to be a simulationChapter 7 Acid-Base Chemistry 271constant (select free when generating the input matrix) and enter pCO2 3:87 104 atm (the abovegroundCO2 g partial pressure). In the second simulation,set up the input matrix similar to the first simulation, except this time enter pCO2 3:87 102 atm (soil-pore CO2 g partial pressure). The pH drops one full unit, from5.5 to 4.5, and the total dissolved carbonate (aqueous carbon dioxide, bicarbonateplus carbonate) increases from 2:18 105 mol L1 to 1:92 103 mol L1.nic eruptions, and the latter being emissions resulting largely from the com-bustion of coal and petroleum.Sulfide minerals in magma react with atmospheric oxygen at high tem-peratures characteristic of eruptions to produce SO2 g and SO3 g in volcanicemissions. Sulfide compounds in coal and petroleum undergo combustionreactions to produce the SO2 g and SO3 g in power plant and auto emissions.Thiophene (Structure 1), thioether (Structure 2), and thiol (SH) representorganosulfur species in petroleum and coal (George and Gorbaty, 1989;Gorbaty, George et al., 1990; Waldo, Carlson et al., 1991; Waldo, Mullinset al., 1992). Coal and crude petroleum also contain sulfide and disulfideminerals.Box 7.1You can verify the impact of increasing pCO2 by performing the following ChemEQLsimulations using the two componentsH and CO2 g . In the first simulation, desig-4. See the ChemEQL Manual under the section Set Up a Matrix.Soil and Environmental Chemistry272Structure 1. ThiopheneStructure 2. ThioetherSulfur dioxide SO2 g is extremely water-soluble. The Henrys Law con-stant for Eq. (7.43) is KH 1:2 mol L1 atm1 (Sander, 2009), but there isno evidence that sulfurous acid H2SO3aq molecules exist in aqueous solu-tion. Aqueous sulfur dioxide SO2 aq has the acid dissociation constant(Eq. (7.44)) of a weak acid.SO2 g $ SO2 aq 7:43SO2 aq H2O l $ H aq HSO3 aq Ka1, SO2 aq 1:5 102 7:44Sulfur trioxide is also extremely water-soluble, combining with water(Eq. (7.45)) to form sulfuric acid H2SO4aq. Sulfuric acid has the acid disso-ciation constant (Eq. (7.46)) of a strong acid, but hydrogen sulfide HSO4 aq (Eq. (7.47)) must be considered a weak acid comparable in strength to aque-ous sulfur dioxide SO2 aq (Eq. (7.44)).SO3g H2Ol $ H2SO4aq 7:45H2SO4 aq H2O l $ H aq HSO4 aq Ka1, SO3 aq 103 7:46HSO4 aq $ H aq SO24 aq Ka1, SO3 aq 1:02 102 7:47The oxidation of sulfur dioxide SO2 g to sulfur trioxide SO3 g appearsto be catalyzed by hydroxyl radicals HO g in the atmosphere (Margitan,1988):SO2 g HO g hydroxylradical! HSO3 g hydroxysulfonylradical7:48HSO3 g hydroxysulfonylradicalO2 g ! SO3 g HOO g hydrogen superoxideradical7:49A major source of hydroxyl radicals HO g is the photolysis of ozone(Eq. (7.50)) to produce photo-excited atomic oxygen O g . Photo-excitedatomic oxygen O g reacts with water molecules (Eq. (7.51)) to yieldChapter 7 Acid-Base Chemistry 273Biogenic nitrogen oxide emissionsdinitrogen oxide N2O g and nitro-gen monoxide NO g are the product of denitrification by soil bacteria.Denitrifying bacteria are anaerobic bacteria that rely on nitrate respiration(see Chapter 8) when soils are waterlogged.Nitrogen compounds in coal and petroleum undergo combustion reactionsto produce the nitrogen oxides NOx in power plant and auto emissions.Pyridine (Structure 3) and pyrrole (Structure 4) represent organonitrogen spe-cies in petroleum and coal (Snyder, 1970; George and Gorbaty, 1989;5. Dinitrogen oxide N2O g is a relatively inert gas in the troposphere but reacts with ultraviolet7.4.4. Nitrogen OxidesAtmospheric chemists use the symbol NOx to denote nitrogen monoxideNO g and nitrogen dioxide NO2 g in Earths atmosphere. Anthropogenicnitrogen oxide emissions from the combustion of petroleum and coal are pre-dominantly NOx compounds.5hydroxyl radicals HO g .O3 g !sunlight O g O2 g 7:50O g H2O g ! 2 HO g hydroxylradical7:51Another source of photo-excited atomic oxygen O g is the photolysis ofnitrogen dioxide NO2 g (Li, Matthews et al., 2008):NO2 g nitrogendioxide!sunlight NO g nitrogenmonoxideO g 7:52Alkaline compounds in atmospheric water droplets catalyzed the conversionof sulfur dioxide to sulfuric acid (Altshuller, 1973), resulting in a plateau ofsulfuric acid levels in acid rain when sulfur dioxide levels exceed a certainthreshold (Appendix 7C).Some of the strong base released by chemical weathering (Eq. (7.24)) isneutralized by sulfuric acid deposition originating with sulfur oxides inthe atmosphere and sulfide mineral weathering (Eqs. (7.35) and (7.36)). Theproduct of this acid-base reaction is the following neutral salt solutionthat requires the sulfate correction in Eq. (7.33) used by Garrels andMackenzie (1971):CaO s strong base H2SO4strong acid!neutralization Ca2 aq SO24 aq H2O l 7:53radiation in the stratosphere to form nitrogen monoxide and, ultimately, nitric acid.Soil and Environmental Chemistry274Gorbaty, George et al., 1990; Waldo, Carlson et al., 1991; Waldo, Mullinset al., 1992).Structure 3. PyridineStructure 4. PyrroleSome of the nitrogen dioxide NO2 g in the atmosphere is produced by theoxidation of nitric oxide NO g :2 NO g N 2 O2 g !oxidation 2 NO2 g N 4 7:54The hydrolysis of nitrogen dioxide NO2 g produces equal quantities of nitricHNO3 aq and nitrous acid HNO2 aq . Reaction (7.55) is a disproportionationreaction because the net formal oxidation state of nitrogen (4) remainsunchanged:2 NO2 g N 4 H2O l !hydrolysis HNO3 aq N 5 HNO2 aq N 3 7:55Benkovitz and colleagues (1996) found that nitrogen emissions from anthropo-genic and biogenic sources were roughly equal on the global scale, while cur-rent sulfur emissions are predominantly anthropogenic. The molar nitrogen-to-sulfur ratio of atmospheric emissions ranges (Figure 7.3) from 6:5 104 to1:0 104. Industrial and population centers with high sulfur oxide emissionsare characterized by N/S ratios 400. This variation in the nitrogen-to-sulfur ratio ofatmospheric emissions reflects the importance of biogenic emissions.Selecting data from Figures 7.4 and 7.5 for sulfate and nitrate wetdeposition and converting units from kg ha1 to mol ha1, we can confirmthe trend in the molar N/S depositional ratios reported by Benkovitz and col-leagues (1996). The molar N/S depositional ratio for a site in western Kansasis 19 compared to a deposition ratio of 0.9 for a site in southeastern Ohio.Latitude500100.0010.001.000.10N/S Molar Ratio0.0150FIGURE 7.3 Mole ratio of nitrogen to sulfur in atmospheric emissions reflects the relativeimportance of industrial and biogenic emissions. Source: Reproduced with permission fromBenkovitz, C.M., Scholtz, M.T., et al., 1996. Global gridded inventories of anthropogenicemissions of sulfur and nitrogen. J. Geophys. Res. 101(D22), 2923929253.Chapter 7 Acid-Base Chemistry 275FIGURE 7.4 Sulfate wet deposition in the contiguous United States during 2008 (NationalAtmospheric Deposition Program, National Trends Network).27FIGURE 7.5 Nitrate wet deposition in the contiguous United States during 2008 (NationalAtmospheric Deposition Program, National Trends Network).Soil and Environmental Chemistry67.5. AMMONIA-BASED FERTILIZERS AND BIOMASSHARVESTINGNitrogen Cycling in Natural LandscapesSoil acidification is a natural consequence of chemical mineral weatheringpromoted by soil respiration and leaching in humid climates. Plant nutrientuptake does not contribute to soil acidification because any components rele-vant to soil acid-base chemistry in standing biomass ultimately return to thesoil when plant residue decomposes. Plant residue removal by agricultureand forestry exports plant ash from managed ecosystems, and the use ofammonia-based fertilizers, imported to replace nutrients lost by harvest, dra-matically accelerates soil acidification.The nitrogen cycle involves several reactions that transform nitrogen by elec-tron transfer. Understanding the acid-base implications of the nitrogen cycle is,therefore, our point of departure. Nitrogen fixation (Eq. (7.56)) consumes eightprotons as it forms two NH4 molecules for every N2 molecule fixed, regardlessof the specific nitrogen fixation process (biological or abioticatmospheric orindustrial). Mineralization of biological nitrogen compounds, leading to the assim-ilation of ammonium nitrogen (regardless of its origin), does not lead to a change innitrogen oxidation state and has no impact on environmental acid-base processes:N2 g N 0 8 H 6 e !nitrogen fixation 2 NH4 aq N 3 7:56Chapter 7 Acid-Base Chemistry 277the soil profile, there is little organic matter to sustain bacterial nitrate respi-ration (see Chapter 8). Remote nitrate reduction is most likely to occur inorganic-rich sediments as groundwater discharges into a stream hyporheic(or lake hypolentic) zone.2 NO3 aq N 5 16 e 14 H2O l !assimilatorynitrate reduction2 NH4 aq N 3 20 OH7:60The only significant contributions to soil acidification from nitrogen cycling innatural landscapes arise from nitrate leaching losses (i.e., remote nitrate reduc-tion). Agricultural landscapes export biomass and rely on fertilization to replacenutrients lost by export. Nitrate fertilizer import constitutes hydroxyl importreleased during assimilation (Eq. (7.60))while the import of ammonia-basedfertilizer (urea, ammonia, and ammonium salts) constitutes acid import2 NO3 aq N 5 12 H 10 e !denitrification N2 g N 0 6 H2O l 7:59At steady state, nitrogen fixation (Eq. (7.56)) replaces NO3 lost by leachingand denitrification. Nitrate leaching is equivalent to hydroxyl export fromthe soil where nitrate reduction occurs at the remote location (Eq. (7.60)).Keeping in mind most soils have little anion exchange capacity (humic col-loids and clay minerals are cation exchangers), once nitrate has leached belowassimilate NO3 taken up from solution, reversing the nitrification reaction:2 NH4 aq N 3 6 H2O l !nitrification 2 NO3 aq N 5 20 H 16 e 7:572 NO3 aq N 5 20 H 16 e !assimilatorynitrate reduction2 NH4 aq N 3 6 H2O l 7:58Denitrification (Eq. (7.59)) is a biological reduction process (see Chapter 8)that consumes 12 protons as it forms 1 N2 molecule for every 2 NO3 mole-cules reduced, completing the nitrogen cycle. The 20 protons consumed bynitrogen fixation (Eq. (7.56)) and denitrification (Eq. (7.59)) balance the 20protons produced during nitrification (Eq. (7.57)).Nitrification (Eq. (7.57)) is a biological oxidation process (see Chapter 8) thatyields 20 protons as it forms 2 NO3 molecules for every 2 NH4 molecules oxi-dized. Nitrification is an essential nitrogen-cycle transformation. Plants, fungi,bacteria, and archaea must reduce NO3 to NH4 (Eq. (7.58)) if they are toreleased during nitrification (Eq. (7.56)).Soil and Environmental Chemistry278Turning our attention to the right-hand side of Figure 7.6, total accumulatedcations in plant tissue is equal to the persistent cations (122.0 cmolc L1), whiletotal accumulated anions (122.0 cmolc L1) is the sum of persistent anions(30.4 cmolc L1), conjugate bases (59.5 cmolc L1) derived from weakorganic acids in plant tissue, and sulfate that has not been assimilated (32.1cmolc L1). Reaction (7.12) relates the formation of organic conjugate basesin plant tissue to the consumption of hydroxyl ions, a reaction that is equiva-lent to the formation of bicarbonate when a strong base reacts with the weakacid aqueous carbon dioxide (Eq. (7.26)).Total cation uptake is the sum of the persistent cations (122.0 cmolc L1)and the organic nitrogen (452.8 cmolc L1)which was taken up as NH4 beforebeing assimilated as organic nitrogen. Excess cation uptakewhich must equalthe hydrogen ions excreted by roots into the rhizosphere (362.9 cmolc L1)7.6. CHARGE BALANCING IN PLANT TISSUEAND THE RHIZOSPHERECharge neutrality constrains ion uptake by plant roots, ion composition inplant tissue, and ion composition of the rhizosphere. The plant tissue chargebalance, however, must account for postuptake assimilatory nitrate reduction(Eq. (7.60)) and sulfate reduction (Eq. (7.61)).SO24 aq S 6 8 e 5 H2O l !assimilatorysulfate reductionHS aq S 2 9 OH 7:61An excellent accounting of plant tissue and rhizosphere charge balancing inresponse to nitrate and ammonium uptake appears in van Beusichem andcolleagues (1988). Unfortunately, the results appear in tabular form, makingit difficult to visualize the contributions of each component to respectivecharge balance equations.Figure 7.6 illustrates the cation and anion accounting required to balancecharge in plant tissue and in the soil rhizosphere. The data are from an uptakeexperiment where nitrogen is supplied as the ammonium cation (van Beusi-chem, Kirby et al., 1988). Persistent cations (122.0 cmolc L1)Na, K,Ca2, and Mg2and persistent anions (30.4 cmolc L1)Cl andH2PO4 appear on the left side of Figure 7.6. The ammonium-N in theexperiment has been completely assimilated, which means that all NH4 accu-mulated in plant tissue has been converted into organic nitrogen (330.8 cmolcL1). Sulfate is not persistent because a fraction is reduced to sulfide(Eq. (7.61)) and converted to bioorganic sulfur compounds. Total sulfur accu-mulated in plant tissue exists either as sulfate-S (32.1 cmolc L1) or assimi-lated organic sulfur (20.7 cmolc L1). Ion uptake in this experiment resultsin a net excretion of hydrogen ions by the roots into the rhizosphere (362.9cmolc L1).is equal to the total cation uptake minus the total accumulated anions.FIGURE 7.6 Cation and anion balances in plant tissue must account for the assimilation of both nitrate and sulfate. The ion components appear on the left, andsummed components appear on the right, based on data from (van Beusichem, Kirby et al., 1988).Chapter7Acid-BaseChemistry279(7.60) is less than the base counted as EB. If the EB=N ratio of harvested bio-Soil and Environmental Chemistry2807.6.1. Water AlkalinityEarlier in this chapter, we learned that water containing dissolved carbondioxide requires a special reference point to distinguish the presence of strongacids and bases. Absent weak acids or bases, acidity and basicity are definedrelative to pH 7 or the water reference level determined by the equilibriumconstant Kw for the spontaneous dissociation of water (Eq. (7.6)).Earths atmosphere (Table 7.4) contains CO2 g at a partial pressure ofpCO2 3:87 104 atm, and, as a consequence, all natural waters are steepedin CO2 aq . The presence of CO2 aq demands a pCO2 -dependent referencepoint to distinguish the presence of strong acids and bases in aqueous solu-tion: the aqueous carbon dioxide reference level (Eq. (7.20)). Environmentalchemists distinguish between mineral acidity AM and total alkalinity AT rela-tive to the aqueous carbon dioxide reference level. The following sectionextends the chemical concept of the aqueous carbon dioxide reference levelto the geochemical concept of alkalinity AT .mass is greater than 1, the loss of organic nitrogen in the biomass will increaseacidity because the export of base associated with remote denitrification (7.59)and assimilatory nitrate reduction (7.60) is greater than the base counted asEB. Plants that have high rates of nitrogen assimilation relative to their ten-dency to accumulate excess base in their biomass have low EB=N ratios.Barak and colleagues (1997) trace the impact of agriculture on soil acidifica-tion to two factors: nitrification (Eq. (7.56)) of nitrogen fertilizer in excess of thenitrogen assimilated in biomassobviously nitrate fertilizers do not contribute toacidity arising from nitrificationand biomass harvest preventing organic conju-gate bases (see Figure 7.6) in plant tissue from returning to the soil.Net assimilated cations equals organic nitrogenrepresenting assimilatedNH4 minus organic sulfurrepresenting SO24 anions lost by assimilation.Plant species vary considerably in their tendency to accumulate cationsand anions and to assimilate ammonium, nitrate, and sulfate. Pierre andBanwart (1973) devised a plant tissue parameter that rates the impact of bio-mass harvest on soil acidification. The Pierre-Banwart EB=N ratio comparesthe total hydroxyl content of plant tissue EB (total persistent cations minustotal persistent anions equivalent to assimilated sulfate plus accumulatedorganic conjugate base in Figure 7.6) with the hydroxyl content derived fromnitrogen assimilation Norg:Excess BaseNorg EBN7:62If the EB=N ratio of harvested biomass is less than 1, then the export of baseassociated with remote denitrification (7.59) and assimilatory nitrate reductionChapter 7 Acid-Base Chemistry 281silicic acid H4SiO4 aq ) to the acid-base chemistry of natural waters. Theconjugate base H3SiO4 is the only significant contributor to silicate alkalinityASi in natural waters:ASi CH3SiO4 2 CH2SiO24 CH3SiO4 7:67The dissolution reaction (7.68) of the silicon dioxide mineral opalan amor-phous polymorph of quartzcombined with the first aqueous silica acid dis-sociation reaction (7.69) yields an expression (7.70) for the activity of theThe first term subtracts the chloride concentration from the two most abundantalkaline ions, correcting for the dissolution of halite NaCl s and sylvite KCl s in evaporite rocks. The second term is simply the right-hand side of the Garrelsand Mackenzie expression, which subtracts the sulfate concentration from thetwo most abundant alkaline earth cations, corrected for the dissolution of theevaporite mineral gypsum.AC CNa CK CClevaporites 2 CCa2 CMg2 CSO24evaporites !7:667.6.3. Silicate AlkalinitySilicate alkalinity ASi accounts for the contribution of aqueous silica (i.e.,Carbonate alkalinity ACas it is defined by water chemists and geochemistsis simply an expression of the aqueous carbon dioxide proton reference level asit appears on the right-hand side of expression (7.21):AC CHCO3 2 CCO23 COH CH3O 7:63Deffeyes (1965) observed that regrouping the charge balance expression for natu-ralwaters into the total charge concentration of permanent ions and the total chargeconcentration of changeable ions results in an expression where carbonate alkalin-ity AC (Eq. (7.63)) is nothing more than the sum of the permanent-ion charges(Eq. (7.64)). Deffeyes simply extended (Eq. (7.19)) by including all of the majorstrong base cationsCa2 aq , Mg2 aq , Na aq , and K aq and all ofthe major strong acid anionsSO24 aq and Cl aq in natural waters:CH CNa CK 2 CCa2 2 CMg2 CCl 2 CSO24 CHCO3 2 CCO23 COH 7:64AC CNa CK 2 CCa2 2 CMg2 CCl 2 CSO24 7:65Expression (7.65) (which combines Eq. (7.63) and Eq. (7.64)) resembles an ear-lier empirical expression (7.33) proposed by Garrels and Mackenzie (1971).Regrouping (7.65) by taking (7.33) into account results in expression (7.66).7.6.2. Carbonate Alkalinityconjugate base appearing in (7.67).ate alkalinity AC.7.6.4. The Methyl Orange End-PointTotal alkalinity is the equivalent6 concentration (molc L1) of all weak-acidconjugate bases in solution (carbonates and silicates).7 The operational defini-tion of total alkalinity is the methyl orange (CAS 547-58-0) end-point in aTABLE 7.5 Conjugate Acid-Base Pairs in Aqueous Silica SolutionsWeak Acid Conjugate BaseH O+ H O6. An acid-base equivalent is the amount of a conjugate base that will combine with a mole ofhydrogen ions H.7. Phosphates and other weak acids are typically insignificant compared to the carbonates andSoil and Environmental Chemistry282silicates in freshwater systems. Borate conjugate acid-base pairs attain significant concentrationsopalKs0 Ka1 aH aH2SiO24 102:71 109:847:70Table 7.5 lists the conjugate acid-base pairs in an aqueous silica solution. Theboldface solute species are the same species that define the aqueous silica pro-ton reference level:COH CH3SiO4 2 CH2SiO24 CH3O 0 7:71The boldface species designate the proton balance species of the aqueous sil-ica SiO2 aq reference level at pH 6.3, which is a bit less than pH unit higherthan the aqueous carbon dioxide proton reference level used to define carbon-H4SiO4 aq $ H aq H3SiO4 aq Ka1 aH aH3SiO4aH4SiO4 109:847:69SiO2 s 2 H2Ol $ Haq H3SiO4 aqSiO2 s opal2 H2O l $ H4SiO4 aq aqueous silicaKs0 aH4SiO4 102:71 7:683 2H4SiO4 aq H3SiO4 aq H3SiO4aq H2SiO24 aq H2O OHin marine systems.earth cations in Earths crustsodium, potassium, magnesium, and calciumChapter 7 Acid-Base Chemistry 283soil pore water is typically dominated by Ca2 ions unless saline groundwaterdischarge or mineral weathering in arid climates alters the pore water chemistry.In Chapter 3 we learned that smectite clay minerals were capable of osmoticswelling if saturated by either Na or Li ions (the latter being inconsequentialin most soil or groundwater settings), but smectite clays were limited to crystal-line swelling if saturated by larger alkali ions and divalent alkaline earth cations.This section extends the clay chemical impact of Na ions beyond swellingbehavior and considers the role of alkalinity in altering pore water chemistry.We begin with a discussion of the impact of the clay fraction on soilmechanical and physical properties (soil strength, hydraulic conductivity,strong acid titration. The color change associated with the methyl orange end-point begins at pH 4.4, near the second equivalence point for carbonate:HInredaq $ H aq Inyellowaq Ka aH aInaHIn 103:7 7:72Alkalinity defined by the methyl orange end-point titration measures all of theconjugate bases in a water sample whose proton reference level is at a pHabove 3.7. The most important conjugate base in groundwater besides the car-bonate species is H3SiO4 aq .7.6.5. Mineral AcidityMineral acidity AM (e.g., acid rain or acidic mine drainage water) applies tosolutions whose pH is lower than solutions containing only aqueous carbondioxide CO2 aq , indicating the presence of strong mineral acids, typicallynitric or sulfuric acid. For solutions containing sodium hydroxide NaOH,nitric acid HNO3, and aqueous carbon dioxide CO2 aq , mineral acidity AMis simply the negative of carbonate alkalinity AC:Charge Balance : CNa CH CHCO3 2 CCO23 COH CNO3CO2aq Reference Level : CNO3 CNa CH COH CHCO3 2 CCO23 Mineral Acidity : AM AC 7:737.7. MECHANICAL PROPERTIES OF CLAY COLLOIDSAND SOIL SODICITYThis section examines the impact of Na ions on clay colloid chemistry.Given the relative abundance of the four most common alkali and alkalineand erodibility) and continue with an examination of the effect that Na ionshave on these same properties. Finally, we discuss the pore water chemistryrequired to enrich the exchange complex in Na ions while depleting it ofCa2 and Mg2 ions.7.7.1. Clay Plasticity and Soil Mechanical PropertiesThe geotechnical properties of soilthe strength and hydraulic conductivityof the soil fabric and its resistance to particle detachment during erosiondepend on the relative amount of clay-size mineral particles. Clay-size min-eral particles, regardless of mineralogy, exhibit behavior unlike granular-size(i.e., silt and sand) particles. The specific particle diameter separating theclay- and granular-size fractions varies somewhat among Earth science andengineering communities, but the primary distinction appears when thewithout cracking. A medium plastic soil forms a ribbon 2.5 to 5 cm in length with-Soil and Environmental Chemistry284out cracking. A slightly plastic soil forms a ribbon less than 2.5 cm without crack-ing. Soil textural classes that are typically nonplastic include sand, loamy sand,and silt. These textural classes contain less than 7 to 15% clay, depending on siltcontent.surface-to-volume ratio or surface area per unit mass has a measureableimpact on the interactions between water and mineral surfaces.Soil mechanics distinguishes between the granular-size fraction (silt plussand: 2 mm < d < 2 mm) and the clay-size fraction (d < 2 mm) because thegranular-size fraction is never plastic, while the clay-size fraction exhibitsplasticity over a range of water contents. The USDA defines plasticity asthe property of a soil that enables it to change shape continuously underthe influence of applied stress and to retain that shape on removal of thestress (Staff, 1987). In other words, a soil- or particle-size fraction is plasticif it can be molded (i.e., retain its shape) and deformed without cracking (i.e.,change shape continuously). Soil scientists use the ribbon test (Box 7.2) as afield estimate of soil clay content. Here, a moist soil sample is moldedinto a ball and then pressed into a ribbon between the thumb and forefinger(Figure 7.7). Material composed solely of granular particles (silt and sand)is nonplastic and cannot be molded into a ribbon. Soil containing significantamounts of clay can be molded into a ribbon. As the clay-size fractionBox 7.2 The Ribbon TestSoil mineral particles are typically separated into three particle-size fractions:sand (50 mm to 2.0 mm), silt (2 mm to 50 mm), and clay (d 2 mm)soil beingrestricted to the solid fraction that passes a 2 mm sieve. Soil texture is usually acomplex size distribution represented by the relative proportions of the three par-ticle-size fractions (Staff, 1987): sand, silt, and clay.A highly plastic soil can be molded into a ribbon greater than 5 cm in length5increasesregardless of mineralogythe force required to mold a soil sam-ple and form a ribbon increases.Plasticity arises from the interaction between water molecules and particlesurfaces. These interactions are always present but have a discernible effecton soil mechanical properties when clay-size particles are present in sufficientquantities to influence the contact between granular particles. When the meandiameter of mineral particles, regardless of mineralogy, falls below 2 mmcorresponding to roughly 5 m2 g1the interaction of water with the mineralsurface lead to the behavior we know as plasticity.Nonswelling claysiron oxides, aluminum oxides, and nonswelling claymineralsexhibit more or less the same plasticity characteristics. Although itis possible to synthesize oxide particles in the laboratory with surface areas of100200 m2 g1, oxide minerals rarely occur in the fine clay fraction (d 0.2mm) where the surface area exceeds 50 m2 g1. Swelling clay minerals exhibitplasticity over a larger moisture range because the interlayer adds to the effectivesurface area. The typical surface area of a swelling clay mineral is 750 m2 g1.The geotechnical engineering community assesses the mechanical propertiesof soil and the clay-size fraction using Atterberg Limits: shrinkage limit, plasticFIGURE 7.7 Molding moistclay between forefinger andthumb produces a clay ribbon.Chapter 7 Acid-Base Chemistry 28limit, and liquid limit. Our focus will be on the plastic and liquid limits. Asso-ciated with the Atterberg Limits are several derived parameters: plasticityindex, liquidity index, and activity index.The geotechnical community expresseswater contentw as a fraction of themin-eral-solids massms (Figure 7.8). The plastic limit wP is the lowest water content wat which clay or soil exhibits plastic behavior, the highest water content being theliquid limitwL. BetweenwP andwL there is sufficientwater formoldedmineral par-ticles to deform without cracking. Above wL, plasticity is lost and the materialbehaves like a liquid, unable to retain a molded shape. Below wP, soil containingsufficient clay for plasticity cannot be molded into a ribbon for lack of moisture.The plasticity index IP is a measure of the water content range over whichthe soil is plastic:IP wL wP 7:7428The activity index IA normalizes the plasticity index IP of a soil by its claycontent. A plot of IP as a function of clay content c (assuming the mineralogyof the clay remains unchanged) yields a straight line whose slope is the activ-ity index IA. Swelling clays have a significantly higher activity index IA(1 < IA < 7) than nonswelling clays (IA 0:5):IA IP100 c 7:757.7.2. Clay Content and Granular Particle ContactsWe can estimate the amount of clay needed to prevent direct contact betweengranular mineral particles at water contents typical of a saturated soil. Refer-ring to Figure 7.8, the volume available for water and clay in a soil consistingof clay and granular particles is the product of the void ratio of the granularfraction eg and the total volume of all granular particles Vg:Vvoids eg Vg eg 1 c msr 7:76FIGURE 7.8 Mass-volume relations in a water-saturated soil mixture.Soil and Environmental Chemistry6mineralThe void ratio eg is related to bulk density rbulk and mineral particle densityrmineral as follows:eg VvoidsVs rmineral rbulkrbulk7:77The volume of water saturating all pores Vw and the volume occupied by clayVc are both a function of the mass of the mineral solids ms, the mass fraction(as defined in Figure 7.8) and the density of each component:Vvoids Vw Vc w Mg Mg1 ms Mg rw Mg m3 c Mg Mg1 ms Mg rmineral Mg m3 7:78Setting these expressions equal to one another and simplifying yield the fol-lowing expression for the amount of clay needed to prevent direct contactChapter 7 Acid-Base Chemistry 287between granular particles:1 c ms egrmineral w msrw c msrmineral c eg1 eg rmineralrw eg rw !w eg1 eg rmineral1 eg wThe void ratio eg is typically 0.85, and the geotechnical community uses amineral particle density of rmineral 2:75 Mg m3. The water content ofgranular particles at field capacity wFC is on the order of 0.10 to 0.20:c 0:46 wFC 1:43 7:79The amount of clay c sufficient to coat granular particles and prevent directcontact (7.79) is on the order of 17% for a granular fraction consisting of siltand as high as 30% for a granular fraction consisting of sand.The activity index IA of the clay fractionits tendency to confer plasticityon the whole soilalso depends on the exchangeable cations. In particular,clay activity index IA tends to decrease as the clay fraction becomes saturatedby Na ions; activity index IA increases as the exchange complex is domi-nated by Ca2 (and to a lesser extent, Mg2) ions.Soil fabric derives its load bearing and shear strength from the contactbetween mineral grains, and clay plasticity adds considerably to soil fabricstrength. Furthermore, the pore structure in soil results from particle displace-ment during wetting-drying cycles, freezing-thawing cycles, and bioturba-tion.8 Clay plasticity preserves an open soil fabric, promoting gas exchangebetween the soil and aboveground atmosphere andof particular interest inthis sectionhydraulic conductivity.The empirical hydraulic conductivity parameters in Chapter 2, Appendix 2F,represent the maximum hydraulic conductivity for each soil texturethat is, theclay fraction retains sufficient plasticity to maintain an open soil fabric with max-imum pore size and, hence, hydraulic conductivity. Chemically altering soils bysaturating the exchange complex with Na ions lowers the activity index IA ofthe clay fraction, resulting in significantly lower hydraulic conductivity values.Figure 7.9 illustrates this behavior by showing the effect of two soil treat-ments on the activity index IA of soil clay (Lebron, Suarez et al., 1994). Thenatural soils (filled circles) are saline-sodic, with Na ions occupying 90% ormore of the exchange complex and a pore water electrical conductivity EC in8. Bioturbation is the rearrangement of solid particles in soil and sediment caused by the activityof organisms.Soil and Environmental Chemistry288FIGURE 7.9 The activity index IA of soil clay in 19 saline-sodic soils from Spain: (a) filled cir-the range of 6.2 to 40.5 dS m1. Replacing Na ions with Ca2 ions by wash-ing the soils with calcium chloride solutions (open triangles) increases theactivity index IA of the clay fraction. Washing the soils with pure water tolower salinity reduces the fraction of Na ions occupying the exchange com-plex to 20 to 30% and significantly lowers clay index IA.Geotechnical engineers and soil scientists (Resendiz, 1977; Lebron, Suarezet al., 1994) associate soil erodibility with both clay content and activity indexIA. Soil erosion begins with the detachment of soil particles by raindropimpact or the impact of fine windblown mineral particles bouncing acrossthe soil surface. Soils with low clay contents or containing low-activity indexIA clay are more susceptible to detachment and thus are more erodible. Theaccumulation of sodium ions in the exchange complex of soil clays is knownto increase soil erodibility.7.7.3. SodicitySoil scientists apply several criteria to identify soils that either exhibit lowhydraulic conductivity or are at risk for developing low hydraulic conductivityas a result of clay chemistry changes caused by Na ions accumulating on theclay exchange complex. Geotechnical engineers have no universal term forcles represent the untreated soil activity index IA, (b) open triangles represent the activity index IAfor soils washed with calcium chloride to replace exchangeable Na ions with Ca2 ions, and(c) open squares represent the activity index IA for soils washed with pure water to lower salinity.(modified from Lebron, Suarez et al., 1994).TABLE 7.6 USDA Natural Resource Conservation Service SodicityClassification and CriteriaSoil Type Exchangeable Sodium Soil Water Electrical Soil pHChapter 7 Acid-Base Chemistry 289soils that lose strength when Na ions accumulate on the clay exchange com-plex. Both ESP and clay activity index IA are used to identify highly erodibleor dispersive soils (Resendiz, 1977; Lebron, Suarez et al., 1994). The erodibilitycriterion based on clay activity index IA does not explicitly assess the exchange-able Na ion fraction. Quick clays9 owe their susceptibility to liquefaction toNa ion accumulation on the clay exchange complex, but the criteria used toassess quick clays do not explicitly assess the exchangeable Na ion fraction.The USDA Natural Resource Conservation Service employs three criterialisted in Table 7.6to identify sodicity risk: exchangeable sodium percentage,total dissolved salts as measured by electrical conductivity of soil pore water,and soil pH. We will examine the implications of each criterion to gain anunderstanding of the chemical processes at work in sodic soils.7.7.4. Sodium-Ion Accumulation on the Clay ExchangeComplex: ESPPercentage Conductivity*Saline ESP < 15 ECsw > 4dS m1 pH < 8:4Saline-Sodic ESP > 15 ECsw > 4dS m1 pH < 8:4Sodic ESP > 15 ECsw < 4dS m1 pH > 8:4*SI units for electrical conductivity are siemens per meter: S m1.The exchangeable sodium percentage ESP is a familiar ion exchange param-eter: the equivalent fraction of exchangeable sodium ~ENa multiplied by 100(Eq. (7.80)). A common alternative parameter is the exchangeable sodiumratio ESR (Eq. (7.81)).ESP mNamNa 2 mCa2 2 mMg2 100 ~ENa 100 7:809. Quick clays are typically clay-rich coastal soils that owe their relatively high exchangeableNa equivalent fraction to their location and depositional history. Quick clays are usually depos-ited in coastal seawater followed by uplift above sea level. Quick clay formations remain rela-tively stable in situ but liquefy when remolded (i.e., disturbance of the soil fabric duringexcavation or construction of earthen structures). Liquefaction occurs because the in situ liquidlimit wL is metastable. Remolding disturbs the soil fabric, thereby eliminating metastability.ESR ~ENaCEC ~ENa~ENa~ECa2 ~EMg2 ESP=100 1 ESP=100 7:81The ESP is difficult to measure, leading the USDA Salinity Laboratory Staff(Allison, Bernstein et al., 1954) to search for an empirical relation betweensolution composition and the composition of the exchange complex. They dis-covered a linear relation between the solution sodium adsorption ratioSARP10defined by expression (7.82)and ESR. The solution SARP hasunits ofmmolc L1pbecause the charge concentration of each ion is typi-cally expressed in units of mmolc L1.SARP nNa mmolc L1 1=2 nCa2 nMg2 mmolc L1 q cNa mmol L1 cCa2 cMg2 mmol L1 q7:82Figure 7.10 plots the data from Allison and colleagues (1954) and lists the USDASalinity Laboratory empirical ESR, SARP relation. Most current references sim-plify the original empirical expression by dropping the intercept and shorteningSoil and Environmental Chemistry290sodium adsorption ratio SARP for arid U.S. soils. Source: Reproduced with permission fromAllison, L.E., Bernstein, L., et al., 1954. Diagnosis and Improvement of Saline and Alkali Soils.U. S. S. Laboratory. Washington, D.C., United States Government Printing Office, 160.FIGURE 7.10 The exchangeable sodium ratio (see Eq. (7.81)) is proportional to the practical10. The SARP does not apply activity corrections to ion concentrations.the proportionality factor to two significant digits. Relating ESR to SARP usingexpression (7.83) gives an alternative criterion for sodic soils: SARP > 12.ESR 1:5 102 SARP 7:83Appendix 7H summarizes Na,Ca2 cation exchange results for twoclosely related Wyoming smectite samples: American Petroleum Institutesample API-25 and Clay Minerals Society sample SWy-1. Appendix 7H alsoshows the effect of sodium exchange on the critical coagulation concentrationof smectite (Oster, Shainberg et al., 1980). Figure 7.11 plots data points alongthe critical coagulation concentration curve (Oster, Shainberg et al., 1980)(see Figure 7H.1) using the same relation as that appearing in Figure 7.10.Figures 7.10 and 7.11 demonstrate that Na,Ca2 exchange by soil clays(Figure 7.10) is closely related to the Na,Ca2 exchange behavior of smec-tite clays (Figure 7.11).The sodium adsorption ratio SARP (Eq. (7.82)) is related to the Gaines-Thomas exchange selectivity quotient (Eq. (7.84)) discussed previously inChapter 4. Despite references to the Gapon exchange selectivity quotient byUSDA Handbook 60 (Allison, Bernstein et al., 1954), a quasi-linear relationbetween ESR (Eq. (7.81)) and SARP (Eq. (7.82)) appears in Figure 7.11.The subtle curve and negative intercept in the data plotted in Figure 7.11are obscured by experimental and sample variation in Figure 7.10.Chapter 7 Acid-Base Chemistry 291FIGURE 7.11 The exchangeable sodium ratio (Eq. (7.81)) is proportional to the practicalsodium adsorption ratio SARP for Na,Ca2 cation exchange on Wyoming smectite API-25(data points follow critical coagulation concentration curve from Oster and colleagues (1980)using KGT 0:30 plotted in Appendix 7H, Figure 7H.2).2 NaexchangerCa2aq $solution2 Naaqsolution Ca2exchangerKcGT ~ECa2 C2Na~2Soil and Environmental Chemistry292KGT ~ENa~ECa2@ A CNaC1=2Ca2 cNa=1000cCa2p=1000pSARP 1000p KcGT ~E2Na~ECa2 !1=2 1000 KcGTp ~ENa~ECa2p !7:847.7.5. Pore Water Electrical Conductivity ECWA contributing factor to sodification is the combination of low annual rainfalland high rates of evapotranspiration that concentrate soluble salts in soil porewater. The USDA Soil Taxonomy defines the aridic soil moisture regime assoils whose moisture-control section11 is as follows:Dry12 in all parts for more than half of the cumulative days per year when the soil tem-perature at a depth of 50 cm from the soil surface is above 5C and moist in some orall parts for less than 90 consecutive days when the soil temperature at a depth of 50cm is above 8C.Empirical expression (7.85) is widely used by soil chemists to estimateionic strength I from electrical conductivity ECW (Griffin and Jurinak,1973). Previously (see Figure 3.13 and Appendix 3D), we discussed the effectof ionic strength on the osmotic swelling of Na-saturated smectite clays.Figure 7H.1 offers additional evidence that the exchanger Na equivalentfraction ~ENa correlates with an increased critical coagulation concentration(i.e., ionic strength at which coagulation begins to occur) for smectite claysuspensions.I mol L1 0:013 ECW dS m1 7:85The electrical conductivity ECW criterion (see Table 7.6) predicts clay miner-als will either disperse or swell when the exchanger Na equivalent fraction~ENa exceeds a critical threshold.11. The moisture control section of a soil extends approximately (1) from 10 to 30 cm below thesoil surface if the particle-size class of the soil is fine loamy, coarse-silty, fine-silty, or clayey;(2) from 20 to 60 cm if the particle-size class is coarse-loamy; and (3) from 30 to 90 cm if theparticle-size class is sandy.ENa CCa2c 20 11=212. pWP 1500 kPa or hWP 153:0 m7.7.6. Extreme Alkalinity: Soil pH>8.4The pH criterion used by the USDA to assess sodicity risk (see Table 7.6),unlike the other two criteria, does not distinguish sodic from nonsodic behaviorbut serves as a predictor of sodicity risk. As we will see in this section, thereare circumstances where soils exhibit low hydraulic conductivity characteristicof sodicity, meet both ESP (or SARP) and ECW criteria, and yet still fail thepH > 8:4 criterion.Pore water chemistry related to sodicity is best understood on a continuumbetween two end-points. The low-alkalinity end-point is the chemistry ofcalcite-saturated seawater or calcite-saturated saline groundwater. The alka-linity of the low-alkalinity end-point is derived solely from calcite dissolutionbecause the other solutes are derived from neutral salts: chlorides and sulfates.The major cations in seawater (Table 7.7) originate from chemicalweathering of Earths crust. The major anions result from acid depositionfrom volcanic activityhydrochloric and sulfuric acidand atmosphericTABLE 7.7 Standard Mean Chemical Composition of Seawater: IonicStrength I 0:72molc kg1H2O, Total Alkalinity AC 2:4 103 molc kg1H2Oand pH 8.1Species Concentration, mol kg1H2ONa 0.48616Mg2 0.05475Ca2 0.01065Chapter 7 Acid-Base Chemistry 293K 0.01058Sr2 0.00009Cl 0.56576SO24 0.02927Br 0.00087F 0.00007HCO3 0.00183CO23 0.00027B OH 03 0.00033B OH 4 0.00010OH 0.00001Source: Dickson and Goyet, 1994.CO2. Acid deposition neutralizes most of the alkalinity resulting from chemi-cal weathering of the silicate crust; most of the total alkalinity derives fromcalcite saturation.Diluting seawater to ECW 4dS m1 while maintaining calcite saturationresults in pore water composition that satisfies the first two criteria inTable 7.6 but fails the pH criterion. The residual sodium carbonate RSC isnegative, consistent with the low pH:RSC CHCO3 2 CCO23 2 CCa2 2 CMg2 7:86The pore water chemistry in Table 7.8 is representative of the low-alkalinityend-point found in incompletely leached marine quick clay deposits and soilsthat develop sodicity from saline groundwater discharge or irrigation withsaline groundwater.The high-alkalinity end-point results solely from the chemical weatheringof silicate rocks. Figure 7.12 illustrates the dissolution of Earths silicate crustby reaction (7.23), where solution Ca2 aq activity aCa2 is constrained bycalcite solubility. The process depicted in Figure 7.12 is equivalent to the irre-versible dissolution of orthoclase KAlSi3O8 described by Helgeson and collea-gues (1969). Rhoades and colleagues (1968) measured significant chemicalSoil and Environmental Chemistry294Mg 3:93 10 mol LCa2 3:92 103 mol L1K 7:06 104 mol L1Cl 4:07 102 mol L1SO24 2:10 103 mol L1AC 8:11 103 molc L1pH 6.96SARp 12:2mmol L1pRSC 6:98 103 molc L1weathering and increasing alkalinity when leaching arid-region soils with irri-gation water. Much of the alkalinity recorded by Rhoades and colleagues,however, resulted from calcite dissolution.TABLE 7.8 Seawater Diluted to Ionic Strength I 0:05molc L1ECW 4 dS m1 While Maintaining Calcite Saturation and Soil Pore CO2Levels: pCO2 3:87 102 atmSpecies ConcentrationNa 3:49 102 mol L12 3 1Chapter 7 Acid-Base Chemistry 295Expression (7.65) (Deffeyes, 1965) defines alkalinity as the differencebetween the sum over the major alkali and alkaline earth cationsCa2 aq , Mg2 aq , Na aq , and K aq minus the sum over all majorstrong acid anionsSO24 aq and Cl aq in natural waters. Calcite solu-bility imposes no global constrain on alkalinity.Equation (7.65) implies another mechanism for increasing alkalinity with-out the need for chemical weathering of silicate rocks: conversion ofSO24 aq to OH aq by biological sulfate reduction. Whittig and Janitzky(1963) identified anaerobic dissimilatory sulfate reduction as an alternatesource of hydroxyl ions in landscape settings where poor drainage, high levelsof dissolved sulfate, and abundant soil organic matter are present:SO24 aq S 6 8 e 5 H2O l !dissimilatorysulfate reductionHS aq S 2 9 OH 7:87Though conditions favoring dissimilatory sulfate reduction (7.87) are rarein arid environments and incompatible with the pH > 8:4 criterion (seeTable 7.6), under most circumstances dissimilatory sulfate reduction couldFIGURE 7.12 The irreversible dissolution of Earths crust according to reaction (7.23) neglectsthe solubility of Al2O3, Fe2O3, and SiO2. Calcium solubility is constrained by calcite solubilityand atmospheric CO2 g pCO2 3:89 104 atm . Solution pH (diamond symbol) increases onthe logarithmic scale once 105 mol L1 of the crust has dissolved. Maximum calcium solubility(square symbol) is attained at pH 8.4 when the solution becomes saturated by calcite (dissolution 102 mol L1) and then declines as pH and sodium solubility (triangle symbol) continue toincrease.be a significant source of alkalinity in soils at the low-alkalinity end-pointdescribed earlier. Geotechnical engineers studying marine quick clays noteBower (Bower, Wilcox et al., 1963; Bower, Ogata et al., 1968) usedSoil and Environmental Chemistry296expression (7.91) to predict changes in the SAR resulting from calcite precip-itation. Bower assumed that the soil pH buffer capacity immediately shiftsirrigation water pH to the prevailing soil pH (assumed to be the pH of typical13. pKa2,CO aq 10:26 in Langelier; pKa2,CO aq 10:33 in the ChemEQL database.Kca2,CO2 aq Ka2,CO2 aq 3gH gCO23 3CHCO37:89Kcs0 Ks0 1gCa2 gCO23 ! CCa2 CCO237:90The empirical formula for calculating an ion activity coefficient and the ther-modynamic constants for carbonate hydrolysis13 and calcite solubility14 havechanged since Langelier published his paper. Table 7.9 lists parameters calcu-lated from data listed in Table 3 in Langeliers paper; the differences betweenthe last two columns illustrate the effect of revised constants and current meth-ods for calculating ion activity coefficients. Alkalinity AC consistently increasesand calcium solubility consistently decreases as pH increases above 8.4 (seeFigure 7.12).negative logarithm of the carbonate alkalinity or pAC log AC ) of waterin contact with the pipes, Langelier derived an expression for the pH at whichthe water is saturated by calcite: pHc:pHc pKca2 pKcs0 pCa pAC 7:88The first term on the right-hand side of expression (7.88) is the conditionalhydrolysis coefficient (7.89) derived from Eq. (7.42); the second term is theconditional calcite solubility coefficient (7.90).gHCO !CH CCO2that conditions favoring dissimilatory sulfate reduction can generate sufficientalkalinity to alter the univalent-to-divalent cation ratio of pore water in quickclay formations (Lessard, 1981).7.7.7. Predicting Changes in Pore Water SARLangelier (1936) developed a method for calculating the calcite saturationindex, the motivation being corrosion prevention by depositing and maintain-ing a calcite layer on the interior of cast iron pipes. Given the calcium concen-tration (expressed as the negative logarithm of the total soluble calciumconcentration or pCa log CCa Total ) and alkalinity (expressed as the2 214. pKs0 8:32 in Langelier; pKs0 8:48 in the ChemEQL database.TABLE 7.9 Negative Logarithm of the Ion Activity Product for CalciteSolubility pIAP, pHc, and Calcite Saturation Index pHpHc Chapter 7 Acid-Base Chemistry 297calcareous soils: 8.4) and used the Langelier Saturation Index to predictwhether calcite precipitation would raise or lower SARiw. The pH at whichCalaveras Reservoir 8.14 7.41 0.34 0.15San Mateo 8.33 7.40 0.15 0.12Milpitas 8.31 7.65 0.17 0.13Hayward 8.39 7.71 0.09 0.10Crystal Springs Reservoir 8.72 8.44 0.24 0.07Irvington 8.84 9.23 0.38 0.11Berkeley 8.08 9.55 0.40 0.12Note: Calculated values are based on ChemEQL simulations, except column 4 ({), which listsoriginal published values.Source: Langelier, 1936.Water Source pIAP pHc pHpHc pHpHc {calcite precipitatespHcis calculated from the chemical composition ofthe irrigation water using expression (7.88).adjSARiw SARiw 1 8:4 pHc 7:91Bowers adjSARiw tends to overestimate changes in irrigation water SAR.Suarez (1981) proposed a more direct expression (7.92) for calculatingchanges in irrigation water SAR.15 Expression (7.92) contains the predictedcalcium concentration c0Ca2 mmol L1 at the soil pH, taking into accountthe soil CO2 g partial pressure pCO2 g and the bicarbonate-to-calcium ratioCHCO3=CCa2 of the irrigation water.SARadj cNa mmol L1 c0Ca2 mmol L1 p 7:92Water chemistry simulation applications such as ChemEQL and MINTEQallow you to calculate c0Ca2 without resorting to tables such as those pub-lished by Langelier and Suarez. An example appears in Appendix 7I.15. Suarez (1981) includes the magnesium concentration cMg2 mmol L1 in his original expres-sion: SARajd cNacMg2c0 Ca2pextracted by distilled water. Extracting soil acidity required adding some typeSoil and Environmental Chemistry2987.8.1. Exchangeable Calcium and Soil AlkalinitySoils containing calcite are buffered at roughly pH 8.4 (see Appendix 7A);they resist becoming either more alkaline or more acidic as long as calciteremains in the soil. Although chemical weathering in humid climates willeventually remove all traces of the mineral calcite, the mineral and organicsoil colloids (smectite clay minerals and humic substances) will remainlargely saturated by Ca2 ions, a consequence of the natural abundance of thiselement. Absent calcite, there is little to prevent a drop in soil pH. Thoughcontinued chemical weathering and leaching drive the pH ever lower, soil col-loids remain Ca2-saturated until pH 6.5, the pH of minimum aluminumsolubility.As soil pH drifts below pH 6.5, aluminum solubility begins to graduallyincrease, displacing the exchangeable Ca2 ions. As we have already seen,asymmetric ion exchange tends to favor the ion with higher valence, shiftingthe advantage decidedly in the favor of Al3 (Figure 7.13).7.8.2. Gibbsite SolubilityExample 5.16 in Chapter 5 examines the solubility of a common hydrous alumi-num oxide mineral: gibbsite (Eq. (7.93)). Our model for exchangeable acidity isof soluble salt to displace the insoluble acids. Vieth (1904) reported a compar-ison of his limewater (calcium hydroxide) method (Vietch, 1902) and thesodium-chloride extraction developed by Hopkins and colleagues (1903).Hopkinss sodium chloride extract released considerable quantities of iron,alumina, and manganese into solution that precipitated when the extractwas titrated with sodium hydroxide to quantify acidity. Vietch (1904) foundthat extracting acid soils with a neutral sodium salt solution resulted in thereplacement of aluminum by sodium. He also found that potassium saltswere more efficient at replacing aluminum than sodium.Vietch coined the term active acidity to describe the acidity displaced byneutral salts such as sodium and potassium chlorides in Hopkinss methodand total apparent acidity to describe the much greater acidity measured byhis limewater (calcium hydroxide) method. The debate over soil aciditycontinued for another 60 years (Thomas, 1977), but no study during that spanof years altered the conclusions one could easily drawin hindsightfromthe work of Vietch and Hopkins.7.8. EXCHANGEABLE ACIDITYThe earliest studies of soil acidity (Vietch, 1902; Hopkins, Knox et al., 1903)found that the unidentified acids responsible for soil acidity could not bebased on gibbsite solubility (Eq. (7.94)), but one could easily prepare similar9Chapter 7 Acid-Base Chemistry 29models based on other naturally occurring aluminum oxide, hydroxide, oroxyhydroxide minerals.Al OH 3 s GIBBSITE$ Al3 aq 3 OH aq 7:93Ks0 1:29 1034 aAl3 a3OH 7:94Solubility expression (7.95) is a more convenient expression of pH-dependentgibbsite solubility. The net equilibrium constant (7.96) for reaction (7.95)results from dividing (7.94) by the water hydrolysis constant Kw (6) to thethird power.Al OH 3 s 3 H aq Al3 aq 3 H2O l 7:95Knet Ks0 K3w 108:11 aAl3a3H7:96Taking the logarithm of solubility expression (7.96) yields a linear expression(7.97) between the logarithm of Al3 aq activity and solution pH.8:11 log aAl3 3 log aH log aAl3 8:11 3 pH 7:97FIGURE 7.13 This graph plots the asymmetric Ca2,Al3 exchange isotherm from Coulterand Talibudeen (1968): KGT 40.Soil and Environmental Chemistry300Figure 7.14 (see Figure 5.3) plots the activity of the most abundant solutionaluminum species in equilibrium with gibbsite. The trivalent Al3 aq speciesis the most abundant aluminum species below pH 5, where aluminum solubil-ity reaches millimolar concentrations. The univalent Al OH 2 aq species isthe dominant species in a pH range5:10 < pH < 6:80where aluminumsolubility remains below 3 105 M. The divalent Al OH 2 aq species isnever the most abundant species.7.8.3. The Role of Asymmetric (Al3,Ca2) ExchangeThe relative abundance of univalent, divalent, and trivalent species as solubil-ity increases is very important because these solution aluminum speciesbecome increasingly competitive with Ca2 aq for cation exchange sites assoil pH decreases. If we assume a representative soil pore water ionic strengthof 103 M, the univalent Al OH 2 aq species is never competitive for asym-metric cation exchange with Ca2 aq in the pH range, where it is dominantbecause of its valence and low relative solubility. We can ignore symmetricAl OH 2,Ca2 cation exchange because Al OH 2 aq is never the mostabundant soluble aluminum species. By process of elimination, the only sig-nificant cation exchange reaction that is relevant to soil acidity is theFIGURE 7.14 This graph plots the logarithm of ion activity for the five most abundant alumi-num solution species as a function of pH from simulation using ChemEQL. The solubility ofAl3 aq is constrained by gibbsite solubility, as discussed in Example 5.16, except hereH aq is treated as an independent variable covering the range depicted in the graph.1FIGURE 7.15 This graph plots the exchangeable Al3 equivalent fraction ~EAl3 for asymmetric3 2Chapter 7 Acid-Base Chemistry 30asymmetric Al3,Ca2 cation exchange; the advantage lies with Al3 aq because of its valence and high relative solubility when soil pH dropsbelow 5.The complete solution of the cubic asymmetric Al3,Ca2 exchange iso-therm is found in Appendix 7E. The combined effect of pH-dependent alumi-num solubility (Figure 7.14) and asymmetric Al3,Ca2 exchange(Figure 7.13) are plotted in Figure 7.15.7.8.4. Neutralizing Exchangeable Soil AcidityHydrolysis reactions (7.98), (7.99), and (7.100) identify exchangeable alumi-num Al3 ex as a weak acid. Exchangeable calcium Ca2 ex is not a baseaccording to acid-base chemistry, but is simply the cation associated withthe true base OH aq . The accumulation of exchangeable aluminumAl3 ex portrayed in Figure 7.15 leads to the accumulation of an exchange-able weak acid that requires three equivalents of base to fully neutralize.Al3weak acidaq $ H aq Al OH 2conjugatebaseaq Ka1 1:0 105 7:98Al ,Ca exchange as a function of pH. Solution parameter C0 (Appendix 7C) is restricted to1:0 103 molc L1 < C0 < 2:0 103 molc L1. The Gaines-Thomas selectivity coefficient isKcGT 160 (Foscolos, 1968). Gibbsite solubility is simulated using ChemEQL as discussed inExample 5.16.of exchangeable Al ex by soluble Ca aq is precisely the reactioninduced by the limewater extraction used by Vietch (1902) to measure totalSoil and Environmental Chemistry302aqueous carbon dioxide. Bicarbonate ions are the basis of water alkalinity; theproton reference level used by environmental chemists shifts below pH 7 ashydroxyl ions are converted into bicarbonate ions.Climatic conditions determine whether soils tend to be acidic or alkaline;the former are common in humic climates, while the latter are common in aridand semiarid climates. Land degradation can occur in arid and semiaridclimates when the accumulation of sodium ions by clay minerals reducesthe activity index IA of soil clays, reducing soil mechanical strength and7.9. SUMMARYEnvironmental acidity and basicity arise from numerous sources: the dissolu-tion of atmospheric gases in water and their subsequent wet deposition on theland surface, fertilization and harvest in agriculture, and chemical weatheringof minerals in soils and aquifers. The criteria for measuring acidity or basicityin the environment must account for the dissolution of carbon dioxide in waterand the production of bicarbonate ionsthe conjugate base of the weak acidapparent acidity.2 Al3exchanger3 Ca2aqsolution$ 2 Al3aqsolution 3 Ca2exchanger7:102Soluble Al3 aq reacts with bicarbonate HCO3 aq and carbonateCO23 aq conjugate bases of aqueous carbon dioxidein solution resultingin the precipitation of the aluminum hydroxide gibbsite Al OH 3 s , the veryprecipitate described by Vietch.Al OH 2weak acidaq $ H aq Al OH 2conjugatebaseaq Ka2 7:9 106 7:99Al OH 2weak acidaq $ H aq Al OH 03conjugatebaseaq Ka3 1:6 107 7:100Combining reactions (7.99) through (7.100) with the conjugate base hydroly-sis reaction (7.32) yields the neutralization-exchange reaction (7.101) betweenexchangeable Al3 ex and the solid base calcite CaCO3 s .2 Al3 ex 3 CaCO3 s calcite! 3 Ca2 ex 2 Al OH 03 aq 3 CO2 aq 7:101The dissolution of calcite CaCO3 s releases soluble Ca2 aq that undergoesasymmetric exchange (7.102) with exchangeable Al3 ex . The displacement3 2as a consequencesoil-water hydraulic conductivity. Sodification is aKw 1014 aH aOH 7A:43Cbase aOH CNa 7A:5Cacid aH CNO37A:6Cbuffer CHA CA 7A:7The preceding relations determine the concentration of the conjugate baseA aq :aH CA acid or strong base must be added to change pH by a fixed amount. Bufferingis an important concept because a variety of chemical substances dissolved insurface and pore water of the saturated and vadose zones contribute to the sol-uble buffer capacity, poising the pH in these systems.The buffer index b is defined in the following equations. Adding a strongbase causes pH to increase, while adding a strong acid causes pH to decrease;the buffer index b > 0 regardless.b DCbaseDpH DCacidDpH7A:1b DCbaseDaH DaHDpH 2:303 aH DCbaseDaH 7A:2If the buffer is based on a generalized weak acid HA aq , then the completedissociation of the strong base NaOH and acid HNO3 results in the followingrelations (neglecting activity corrections):Kca aH CACHA7A:3lowering calcium solubility. At the other extreme, land degradation in humid cli-mates can result in soil acidification. This process also involves interactionsbetween pH-dependent changes in aluminum hydrous oxide solubility and cationexchange, leading to the accumulation of exchangeable aluminum ions.Exchangeable aluminum ions behave as weak acids, and their accumulationamounts to a chemically active but insoluble formof acidity in humid region soils.APPENDIX 7A. BUFFER INDEXA pH buffer is composed of one or more weak acids or bases (including con-jugate acids and conjugate bases) that resist changes in pH when either strongacid or strong base is added. Buffer capacity is a measure of how much strongcomplex process that involves cation exchange, pH-dependent calcite solubility,and extreme alkalinity that increases the sodium-to-calcium ratio in solution byChapter 7 Acid-Base Chemistry 30Cbuffer CA CHA CA Kca7A:8Soil and Environmental Chemistry304Kca aH 2 aHb 2:303 Cbuffer Kca aHKca aH 2 KwaH aH !7A:12The buffer index b (7A.12) depends on both buffer concentration Cbuffer andb 2:303 aH Cbuffer KaKca aH 2@ A Kwa2H@ A 1@ Ab 2:303 Cbuffer Kca aH 0@1A Kw0@1A aH0@1Ab 2:303 aH ddaHCbuffer KcaKca aH0@1A ddaHKwaH0@1A daHdaH0@1Ab 2:303 aH Cbuffer KcaKca aH 20@1A Kwa2H0@1A 10@1Ac0 1 0 10 1Cbuffer CA 1 aHKca CA Kca aHKca CA Cbuffer KcaKca aH7A:9Total cation charge must equal total anion charge:aH CNa aOH CNO3 CA 7A:10Solving the charge balance condition (7A.10) for Cbase and replacing termsusing Eqs. (7A.4), (7A.6), and (7A.9) result in Eq. (7A.11):Cbase CNa Cacid CA aOH aHCbase Cacid Cbuffer KcaKca aH KwaH aH 7A:11Applying the differential definition of buffer index b (7A.2) to expression(7A.11) yields the more tractable expression (7A.12):b 2:303 aH dCbasedaH0@1Ab 2:303 aH ddaHCacid Cbuffer KcaKca aH0@1A KwaH0@1A aH0@1Athe dissociation constant Kca of the weak acid used as buffer.at the moles of charge per gram.Since the requirement of charge neutrality applies to Earths crust, itshould come as no surprise that the 10 most abundant elements in Earthscrust account for all but 0.6% of the charge.Table 7.3 lists the oxide mole-per-mass mol kg1 composition of Earthscrust (column 2) based on the listed oxides (column 1). The oxides are basedon the valence of each element in crustal rocks. You will notice that the oxidemole-per-mass mol kg1 composition (Table 7.1, column 2) is a multiple ofmole-per-mass mol kg1 composition in Table 7B.1 (column 4).TABLE 7B.1 Composition of the Outer (Continental) Crust for Planet EarthAtomicSymbolMassFractionAtomic Mass,g mol1Moles,mol kg1Moles of Charge,molc kg1O 4:55 101 15.9994 28.4 56.88Si 2:72 101 28.0845 9.68 38.74Al 8:30 102 26.9815 3.03 9.23Chapter 7 Acid-Base Chemistry 305APPENDIX 7C. SATURATION EFFECT: ATMOSPHERICCONVERSION OF SULFUR TRIOXIDE TO SULFURIC ACIDAltshuller (1973) demonstrated the saturation effect that occurs when atmo-spheric sulfur dioxide concentrations exceed a certain threshold (Figure 7C.1).Below the threshold, the sulfur dioxidetosulfate ratio in the atmosphere ofmajor cities increases linearly. Beyond the saturation threshold (80 mg m3 inFigure 7C.1), atmospheric sulfuric acid levels cease to increase regardless ofFe 6:20 102 55.8452 1.11 2.22Ca 4:66 102 40.0784 1.16 2.33Na 2:27 102 22.9898 0.987 0.99Mg 2:76 102 24.3051 1.14 2.27K 1:84 102 39.0983 0.471 0.47Source: Greenwood and Earnshaw, 1997.APPENDIX 7B. CONVERTING MASS FRACTION TO SUM-OF-OXIDES COMPOSITIONTable 7B.1 lists the mass fraction composition of Earths outer crust in col-umn 2. Dividing each entry in column 2 by the atomic mass (column 3) andmultiplying by 1000 to convert from grams to kilograms yields the molarcomposition of each element (column 4). Multiplying each entry in column4 by the valence of each elementiron is Fe(II) in crustal rockswe arrivethe sulfur dioxide concentration.0 20 40 60 80 100 120 140 160 180 200 220Soil and Environmental Chemistry306Sulfur Dioxide Concentrationg m3FIGURE 7C.1 The relationship between annual average sulfur dioxide concentration and theratio of sulfur dioxide to sulfate for 18 U.S. cities. Source: Reproduced with permission fromAltshuller, A.P., 1973. Atmospheric sulfur dioxide and sulfate: Distribution of concentration aturban and nonurban sites in United States. Environ. Sci. Technol. 7, 709712.3020Atmospheric Sulfur DioxidetoSulfate Ratio100Ammonia and other alkaline substances in the atmosphere catalyze theoxidation of sulfur dioxide to sulfuric acid (Scott and Hobbs, 1967). Once sul-fur dioxide levels reach a certain threshold, the acidity from the sulfuric acidexceeds the alkalinity, resulting in a drop in the pH of water droplets in theatmosphere and effectively eliminating the further conversion of sulfur diox-ide to sulfuric acid.APPENDIX 7D. BICARBONATE AND CARBONATE REFERENCELEVELSThe weak acids in carbonate solutions encompass three proton referencelevels. Table 7D.1 (identical to Table 7.2) lists the species that appear in theproton balance defined for the aqueous carbon dioxide CO2 aq reference level(boldface species).Table 7D.2 lists the proton balance expression defined for the aqueouscarbon dioxide CO2 aq reference level (row 4) and is assembled from thespecies representing a proton surplus (row 2) and the species representing aproton deficit (row 3).Table 7D.3 lists the species that appear in the proton balance defined forthe bicarbonate HCO3 aq reference level (boldface species).Table 7D.4 lists the proton balance expression defined for the bicarbonateHCO3 aq reference level (row 4) and is assembled from the speciesTABLE 7D.2 Proton Balance Relative to the Aqueous Carbon DioxideCO2 aq Reference LevelProton Reference Level CO2 aq Proton Surplus CH3OProton Deficit COH CHCO3 2 CCO23Proton Balance CH3O COH CHCO 3 2 CCO23TABLE 7D.1 Conjugate Acid-Base Pairs in Aqueous Carbonate SolutionsWeak Acid Conjugate BaseH3O+ H2OCO2(aq) HCO3HCO3 CO23H2O OHTABLE 7D.3 Conjugate Acid-Base Pairs in Aqueous Carbonate SolutionsWeak Acid Conjugate BaseH3O+ H2OCO2 aq HCO3HCO3 CO23H2O OHTABLE 7D.4 Proton Balance Relative to the Bicarbonate HCO3 aq Reference LevelProton Reference Level HCO3 aq Proton Surplus CH3O CCO2 aq Proton Deficit COH CCO23Proton Balance CH3O COH CCO23 CCO2 aq Chapter 7 Acid-Base Chemistry 307H3O+ H2OSoil and Environmental Chemistry308CO2 aq HCO3HCO3 CO3H2O OHTABLE 7D.6 Proton Balance Relative to the Carbonate CO23 aq ReferenceLevelProton Reference Level Strong Base KOHProton Surplus CH3O 2 CCO2 aq CHCO3Proton Deficit COHTABLE 7D.5 Conjugate Acid-Base Pairs in Aqueous Carbonate SolutionsWeak Acid Conjugate Baserepresenting a proton surplus (row 2) and the species representing a protondeficit (row 3). The proton surplus lists H3O (H2O plus a H) andCO2 aq (HCO3 plus a H). The proton deficit lists OH (H2O minus aH) and CO23 (HCO3 minus one H). The bicarbonate HCO3 aq speciesdoes not appear in the proton balance in Table 7D.4.Table 7D.5 lists the species that appear in the proton balance defined forthe carbonate CO23 aq reference level (boldface species).Finally, Table 7D.6 lists the proton balance expression defined for the car-bonate CO23 aq reference level (row 4) and is assembled from the speciesrepresenting a proton surplus (row 2) and the species representing a protondeficit (row 3). The proton surplus lists H3O (H2O plus a H), CO2 aq (CO23 plus two H), and HCO3 (CO23 plus one H). The proton deficit listsOH (H2O minus a H). The carbonate CO23 aq species does not appear inthe proton balance in Table 7D.6.APPENDIX 7E. CALCULATING THE pH OF A SODIUMCARBONATE SOLUTIONThe carbonate ion CO23 aq is an extremely important diprotic conjugatebase in water chemistry. What is the pH of a 0.1 M solution of Na2CO3?Proton Balance CH3O COH 2 CCO2 aq CHCO3 x Chapter 7 Acid-Base Chemistry 309We estimated the pH of a 0.10 M sodium carbonate solution by assuming thatthe second hydrolysis step, the hydrolysis reaction that produces carbonic acidfrom bicarbonate, is negligible relative to the first hydrolysis step. The resultconfirms the validity of the simplifying assumption.APPENDIX 7F. CALCULATING THE AQUEOUS CARBONDIOXIDE CONCENTRATION IN A WEAK BASE SOLUTIONSuppose we estimate the concentration of aqueous carbon dioxide CO2 aq ,Since x 4:63 10 , the approximation 0:10 x 0:10 is acceptable.COH 4:66 103 102:33pOH 2:33pH 14 pOH 11:7the product3of the secon 2:14 105d hydrolysis step,4:63 103from Appendp2:14 10 0:10 assign values to each component in equilibrium expression.Stage CO23 aq $ HCO3 aq OH aq Initial 0.10 0 0Reaction x x xEquilibrium 0.10 x x xThe equilibrium expression using concentrations from the preceding tablefollows:Kb1 2:14 104 COH CHCO3CCO23Kb1 x x0:10 x 4 x xBecause the second base association constant Kb2 is much smaller than thefirst base association constant Kb1, the hydroxide ion OH aq concentrationresults almost entirely from the first hydrolysis step. Assume, as a firstapproximation, that only the first step occurs. Use an equilibrium table toHCO3 aq $ CO2 aq OH aq Kb2 2:33 108 COH CCO2CHCO3CO23 aq H2Ol $ HCO3 aq OH aq Kb1 2:14 104 COH CHCO3CCO23ix 7E.stepthe conversion of bicarbonate to aqueous carbon dioxideto assignmuch smal 2 3 h a h CHCO3and COH a seIt is imp l g o dixes 7Eand 7F wou l ncentra-tions in a re m dispenseSoil and Environmental Chemistry310APPENDIX 7G. ION EXCHANGE ISOTHERM FOR ASYMMETRIC(Ca2, Al 3) EXCHANGEThe trivalent-divalent Al3,Ca2 exchange isotherm is significantly morecomplex than the univalent-divalent Na,Ca2 exchange isotherm becausethe former requires solving cubic equations throughout the exchange iso-with simplifying assumptions and rely in ChemEQL to simulate the reactions.therm, whilld be difficual water chee the latter it to make when attempting to predict solute coistry problem. An accurate calculation wouldortant to rea ize the simplifyinnvolves relativelyassumptisimple quns used in Appenre very clo to 4:52 103 M.ler than 4:5 10 M. It is t erefore re sonable that botvalues to each component in equilibrium expression as before.Stage HCO3 aq $ CO2 aq OH aq Initial 4:52 103 0 4:52 103Reaction y y yEquilibrium 4:52 103y y 4:52 103+yThe equilibrium expression using concentrations from the preceding tablefollows:Kb2 COH CH2CO3CHCO3Kb2 4:52 103 y y4:52 103 y 2:33 108 4:52 103 y4:52 103 y 2:33 108Because the second base association constant Kb2 is relatively small, the sec-ond ionization step occurs to a much smaller extent than the first. This meansthe amount of H2CO3 aq and OH aq produced in the second step (y) isHCO3 aq $ CO2 aq OH aq Kb2 2:33 108 COH CCO2CHCO3To do this, we will construct an equilibrium table for the second hydrolysisadratic equations.Chapter 7 Acid-Base Chemistry 3111 3 ~EAl3 3 ~E2Al3 ~E3Al3 9 C0 1 EAl3 38 KcGT E2Al3 ~E2Al3 7G:6The term in parentheses on the right-hand side of (7G.6) contains the entire39 C0@ A E2Al3 1 ~EAl3 38 KcGT E2Al39 C00@1A 1 3 ~EAl3 3 ~E2Al3 ~E3Al3 1 EAl3 3 ~E2Al3 !C0 3 Al3 2 Ca2 7G:2ECa2 2 Ca2 3 Al3 2 Ca2 2 Ca2 C07G:3EAl3 3 Al3 3 Al3 2 Ca2 3 Al3 C07G:4KcGT C0 ECa22 3 ~E2Al3~E3Ca2 C0 EAl33 20B@1CA 7G:5KcGT 9 C08 1 EAl3 3 ~E2Al3E2Al3 1 ~EAl3 3 !7G:5Expression (7G.5), after rearrangement, is revealed to be a cubic function (7G.6)whose independent variable is the Al3 equivalent fraction on the exchanger~EAl3 and dependent variable is the Al3 equivalent fraction in solution EAl3 .8 KcGT0 11 EAl3 3 ~E2Al32 Al3aqsolution 3 Ca2exchanger$ 2 Al3exchanger3 Ca2aqsolutionThe conditional Gaines-Thomas selectivity expression for the asymmetricAl3,Ca2 exchange reaction is given by expression (7G.1):KcGT Ca2 3 ~E2Al3~E3Ca2 Al3 27G:1Solution parameter C0 is the solution normality summed over all ions involvedin the exchange (7G.2). The solution equivalent fractions are defined inexpressions (7G.3) and (7G.4), which are substituted into Gaines-Thomasselectivity expression (7G.2) to yield new expression using only equivalentfractions (7G.5).functional dependence of this cubic expression on the Al equivalent fraction31q 2 bc27 bc 1 7G:12r p327 q24 7G:13The exchangeable equivalent fraction ~EAl3the only real root of (7G.8)isgiven by (7G.14) where the value of r determines the appropriate expressionfor the term y in (7G.14).~EAl3 ybc 7G:14b2 9 7G:99 C0 1 EAl3 38 KcGT E2Al30@1A 30@1A2 99 C0 1 EAl3 38 KcGT E2Al30@1A2 6 9 C0 1 EAl3 38 KcGT E2Al30@1A 9 99 C0 1 EAl3 38 KcGT E2Al30@1A2 6 9 C0 1 EAl3 38 KcGT E2Al30@1A 09 C0 1 EAl3 38 KcGT E2Al3 ! 6 7G:10Define three new functions p (7G.11), q (7G.12) and r (7G.13).p 9 b2c37G:113 bc 9 C0 1 EAl3 38 KcGT E2Al3 ! 3 7G:7~E3Al3 bc ~E2Al3 3 ~EAl3 1 0 7G:8Cubic function (7G.8) is a perfect cube when (7G.9)or by extension(7G.10)is true. Since (7G.10) is dependent on solution parameter C0,exchange selectivity coefficient KcGT , and the solution equivalent fractionEAl3 , we must assume that (7G.10) is not satisfied in general.in solution EAl3 , leading to a new function (7G.7). Using function (7G.7), thecubic expression (7G.6) becomes (7G.8). The exchange isotherm is one of theroots of cubic function.Soil and Environmental Chemistry23When r 0 the term y in (7G.14) is given by (7G.15), using expressions u(7G.16) and v (7G.17).Chapter 7 Acid-Base Chemistry 313montmorillonite clay coagulate at solution concentrations exceeding thevalues represented by the curve plotted in Figure 7H.1 or remain dispersedat solution concentrations less than the values represented by the line. Thisphenomenon is related to the concentration-dependent osmotic swelling men-tioned earlier (see Figure 3.13 and Appendix 3D). The CCC is very sensitiveto the equivalent fraction ~ENa of exchangeable Na.Changes in clay chemistry appear when Na ions occupy a significantfraction of the exchange complex. Recall the equivalent fraction-dependent16. The aggregation of colloidal particles is called coagulation or flocculation. Aggregates settleAPPENDIX 7H. THE EFFECT OF (Na, Ca2) EXCHANGE ONTHE CRITICAL COAGULATION CONCENTRATION OFMONTMORILLONITEOster and colleagues (1980) published a report correlating the concentration atwhich a colloidal suspension of montmorillonite clay (American PetroleumInstitute API-25, montmorillonite, Upton, Wyoming) becomes unstable andcoagulates.16 Figure 7H.1 plots the critical coagulation concentration CCCas a function of the exchange equivalent fraction ~ENa . Suspensions of thisy u v 7G:15u q2 rp 1=3 7G:16v q2 rp 1=3 7G:17When r < 0 the term y in (7G.14) is given by (7G.18), using the expressionsw (7G.19) and function a (7G.19), the latter in radians.y 2 p3 1=2 cos a3 7G:18w q2 p=3 3q 7G:19a cos1 w 7G:20A spreadsheet model of the asymmetric exchange isotherm (7G.8) requires alogical IF functionIF logical test, value if true , value if false to testthe value of r (7G.13) and assign an appropriate value to y in (7G.14) usingeither (7G.15) or (7G.18) depending on the outcome of the logical test.much more rapidly than unaggregated (dispersed) particles.Soil and Environmental Chemistry314FIGURE 7H.1 The line represents the effect of exchangeable Na on the critical coagulationconcentration mmolc L1 of montmorillonite API-25 (Upton, Wyoming). Experimental dataplotted as open circles (modified from Oster, Shainberg et al., 1980).selectivity coefficient for Mg2,Ca2 exchange on the Libby Vermiculite(see Appendix 4C). Selectivity favors Ca2 ions at the Ca2-rich limit ofthe exchange isotherm, while favoring Mg2 ions at the Mg2-rich limit ofthe exchange isotherm. The shift in ion selectivity away from Ca2 occurswhen the equivalent fraction of exchangeable Mg2 ions increases from tracelevels to chemically significant levels, altering the character of the interlayer.Similarly, as the equivalent fraction of exchangeable Na ions increases, thecharacter of the interlayer gradually changes from an environment limited tocrystalline swelling to an interlayer capable of osmotic swelling.Oster and colleagues used a montmorillonite clay sample collected at thesame site as that used by Sposito and colleagues (1983) in their study of asymmet-ric Na,Ca2 exchange: ClayMinerals Society sample SWy-1 (Upton,Wyom-ing). Figure 7H.2 plots the exchange isotherm reported by Sposito and colleagues;the exchange isotherm results from Oster and colleagues appear in Figure 7H.3.Despite employing a significantly higher salt concentration;C0 0:05 molc L1 than Oster and colleagues, the Gaines-Thomas selec-tivity coefficient KGT 0:30 derived from fitting data from Sposito and col-leagues provides an excellent fit of data reported by Oster and colleagues.The shift in position of the exchange isotherm going from Figure 7H.2 to7H.3 results from the different salt concentrations used in the two studies.The effect of Na,Ca2 exchange on the CCC (see Figure 7H.1) andswelling behavior (see Figure 3.13) of smectite clays has profound implicationsFIGURE 7H.2 The experimental exchange isotherms for asymmetric Na,Ca2 exchange forWyoming smectite SWy-1 (Sposito, Holtzclaw et al., 1983). The exchange isotherm representingGaines-Thomas selectivity coefficient KGT 0:30 is plotted as a smooth line, and the nonselec-tive exchange isotherm appears as a dashed line.FIGURE 7H.3 The experimental exchange isotherms for asymmetric Na,Ca2 exchange forWyoming smectite API-25 (Oster, Shainberg et al., 1980). The exchange isotherm representingGaines-Thomas selectivity coefficient KGT 0:30 is plotted as a smooth line.for the hydr v region soils. Modest increases in the equiv-alent fractio ha a reduces the plasticity index of smectiteclays (and s o ficantly lowering the activity index of soilscontaining .9). The reduction of plasticity lowers themechanical e and sharply decrease water hydraulic con-ductivity th p w hydraulic conductivity at the soil surfacelowers wate a creases runoff while also reducing the effi-ciency of bo re and internal drainage. Internal soil drainagecontrols the xc from the soil profile.APPENDI IC HANGES IN SAR BY WATERCHEMIST TThe follow y a groundwater sample with an electricalpSoil and Environmental Chemistry316A ChemEQL water chemistry simulation that replaces component Cawith calcite (insert solid) and uses pCO2 3:5 102 atm yields the followingresults (numerous minor species have been deleted).Species ActivityCa 4.33E-06K 6.80E-05Mg 9.71E-04MgSO4 7.44E-05MgHPO4 2.75E-05Na 2.94E-03CO2(aq) (atm) 1.71E-03HCO3 (atm) 1.33E-01CO3 (atm) 1.13E-03Cl 3.49E-03NO3 1.43E-07SO4 4.51E-04HPO4 3.49E-05CaCO3(aq) 5.01E-06CaHCO3 1.10E-05OH 1.82E-06CO3H0.005.50E-090.00E00HCO3 228.80 3.75E-03NO3 (N) 0.01 7.14E-07PO4 0.01 1.05E-07Cl 139.00 3.92E-03SO4 77.00 8.02E-04Ca 50.00 1.25E-03Mg 40.00 1.65E-03K 3.00 7.67E-05Na 76.00 3.31E-03Ion ppm, mg L1 M, mol L1conductivity ECW 0:77 dS m1 and SARP 1:94 mmolc L1. The ionicstrength estimated from ECW 0:77dS m1 using expression (7.85) isI 1:04 102 molc L1.ing water anal sis is fromRY SIMULA IONX 7I. PRED TING Cleaching of e ess saltsth soil moistu recharger infiltration r tes and inrough the soil rofile. Lostrength of th soil fabricsmectite clays (Figure 7oil humic coll ids), signiNan ~E of exc ngeable Naulic conducti ity of aridWilco ,highe :SARPro1.Chapter 7 Acid-Base Chemistry 317following solution species.Species Concentration,mol L1Species Concentration,mol L1Ca 9.57E-04 Mg(H3SiO4)2(aq) 2.26E-13CaOH 4.59E-09 Na 1.44E-04CaCO3(aq) 5.42E-06 NaOH 3.00E-11CaHCO3 2.71E-05 NaCO3 1.20E-08CaSO4 8.40E-06 NaHCO3 2.04E-07CaH2SiO4(aq) 1.20E-12 NaSO4 4.07E-08CaH3SiO4 9.13E-10 H2CO3 1.71E-04Ca(H3SiO4)2(aq) 1.26E-13 HCO3 2.90E-03HSiO4 1.22E-14 CO3 5.90E-06typical groundwater has the following composition: pH 7.55, total Ca 40.0 mg L-1, total Mg 5.2 mg L-1, Na 3.3 mg L-1, K 0.9 mg L-1, totalcarbonate (as bicarbonate) 190 mg L-1, total chloride 5.9 mg L-1, total sul-fate 8.1 mg L-1, and total silica 6.3 mg L-1.Use ChemEQL to simulate the alkalinity of this groundwater sample.SolutionBased on the results of this simulation, calculate the alkalinity of this solutionusing the definition of alkalinity AT : Eqs. (7.63) and (7.67). NOTE: Subscript Tindicates the total concentration of the species in the solution as measured,taking into account ion pair interactions.AT Cbicarbonate 2 Ccarbonate Csilica Chydroxyl Cproton The ChemEQL simulation of groundwater with this composition yields theblemsCrandall and colleagues (1999) published a study of groundwater and riverwater mixing, listing dissolved salts in groundwater from a number of wellsand sinkholes and surface water from the Suwannee and Little Springs riversin Suwannee County, Florida. Under low flow (i.e., low rainfall) conditions,wx et al., 1963) is adj SAR 2:55assuming pH 8:4once againr than the sodium adsorption ratio calculated from the water analysis 1:94.The adjusted sodium adsorption ratio calculated using (7.92) (Suarez,1981) is SARadj 2:65assuming the pH is set by calcite solubility andpCO2 3:5 102 atmhigher than the sodium adsorption ratio calculatedfrom the water analysis: SARw 1:94. This increase results from calcite pre-cipitation. The Langelier calcite saturation pHC 8:09 is calculated from thepreceding simulation results using the following expression:pHc 1:85 log aCa2 log aHCO3 pHc 1:85 5:36 0:88The adjusted sodium adsorption ratio calculated using Eq. (7.91) (Bower,K 2.30E-05 Cl 1.66E-04te2.Soil and Environmental Chemistry318num in this soil? Is there any nonexchangeable aluminum in this soil? Doesnonexchangeable aluminum contribute to soil acidity?SolutionThe exchangeable aluminum content of the soil amounts to 4:45 102 molesof charge for every kilogram of soil. The following reactions demonstrate thateach mole of charge (as exchangeable aluminum) is equivalent to a mole ofexchangeable acidity.Al3 ex interlayer3 H2O l ! Al OH 03interlayerpolymeric Al 3 H ex interlayerOnemole of limestone (calcite) neutralizes twomoles of acidity (i.e., threemoles ofcalcite neutralizes the acidity from two moles of exchangeable arelevant to acidity of the Hongmaochong Inceptisol (surface 010 cm) are pH(1 M KCl) 3.91, CEC 22.5 cmolc kg1, exchangeable Al of 4.45cmolc kg1, and exchangeable base cations occupying 9.12% of the CEC.How much limestone would you need to eliminate the exchangeable alumi-neglect species whose concentrations are three orders of magnitude lowerthan HCO3 , the most concentrated species.AT 2:90 103 2:71 105 bicarbonate 2 5:90 106 5:42 106 carbonaAT 2:90 103 0:027 103 0:018 103 0:012 103 AT 2:94 103Dai and colleagues (1998) studied the effect of acid rain on soils from the pro-vinces of Hunan and Guangxi in southern China. The soil chemical properties4The ChemEQL simulation contains two significant figures. This means we can HSO H T 3 3 3 3bicarbonate 2 CO23 Ca CO3 0h i Mg CO3 0h i Na CO3 carbonate H3SiO4 Ca H3SiO4 Mg H3SiO4 silica2 Ca H3SiO4 02h i Mg H3SiO4 02h i silica OH Mg 2.07E-04 H3SiO4 5.00E-07MgOH 2.17E-08 H4SiO4(aq) (SiO2) 1.05E-04Mg4OH4 5.47E-25 H2(SiO4)2 7.19E-13MgCO3(aq) 6.72E-07 H4(SiO4)4 4.48E-22MgHCO3 5.34E-06 H6(SiO4)4 3.13E-15MgSO4 1.51E-06 OH 3.80E-07MgH2SiO4 3.05E-12 H 2.82E-08MgH3SiO4 3.42E-10Subscript T indicates the total concentration of the species in the solutionas measured. This is opposed to the free concentration, which does notaccount for ion pair species. The following formula includes the most impor-tant ion pairs contributing to alkalinity in the solution under consideration.A HCO Mg HCO Ca HCO Na HCO 0h i KOH 2.41E-12 SO4 7.43E-05KSO4 9.20E-09 HSO4 1.67E-10Mg(OH)2(aq) 2.02E-17 H2SiO4 1.73E-12luminum).3.4.Chapter 7 Acid-Base Chemistry 319tent cmolc kg1 of this soil.PO4 0.01NO3 (N) 0.01HCO3 250.7CO3 0.0The subsurface soil chemical properties of a Rhodiudult from Guangxi Prov-ince (China) are (Dai, Liu et al., 1998) pH (1 M KCl ) 4.0 and CEC 29.8cmolc kg1. Using Figures 7.13 and 7.14, estimate the exchangeable Al con-Na 79.0K 5.0Mg 38.0Ca 78.0SO4 85.0Cl 190.0Component ppm, mg Lcbut does not contribute to soil acidity and can be ignored when estimatingthe amount of limestone required.The following table lists the chemical analysis of a groundwater sample fromWaukesha, Wisconsin. The electrical conductivity of the water is 1.05dS m1, and the pH is 8.0. Calculate the following: carbonate alkalinity,ionic strength, and SARP . Using ChemEQL, calculate SARadj using expression(7.92) for a soil pH of 8.4, and pCO2 3:5 102 atm (approximate soilatmosphere).12 Al3 ex interlayer3 CaCO3calcite3 H2O l ! 2 Al OH 3interlayerpolymeric Al3 Ca2 ex interlayer3 CO2 g Remember: The exchangeable aluminum content is expressed as moles ofcharge, eliminating the need to balance moles of exchangeable aluminumwith moles of calcite as shown in the overall reaction.Adding 2.23 grams of limestone (assuming the limestone is pure calcite) toeach kilogram of soil would neutralize the acidity from the exchangeablealuminum.4:45cmolc,Alkgsoil0@1A 102 molccmolc0@1A 4:45 102 molHkgsoil0@1A4:45 102 molHkgsoil0@1A molCaCO32 molH0@1A 2:23 102 molCaCO3kgsoil0@1A2:23 102 molCaCO3kgsoil0@1A 100 gCaCO3molCaCO30@1A 2:23 gCaCO3kgsoil0@1ANonexchangeable aluminum accounts for 71% of the CEC (16 cmol kg1)CaCO3 s calcitelimestone2 H aq !Ca2 aq CO2 g H2O l 8.5 Summary 361Appendix 8A. Assigning FormalPotential Using PlatinumORP Electrodes 3658.1Ox er inen ofma th o-ch h atyo xrea ntransport chain. Respiration is a complex series of electron-transfer reactionsthat ultimately couples to the environment, consuming electron acceptorsranging from molecular oxygen to carbon dioxide in order to release the-as electron donorsby a variety of oxidizing agentselectron acceptorsthrough the respiration of living organisms. This means that the locus of mostenvironmental redox reactions is the zone of biological activity, the zone oforganic carbon accumulation.Soil and Environmental Chemistry.# 2012 Elsevier Inc. All rights reserved.chemical energy stored in reduced carbon compounds.Environmental redox chemistry has at its source the oxidation of reduced carbon compounds biomolecules, organic compounds, and organic matter servingu learned in general chemistry challenging. The driving force behind redoctions in the environment is a key component in respiration: the electroOxidation Numbers 362. INTRODUCTIONidation-reduction or electron-transfvironmental chemistry, affecting theny elements. Redox chemistry inemistry and geochemistry in ways treactions are extremely importantbiological availability and mobilitye environmental context blends biat can make the transition from whChapter 8Redox ChemistryChapter Outline8.1 Introduction 3218.2 Redox Principles 3228.3 Interpreting Redox StabilityDiagrams 3318.4 Microbial Respiration andElectron TransportChains 345Appendix 8B. Converting(pe, pH) RedoxCoordinates into (EH, pH)Coordinates 363Appendix 8C. Limitations inthe Measurement of theEnvironmental Reduction321Soil and Environmental Chemistry322The progress of environmental redox reactions and development of zoneswhere certain redox processes dominate are both governed by the level ofbiological activity. The seeming absence of molecular oxygenanoxia beingconditions where the concentration of dissolved molecular oxygen is verylowis necessary but not sufficient for reducing conditions. The developmentof anoxia leads to changes in the active microbial population from communitiesthat rely on aerobic respirationmolecular oxygen serving as the terminal elec-tron acceptorto anaerobic respiration, where other chemical substances replacemolecular oxygen as the terminal electron acceptor supporting respiration.This transition from one microbial community to anotherfrom one typeof respiration to anothersets the stage for the chemical reduction of theenvironment that will ultimately couple the redox reactions required forbiological respiration to a host of redox reactions that occur simply becausethe redox potential is drawn down by anaerobic respiration.This chapter is organized into three major sections. The first is a reprise ofredox chemistry principles that are essential for a complete understanding ofenvironmental chemistry, designed to bridge the gap between general chemis-try and environmental chemistry. The second develops the methods used bygeochemists to quantify and interpret redox conditions as they occur in theenvironment. The final section provides the mechanism that generates reduc-ing conditions in soils and groundwater: anaerobiosismicrobial respirationin the absence of molecular oxygen. Respiration consists of a sequence ofbiological redox reactions organized as an electron transport chain coupledto select electron acceptors in the environment, and anaerobic respiration isthe source of the compounds characteristic of reducing conditions.8.2. REDOX PRINCIPLES8.2.1. Formal Oxidation NumbersRedox reactions are chemical reactions involving the transfer of one or more elec-trons from an electron donorthe reducing agentto an electron acceptorthe oxidizing agent. General chemistry books typically discuss the assignmentof formal oxidation numbers because it can be difficult in many cases to recog-nize whether electron transfer has occurred in a given chemical reaction and toidentify electron donors and acceptors. Formal oxidation numbers are also usedfor electron accounting in redox reactions.The formal oxidation number of an element in a compound is usually a poorestimate of the actual oxidation state of that element in this compound; subtledetails in chemical bonding determine the true oxidation state. Regardless, anelectron transfer reaction always results in the loss of one or more electrons fromthe electron donor compound and the acquisition of an equal number of electronsby the electron acceptor compound. The assignment of formal oxidation numbersis sufficiently accurate to demonstrate that electron transfer has occurred, to iden-tify electron donors and acceptors, and to balance redox reactions.Table 8.1 lists the chemical rules for assigning formal oxidation numbersto elements in ions and compounds. There are exceptions, but they are rela-tively inconsequential for environmental chemistry. Appendix 8A gives twoexamples to demonstrate the assignment of formal oxidation numbers.TABLE 8.1 Rules for Assigning Formal Oxidation Numbers to ElementsRule Examples and Exceptions1. The oxidation number of a freeelement is always (0).Theelements inS s andO2 g havea formal oxidation number of (0).2. The oxidation number of amonatomic ion equals the chargeof the ion.The oxidation number of the ionNa aq is (1).3. The oxidation number ofhydrogen in a compound isusually (1).Exception: The oxidation numberof hydrogen is (1) in compoundscontaining elements that are lesselectronegative than hydrogen(Figure 8.1)for example, alkalihydrides such as NaH s orCaH2 s .4. The oxidation number of oxygenin compounds is usually (2).Exception: Since F is moreelectronegative than O(Figure 8.1), its oxidation numbertakes precedence. The formaloxidation number of O in oxygendifluoride OF2 g is (2).5. The oxidation number of aGroup IA (alkali) element in acompound is (1).The oxidation number of K in themineral orthoclase KAlSi3O8 s is (1).6. The oxidation number of aGroup IIA (alkaline earth)element in a compound is (2).The oxidation number of Ca inthe mineral anorthiteCaAl2Si2O8 s is (2).7. The oxidation number of aGroup VIIA (halogen) element ina compound is (1).Exception: Since O is moreelectronegative than Cl(Figure 8.1), its oxidation numbertakes precedence. The formaloxidation number of Cl in HOClis (1).8. The sum of the oxidation The sum of the oxidation numbersChapter 8 Redox Chemistry 323numbers of all of the atoms in aneutral compound is (0).for ascorbic acid C6H8O6 is (0).9. The sum of the oxidationnumbers in a polyatomic ion isequal to the charge of the ion.The sum of the oxidation numbersfor SO24 aq is (2).Soil and Environmental Chemistry3248.2.2. Balancing Reduction Half ReactionsThe primary utility of formal oxidation numbers comes when balancing redoxreactions: verifying that electron transfer occurs, identifying electron donorFIGURE 8.1 Periodic table of Pauling electronegativity values.and acceptor atoms, and balancing the electron count. General chemistryintroduces the concept of the reduction half reaction:Asacceptorm H n e ! Drdonor8:1Table 8.2 lists the steps you should follow when balancing a reduction halfreaction (8.1). The balancing steps 25 (see Table 8.2) should be executed inthe order given to avoid confusion and error (see Example 8.1).TABLE 8.2 Steps for Balancing Reduction Half ReactionsStep Example1. Assign formal oxidation numbers toidentify electron acceptor atom in theeduct (left-hand) side and the electrondonor in the product (right-hand) side.N2ON1 . . .! NH4N3 . . .2. Balance atoms involved in electrontransfer.N2ON1 . . .! 2 NH4N3 . . .ContinuedChapter 8 Redox Chemistry 325Example 8.1Balancing the reduction half reaction involving ascorbic acid (CAS 50-81-7,Structure 1) and dehydroascorbic acid (CAS 490-83-5, Structure 2) begins withstep 1; the identity of electron donor and acceptor compounds may not be imme-diately evident from inspection.TABLE 8.2 Steps for Balancing Reduction Half ReactionsContdStep Example3. Determine the change in formaloxidation number and assign thatintegral number to the number ofelectrons n on the electron acceptor(or educt) side of the reactionequation (8.1).N2ON18 e . . .! 2 NH4N3 . . .4. Balance the net charger s m n by addingm protonsH to the left-hand side of the reactionequation (or an appropriate number ofhydroxyl ions to the right-hand side).N2ON110 H 8 e ! 2 NH4N3 . . .5. Balance proton (or hydroxyl) massby adding an appropriate number ofH2O.N2ON 1 10 H 8 e ! 2 NH4N 3 H2OStructure 1. Ascorbic acidStructure 2. Dehydroascorbic acidStep 1: These two compounds differ at carbons C4 and C5: the formal oxida-tion states of carbon C4 are (1) and (2), and carbon C5 are (2) and (3) inascorbic and dehydroascorbic acid, respectively. This identifies dehydroascor-bic acid as the electron acceptor and ascorbic acid as the electron donor. Thereduction half reaction places the electron acceptor dehydroascorbic acid onthe left-hand (educt) side and the electron donor ascorbic acid on the right-hand(product) side.Step 2: The stoichiometric coefficients on the electron donor and acceptorcompounds are identical: 1.Step 3: The net change in formal oxidation state summed over both carbons is(2). The required electron stoichiometric coefficient n is 2, as shown in Eq. (8.2):C6H6O6electronacceptor2 e . . . C6H8O6electrondonor . . . 8:2Steps 4 and 5: Charge balance in expression (8.2) requires a proton stoichio-metric coefficient m of 2, as shown in Eq. (8.3). The proton mass balance doesSoil and Environmental Chemistry326FIGURE 8.2 A complete gal-vaniccellconsistsofacathodeandananode; thecathode is a standardcupric Cu2 1 M Cu s j half-cell, and the anode is a standardhydrogen H2 1 atm Hj 1M half-cell.8.2.3. Reduction Half Reactions and Electrochemical CellsFigure 8.2 illustrates the standard galvanic cell, a common illustration found ingeneral chemistry books. The solutes are all 1 M, the electrode materials arepure elements (copper metal cathode capable undergoing oxidation to Cu2ions and an inert platinum anode), all gas pressures are 1 atmosphere. A saltbridge permits the diffusion of inert ions to maintain charge neutrality duringelectron transfer, and a high impedance1 voltmeter measures the cell potential.The standard reduction potential for a hydrogen half-cell ESHE is, by defi-nition, equal to zero volts (ESHE 0:0V). Consequently the cell potential Ecellnot require any additional water molecules; reaction (8.3) is the fully balancedreduction half reaction.Reaction1. A high impedance voltmeter requires a very small current to record the potential difference.Chapter 8 Redox Chemistry 327TABLE 8.3 Reduction Potentials for a Selection of Reduction Half ReactionsReduction Half Reaction StandardBiologicalReductionPotential,E{H , mVStandardReductionPotential,EH, mV2 H aq 2 e ! H2 g 414 0CO2g 8 H aq 8 e ! CH4g 2 H2O l 245 1696 N2 g 8 H aq 6 e ! 2 NH4 aq 278 2742SO24 aq 10 H aq 8e!S2O23 aq 5H2O l 130 284SO24 aq 8 H aq 6 e ! S s 4 H2O l 61 353Fe3 aq e ! Fe2 aq 771 771NO3 aq 2 H aq 2 e ! NO2 aq H2O l 407 821NO2 aq 2 H aq e ! NO aq H2O l 238 1066Fe OH 3s 3 H aq e ! Fe2 aq 3 H2O l 262 981recorded in Figure 8.2 is equal to the standard reduction half-cell potential2EH of the other half-cell: Cu2 1 M Cu s j .Most electron transfer reactions encountered in biology, geochemistry, andenvironmental chemistry cannot be replicated using galvanic cells of the typeshown in Figure 8.2. Regardless, it is possible to use Gibbs energy relations todetermine standard reduction half reaction potentials for all relevant electrontransfer reactions. We will explain this in the following sections.Standard conditions and standard reduction potentials EH (Table 8.3) arenot found in nature. Biochemists typically tabulate standard biological reduc-tion potentials E{H that approximate physiological conditions. Most environ-mental chemists either tabulate or describe methods for computing standardenvironmental reduction potentials (which are identical to standard biologicalreduction potentials E{H ) from standard reduction potentials.8.2.4. The Nernst EquationThe Nernst equation, which you first encountered in general chemistry, allowsyou to calculate a half reaction potential under any nonstandard condition.This equation is derived from the Gibbs energy expression under nonstandardO2 g 4 H aq 4 e ! 2 H2O l 815 12292. The H subscript in the symbol for reduction half-cell potentials EH indicates that the potentialis based on the hydrogen half-cell ESHE.conditions (Eq. (8.4)) and the expression relating Gibbs energy to the halfSoil and Environmental Chemistry328aA aHDG n F E 8:5Expression (8.4) represents the change in Gibbs energy DG in anychemical reaction. The symbols in Eq. (8.4) are reaction quotient Q,ideal gas constant R (8.314472 103 kJ mol1 K1), and the absolute tem-perature T (K). Expression (8.5) in the context of a redox reaction representsthe change in Gibbs energy DG as electrons move from one electrostaticpotential to another; the initial and final electrostatic potentials are thoseexisting in the electron acceptor and donor compounds. The symbols inEq. (8.5) are the Faraday constant F (98.48534 kJ mol1 V1) and thestoichiometric electron coefficient n for the reduction half reaction.Expression (8.5) applies to any balanced electron transfer reaction,including reduction half reactions. The electron transfer potential for abalanced electron transfer reaction is denoted E, while the electrontransfer potential for the half reaction3 is denoted EH. Similarly, thechange in Gibbs energy for a balanced electron transfer reaction is de-noted DG, while the change in Gibbs energy for a reduction half reactionis denoted DGH.Setting Eq. (8.4) equal to (8.5) results in the seminal Nernst equation (8.6).Solving Eq. (8.6) for half reaction potentials yields the Nernst equation in itsmost familiar form: (8.7). Most expressions replace the natural logarithm withthe logarithm to the base 10 (Eq. (8.8)): ln x ln 10 log10 x .n F EH n F EH R T ln aDraAs amH ! !8:6EH EH R Tn F ln aDraAs amH !8:7EH EH R T ln 10 n F log10aDraAs amH 8:8At 298.15K (25C), Eq. (8.8) reduces to a simpler approximate expression (8.9):R T ln 10 n F 8:314 103 kJ mol1 K1 T 2:303 n 96:49 kJ mol1 V1 !reaction potential (Eq. (8.5)).DG DG R T ln aDrs m ! DG R T ln Q 8:43. The convention we use is all half reactions are written as reduction half reactions (8.1).Chapter 8 Redox Chemistry 329Example 8.3 illustrates the calculation of standard biological reduction halfpotentials E{H for the reaction H107MjH21 atm using the Nernst equa-pressures equal to 1 i:e:, Q 1 or log10Q 0 .Example 8.2Calculate the standard biological reduction half potential E{H for the reactionH2O jO21 atm,H107M (see Table 8.3) using the Nernst equation.The reactionH2O jO21atm,H1M and its standard reduction half potentialEH appear following. Under standard conditions the proton activity is aH 1.O2 4 H 4 e ! 2 H2O E H 1:229VUnder physiological conditions the reaction becomes H2O jO21 atm,H10 7M, and the proton activity is aH 107 because standard biologicalconditions are defined as pH 7.Substituting these conditions into the Nernst equation and simplifying yieldthe following expressions.E{H EH R T4 F0@1A ln 1pO2 107 4E{H EH R T4 F0@1A ln 1107 40B@1CA R T4 F0@1A ln 1pO20@1AE{H EH 4 R T ln 10 7 4 F0@1AApplying the simplification in Eq. (8.9) yields the following, which appears inTable 8.3, column 3.E{H 1229mV 59:16mV 7 E{H 1229mV 414:1mV 814:9mVThe following two examples (Examples 8.2 and 8.3) demonstrate the calcula-tion of standard biological reduction half potentials E{H using the Nernstequationeither (8.8) or (8.9). A standard biological reduction potential E{Hrequires that all componentsother than H aq have activities or partialEH, 25C EH 59:16mVn 25C log10aDraAs amH 8:9tion. You will notice that it is very similar to the previous example.Soil and Environmental Chemistry330EH E H mn 2:303 R T pHF 2:303 R Tn F log10aD mn aA 8:11The first and second terms in Eq. (8.11) combined define the standardbiological (or environmental) reduction half potential E{H (Eq. (8.12)), regard-less of the values assigned to the remaining terms in the reaction quotient Q.H H 2 FApplying the simplification in Eq. (8.9) yields the following, which appears inTable 8.3, column 3.E{H 0:0mV 59:16mV 7 E{H 414:1mVThe general reduction half reaction (8.1) yields a general reaction quotientQ as shown in Eq. (8.10).EH E H R Tn F ln aD mn aA amH !8:10Rearranging expression (8.10) yields (8.11), which explicitly lists protonm and electron n coefficients.E {H EH 2 F@ A ln107 2 2 F@ A lnpH2E{ E 2 R T ln 10 7 0@1Adefined as pH 7.Substituting these conditions into the Nernst equation and simplifying yieldthe following expressions.E{H EH R T2 F0@1A ln pH2107 2 R T0 11 R T0 1Calculate the standard biological reduction half potential EH for the reactionH107MjH21 atm (see Table 8.3) using the Nernst equation.The reaction H1MjH21 atm and its standard reduction half potential E Happear following. Under standard conditions proton activity is aH 1.2 H 2 e ! H2Under physiological conditions the reaction becomes H107MjH21 atm,and the proton activity is aH 107 because standard biological conditions areExample 8.3{Expression (8.13) allows you to calculate a nonstandard reduction potential noChapter 8 Redox Chemistry 331matter what activity is assigned to other components in the reaction quotientQ, including gas partial pressures other than 1 atm.E{H EH mn 2:303 R T 7 F 8:12EH E{H 2:303 R Tn F log10QpH7 8:138.3. INTERPRETING REDOX STABILITY DIAGRAMSOne of the most important tasks facing an environmental chemist is assessingchemical conditions at a site and interpreting the implications of those condi-tions. Chapter 5 discussed the use of water chemistry simulations to identifyminerals that potentially control water chemistry in environmental samples.Chapters 4 and 9 discuss the use of adsorption and exchange isotherms toquantify an insoluble but chemically active reserve that sustains solute con-centrations without the involvement of precipitation reactions. The assessmentand interpretation of redox conditions require chemical coordinates that char-acterize redox conditions and a means of interpreting the significance of thosechemical coordinates.Tables 8.3, 8.7, 8.9, 8.10, and 8.11 list reduction half reactions for numer-ous environmentally relevant redox reactions. All of these tables list standardbiological reduction potential E{H , calculated from the standard reductionpotential EH for each reduction half reaction. The only reduction half reactionin Table 8.3 where the standard biological reduction potential E{H and thestandard reduction potential EH are equal is the reduction of Fe3 aq toFe2 aq the only reaction where H aq does not appear as an educt. Ifreduction half reactions contain H aq as an educt, then expression (8.11)predicts that the reduction potential will be pH-dependent.The two chemical coordinates that chemists use to characterize redox con-ditions are the experimental potential EH and pH. The electrochemist MarcelPourbaix (1938) was the first to prepare stability diagrams to interpret redoxconditions using EH, pH coordinates. Pourbaix studied corrosion; corrosionscientists were the first to employ Pourbaix diagrams, but environmental che-mists, soil chemists, and geochemists quickly adopted them to interpret geo-chemical and environmental redox conditions.8.3.1. Environmental Redox ConditionsBaas-Becking and colleagues (1960) published a Pourbaix diagram plotting ahost of experimental EH, pH coordinates from scientific papers reportingenvironmental redox conditions (Figure 8.3). Few of the experimentalEH, pH coordinates fall outside of the pH range 4 to 8. The lower limit isSoil and Environmental Chemistry332FIGURE 8.3 This Pourbaix diagram plots more than 6,200 experimental EH , pH coordinatesthe pH of maximum buffering by exchangeable Al ions (see Chapter 7), whilethe upper limit is the pH at which carbonate buffering resists further increases.Environmental reduction potentials EH at the upper limit plot roughly parallelto the line defining the limit of water stability (Delahay, Pourbaix et al.,1950)the line labeled O2 H2Oj representing the O2 reduction half reactionfrom Table 8.3and never approach the lower limit of water stabilitytheline labeled H2 Hj representing the H aq reduction half reaction fromTable 8.3below pH 6.HCO3 aq 7 H 8 e ! CH4g 2 H2O E{H 245 mV8:14Baas-Becking and colleagues (1960) attribute the significant increase in therange of environmental redox conditions centered on the alkaline pH limitto microbial sulfate respiration; however, there is no significant change in sul-fate solubility in this pH range. An alternative interpretation supported by thebicarbonate reduction potential (Eq. (8.14)) would assign the dramatic expan-sion of reducing conditions at the alkaline pH limit to microbial carbonate res-piration. Carbonate solubility increases dramatically above pH 6 (see Chapter7), increasing both buffering capacity and the availability of the terminal elec-tron donor required for carbonate respiration.representative of the redox conditions found in the environment. Source: Reproduced with permis-sion from Baas-Becking, L.G. M., Kaplan, I.R., et al., 1960. Limits of the natural environment interms of pH and oxidation-reduction potentials. J. Geol. 68, 243284.Regardless of why the range of reducing conditions recorded in soilsexpands with increasing pH, Figure 8.3 confirms the profound importanceof anaerobic microbial respiration in defining environmental redox conditions.8.3.2. Measuring Environmental Reduction Potentials UsingPlatinum Oxidation-Reduction ElectrodesEnvironmental reduction potentials are measured using some variation of aplatinum combination oxidation-reduction potential ORP electrode, illustratedin Figure 8.4. The electrode is a compact version of the galvanic cell inChapter 8 Redox Chemistry 333FIGURE 8.4 A typical platinum oxidation-reduction potential (ORP) electrode is a combinationelectrode. The reference half-cell potential in this case is based on the calomel reduction potentialWilde (1998) outline the limitations of measuring environmental reductionpotentials using platinum ORP electrodes. These limitations are discussed inAppendix 8B.The true redox potential of a soil that is rich in organic matter is highlyreducing, but the reducing potential of natural organic matter is blocked byan activation barrier that prevents the transfer of electrons from organic matterto dioxygen (see Chapter 6). Aerobic respiration eliminates the aforemen-tioned activation barrier through catabolism and the aerobic electron transportchain.Figure 8.2. The standard hydrogen half-cell (anode, Figure 8.2) is not practi-cal for environmental measurements and is replaced by a reference half-cellsuch as the calomel reduction half reaction (8.60). The voltmeter employs ahigh-impedance design that requires a very small current to record an accuratepotential.Hg2Cl2s 2 e ! 2 Hgl 2 Cl EH 244:4 mV 8:15The platinum ORP combination electrode includes two porous ceramic junc-tions that function as salt bridges, allowing an ion current to flow between ref-erence electrode and the external solution being measured. The electroncurrent passes through a voltmeter in the circuit connecting the platinumsensing wire and the liquid mercury of the reference cell. Nordstrom and(8.15). The reduction potential is measured using a platinum wire as the second electrode.8.3.3. Pourbaix Stability Diagrams: Preparationand InterpretationThis section describes the components in a Fe-O-C-H Pourbaix stability dia-gram to illustrate the essential features found in all Pourbaix diagrams. Thepreparation of accurate Pourbaix diagrams is beyond the scope of this book,since it requires an advanced understanding of chemical thermodynamicsand redox chemistry. This section, however, will provide the foundation thatSoil and Environmental Chemistry334the interpretation is surprisingly simple because Pourbaix diagrams providea limited representation of the chemical system.8.3.4. Water Stability LimitsThe two boundaries in Figure 8.3 delineate the stability domain of water (seeDelahay, Pourbaix et al., 1950). These boundaries are derived from the tworeduction half reactions (8.16) and (8.17).O2 g 4 H aq 4 e ! 2 H2O l EH 1229 mV 8:162 H aq 2 e ! H2 g EH 0:0 mV 8:17Expression (8.18) is the Nernst expression for reduction half reaction (8.16)defining the boundary labeled O2 H2Oj in Figure 8.3.EH EH R Tn F ln1pO2 a4H ! EH R T ln10 4 F log101pO2 a4H !8:18TABLE 8.4 The Essential Features Needed to Interpret a Pourbaix Diagram1. The elemental components whose chemical stability the diagram is designed toportray.2. Total dissolved concentration of all solutes and partial pressure of all gases influen-cing the chemical stability of the defined system.3. The nature of each stability field: solute or precipitate.4. The nature of each boundary separating two fields: solute-solute, solute-precipitate,or precipitate-precipitate.will allow you to interpret virtually any Pourbaix diagram you will encounter,however complex.Table 8.4 lists the features found in any complete Pourbaix diagram. Inter-pretation begins with identifying each of these features. Most of these featureswill be readily apparent, but some may be listed in the caption or text accom-panying the diagram. The absence of these features makes interpretationimpossible. Once you have correctly identified all of the essential features,5EH 1229 mV 59:16 mV pH 8:20The O2 g H2O l j stability boundary is usually drawn assuming an O2 partialpressure of 1 atm (Eq. (8.20)). To demonstrate the effects of anoxia, expres-sion (8.21) gives the pH-dependent reduction potential for the O2 g H2O l jcouple at pO2 106 atm. The intercept of Eq. (8.21) is shifted downward amere 88.8 mV relative to the intercept of Eq. (8.20), a relatively minor shiftconsidering the 700800 mV potential recorded by a typical platinum ORPelectrode EPt in aerated water (Appendix 8B).EH 1229 mV 59:16 mV 6 4 59:16 mV pHEH 1141 mV 59:16 mV pH 8:21Expression (8.22) is the Nernst expression for reduction half reaction (8.17)defining the boundary labeled H H2j in Figure 8.3.EH EH R T ln10 2 F log10pH2a2H 8:22Factoring the second term on the right of expression (8.22) results in expres-sion (8.23), containing three terms on the right: the standard reduction poten-tial EH, the dependence on the H2 partial pressure (see Table 8.4, item 2), andthe dependence on proton activity. The stoichiometric coefficients forthe electrons n and protons m are identical and cancel in the third term.The H aq H2 g j stability boundary is usually drawn assuming a H2 partialpressure of 1 atm (8.24).EH EH 59:16 mV2 log10 pH2 59:16 mV log10 aH EH EH 59:16 mV2 log10 pH2 59:16 mV pH 8:23Factoring the second term on the right of expression (8.18) results in expres-sion (8.19), containing three terms on the right: the standard reduction poten-tial EH, the dependence on the O2 partial pressure, and the dependence onproton activity. Notice that the stoichiometric coefficients for the electronsn and protons m are identical and cancel in the third term.EH EH 59:16 mV4 log10 pO2 59:16 mV log10 aH EH EH 59:16 mV4 log10 pO2 59:16 mV pH 8:19Chapter 8 Redox Chemistry 33EH 59:16 mV pH 8:24Soil and Environmental Chemistry336The first boundary unique to the Fe-O-C-H Pourbaix diagram we are prepar-ing is the reduction equilibrium boundary for pHindependent reduction halfreaction (8.25).Fe3 aq e ! Fe2 aq EH 771 mV 8:25The Nernst expression for this half reaction is (8.26). Since this reduction halfreaction is independent of pH, we can anticipate the boundary runs perpendic-ular to the EH axis of our Pourbaix diagram.EH EH R T ln10 n F log10aFe2aFe3 EH 771 mV 59:16 mV log10aFe2aFe3 8:26The convention used to define a solute-solute reduction equilibrium boundaryis to draw the boundary where the activities of the two solutes are equalinthis case aFe2 aFe3 . Expression (8.26) reduces to solute-solute reductionequilibrium boundary expression (8.27).EH 771 mV 8:27Figure 8.5 illustrates the Pourbaix diagram with the three boundaries (8.20),(8.24), and (8.27).Solute Fe3 aq undergoes hydrolysis (8.28) and (8.29) as the pHincreases.Fe3 aq H2O l ! Fe OH 2 aq H aq Ka1 102:19 8:28Fe OH 2 aq H2O l ! Fe OH 2 aq H aq Ka2 103:508:29Solution specie Fe OH 2 aq appearing in both (8.28) and (8.29) neverreaches an activity where it accounts for 50% of the soluble Fe. Hydrolysisequilibrium involving the two dominant solute species is defined by reaction(8.30), which combines (8.28) and (8.29).Fe3 aq 2 H2O l ! Fe OH 2 aq 2 H aq Ka1 Ka2 b2 8:30The equilibrium expression for hydrolysis reaction (8.30) is given byBoundary lines (8.20) and (8.24) are parallel and differ only in their intercept,which at pH 0 are the standard reduction potentials EH for the two reductionhalf reactions.8.3.5. The Solute-Solute Reduction Boundaryexpression (8.31).Chapter 8 Redox Chemistry 337b2 105:69 aFe OH 2 a2HaFe38:31Since electron acceptor Fe OH 2 aq will exceed 50% of the total soluble Fein the pH range > 2.84, we require a solute-solute reduction equilibriumboundary. This boundary is found by adding reduction half reaction (8.25)and hydrolysis reaction (8.30). The combined reaction is given by (8.32).Fe OH 2 aq 2 H aq e ! Fe2 aq 2 H2O l 8:32The reduction potential for this half reaction is calculated from the standardGibbs energy DGH for reduction half reaction (8.32) using the standard Gibbsenergy of formation DGf for each educt and product (8.33).4 The source forFIGURE 8.5 An incomplete Pourbaix diagram plotting the two water stability boundary lines,(8.20) and (8.24), and one solute-solute reduction equilibrium boundary (8.27). The positions of thewater stability boundaries are determined by pO2 1 atm, pH2 1 atm , as reported in the diagram.4. The standard Gibbs energy of formation DGf for H aq is defined as 0:00 kJ mol1.Soil and Environmental Chemistry338the two solutes are equalin this case aFe3 aFe OH 2 :Expression (8.37) reduces to boundary expression (8.38). Since this hydro-lysis reaction is independent of EH, boundary (8.38) runs perpendicular to thepH axis of our Pourbaix diagram.a2H b2 aFe3aFe OH 2 ! 105:69 aFe3aFe OH 2 !8:37pH 2:84 8:38Solute hydrolysis is a common equilibrium included in Pourbaix diagrams.Solute Fe3(aq) undergoes hydrolysis (8.28) through (8.30), as noted in thepreceding section. Solving expression (8.31) for the proton activity resultsin expression (8.37). Following the convention used to derive (8.27), we willdraw the solute-solute hydrolysis equilibrium boundary where the activities ofThe convention used to define solute-solute reduction equilibrium boundariesis to draw the boundary where the activities of the two solutes are equalinthis case aFe2 aFe OH 2 . Expression (8.35) reduces to boundary expression(8.36).EH 1108 mV 118:3 mV pH 8:368.3.6. The Solute-Solute Hydrolysis Boundarystandard Gibbs energy of formation DGf values, formation constants, stabilityconstants, and solubility constants is Lindsay (1979).DGH DGf ,Fe2 2 DGf ,H2O DGf ,Fe OH 2 2 DGf ,H 8:33DGH 91:21 kJ mol1 2 237:2 kJ mol1 458:7 kJ mol1 The reduction potentiala function (8.5) of the standard Gibbs energy changeDGH for the reduction half reaction (8.32)is given in expression (8.34).EH DGHn F 106:9 kJ mol1 1 96:485 kJ mol1V1 1:108V 8:34The Nernst expression for this half reaction is (8.35).EH EH R T ln10 n F log10aFe2aFe OH 2 a2H !EH 1108 mV 59:16 mV log10aFe2aFe OH 2 ! 2 59:16 mV log10 aH 8:35Chapter 8 Redox Chemistry 339Fe, total Fe OH 2equilibrium boundary for this choice is (8.42).aH 107:00102:15 104:85 8:42The condition CFe, total 107:00 M (Table 8.4) is reported by labeling thePourbaix diagram itself (Figure 8.6).Carbon dioxide gas dissolved in water will cause solute Fe2 aq to pre-cipitate as siderite FeCO3 s under alkaline conditions. This solute-precipitateequilibrium boundary depends on the carbon dioxide partial pressure, asshown in reaction (8.43).FeCO3 s siderite2 H aq ! Fe2 aq CO2 g H2O l 8:43The equilibrium solubility expression (8.44) is rearranged to obtain expression(8.45).Ksp aFe2 pCO2a2H 107:92 8:44a2H aFe2 pCO2 K1spKs2 a3HaFe3aFe OH 2 10aH aFe OH 2102:158:41The position of the solute-precipitate equilibrium boundary (8.41) depends onthe activity of solute aFe OH 2 , the numerator. The selection of this valuerelates to the second item in Table 8.4 that must be identified before youcan interpret the diagram. In this example, the total soluble iron concentration ischosen to be C 107:00 M, so a 107:00. The solute-precipitatesolute (8.39). Solute-precipitate equilibrium involving the dominant specieFe OH 2 aq is defined by reaction (8.40), which combines hydrolysisreactions (8.28) and (8.29) with solubility reaction (8.39).Fe OH 3 s 3 H aq ! Fe3 aq 3 H2O l Ks0 K3w 103:548:39Fe OH 3 s H aq ! Fe OH 2 aq H2O l Ks2 8:40aFe3 aFe OH 2 aH aFe OH 2 aH ! 2:158.3.7. The Solute-Precipitate BoundarySolute precipitation is a common equilibrium included in Pourbaix diagrams.Solute Fe3 aq undergoes hydrolysis as the pH increases until precipi-tation occurs in a pH range where Fe OH 2 aq is the most abundant ferricSoil and Environmental Chemistry340pH 12 log10 aFe2 log10 pCO2 7:92 8:45The solute-precipitate equilibrium boundary (8.46) is found by applying ourearlier condition on total soluble CFe, total 107:00M and choosing pCO2 103:45 atm (the atmospheric carbon dioxide level at mean sea level):pH 12 7:00 3:45 7:92 9:19 8:468.3.8. The Solute-Precipitate Reduction BoundaryAdding reduction half reaction (8.25) to solubility reaction (8.39) generates areduction half reaction (8.47) where the educt is a solidamorphousFe OH 3sand the product is the solute Fe2 aq . Reduction half reactionsof this type are common in environmental systems.FIGURE 8.6 An incomplete Pourbaix diagram displaying two water stability boundary lines,one solute-solute reduction equilibrium boundary (8.27), a solute-solute hydrolysis equilibriumboundary (8.33), and a solute-precipitate equilibrium boundary (8.42). The total soluble iron con-centration is CFe, total 107:00 M.1ferrous carbonate mineral siderite FeCO3 s . The reduction half reactionincludes CO2g as an educt, making this reaction dependent on pCO2 :Fe OH 3 s CO2g H aq e ! FeCO3 s 2 H2O l 8:53Earlier, when drawing the solute-precipitate equilibrium boundary (8.42),the following condition was adopted: CFe, total 107:00M. This conditionalso applies to (8.51): aFe2 107:00 or log10 aFe2 7:00. The solute-precipitate reduction equilibrium boundary for this choice is (8.52) and isplotted in Figure 8.7.EH 981 mV 59:16 mV 7:00 177:5 mV pHEH 1395 mV 177:5 mV pH 8:528.3.9. The Precipitate-Precipitate Reduction BoundaryReduction equilibrium can involve two solids. In this case the electron accep-tor is amorphous ferric hydroxide Fe OH 3 s , and the electron donor is theEH EH 1 F log10Fea3H8:50EH 981mV 59:16 mV log10 aFe2 3 59:16 mV pH 8:51Every Pourbaix diagram that includes reduction half reactions where an eductor product is a solid will result in an expression much like (8.51). The positionof the solute-precipitate reduction equilibrium boundary (8.51) depends on theactivity of solute Fe2 aq the second term on the right.Fe OH 3s 3 H aq e ! Fe2 aq 3 H2O l 8:47You will not find the reduction potential for (8.47) tabulated in any databasebut it is readily computed using the same approach applied to (8.28). Thereduction potential for this half reaction is calculated from the standard Gibbsenergy DGH for reduction half reaction (8.47) from the standard Gibbs energyof formation DGf for each educt and product (8.48). The standard reductionpotential EH is given by (8.49).DGH DGf ,Fe2 3 DGf ,H2O DGf ,Fe OH 3 s 3 DGf ,H 8:48DGH 91:21 kJ mol1 3 237:2 kJ mol1 708:1 kJ mol1 EH DGHn F 94:6 kJ mol1 1 96:485 kJ mol1V1 0:981V 8:49The Nernst expression for this half reaction is (8.50). Substituting the standardreduction potential EH (8.49) into (8.50) and separating terms for the contribu-tions from Fe2 aq and H aq yield expression (8.51). RT ln10 a 2 Chapter 8 Redox Chemistry 3434 Soil and Environmental Chemistry2The reduction potential for half reaction (8.53) is calculated from the standardGibbs energy of formation DGf for each educt and product (8.54). The stan-dard reduction potential EH is given by (8.55).DGH DGf ,FeCO3 s 2 DGf ,H2O DGf ,Fe OH 3 s DGf ,CO2 g DGf ,H 8:54DGH 677:6 kJ mol1 2 237:2 kJ mol1 708:1 kJ mol1 394:4 kJ mol1 EH DGHn F 49:43 kJ mol1 1 96:485 kJ mol1 V1 0:5123V 8:55The Nernst expression for this half reaction is (8.56). Substituting the standardreduction potential EH (8.55) into (8.56) and separating terms for the contribu-tions from CO2 g and H aq yield expression (8.57).FIGURE 8.7 An incomplete Pourbaix diagram plotting the following equilibrium boundaries:solute-solute reduction equilibrium boundary (Eq. (8.27)), solute-solute hydrolysis equilibrium bound-ary (Eq. (8.38)), solute-precipitate equilibrium boundary (Eq. (8.42)), and solute-precipitate reductionequilibrium boundary (Eq. (8.48)). The domains where CFe, total 107:00 M are shaded gray.3 2Chapter 8 Redox Chemistry 343and precipitate-precipitate reduction.l Experimental EH, pH coordinates plotting along solute-solute reductionboundaries indicate that the activities of the electron donor and theelectron acceptor are equal.l Experimental EH, pH coordinates plotting along solute-solute hydrolysisboundaries indicate that the activities of the two solute species separatedare labeled as solutes: Fe aq , Fe OH 2 aq , and Fe aq . Domainswhere the solute concentration is less than the defined limit (Figure 8.8)are labeled as solids: Fe OH 3 s and FeCO3 s . This labeling convention(Table 8.4, item 3) is a reminder regarding the total solute concentration.Each boundary represents a specific type of equilibrium (Table 8.4, item 4):solute-solute reduction, solute-solute hydrolysis, solute-precipitate reduction,EH EH R T ln10 n F log101pCO2 aH 8:56EH 512:3 mV 59:16 mV log10 pCO2 59:16 mV pH 8:57Earlier, when drawing the solute-precipitate equilibrium boundary (8.52), thefollowing condition was adopted: pCO2 103:45 atm. This condition alsoapplies to (8.57): log10 pCO2 3:45. The precipitate-precipitate reductionequilibrium boundary for this choice is (8.58).EH 308:2 mV 59:16 mV pH 8:588.3.10. Simple Rules for Interpreting Pourbaix DiagramsThe complete Pourbaix diagram in Figure 8.8 was earlier identified as a Fe-O-C-H Pourbaix diagram because these four elements are the only componentsdisplayed in the diagram (Table 8.4, item 1). Adding other components willintroduce new solutes and solids, altering the appearance of the diagram.A Fe-O-C-H Pourbaix diagram has no value when interpreting Fe chemistryof a system containing components besides O-C-H.The position of numerous boundary lines depends on solute concentrationsand gas partial pressures: boundary (8.20) depends on pO2 , boundary (8.24)depends on pH2 , boundaries (8.46) and (8.58) depend on pCO2 , and boundaries(8.42), (8.46), and (8.52) depend on the total soluble iron concentrationCFe, total (Table 8.4, item 2).Experimental EH, pH coordinates plotting to the left of boundaries(8.42), (8.46), and (8.52) encompass conditions where CFe, total 107M.Experimental EH, pH coordinates plotting to the right of these sameboundaries cover conditions where CFe, total 107M. Notice that domainswhere the solute concentration exceeds the defined limit (Figure 8.8)by the boundary are equal.Soil and Environmental Chemistry344l Experimental EH, pH coordinates plotting along solute-precipitate bound-aries indicate that the activity of the solute species is equal to the definedlimit and the designated solid controls solubility. For example, EH, pH coordinates along boundary (8.42) indicate that Fe OH 3 s is the solidcontrolling iron solubility, iron solubility is at the designated limitCFe, total 107M , and the most abundant solute is Fe OH 2 aq .l Experimental EH, pH coordinates plotting along precipitate-precipitatereduction boundaries indicate that solute activities are below the desig-nated level and the two solids separated by the boundary coexist. WhenEH, pH coordinates plot on either side of the boundary, one of the twosolids must transform into the other by reduction or oxidation (dependingon which side of the boundary the EH, pH coordinate lies). For example,FIGURE 8.8 A complete Pourbaix diagram plotting the following equilibrium boundaries: sol-ute-solute reduction equilibrium boundary (8.27), solute-solute hydrolysis equilibrium boundary(8.33), solute-precipitate equilibrium boundaries (8.42) and (8.52), solute-precipitate reductionequilibrium boundary (8.48), and precipitate-precipitate reduction equilibrium boundary (8.58).The domains where CFe, total 107:00 M are shaded gray.2and Marshall, 1965). Primordial O levels were believed to be sufficient forChapter 8 Redox Chemistry 3452aerobic respiration as early as the beginning of the Paleozoic Era 542 millionyears ago. Estimated atmospheric CO2 levels early in the Paleozoic Era werein the range 0.420.60% or 11- to 15-fold higher than today.Present O2 levels are the result of photosynthesis. The reduction halfreactions for carbon dioxide (8.59) and oxygen (8.60) are combined to yieldthe net redox reaction for biological carbon fixation to form glucose (8.61).6 CO2 24 H 24 e ! C6H12O6glucose 6 H2O E{H 404 mV 8:59EH, pH coordinates along boundary (8.58) represent conditions whereFe OH 3 s and FeCO3 s coexist and iron solubility is below the desig-nated limit CFe, total 107M . If experimental EH, pH coordinates ploton the reducing side of boundary (8.58) (i.e., below), then Fe OH 3 s isunstable and will transform into siderite under prevailing conditionspCO2 103:45 atm . If experimental EH, pH coordinates plot on theoxidizing side of boundary (8.58) (i.e., above), then FeCO3 s is unstableand will transform into Fe OH 3 s under prevailing conditions.8.4. MICROBIAL RESPIRATION AND ELECTRON TRANSPORTCHAINSSection (8.3) provides the chemical basis for interpreting redox conditions insoils and the saturated zone, but it does not supply the mechanism and drivingforce behind the development of reducing conditions in these environments.Experimental EPt, pH coordinates reflect the profound impact of biologicalactivity. Absent biological respiration, the reducing potential of natural organicmatter remains blocked (see Chapter 6). Respiration, particularly microbialanaerobiosis, removes the activation barriers blocking the oxidation of organicmatter and releases reduced solutes that a platinum ORP electrode can detect asa voltage displacement (see Figure 8.3).Planet Earthmetallic core, mantle, and crust as a wholeis chemicallyreduced. Even though oxygen is the most abundant element in crustal rocks,the most abundant transition elements are not completely oxidized. The tenmost abundant elements in Earths (Table 8.5) crust account for 99.48% ofthe mass and, based on the listed formal oxidation numbers, 99.86% of thecharge. The most probable formal oxidation number for iron is (2), indicat-ing that the formation of the crust resulted in the partial oxidation of iron fromthe elemental state found in the core.The present atmosphere (mean sea level) has the following volume percentcomposition: 78.084% N2, 20.946% O2, 0.9340% Ar, and 0.0387% CO2.The primordial atmosphere contained an estimated 1% of present O2 levels( 0.2% O ), most probably the product of abiotic water photolysis (BerknerSoil and Environmental Chemistry346Fe 0.0620 1.110 2 2.220 87.20%Ca 0.0466 1.163 2 2.325 91.86%Na 0.0227 0.987 1 0.987 94.13%Mg 0.0276 1.137 2 2.274 96.89%K 0.0184 0.471 1 0.471 98.73%TABLE 8.5 Abundance of Elements in Crustal Rocks of Earth and ChargeBalance Based on Formal Oxidation States.Element MassFractionmol kg1 FormalOxidationNumbermolc kg1 Cumulative% MassO 0.4550 28.439 2 56.877 45.50%Si 0.2720 9.685 4 38.739 72.70%Al 0.0830 3.076 3 9.229 81.00%6 O2 24 H 24 e ! 6 H2O E{H 814:9 mV 8:606 CO26 H2O!C6H12O6glucose6 O2 E{1219mV; DG{2823 kJ mol18:61Carbon dioxide fixation occurs when the enzyme rubisco (ribulose 1,5-bisphosphate carboxylase) catalyzes the conversion (8.61) of RuBP (ribulose1,5-bisphosphate), carbon dioxide, and water into PGA (3-phosphoglycericacid). The energy required for this process (8.61) is provided by the captureof light energy in earlier steps of the photosynthetic process.C5H8O5 PO4 2RuBPCO2H2O!rubisco 2 C3H4O4 PO4 PGAO2 2 H H2PO48:62The chemical energy captured during photosynthesis is released duringrespirationthe reverse of reaction (8.61).Ti 0.0063 0.132 4 0.528 99.37%P 0.0011 0.036 5 0.181 99.48%Source: Greenwood and Earnshaw, 1997.Chapter 8 Redox Chemistry 347Table 8.6 lists a classification of living organisms. Plants and other pho-tosynthetic organisms are classified as photolithotrophs that assimilate car-bon dioxide. Chemolithotrophic bacteria assimilate carbon dioxide byoxidizing a variety of inorganic electron donors (ferrous iron Fe2, thiosul-fate S2O23 , elemental sulfur, ammonium NH4 , nitrite NO2 , and dihydrogenH2). Chemolithotrophic bacteria make an insignificant contribution to netcarbon dioxide assimilation but play a prominent role in environmentalredox cycling.Organotrophic organisms cannot assimilate carbon dioxide but ins-tead assimilate organic compounds produced by lithotrophic organisms.Chemoorganotrophsall eukaryotic organisms that are not photolitho-trophs and most prokaryotesderive their energy from the oxidation oforganic compounds.When lithotrophs assimilate carbon dioxide, they generate small organicmolecules used to synthesize complex biomolecules that comprise livingbiomass while simultaneously capturing the chemical energy necessary foranabolic (i.e., biosynthetic) processes. Both lithotrophs and organotrophsTABLE 8.6 Classification of Living Organisms: Carbon Source and EnergySourcePrimary Energy SourceLight Oxidation of ElectronDonorsCarbonSourceCarbon dioxide Photolithotrophs ChemolithotrophsOrganic carbon Photoorganotrophs Chemoorganotrophsrelease stored chemical energy by catabolic pathways that disassemble largemolecules into fragments and oxidize the fragments.8.4.1. Catabolism and RespirationThe release of chemical energy stored in organic compounds occurs in twostages: catabolism and respiration. Reduction leading to carbon dioxiderelease occurs during catabolism: the electron donor is the organic compoundbeing catabolized, while the electron acceptor is the oxidized form of nicotin-amide adenine dinucleotide NAD (CAS 53-84-9, Structure 3) or a similarcompound (e.g., flavin adenine dinucleotide FAD or nicotinamide adeninedinucleotide phosphate NADP).Soil and Environmental Chemistry348Structure 4. NADHNAD H 2 e ! NADH 8:63Catabolism reduces NAD to NADH (CAS 606-68-8, Structure 4) in reductionhalf reaction (8.63). For example, glucose catabolism involves three processes:glycolysis, pyruvate oxidation, and the tricarboxylic acid cycle. Reduction halfreaction (8.64) represents glucose catabolism by this pathway.6 CO2 24 H 24 e ! C6H12O6glucose6 H2O 8:64Combining reduction half reactions (8.63) and (8.64) illustrates glucose dis-Structure 3. NADsimilation to carbon dioxide (8.65). Notice that the electron acceptor is NADrespirationby utilizing a variety of terminal electron acceptors as the need9arises.Anaerobiosis eliminates the activation barrier impeding the abiotic oxida-tion of nitrate and sulfate through the specialized electron transport chains ofnitrate- and sulfate-reducing bacteria. While platinum ORP electrodes mayhave limited sensitivity to these redox couples, some of the reduction products(ferrous iron, thiosulfate, etc.) are sufficiently electroactive and soluble toyield measureable platinum ORP electrode voltage displacements.8.4.2. Electron Transport ChainsAerobic respiration uses an electron transport chain whose electron donor isNADH (8.62) and whose terminal electron acceptor is O2 (8.65).O2 4 H 4 e ! H2O 8:66The net redox reaction in aerobic respiration (8.67) combines reduction halfreactions for the electron donor (8.63) and the terminal electron acceptor(8.66).6 O2 12 NADH 12 H ! 12 H2O 12 NAD 8:67Aerobic glucose dissimilation (8.68) combines glucose dissimilation (8.65)with aerobic respiration (8.67). The NAD NADHj couple (8.63) does notappear in (8.68) because it is recycled between the catabolic pathway andelectron transport chain.C6H12O6 aq 6 O2 g ! 6 CO2 aq 6 H2O l 8:68ous catabolic pathways to the electron transport chain, and functions as theelectron donor feeding electrons into the electron transport chain.While all organisms employ numerous catabolic pathways, bacteria haveevolved a broader array of catabolic pathways than other organisms, makingthem important players in the environmental degradation of organic contami-nants. Bacteria also draw upon a more flexible electron transport chain,providing them with respiratory alternatives absent in eukaryotes. Manybacteria continue to respire in the absence of O2a process called anaerobicglucose nicotinamideadeninedinucleotideReduced nicotinamide adenine dinucleotide NADH functions as a redoxcofactor. Reduced NADH is an electron carrier, shuttling electrons from vari-(8.63), not O2: the electron transport chain, and not the catabolic pathway,defines the terminal electron acceptor.C6H12O612 NAD 6 H2O! 6 CO2 12 NADH 12 H 8:65Chapter 8 Redox Chemistry 34glucoseSoil and Environmental Chemistry350The glucosetocarbon dioxide half-reaction standard biological reductionpotential (8.72) requires expression (8.12).E{H 9:976 mV 2424 414:1 mV 404:1 mV 8:72The calculation illustrated in expressions (8.69) through (8.72) is quite gen-eral. We used this approach earlier in this chapter to demonstrate the prepara-tion and interpretation of redox stability diagrams.Aerobic Electron Transport ChainsThe reduction half reactions listed in Table 8.7 are components of the electrontransport chain typical of aerobic bacteria and prokaryotes. The electron donorfor the sequence is typically NADH or NADPH, and the terminal electronacceptor is O2.The reactive center in iron sulfur proteins and the cytochromesb, c, a,and a3is ferrous iron in iron sulfide clusters and heme groups, respectively.Subtle changes in the iron bonding environment determine the reductionThe change in Gibbs energy under standard conditions DGH for the glucosetocarbon dioxide reduction half reaction (8.64) is (8.70). Applying (8.5) to(8.70) yields the glucosetocarbon dioxide half reaction standard reductionpotential (8.71).EH DGHn FEH 2:3100 104 J mol124 9:6485 104 J V1 mol1 ! 9:976 mV 8:71DGH DGf , glucose 6 DGf ,water 6 DGf ,CO2 24 DGf ,H 8:69DGH 915:90 kJ mol1 6 237:18 kJ mol1 6 385:98 kJ mol1 24 0:0 kJ mol1 DGH 23:100 kJ mol1 8:70The glucosetocarbon dioxide reduction half reaction (8.64) does not lista reduction potential. It would be impossible to construct a galvanic cell simi-lar to the one shown in Figure 8.2 to measure this potential, but we can calcu-late the reduction potential using Gibbs energy expression (8.5).We begin with (8.69)an expression you will recognize from generalchemistrythe change in Gibbs energy for reduction half reaction (8.64) understandard conditions DGH being the sum of the standard Gibbs energy of forma-tion for each product minus the sum of the standard Gibbs energy of formationfor each educt (Amend and Plyasunov, 2001; Amend and Shock, 2001). potential E{H of each species.Chapter 8 Redox Chemistry 351TABLE 8.7 Standard Biological Reduction Half Reactions of the AerobicElectron Transport ChainReduction Half Reaction Reduction Potential, E{H , mVNAD H 2 e ! NADH 320NADP H 2 e ! NADPH 324FMN 2 H 2 e ! FMNH2 212Fe32 S2P :putidia 2 e ! Fe22 S2P :putidia30cytochrome boxidized e ! cytochrome breduced75ubiquinone 2 H 2 e ! ubiquinol 100cytochrome coxidized e ! cytochrome creduced235cytochrome aoxidized e ! cytochrome areduced290cytochrome a3oxidized e ! cytochrome a3reduced305 The half reactions listed in Table 8.7 combine to yield the redox reactionsequence of the aerobic electron transport chain, where NADH (or NADPH)serves as the electron donor (Table 8.8). These reactions release the chemicalenergy carried to the electron transport chain by the electron donor in rela-tively small increments.Figure 8.9 illustrates the aerobic electron transport chain as a simplifiedredox cascade. Electrons enter the redox cascade from the electron donorNADH and release energy as they cascade over each reduction step until theyreach the terminal electron acceptor, which defines the terminus of the cas-cade. The floor of the redox cascade representing the aerobic electron trans-port chain is half reaction for reduction of O2 to water (8.66).Although the reduction potential of each step in the redox cascade is morepositive than the preceding step, using the Gibbs energy expression (8.5)requires each step in the cascade to lie at a more negative Gibbs energy thanthe preceding step. The complete redox reaction represented by the aerobicelectron transport chain in Figure 8.9 is reaction (8.67), and the total Gibbsenergy DG{ change associated with the complete cascade of electrons fromNADH to O2 in (8.67) is 435.8 kJ mol1.Chemolithotrophic eukaryotes utilize a variety of inorganic electrondonors (Table 8.9) as a source of chemical energyferrous iron Fe2, thio-sulfate S2O23 , elemental sulfur, ammonium NH4 , nitrite NO2 , and H2. TheseO2 4 H 4 e ! H2O 815FIGURE 8.9 The simplified redox cascade for the aerobic electron transport chain begins withthe electron donor NADH and ends with the terminal electron acceptor O2.TABLE 8.8 Reduction Reactions of the Aerobic Electron Transport ChainNADH H FMN!1 NAD FMNH2FMNH2 2 Fe4S4 2!2 FMN 2 Fe4S4 2 H2 Fe4S4 2 H Q!3 2 Fe4S4 2 QH2QH2 2 cytochrome boxidized!4 Q 2 H 2 cytochrome breduced2 cytochrome breduced 2 cytochrome coxidized!5 2 cytochrome boxidized 2 cytochrome creduced2 cytochrome creduced 2 cytochrome aoxidized!6 2 cytochrome coxidized 2 cytochrome areduced2 cytochrome areduced 2 cytochrome a3oxidized!7 2 cytochrome aoxidized 2 cytochrome a3reduced4 cytochrome a3reduced 4 HO2 !8 4 cytochrome a3oxidized 2 H2OSymbols: flavin mononucleotide FMN, iron-sulfur protein Fe4S4 , ubiquinone Q.Soil and Environmental Chemistry352Chapter 8 Redox Chemistry 353inorganic electron donors feed electrons directly into the aerobic electrontransport chain instead of relying on the catabolism of organic compoundsfor chemical energy. Each inorganic electron donor couples to the electrontransport chain at one of three points, defined by the reduction half reactionpotential of the electron donor and the electron chain half reaction (seeTable 8.7). The highest entry point uses NAD or NADP as electron accep-tors (reaction 1, Table 8.8). The next entry point uses ubiquinone as the elec-tron acceptor (reaction 3, Table 8.8). The lowest level, the entry point with theleast energy recovery, uses ferrous cytochrome c as the electron acceptorTABLE 8.9 Standard Biological Reduction Half Reactions of ElectronDonors Used by Chemolithotrophic BacteriaReduction Half Reaction ReductionPotential, E{H , mV2 H aq 2 e ! H2 g 4142 SO24 aq 10 H aq 8 e ! S2O23 aq 5 H2O l 233SO24 aq 8 H aq 6 e ! S s 4 H2O l 199NO3 aq 2 H aq 2 e ! NO2 aq H2O l 407NO3 10 H 8 e ! NH4 3 H2O 363Fe3 aq e ! Fe2 aq 771O2 g 4 H aq 4 e ! 2 H2O l 815(reaction 5, Table 8.8). These levels correspond to successively more positiveredox potentials and, therefore, decreased potential differences relative to theO2, the terminal electron acceptor. The redox cascades are similar to the onein Figure 8.9, all with the same floor, but each begins at progressively lowerentry points and releases less energy.Facultative and Obligate AnaerobesReaction 4 in Table 8.8 (ubiquinol reduction to ubiquinone) in the aerobic elec-tron transport chain is particularly problematic for aerobic organisms becauseelectrons divert prematurely to O2 at this stage. The normal electron transferprocess begins with the oxidation of ubiquinol QH2, delivering one electronto two different one-electron acceptors, one being cytochrome b (see Table 8.7)in a bifurcated pathway. Disruption occurs when the one-electron transfer tocytochrome b fails, leaving an unstable ubisemiquinone radical Q. The ubi-semiquinone radical Q reacts with O2 to form superoxide anion radical O2 .The occurrence of this electron transport disruption has resulted in theevolution of two key enzymes in aerobic organisms: superoxide dismu-tasean enzyme that swiftly and safely converts the superoxide anion radicalSoil and Environmental Chemistry354fermentation (8.75) uses NADH as an electron donor and pyruvic acid as anelectron acceptor to produce lactic acid (CH3 COH COOH, CAS 598-82-3,Structure 6).2 CH3 CO COOH NADH H ! 2 CH3 COH COOH NAD8:75Alcohol (ethanol) fermentation (8.76) uses NADH as an electron donor andpyruvic acid as an electron donor to produce ethanol (CH3CH2OH, CAS 64-17-5). Pyruvic acid, however, does not appear in (8.76), and the electronanaerobic respiratory processes, does not use the electron transport chain.Organisms capable of fermentationcertain fungi and many bacteriaarefacultative anaerobes. During fermentation the electron transport chain isinactive; oxidation occurs during catabolism.Structure 5. Pyruvic acidStructure 6. Lactic acidThe first stage of glucose catabolism (glycolysis) produces two moleculesof pyruvic acid (CH3 CO COOH, CAS 127-17-3, Structure 5). Lactic acidposes hydrogen peroxide into water and O2 (8.74).2 O2 2 H !superoxidedismutaseO2 H2O2 8:732 H2O2!catalaseO2 2 H2O 8:74Facultative anaerobic bacteria possess superoxide dismutase, enabling themto tolerate disruption of the aerobic electron transport chain in reaction (8.4)by decomposing the reactive oxygen species it produces. Obligate anaerobicbacteria lack superoxide dismutase and, as a consequence, cannot tolerate sig-nificant levels of O2.Fermentative Anaerobic BacteriaOne anaerobic respiratory process is fermentation. Fermentation, unlike otherO2 into hydrogen peroxide (8.73)and catalasean enzyme that decom-donor appears to be acetaldehyde (CH3 CO H, CAS 75-07-0).CH3 CO H NADH H ! CH3CH2OH NAD 8:76Pyruvic acid is the true electron donor in alcohol fermentation but its transfor-mation to acetealdehyde by pyruvate decarboxylase (8.77) cannot be classi-fied as a redox or electron transfer reaction.CH3 CO COOH ! CH3 CO H CO2 8:77Bacteria use other fermentation pathways to produce many of the low molec-ular weight organic acids found in the pore water of soils and sediments.Nitrate Respiratory Chain of Nitrate-Reducing BacteriaThe electron transport chain of nitrate-reducing bacteria utilizes most of theaerobic electron transport chain, diverting electrons from cytochrome c tonitrate and eliminating reactions 6 through 8 in Table 8.8. The use of nitrateas the terminal electron acceptor, however, requires an enzyme system thattransfers electrons from cytochrome c to nitrate. The reduction of nitrate toChapter 8 Redox Chemistry 35535. The aerobic redox cascade (Figure 8.9) is used in Figures 8.11 and 8.12 to illustrate theNO2 aq 2 H aq e ! NO aq H2O l 2382 NO aq 2 H aq 2 e ! N2O aq H2O l 1285N2O aq 2 H aq 2 e ! N2 g H2O l 14032 NO aq 12 H aq 10 e ! N2 g 6 H2O l 748N2 involves the transfer of five electrons per nitrogen. Since biological redoxreactions typically are one- and two-electron reductions, the complete reduc-tion of nitrate to N2 cannot occur in a single redox reaction (Table 8.10).Figure 8.10 illustrates the components of the nitrate reduction system innitrate-reducing bacteria. The first stepthe reduction of nitrate to nitriteiscatalyzed by a nitrate reductase NAR bound to plasma membrane. The nitritereductase NIRreducing nitrite to nitric oxideis located in the periplasmbecause nitric oxide NO is cytotoxic. The remaining steps occur in the periplasm:nitric oxide reduction to nitrous oxide N2O and nitrous oxide reduction to N2.Figure 8.11 illustrates the anaerobic electron transport chain of nitrate-reducing bacteria as a simplified redox cascade.5 Electrons enter the redoxTABLE 8.10 Standard Biological Reduction Half Reactions of the NitrateRespiratory ChainReduction Half Reaction Reduction Potential,E{, mVNO3 2 H 2 e ! NO2 H2O 407submergence of the electron transport chain when alternative electron acceptors replace O2.Soil and Environmental Chemistry356cascade from the electron donor NADH and release energy as they cascadeto the level set by the electron acceptor, defined in this example as the halfreaction for reduction of nitrate to nitrite. The complete redox reaction repre-sented by the aerobic electron transport chain in Figure 8.11 is reaction(8.78), and the total Gibbs energy change DG{ associated with the completecascade of electrons from NADH to O2 is 217.9 kJ mol1 per NADH. Thesubmerged portion of the electron transport chain makes no contribution tothe Gibbs energy change DG{ because nitrate terminates the cascade at ahigher level than aerobic respiration (see Figure 8.9). The Gibbs energy changeDG{ for electron transfer from NADH to N2 is 205.0 kJ mol1 per NADH.2 NO3 5 NADH 7 H ! N2 6 H2O 5 NAD 8:78Ferric Iron Respiratory Chain of Metal-Reducing BacteriaMost iron-reducing bacteria are capable of using several terminal acceptorsbesides ferric iron (Ruebush, Brantley et al., 2006), but their distinguishingcharacteristic is their ability to grow under anaerobic conditions where theFIGURE 8.10 Components of the nitrate reduction system of nitrate-reducing bacteria arelocated in the inner or plasma membrane and the periplasm. Source: Reproduced with permissionfrom Zumft, W.G., 1997. Cell biology and molecular basis of denitrification. Microbiol. Mol. Biol.Rev. 61 (4), 533616Chapter 8 Redox Chemistry 357sole electron acceptor is either Fe(III) or Mn(IV). The relative natural abun-dance of iron and manganese makes Fe(III) a more abundant terminal electronacceptor in the environment, hence the use of iron respiratory chain andiron-reducing bacteria.The iron respiratory chain faces a singular challenge: the terminal electronacceptor is insoluble and cannot be taken up into the cytoplasm like nitrate,sulfate, or carbonate. There is considerable evidence for membrane-bound ter-minal ferric reductase enzymes (Lovley, 1993) that overcome the need for asoluble terminal electron acceptor, relying on direct contact between cell sur-face and insoluble ferric minerals. Some studies (Lovley, Holmes et al., 2004)suggest that some iron-reducing speciesShewanella and Geothrixmaysecrete soluble electron shuttles capable of reducing ferric oxide mineralswithout coming into direct physical contact. Microbiologists studying the ironrespiratory chain have identified several components of an electron transportchain that couples to outer-membrane-bound terminal ferric reductaseenzymes. Identification of soluble electron shuttles, however, remains elusive.One of the more unusual features of the terminal ferric reductase is itslocation. The position of reductase enzymes in the nitrate respiratory chain(see Figure 8.10) in the inner or cytoplasmic membrane and the peri-plasmthe location of the cell wall of Gram negative bacteria separatingthe inner and outer membranesalso applies to the reductase enzymes ofFIGURE 8.11 The simplified redox cascade for the anaerobic electron transport chain in nitrate-reducing bacteria begins with electron donor NADH and ends with the electron acceptor nitrate.Soil and Environmental Chemistry358the sulfate and carbonate respiratory chains. The placement of the terminalferric reductase, however, is on the outer surface of the outer membrane(DiChristina, Moore et al., 2002; Myers and Myers, 2002).Figure 8.12 shows the simplified redox cascade for the iron respiratorychain. The level in the pool has risen to 262 mV, submerging much of theaerobic redox cascade and limiting the recovery of chemical energy in elec-tron donor NADH.The complete redox reaction represented by the aerobic electron transportchain in Figure 8.12 is reaction (8.79), and the total Gibbs energy changeDG{ associated with the complete cascade of electrons from NADH toFe2 is 46.51 kJ mol1 per NADH. The submerged portion of the electrontransport chain makes no contribution to the Gibbs energy DG{ changebecause Fe OH 3 s sets the floor of the cascade at a higher level.2 Fe OH 3 s NADH 5 H ! 2 Fe2 NAD 6 H2O 8:79Sulfate Respiratory Chain of Sulfate-Reducing BacteriaTable 8.11 lists reduction half reactions and potentials of what is considered thelikely reduction pathway from sulfate SO24 the terminal electron acceptor ofFIGURE 8.12 The simplified redox ladder for the anaerobic electron transport chain in iron-reducing bacteria begins with electron donor NADH and ends with the electron acceptor ferriciron in mineral form Fe OH 3 s .9NADH is 320 mV (see Table 8.7), which represents a significant hurdle: theGibbs energy change for sulfate reduction by NADH is positive and, there-fore, the reaction would absorb rather than releases energy.NADH SO24 aq 2 Haq NAD HSO3 aq H2OaqDG{ 38:76 kJ mol1 8:80All bacteria capable of growth when the sole electron acceptor is sulfate SO24 acti-vate sulfate for assimilatory and dissimilatory reduction by forming 50-adenylylsulfate (C10H14N5O10PS, CAS 485-84-7, Structure 7) from adenosine-50-triphos-phate ATP and sulfate in reaction (8.81), coupled to the hydrolysis of a high-energy phosphate ester bond (8.82) in guanosine-50-triphosphate GTP (Liu, YaSuo et al., 1994).the sulfate respiratory chainto hydrogen sulfide HSthe final product ofdissimilatory sulfate reduction. Sulfate-reducing bacteria are obligate anaerobes,unlike the facultative anaerobes: iron-reducing and nitrate-reducing bacteria.The reduction half reaction of the electron donor for this respiratory chainHSO3hydrogensulfite 6 H 6 e ! HShydrogensulfide 3 H2O 76APS 7 H 8 e ! HS 3 H2O AMP 72TABLE 8.11 Standard Biological Reduction Half Reactions of the SulfateRespiratory ChainReduction Half Reaction ReductionPotential, E{, mVAPS H 2 e ! HSO3 AMP 60Chapter 8 Redox Chemistry 35ATP3 SO24 !ATP sulfurylaseAPS2 HP2O37pyrophosphate8:81GTP3 H2O! GDP2 H2PO4 8:82Structure 7. 50-adenylyl sulfate APSNNOOOOS POOOOHO OHNNH2NActivation of the sulfate lowers the potential for the reduction of sulfate toSoil and Environmental Chemistry3608.4.3. Environmental Redox Conditions and MicrobialRespirationThe energy yield from each of these respiratory chains is progressively less. As aresult, metabolic activity by facultative anaerobic bacteria is lower than that ofaerobic bacteria; the activity of obligate anaerobic bacteria is the lowest of all.Reducing conditions in the environment are usually the result of anaerobicmicrobial respiration. Biologically generated reducing conditions develop inwater-saturated soil and sediments when there is abundance of carbon, a suitableterminal electron acceptor, and temperatures favoring biological activity.Anoxia develops as aerobic organisms deplete pore water of dissolved O2,setting the stage for the sequential rise and decline in the activity of nitrate-reducing bacteria, followed by iron-reducing, sulfate-reducing, and, ultimately,methanoarchaea. Each succeeding population drives the reducing potentiallower as each electron acceptor pool is depleted and a new terminal electronacceptor is sought. With each new terminal electron acceptor, a new populationof anaerobic bacteria becomes active.The respiration of each anaerobic population pumps electron donors intothe environment, reducing the conditions that propagate throughout the zonehydrogen sulfite to 60 mV (see Table 8.11) and allows the remaining reduc-tion steps to follow. The Gibbs energy change DG{ for electron transfer fromNADH to HS aq is 22.92 kJ mol1 per NADH (accounting for the energycost of activation).Methanogenic Anaerobic ArchaeaThere are no carbonate-reducing bacteria; methanogenic organisms belong tothe domain archaea (Thauer, 1998). Bacterial fermentation supports methano-genesis by converting organic matter into acetate CH3COO, dihydrogen H2and either formate HCOO or bicarbonate HCO3 . Methanoarchaea derivemetabolic energy by either disproportionating6 one-carbon compounds (e.g.,reactions (8.83) through (8.85)) or using dihydrogen H2 to reduce bicarbonateHCO3 (8.14).CH3COO aq H aq ! CO2 aq CH4 g 8:834 HCOO aq 4 H aq ! 3 CO2 aq CH4 g 2 H2O l 8:844 CH3COH aq ! CO2 aq 3 CH4 g 2 H2O l 8:85Other carbon compounds used by methanoarchaea include carbon monoxide,methylamines NCH3n1 n 3, and methylsulfide HSCH3.6. Disproportionation is not a redox reaction as defined by reaction (8.1).Chapter 8 Redox Chemistry 361of biological activity as abiotic electron transfer reactions reduce com-pounds that bacteria do not utilize for respiration. Percolating water carriesthe electron donors generated by anaerobic bacteriaand those generatedby abiotic electron transfer reactionsbeyond the zone of biological activityinto aquifers, where carbon levels are too low to sustain appreciablemetabolism.The fate of nitrate in groundwater illustrates the role of anaerobic respirationon nitrate levels. Nitrate readily leaches through soil because ion exchangecapacity of soils is overwhelmingly cation exchange capacity. Denitrifyingbacteria in water-saturated soil reduce nitrate, but the likelihood of that happen-ing drops dramatically once the nitrate leaches into the subsoil and underlyingsurficial materials, where organic carbon levels and biological activity tend tobe quite low. Nitrate in the groundwater persists until it enters a surface waterrecharge (hyporheic) zone in a wetland or sediment zone of a stream or lake.Biological activity in these zones is much higher because these zones arecarbon rich. Dissolved nitrate rapidly disappears as nitrate-reducing bacteriain the recharge zone utilize the nitrate to metabolize available carbon.8.5. SUMMARYThis chapter began with a review of redox principles from general chemistry: for-mal oxidation numbers, balancing redox and reduction half reactions, and theNernst equation. These are the basic tools needed to calculate standard biological(or environmental) reduction potentials E{H and to understand biological electrontransfer reactions.Section 8.3 focused on the measurement and interpretation of redox condi-tions by plotting experimental Ered, pH coordinates on Pourbaix diagrams.Table 8.4 summarizes the essential features common to Pourbaix diagramsand the foundation for interpreting reducing conditions using Ered, pH coordinates.Reducing conditions in the environment result from a key biological pro-cess: respiration (Baas-Becking, Kaplan et al., 1960). Section 8.4 explainedhow catabolism and electron transport are fundamentally chemical reductionprocesses that release the chemical energy stored in bioorganic compounds.Numerous catabolic pathways feed electrons into electron transport chainsthat harvest the chemical energy released during catabolism.Since biological activity requires an energy (i.e., carbon) source and suit-able temperatures, reducing conditions develop when and where there is a sig-nificant biological activity. Anaerobic respiration effectively pumps reactiveelectron donors into the environment, depending on the type of anaerobic res-piration. These electron donorsespecially thiosulfate, hydrogen sulfide, andferrous irontransfer electrons to a host of electron acceptors through abioticreduction reactions. The mobility and biological availability of many inorganiccontaminants are sensitive to prevailing redox conditions. Solubility increasesPHENOLBonding Charge TransferC1$C2 0C1$C6 0C1!O 1Formal Oxidation Number NC11Bonding Charge TransferC2$C1 0C2$C3 0C2 H 1Formal Oxidation Number NC2 NC3 NC4 NC5 NC6 1Soil and Environmental Chemistry362The formal oxidation sum for phenol verifies that Rule 8 is not violated.Ntotal 6 NH NO XiNCiNtotal 6 1 2 NC1 X6i2NCiNtotal 6 2 1 5 0Structure 8. Phenolunder reducing conditions for some contaminants and decreases for others.Regardless, prevailing redox conditions determine environmental risk for manycontaminants.APPENDIX 8A. ASSIGNING FORMAL OXIDATION NUMBERSExample 8A.1The formal oxidation numbers of carbon atoms in phenol (CAS 108-95-2, Struc-ture 8) distinguish between carbon C1 bonded to oxygen and the remaining fivecarbon atoms bonded to hydrogen.Structure 9. Acetic acidThe formal oxidation sum for acetic acid verifies that Rule 8 is not violated.Ntotal 4 NH 2 NO XiNCiNtotal 4 1 2 2 NC1 NC2 Ntotal 4 4 3 3 0Bonding Charge TransferC2 H 3C2$C1 0Formal Oxidation Number NC23Chapter 8 Redox Chemistry 363APPENDIX 8B. CONVERTING (pe, pH) REDOX COORDINATESINTO (EH, pH) COORDINATESSubstituting the half-cell reduction potential under standard conditions EHinto the Nernst equation (8.7) yields a relation between the half-cell reductionpotential EH and the conceptual redox parameter pe. Redox parameter pe isexample for phenol. Rules 3 and 4 (see Table 8.1) apply to O and H.ACETIC ACIDBonding Charge TransferC1$C2 0C1!Ocarbonyl 2C1!Ohydroxyl 1Formal Oxidation Number NC13Example 8A.2The formal oxidation numbers of carbon atoms in acetic acid (CAS 64-19-7,Structure 9) distinguish between carbon C1 bonded to oxygen and the carbonatoms bonded to hydrogen.The effect of relative electronegativity (see Figure 8.1) is the same as theSoil and Environmental Chemistry364Expression (8B.4) defines the conceptual redox parameter pe by analogy withthe definition of pH. log10 ae pe 8B:4Notice that the Nernst equation (8B.5) for reduction half reaction (8B.1) doesnot list the electron as an educt.EH EH R T ln 10 n F log10aDraAs amH 8B:5The development of conceptual redox parameter pe begins with equilibriumexpression (8B.2) for the reduction half reaction (8B.1) that includes electronactivity ae . Expression (8B.2) is not consistent with convention for writingreduction half reactions (8B.1). Chemists list the electron e and its stoichio-metric coefficient n in reduction half reactions as a convenient means oftracking electron transfer between the donor Dr and the acceptor As. Onecan imagine other conventions for writing reduction half reactions that dis-pense with listing electrons e as an educt.Kred aDraAs amH ane aDraAs amH ane 8B:2The convention for writing reduction half reaction (8B.1) was adopted withthe understanding that listing the electron e as an educt did not imply theexistence of free electrons. Electron activity ae (8B.2) in solution has nophysical basis; electrons do not exist as free particles, unlike hydronium ionsH3O aq .Taking the base-10 logarithm of all of the terms in (8B.2) results inexpression (8B.3).log10 Kred log10aDraAs amH n log10 ae n log10 ae log10 Kred log10aDraAs amH 8B:3ple, uses redox parameter pe to plot pe, pH Pourbaix diagrams.The general reduction half reaction is given by (8B.1).Asacceptorm H3O n e ! Drdonor8B:1not recognized by the International Union of Pure and Applied Chemists(IUPAC). Deriving the relation between EH and pe serves a single purpose:it allows readers to covert pe values reported in the scientific literature intoEH values. The computer-based water chemistry model ChemEQL, for exam-Chapter 8 Redox Chemistry 365ENVIRONMENTAL REDUCTION POTENTIAL USING PLATINUMORP ELECTRODESAqueous solutions saturated with O2 under standard conditions pO2 1 atm,pH 0 typically result in a 700800 mV experimental potential EPt whenusing a platinum ORP electrode (Garrels and Christ, 1965; Stumm andwritten using an numerical parameter (8B.11) appropriate for 25C (298.15 K).EH, 25C 59:16 mV 25C pe 8B:11APPENDIX 8C. LIMITATIONS IN THE MEASUREMENT OF THEEH R T ln 10 F pe 8B:10The equivalence between the experimentally measurable half-cell reduction poten-tial under general conditions EH and the conceptual redox parameter pe is often(8B.3), (8B.4), and (8B.9) yields (8B.10), defining the relation between theconceptual redox parameter pe and EH.n F EHR T ln 10 n pelog10 Kred n F EHR T ln 10 8B:8Rearranging expression (8B.5) and combining it with (8B.8) yields (8B.9).n F EHR T ln 10 log10 Kred log10aDraAs amH 8B:9The two terms on the right side of (8B.9) also appear in (8B.3). Combining10(8B.7), upon rearrangement.log10 Kred DGHR T ln 10 8B:7Using expressions (8.4) and (8.5) from earlier, we can write expression(8B.8).Expression (8B.6) relates the standard change in Gibbs energy DGto theequilibrium constant K for any chemical reaction.DG R T ln K 8B:6Natural logarithms are converted to base-10 logarithms using the followingrelation: ln x ln 10 log x . Applying this conversion to (8B.6) yieldsMorgan, 1970) rather than the expected EH 1229 mV (see Table 8.3). Thediscrepancy results from the detailed electron transfer mechanism betweenthe platinum electrode and O2 molecules adsorbed on its surface and the slowkinetics of the electron transfer process. A thin layer of platinum oxide formswhen O2 is being reduced by electrons at the electrode surface (Liang andJuliard, 1965). This oxide layer passivates the platinum metal, inhibiting elec-tron transfer by forming an insulating layer and altering the experimentalpotential. The net effect of the reduction mechanism and kinetics is a zeroelectrode current over a considerable potential range (Stumm and Morgan,1970).Numerous electrochemically active redox couples are dissolved in anyenvironmental sample. The kinetics, mechanism, and reversibility of electrontransfer and the extent to which each couple deviates from its equilibriumstate ensure that any experimental electrode potential EPt represents a com-posite (i.e., mixed) electron transfer potential between all of these speciesand the platinum electrode surface.TABLE 8C.1 Limitations on Experimental Platinum ORP ElectrodeMeasurements of Reduction Potentials in Environmental Samples1. Many redox species exhibit no tendency to transfer electrons at the platinummetal electrode surface (e.g., nitric oxide NO, dinitrogen gas N2, sulfateSO24 , and methane CH4) and, therefore, fail to contribute to the measuredpotential EPt.Soil and Environmental Chemistry3662. A platinum ORP electrode will record the potential of a couple only if the electrontransfer reaction is reversible. Rosca and Koper (2005) and de Vooys (de Vooys,Koper et al., 2001a, b) discovered at least two pathways for nitric oxide NOreduction at a platinum electrode, one yielding nitrous oxide N2O and the otheryielding ammonia NH3.3. The electron transfer rate at the platinum metal electrode surface is a function ofsolution activity for redox couples where one or both of the electron donor andacceptor species are solutes. Solutes such as Fe3 aq and Mn4 aq , and theirhydrolysis products, are extremely insoluble over a considerable pH range,rendering the measured potential EPt insensitive to significant variations in theredox status of these couples.4. Many redox couples do not attain equilibrium under environmental conditionsregardless of the reversibility or kinetics of the half reaction at the platinum metalelectrode surfacebecause of slow electron transfer kinetics in situ. Theexperimental reduction potential EPt fails to represent the equilibrium redox statusof these couples.Pro1.Chapter 8 Redox Chemistry 367N 1 C 5 1N 1 H 1PYRROLEBonding Charge TransferN 1 C 2 1SolutionblemsDetermine the formal oxidation number of nitrogen in pyrrole (CAS 109-97-7)and calculate the formal oxidation state sum for the molecule.PyrrolePYRROLEBonding Charge TransferN1 C2N1 C5N1 HFormal Oxidation Number NN1 Bonding Charge TransferC2!N1C2$C3C2 HFormal Oxidation Number NC2 NC5 Bonding Charge TransferC3$C2C3$C2C3 HFormal Oxidation Number NC3 NC4 y3682. The incomplete reduction half reaction for the dechlorination of DDT(dichloro-diphenyl-trichloroethane, CAS 50-29-3) to DDD (dichloro-diphenyl-dichloroethane, CAS 72-54-8) appears following.Determine the formal oxidation number of the chlorinated methyl carbon inboth DDT and DDD (show your work, please). Balance the reduction halfreaction (electron balance, charge balance, and mass balance) by insertingthe missing coefficients and product.C 3 $C 4 0C 3 H 1Formal Oxidation Number NC 3 NC 4 1Ntotal 2 NC 2 2 NC 3 5 NH NNNtotal 2 0 2 1 5 1 3 0(DDT (1,1,1-trichloro-2,2-di(4-chlorophenyl)ethane, CAS 50-29-3)Bonding Charge TransferC1!ClC1$C2C 3 $C 2 0FoPYRROLEFormal Oxidation Number NN 1 3Bonding Charge TransferC 2 !N 1 1C 2 $C 3 0C 2 H 1Formal Oxidation Number NC 2 NC 5 0Bonding Charge TransferSoil and Environmental Chemistrrmal Oxidation Number NC1Sol3.FoMoBoCCCFoCh 69utionGiven the relation between the Standard Gibbs Energy of Formation DGf ofrmal Oxidation Number NC1DDT (1,1,1-trichloro-2,2-di(4-chlorophenyl)ethane, CAS 50-29-3)Molecular ChargeBonding Charge TransferC 1 !Cl 3C 1 $C 2 0Formal Oxidation Number NC 1 3DDD (1-chloro-4-[2,2-dichloro-1-(4-chlorophenyl)ethyl]benzene,CAS 72-54-8)lecular Chargending Charge Transfer1!Cl 21$C 2 01 H 1rmal Oxidation Number NC 1 1Bonding Charge TransferC1!ClC1$C2C1 H(DDD (1-chloro-4-[2,2-dichloro-1-(4-chlorophenyl)ethyl]benzene, CAS 72-54-8)apter 8 Redox Chemistry 3the educts and products (below) and the halfreaction reduction potential(DGh nFEh), calculate the reduction potential for DDT dechlorination halfreaction in Problem 1.y3700.800 1 2 3 4 5 6 7 8 9 10 11 12 13 14pHField Cr3 aq :Field Cr OH 2 aq :Field HCrO4 aq :Field CrO24 aq :Field Cr OH 3 s :Boundary (1):0.600.200.40Cr(OH)3 (s)4. The following EH , pH Pourbaix diagram shows the stability fields for severalchromium species. This diagram was prepared using a total soluble chromiumconcentration of 50 ppb (9.62 10-7 mol L-1), the USEPA Maximum Contami-nant Limit for Cr.Interpret the chemical significance of each stability field and boundary.1.201.000.800.600.400.200.00EhCr3+(aq)HCrO4(aq)CrO42(aq)Cr(OH)2+(aq) 7316254Cl aq 131.3 kJ mol1Compound DGfDDT aq 274.9 kJ mol1DDD aq 238.7 kJ mol1H aq 0.0 kJ mol1Soil and Environmental ChemistrBoundary (1):Boundary (3):Boundary (4):Boundary (5):Boundary (6):9.8 Valence Bond Model ofProton Sites 392-with one or more ions bound to sites on the surface of a solid particle or amacromoleculehereafter referred to as the adsorbent. Ion exchange is a spe-cial case of a more general surface chemistry process: adsorption.Adsorption and adhesion share the same root, and both imply binding to asurface. An adsorption process involves the transferto adsorbent surface site surface. The solute does noSoil and Environmental Chemistry.# 2012 Elsevier Inc. All rights reserved.9.1. INTRODUCTIONIon exchange represents a chemical process common in the natural environment but rarely mentioned in general chemistry text books. The ionexchange process involves the exchange of one or more ions from a solutionAdsorption 388Chapter Outline9.1 Introduction 3719.2 Mineral and OrganicColloids as EnvironmentalAdsorbents 3729.3 The Adsorption IsothermExperiment 3749.4 Hydrophobic andHydrophilic Colloids 3799.5 Interpreting the AdsorptionIsotherm Experiment 3799.6 Variable-Charge MineralSurfaces 3879.7 The Adsorption EnvelopeExperiment: MeasuringpH-Dependent Ion9.9 Surface Complexes 3959.10 Summary 399Appendix 9A. ParticleSedimentation Rates inWater: Stokess Law 400Appendix 9B. Linear LangmuirExpression 401Appendix 9C. Hydrolysis Modelof Proton Sites 402Chapter 9Adsorption and SurfaceChemistryof a solute from solutiont have to be an ion, and371adsorption does not require the exchange of a molecule or ion bound to anadsorbent surface site with another molecule or ion in solution.Ion exchange retains ions at surface sites through the electrostatic forcebetween the ion and one or more sites bearing an opposite electrostaticcharge. Adsorption, being a more general chemical process, retains moleculesor ionsadsorbatesthrough the same chemical bonds or intermolecularforces you would have learned about in general chemistry.Protons, for instance, are bound to water molecules and hydroxyl ions insolutionand at mineral surfacesthrough a covalent bond. Protons alsoform hydrogen bonds between adsorbate molecules and surface sites, theadsorbate and the adsorbent acting as a hydrogen-bond donor-receptor pairwhose roles are interchangeable between adsorbate and surface site. Transi-Soil and Environmental Chemistry372tion metal ions form coordinate-covalent bonds when lone-pair electrons ona ligand atom (e.g., oxygen or nitrogen in a molecule or ion) overlap withvacant d-orbitals of the metal ion. As with hydrogen bonds, the adsorbateand the adsorbent constitute an electron-pair donor (the ligand or Lewis base)and an electron-pair receptor (the transition metal ion or Lewis acid), whoseroles are interchangeable between adsorbate and adsorbent site. Weak electro-static forces also bind molecular dipoles in adsorbate molecules to dipoles ofthe adsorbent. These van der Waals forces act in concert, becoming the domi-nant binding-force when the adsorbate is a large neutral molecule.9.2. MINERAL AND ORGANIC COLLOIDS ASENVIRONMENTAL ADSORBENTSAdsorption processes, though ubiquitous, become apparent only when thesurface-to-volume ratio of the adsorbent is extremely high. This condition iscommonly satisfied in environmental systems where clay-size mineral parti-cles (Figure 9.1) or organic matter molecules are present in significantamounts. Table 9.1 lists the size range and specific surface area for the threeFIGURE 9.1 These electron micrographs depict fine grains of the minerals kaoliniteAl4 Si4O10 OH (L; (Roe, 2007)) and hematite Fe2O3 (R; Contributors, 2008). The images8are courtesy of the Clay Minerals Group of the Mineralogical Society.Chapter 9 Adsorption and Surface Chemistry 373TABLE 9.1 Specific Surface Area of Spherical Particles with DiametersDefining Each USDA Particle-Size Class (Particle density is 2.65 Mg m3,the typical density of mineral grains in Earths crust)Particle Class Diameter Specific Area, m2g1Very coarse sand 2 mm 4.53E-03Coarse sand 1.0mm 9.06E-03Medium sand 0.50mm 1.81E-02particle-size classes (sand, silt, and clay), and Table 9.2 lists the specific sur-face area of several soil textural classes. Soil textural classes represent theparticle-size distributions commonly found in soils and sediments.Tables 9.1 and 9.2 demonstrate the importance of clay-size mineral particlesto the specific surface area of surficial material: soils, sediments, and aquifers.A similar case could be made for organic matter that, in the context of thischapter, is considered the organic colloidal fraction in soils and sediments.One further example demonstrates how solute adsorption by the clay-sizefraction can significantly alter pore-water composition. The typical adsorbingcapacity of any mineral surface is on the order of 1 mmol m2. From Tables 9.1and 9.2 we can see that the typical specific surface area of soils and sedimentsFine sand 0.25mm 3.62E-02Very fine sand 0.10mm 9.06E-02Coarse silt 50 mm 1.81E-01Clay is on the order of 2 m3g1. Given a typical 20% volumetric water content ofsoils at field capacity and a typical bulk density of 1.3 Mg m3, a cubic meterof soil will hold about 200 L and have dry mass of 1:3 106 g with a specificsurface area of 2:6 106 m2, most from the clay fraction (see Table 9.2).The adsorbing capacity of mineral particles in a cubic meter of soil isabout 2 moles, which means that adsorption by the mineral fraction in soilcan remove 0.01 moles per liter 2mol m3=200 L m3 from solution.Clearly the adsorption of 0.01 M represents a significant fraction of the totalSoil and Environmental Chemistry374solute concentration in pore water. The capacity of adsorption processes toalter pore-water composition is a direct result of the extremely high specificsurface area of soil colloids.Clays and humic substances are profoundly different colloids, displayingmarkedly different adsorption behavior. To grasp these differences, we mustfirst understand how an adsorption experiment is performed and the generalappearance of the experimental results.9.3. THE ADSORPTION ISOTHERM EXPERIMENTIn this section we describe the adsorption isotherm experiment, one ofmany adsorption experiments designed by surface chemists. The adsorptionisotherm experiment requires a series of solutions containing the samemass of suspended adsorbent madsorbent and the same volume of water V.Varying the initial concentration Ci of solute Sthe potential adsorbateimposes the experimental treatment.Figure 9.2a depicts the initial state of a clay adsorbent suspension. Duringthe equilibration stage the suspension is agitated to ensure ample opportunityfor the solution containing adsorbate to contact the adsorbent (Figure 9.2b).The duration of the equilibration stage (Figure 9.2b) depends on how rapidlythe adsorbate binds to the clay, usually a few minutes to several hours or days.The final stage (Figure 9.2c) requires separation of suspended clay from thesolution for each chemical treatment in the series, usually by filtration oraccelerated sedimentation in a centrifuge (see Appendix 9A). The supernatantsolutions contain varying final concentrations Cf of the solute S (the adsor-bate), representing the quantity of the solute S remaining in solution afterFIGURE 9.2 Measuring the adsorption isotherm by allowing aseries of solutions containing varying concentrations (a) of a sol-uteS aq to adsorb on the clay adsorbent, equilibration duringagitation (b), and separation of adsorbent clay from solution (c).adsorption has reached equilibrium. The amount of solute S adsorbed permass of adsorbent q C is the difference between the initial and final soluteconcentrations multiplied by the total volume V and divided by mass of adsor-bent in the suspension madsorbent :q C Ci Cf Vmadsorbent9:1Figure 9.3 depicts the equilibrium state when adsorption is measured using aChapter 9 Adsorption and Surface Chemistry 375FIGURE 9.3 A semipermeable membrane (dashed line,center) confines the adsorbent (open circles labeled A,right) from diffusing into the left half of the cell. The freesolute (filled circles) concentration is the same on bothsides of the membrane.dialysis cell. If the adsorbent is a molecular adsorbent such as humic sub-stances (see Chapter 6, section 6.5.1), it is impossible to separate the solutionfrom the adsorbent by filtration or centrifugal sedimentation. Separation isachieved by equilibrium dialysis.The appropriate dialysis membrane is permeable to solute S (the adsor-bate) but impermeable to the molecular adsorbent. A series of dialysis cells(Figure 9.3) are prepared, each containing the same total volume of aqueoussolution V, the same mass of molecular adsorbent madsorbentconfined toone-half of the cell by a semipermeable membraneand varying initial con-centrations Ci of solute S. Adsorption of the solute S to the confined adsorbentprevents a fraction of the solute from diffusing across the membrane. The freesolute concentration is the same on both sides of the membrane because it canfreely diffuse across the membrane, but the total concentration is higher in thehalf containing the adsorbent.The amount of solute adsorbed per mass of adsorbent q C is the differencebetween the initial and final solute concentrations divided by the mass of adsor-bent in the suspension (9.1). The final solute concentration is either the soluteconcentration in the supernatant solution (see Figure 9.2) or the solute concen-tration inside of the dialysis chamber lacking adsorbent (Figure 9.3, left).Table 9.3 lists the results from a typical adsorption isotherm. The adsor-bent was a calcareous soil from Grand Bahama Island. The soluteortho-phosphate HPO24 aq is a divalent molecular anion. The data are plottedin Figure 9.4. The adsorption isotherm displays a steep initial slope thatdecreases steadily toward what appears to be a zero slope representing anadsorption maximum. Adsorption isotherms showing this behavior are calledL-type adsorption isotherms.37TABLE 9.3 Adsorption Isotherm for Orthophosphate HPO24 aq by 0.25 gof a Calcareous Soil11Soil and Environmental Chemistry6Environmental chemists commonly encounter linear or C-type adsorptionisotherms (9.2) where the slope apparently remains constant throughout thesolute concentration range used in the adsorption isotherm experiment.q C Ksoil Cf 9:2CHPO24 , f mg L qHPO24 mg kg 2.00 17.822.75 21.854.15 25.675.50 29.349.70 35.1114.50 40.32Source: Data from R. W. Taylor, Alabama A & M University.FIGURE 9.4 This graph plots the adsorption isotherm of the orthophosphate HPO24 aq bya calcareous soil (Grand Bahama Island, Commonwealth of The Bahamas). The estimatedadsorption maximum is qmax 50:0 mg kg1.Lambert (1968) reported linear isotherms for the adsorption of the insecticidechlorfenvinphos (CAS 470-90-6; Structure 1) by two California soil series: Yolosilty clay loam and Hanford (Ripperdan) fine sandy loam. The adsorption iso-therms for chlorfenvinphos (Structure 1) by these two soils appear in Figure 9.5.Structure 1. ChlorfenvinphosThe data are from Lambert (1968), who relied on chlorfenvinphos labeledwith the radioisotope 14C, so concentration is reported as radioactivity withoutspecified units.These linear adsorption isotherms are reminiscent of the results one wouldobtain from a process in which a solute partitions between two immiscible sol-vents: water and an organic solvent. This behavior led Lambert (1965)to hypothesize the adsorption of organic compounds by soil corresponds to par-Chapter 9 Adsorption and Surface Chemistry 377tition of the compound into the organic matter. The Yolo soil clearly adsorbsmuch more of the insecticide than the Hanford soil (Figure 9.5), but if theFIGURE 9.5 This graph plots the adsorption isotherm of the insecticide chlorfenvinphos (CAS470-90-6) by two California soils: Yolo silty clay loam and Hanford (Ripperdan) fine sandy loam.Soil and Environmental Chemistry37840.020.00.00.00 0.05 0.10 0.15C, mL10.20 0.25 0.30 0.35FIGURE 9.6 This graph plots the adsorption isotherm of the insecticide chlorfenvinphos (CAS160.0140.0120.0100.080.060.0q, g1200.0Yolo Hanford180.0quantity adsorbed is normalized by the organic matter content of the soil (9.3),the adsorption isotherms for the two soils are essentially identical (Figure 9.6).q C Ci Cf morganic matter=V 9:3The Lambert hypothesis has been widely adopted by environmental che-mists studying the adsorption of neutral organic compounds by soils and sedi-ments because normalizing the adsorption isotherms for the same compoundon many different soils and sediments typically results in a plot similar to thatin Figure 9.6 and summarized in Eq. (9.4).q C Ci Cf mOM=V KOM Cf 9:4Lambert (1968) states that the adsorption behavior displayed in Figures 9.5and 9.6 may be construed as evidence that the organic matter of soils fromwidely differing locations and of widely differing composition is so similarthat for all practical purposes it can be considered the same. The similaritypertains to the adsorption behavior of neutral organic compounds by naturalorganic matter and should not be construed to apply to other properties of soilorganic matter.470-90-6) by two California soils: Yolo silty clay loam (5% organic matter) and Hanford (1%organic matter) fine sandy loam. The data, from Lambert (1968), are normalized by the organicmatter content of the two soils.9.4. HYDROPHOBIC AND HYDROPHILIC COLLOIDSA dispersion of colloidal particles in a liquid is stable, meaning that the par-ticles will not settle out, because the constant thermal motion of moleculesin the liquid is sufficient to overcome the effects of gravity on the particles(Appendix 9A). The two types of colloidal particleshydrophobic and hydro-philic colloidsare found in soils and sediments. Hydrophobic colloids areChapter 9 Adsorption and Surface Chemistry 379fine-clay-size mineral particles, while hydrophilic colloids are humic substancesand bioamphiphiles secreted by microbes (see Appendix 6A).Humic molecules exhibit amphiphilic properties similar to simple amphi-philes such as phospholipids. It is unlikely, though not impossible, that humicmolecules have a single polar end and a single nonpolar end. A more probablestructure would resemble an amphiphilic block-copolymer (see Figure 6.23), aflexible linear molecule with alternating flexible polar and nonpolar segments.Such molecules would fold and aggregate in water by presenting their polarsegments at the aqueous contact and burying their nonpolar segments withinthe interior.Bacteria secrete a variety of bioamphiphilesglycolipids, lipopeptides,and so onthat form micelles (see Appendix 6A). These bioamphiphiles playa variety of roles, including increasing the biological availability of nonpolarorganic contaminants for degradation. Humic amphiphiles have little tendencyto form aggregates of the type seen in Figure 9.7a, except when concentratedhumic extract solutions are prepared in the laboratory. Otherwise, humicmolecules aggregate at mineral surfaces (Figure 9.7b), folding in such a man-ner as to present their polar segments to either water or the mineral surfaceand withdrawing their nonpolar segments into the aggregate interior to createnonpolar domains much like the interior of the micelles and colloidal filmspictured in Figures 9.7a and b, respectively.9.5. INTERPRETING THE ADSORPTION ISOTHERMEXPERIMENTFigures 9.4 and 9.5 illustrate the two types of adsorption isotherms mostcommonly encountered by environmental chemists. Figure 9.4 is a nonlinearL-type isotherm exhibiting an apparent adsorption maximum. Figure 9.5 is alinear C-type isotherm with no apparent adsorption maximum.FIGURE 9.7 The probable structureof molecular aggregates formed byblock copolymer amphiphiles in aque-ous solution (a) and at the mineral-water interface (b); polar segments areopen circles and nonpolar segmentsare flexible gray lines.L-type adsorption isotherms result from site-limited adsorption processes.Adsorbent particles bind adsorbate molecules at a limited number of sites. Theadsorption maximum, which is characteristic of L-type isotherms, representsthe saturation of a limited number of adsorption sites. C-type adsorption iso-therms result when the adsorbent has solvent-like properties, which is charac-teristic of molecular-aggregate adsorbents. Adsorption processes that produceC-type isotherms are comparable to the adsorbate dissolving (or partitioning)into solvent-like domains found within hydrophilic colloids. The adsorptionisotherm, consequently, reveals the fundamental nature of the adsorption pro-cess, which is determined by the dominant interaction between the adsorbateSoil and Environmental Chemistry380and the adsorbent.The following sections present models for both types of adsorption iso-therms. Nonlinear L-type adsorption isotherms are represented by a particulartwo-parameter function. Linear C-type adsorption isotherms require a singleparameter, represented by the slope of the isotherm; the physical requirementsof the adsorption process demand that the isotherm pass through the origin (i.e., zero intercept).9.5.1. The Langmuir Adsorption ModelIrving Langmuir (1916) derived the model commonly used to represent site-limiting adsorption processes. The assumptions upon which this model wasoriginally based (Table 9.4) are idealized and generally do not apply to site-limiting adsorption processes involving environmental colloids. The use ofthe Langmuir model generated considerable debate within the environmentalchemistry community, particularly the appropriateness of using a modelwhose foundational assumptions are not satisfied. We can apply this modelto parameterize nonlinear adsorption isotherms, provided that we carefullyavoid assigning certain physical interpretations of the L-type isothermparameters.Langmuir (1916; 1918) based his theory of site-limited adsorption on akinetic model. The rate that molecules desorb from a solid surface, by hisTABLE 9.4 The Assumptions Used by Langmuir to Derive the NonlinearL-type Gas Adsorption Isotherm Expressionl The solid surface has a fixed number of adsorption sites. Depending on the tempera-ture and gas pressure, adsorbed molecules occupy a fraction y of the sites, while theremainder (1 y) is vacant.l Only one adsorbed molecule can occupy each site.l The enthalpy of adsorption DHads is the same for all sites and is not influenced by thefraction y of sites occupied.reasoning, is proportional to the fraction of occupied sites y (9.5). The propor-tionality constant kD is the rate constant for desorption:rate of desorption : kD y 9:5The rate that molecules adsorb is proportional to the fraction of unoccu-pied states (1 y) and the adsorbate concentration C when we apply the Lang-muir model to adsorption from solution. The proportionality constant foradsorption kA (9.6) is the rate constant for adsorption from solution. Langmuir(1916) developed the theory for gas molecule adsorption using the partialpressure of the adsorbent instead of the concentration in solution.rate of adsorption : kA C 1 y 9:6Chapter 9 Adsorption and Surface Chemistry 381centration C using three differ-ent values for the adsorptioncoefficient parameter Kac.adsorption sites are completely saturated:FIGURE 9.8 The L-typeadsorption isotherm derived byLangmuir (1916) plots the frac-tion y of adsorption sites occu-pied by adsorbate molecules asa function of the adsorbate con-Equilibrium (9.7) is the state where the rates of adsorption and desorptionare equal.equilibrium state : kD y kA C 1 y 9:7Langmuir (1916) solved this equation for y, defining Kac as the adsorptioncoefficient, which is actually the rate constant ratio kA=kD:kD y kA C kA C y y Kac C 1 Kac C 9:8Plotting y as a function of the adsorbate concentration C illustrates an importantcharacteristic of the Langmuir adsorption isotherm: adsorption approaches aplateau as the occupied sites y approach saturation (Figure 9.8).Langmuir (1918) replaced the symbol y with the ratio between the massconcentration of the adsorbate on the adsorbent as defined by Eq. (9.1)divided by the mass concentration at the adsorption maximum qmax whereSoil and Environmental Chemistry382under the conditions imposed by Langmuir (1916; 1918):kAkD Kac eDGads=RT 9:10Langmuirs conditions (see Table 9.4) are not met for site-limited adsorp-tion processes encountered by environmental chemists. At most we can useadsorption coefficients Kac to compare the relative adsorption affinity of dif-ferent adsorbates on the same environmental colloid or the same adsorbate ondifferent environmental colloids.9.5.2. Ion Exchange Adsorption IsothermsIon exchange is an adsorption process, but the physical characteristics arevery different from those giving rise to the L-type isotherm described byLangmuir (1916). Symmetric exchange reactions yield isotherms that do notchange with salt concentrationlinear if the exchange process is nonselective(see Figure 4.9) and curved if it is selective (see Figure 4.7).There are cases where an asymmetric exchange isotherm closely resem-bles the Langmuir site-limited adsorption isotherm. Consider a hypotheticalnonselective asymmetric exchange isotherm involving the univalent cationNa and the divalent cation Ca2 (Eq. (9.11)) and the Gaines-Thomas selec-tivity expression for the asymmetric exchange process (Eq. (9.12)).2 Naaqsolution Ca2exchanger ! 2 NaexchangerCa2aqsolution9:11y qqmax Kac C 1 Kac C q qmax Kac C 1 Kac C 9:9Take another look at Figures 9.4 and 9.8. In the high adsorbate concentrationrange, specifically wherever Kac C >> 1, then y 1 or q qmax. On theother hand, in the low adsorbate concentration range, specifically whereverKac C Chapter 9 Adsorption and Surface Chemistry 383coefficients KD tend to be nonpolar organic compounds with low watersolubility.As pointed out earlier, L-type nonlinear adsorption processes exhibitbehavior resembling (9.15) at low adsorbate concentration C range, providedtherms involves molecular-aggregate adsorbents and nonpolar adsorbatemolecules. The adsorbate is thought to partition from water into nonpolarsolvent-like domains found within the molecular-aggregate colloid.The slope of the C-type linear adsorption isotherm is often called thedistribution or partition coefficient:KD L kg1 quantity adsorbed per mass adsorbentconcentration dissolved in solution q g kg1 C g L1 9:15Substances that have a very low affinity for the environmental adsorbent havedistribution coefficients near zero. Substances with very high distribution9.5.3. Linear Adsorption or Partitioning ModelAs just mentioned, linear C-type adsorption isotherms result from adsorptionprocesses where the interaction between adsorbate and adsorbent does notinvolve binding to a limited number of sites. Instead, the adsorbent behavessimilar to a solvent, a characteristic of hydrophilic (or molecular-aggregate)adsorbents. The adsorption process yielding C-type linear adsorption iso-and the selectivity of the exchange process KcGT (Eq. (9.14)).Asymmetric Exchange Isotherm~ENa bb2 4 bp29:13b 2 C0 KcGT E2Na1 ENa 9:14Figure 9.9a is a plot of the exchange isotherm for a nonselective asymmetric(9.11) univalent-divalent ion exchange process, plotting the fraction ofexchange sites occupied by the divalent cation as a function of the concentra-tion of the divalent cation in solution. This plot clearly resembles the plot of aprototypical L-type isotherm in Figure 9.4 with a relatively large adsorptioncoefficient K. A plot of the exchange isotherm for the univalent cation(Figure 9.9b) does not remotely resemble the isotherm in Figure 9.4.KcGT Ca2 ~E2Na~ECa2 Na 29:12The asymmetric exchange isotherm (Eq. (9.13)) for reaction (9.11) is aquadratic equation that depends on the normality C0 of the electrolyte solutionSoil and Environmental Chemistry384Kac C Chapter 9 Adsorption and Surface Chemistry 385is fundamentally a partitioning process; a nonpolar organic compound distri-butes itself between two solvents: water and the solvent-like nonpolardomains formed when amphiphiles aggregate in solution (see Figure 9.7a)or on clay surfaces (see Figure 9.7b).Small nonpolar compounds typically have a high vapor pressure and read-ily evaporate from water rather than adsorb to molecular-aggregate colloids.Vapor pressure decreases as molecular weight increases, increasing thetendency of nonpolar organics to adsorb to humic colloids. Water solubilitycorrelates with the overall polarity of organic compounds and is a major factordetermining the distribution tendency between aqueous solution and thenonpolar domains of molecular-aggregate colloids.Lambert (1965) assumed that the adsorption of uncharged (i.e., nonpolar)organic molecules by soil corresponds to partition of the compound intoorganic matter of the soil and chose to base the adsorption of organic com-pounds by soil on the organic matter content (Eq. (9.16)). Lambert citedearlier studies of pesticide adsorption by soil with varying organic matter con-tents that confirm a C-type linear adsorption isotherm.KOM L kg1OM quantity adsorbed per mass organic matterconcentration dissolved in solution q g kg1OM C g L1 9:16While Lamberts simple partitioning model is useful and the generaliza-tion that KOM for a given nonpolar compound is a good predictor of thewhole-soil distribution coefficient KD, it did not provide a basis for predictingthe KOM based on the molecular structure of the compound. Lambert (1967;1968) applied the linear free energy principle to predict changes in KOM fromadding a substituent or otherwise making small changes in molecular struc-ture. The basis for his linear free energy relationship for predicting KOM isbased on the notion (Langmuir, 1925) that a major determinant of solubilityis the energy of creating a cavity in the solvent sufficient to accommodatethe solutethe volume-energy concept.Adding a bulky substituent, for instance, to a nonpolar molecule imposeslittle or no energy cost to creating a solute cavity in a nonpolar domain withina molecular-aggregate colloid (or a nonpolar solvent). The energy cost is sub-stantial if the solute is nonpolar and the solvent is water because water mole-cules are bound together through hydrogen bonds in the liquid state. Thehydrogen bond network in water must be broken to create a cavity for a non-polar molecule.Consequently, any change in molecular structure that increases the volumeof a nonpolar molecule will decrease water solubility, increasing the tendencyof that compound to partition from water into the nonpolar domains providedby the organic matter coating mineral grains in the soil or sediment. Similarly,any change in molecular structure that increases the nonpolar surface area of acomplex moleculemolecules with a mixture of polar and nonpolar groupswill have a similar effect: decreased water solubility and increased distribu-tion coefficient KOM (Eq. (9.16)).This model for predicting the distribution coefficient KOM anticipatesincreasing water solubility and decreasing distribution coefficients KOM(Eq. (9.16)) if changes in molecular structure add polar groups. Adding polargroups to a nonpolar molecule reduces the energy cost of creating a solutecavity in water. Lambert (1968) found a linear correlation between the para-chor value P of similar nonpolar organic compounds and the distributioncoefficient KOM. The parachor value P is a measure of the molecular volumefor a compound.These principles underlying C-type linear adsorption of nonpolar organiccompounds by humic colloids were subsequently confirmed and extendedby Chiou and colleagues (1979) and others (see Doucette and Andren, 1987,1988; Shiu, Doucette et al., 1988). Some of these later studies correlate themolecular volume and total molecular surface area of nonpolar organic com-pounds with the octanol-water partition coefficient KOW. Octanol-water parti-tion coefficients KOW interest environmental chemists because KOW correlateswith fat solubility of a compound and the tendency for biomagnification(Box 9.1).Soil and Environmental Chemistry386Box 9.1 Biomagnification and BioaccumulationThe Office of Pollution Prevention and Toxics (U.S. Environmental ProtectionAgency) maintains an Internet site called the PBT Profiler (Center, 2006) that esti-mates a variety of important environmental characteristics of organic compounds,principally persistence, bioaccumulation, and toxicity. The Office of PollutionPrevention and Toxics defines biomagnification as the concentration of a chem-ical to a level that exceeds that resulting from its diet. Biomagnification is quan-tified using the biomagnification factor BMF, where CB indicates theconcentration in an organism (e.g., zooplankton, fish, etc.) and CA the total con-centration in the organisms diet.BMF CBCABioaccumulation encompasses both bioconcentration and biomagnification,where the former relates to uptake from all sources and the latter specificallyrelates to diet. Bioconcentration is quantified using the bioconcentration factorBCF, where CB indicates the concentration in an organism (e.g., zooplankton,fish, etc.) and CW the total concentration in water.BCF CBCWMackay and Fraser (2000) reviewed models of bioaccumulation and methodsfor estimating BCF. A popular approach draws on the extensive octanol-waterpartition coefficients KOW database for organic chemicals. Mackay (1982)79.6. VARIABLE-CHARGE MINERAL SURFACESEnvironmental acidity is a complex phenomenon that we discuss in Chapter 7.Suffice it to say at this point, pore water pH in soils, sediments, and aquiferscovers a relatively large range. Natural biological and geochemical processescan result in pore water acidities as low as pH 4 and as high as pH 9. Chemistsobserved that ion adsorption, both cations and anions, by environmental col-loids varied significantly with pore water pH. Some of this could be explainedby the hydrolysis of weak acid groups in natural organic matter, but weak acidhydrolysis of organic matter could not explain all of the variability that thechemists measured. Mineral colloids, the clay fraction, account for much ofthe observed variability in ion adsorption in soil and sediments.Parks and de Bruyn (1962) were the first to suggest that the adsorption ofH by mineral colloid surfaces could be described by a hydrolysis reactionwith a characteristic equilibrium constant. They believed that a charge-freemineral surface occurs at a characteristic pH depending on the nature of themineral colloid. The hypothetical charge-free mineral surface develops a pos-itive surface charge through the adsorption of H ionsas illustrated follow-ing, with the neutral amine NH2 designated as the conjugate base:NH3conjugateacidH2O l !Ka NH2weakbaseH3O aq 9:17of the trout.Box 9.1 Biomagnification and Bioaccumulationcontdproposed a simple, one-parameter estimator of BCF for rainbow trout (Oncor-hynchus mykiss) based on a linear regression with KOW for nonpolar organiccompounds.BCF 0:048 KOWMackay observed that the proportionality constant can be regarded as aneffective octanol content of the fish and is related, or equal, to the lipid contentChapter 9 Adsorption and Surface Chemistry 38The hypothetical charge-free mineral surface develops a negative surfacecharge through H ion desorptionas illustrated in Eq. (9.18), with the neutralcarboxyl COOH designated as the weak acid. The desorption of H ions,however, is equivalent to the adsorption of OH ionsas shown in reaction(9.19), where COO is designated as the conjugate base and K0a K0b Kw.COOHweak acidH2O l !K0a COOconjugatebaseH3O aq 9:18COOHweakacidOH aq !K0b COOconjugatebaseH2O l 9:19Soil and Environmental Chemistry388to the suspension. An adsorption isotherm experiment is designed to measureadsorption as a function of varying the adsorbate concentration; control ofsolution pH may or may not be imposed, and measurement of equilibriumsolution pH may or may not be recorded. A pH-dependent adsorption experi-ment explicitly adjusts solution pH so that the equilibrium pH of the treatmentsadequately spans the desired pH range; the initial adsorbate concentration isidentical for all pH treatments.A decrease in adsorbate concentration caused by precipitation of a mineralrather than adsorption should be considered possible when designing a pH-dependent ion adsorption experiment. The simplest way to evaluate whetherprecipitation can explain the observed change in adsorbate ion concentrationis to analyze the equilibrium solution and perform a water chemistry simula-tion to identify whether precipitation involving the adsorbate solute is likely.For instance, suppose the experiment is designed to measure the adsorp-tion of phosphate by the aluminum hydroxide mineral gibbsite Al OH 3 s .A well-designed pH-dependent phosphate adsorption experiment would mea-The model proposed by Parks and de Bruyn, and later Stumm and colleagues(Stumm, Huang et al., 1970), is shown in reactions (9.20) and (9.21). Thehypothetical charge-free mineral surface develops a positive charge throughthe adsorption of H ions (9.20), with the neutral site MeOH designatedas the weak base and the positively charged site MeOH2 as thecorresponding conjugate acid. The hypothetical charge-free mineral surfacedevelops a negative charge through the desorption of H ions (9.21), with theneutral site MeOH now designated as the weak acid and the negativelycharged site MeO as the corresponding conjugate base.MeOH2conjugate acidH2Ol !K1 MeOHweak baseH3Oaq 9:20MeOHweak acidH2Ol !K2 MeOconjugate baseH3Ol 9:21The following two sections describe the experiments that measure pH-dependent ion adsorption by mineral colloids and pH-dependent surfacecharge, the latter being a major determinant of pH-dependent ion adsorption.9.7. THE ADSORPTION ENVELOPE EXPERIMENT: MEASURINGpH-DEPENDENT ION ADSORPTIONThe design of a pH-dependent ion adsorption experiment is very similar to thepreviously described adsorption isotherm experiment. In both experiments thechemists must separate the adsorbent from the solution by either filtration oraccelerated sedimentation in a centrifuge (see Figure 9.2) or equilibrium dial-ysis (see Figure 9.3) in order to analyze the solution.The major experimental design difference relates to the treatments appliedsure the following at equilibrium: total dissolved phosphate concentration andtotal dissolved aluminum concentration. The researcher would then performa water chemistry simulation for each treatment based on the equilibriumsolution concentration, calculating the saturation index of each aluminumphosphate mineral that could potentially form. The researcher can reasonablyassign the decrease in phosphate concentration to an adsorption process for alltreatments where the saturation indices for all potential aluminum phosphateminerals are less than 1. All other treatments where the saturation indices ofpotential aluminum phosphate minerals are 1 or greater represent conditionswhere precipitation of aluminum phosphate minerals is possible and mightaccount for the decrease in phosphate solution concentrations.9.7.1. Adsorption EdgesTypical cation adsorption envelopes appear in Figure 9.10, which shows arapid increase in the percent adsorbed in a narrow pH rangetypicallyChapter 9 Adsorption and Surface Chemistry 3892 pH units from negligible to nearly complete adsorption from solution. Manyenvironmental chemists reporting cation adsorption envelopes similar tothose in Figure 9.10 may also report an adsorption edge, defined as the pHat which cation adsorption is 50% of the initial cation concentration. Theadsorption edges for Co II and Cu II by imogolite are pH 6.0 and pH 7.7,respectively.Typical anion adsorption envelopes appear in Figure 9.11, which shows arapid increase in the percent adsorbed in a narrow pH rangetypically 2 pHunits from negligible to nearly complete adsorption from solution. While cat-ion adsorption is negligible when the solution pH is acidic, anion adsorption isnegligible when the solution pH is basic. The adsorption edges for selenateSeO24 and selenite SeO23 by goethite are pH 4.4 and pH 9.8, respectively.FIGURE 9.10 This graphplots the pH-dependent adsorp-tion results from Clark andMcBride (1984). The initialadsorbate ion concentrationswere 250 mM: Co II (open sym-bol) and Cu II (filled symbol).The adsorbent suspension con-tains 5 g L1 of synthetic imogo-lite Al2SiO3 OH 4 s and anionic strength I of 0.15 M asCa NO3 2.399.7.2. Measuring pH-Dependent Surface ChargeThe design of a pH-dependent surface charge experiment is essentially a titra-tion experiment that is otherwise similar to the previously described pH-dependent ion adsorption experiment. The proton-surface charge experimentmeasures the relative adsorption of protons H or hydroxyls OH by the col-loid over the desired range. The design of a proton-surface charge experimentinvolves titrating the colloid suspension with a strong acid solution (to covertion results from Su and Swarez(1997). The initial adsorbateion concentrations were 100mM: selenate SeO24 (open sym-bol) and selenite SeO23 (filledsymbol). The adsorbent suspen-sion contains 4 g L1 of syn-thetic goethite FeO OH s and an ionic strength I of 0.1M as NaCl.FIGURE 9.11 This graphplots the pH-dependent adsorp-Soil and Environmental Chemistry0the acid pH range) and a strong base solution (to cover the basic pH range).The acid concentration CA and base concentration CB of the titrating solutionsmust be precisely measured because protons H are being adsorbed andhydroxyls OH are being desorbed in the process.Parks and de Bruyn (1962) proposed the following definition of proton sur-face charge sH (9.22) (units: Coulomb per square meter C m2), where Sclay isthe clay (i.e., hydrophobic colloid) surface concentration (9.23) (units: squaremeter per liter m2 L1).sHF CSA 10pH CSB 1014pH Sclay9:22Sclaym2L Aclay m2g Mclay gLh i9:23The Faraday constantF in Eq. (9.22) convertsmole of charge to Coulomb units.F e NAF 1:602 1019 C 6:022 1023 mol1 F 9:649 104 C mol1Chapter 9 Adsorption and Surface Chemistry 391FIGURE 9.12 This graph plots the pH-dependent proton surface charge sH of kaoliniteAl4Si4O10 OH 8 from Zhou and Gunter (1992), with additional data published previously by Bolt(1957) and Spyrcha (1989).Zhou and Gunter (1992) measured the pH-dependent proton surface charge ofkaolinite Al4Si4O10 OH 8, comparing their results with earlier pH-dependentproton surface charge sH measurements of silica (Bolt, 1957) and alumina(Sprycha, 1989). Kaolinite is a layer aluminosilicate, with each layercomposed of a gibbsite sheet and a silica sheet (see Figure 3.9), and developssurface charge at its edge surface. Figure 9.12 demonstrates that the kaolinitelayer-edge develops a considerably greater surface charge than its componentoxides. The kaolinite pH-dependent proton surface charge sH cannot be con-sidered the additive sum of the two components.9.7.3. Proton Surface Charge SitesSoils and sediments are environments exposed to significant chemicalweathering, a geochemical process that transforms primary minerals in rocksinto the secondary minerals constituting the mineral colloid fraction. Thesesecondary clays are typically oxide minerals, and the outermost atomic layerat the mineral-water interface consists of oxygen ions at various stages of pro-tonation. Hence, reactions that confer surface charge (9.20) and (9.21) are areasonable representation of the surface charging process.The nature of the surface sites in the Langmuir model (Langmuir, 1916)and the pH-dependent surface charge model (Stumm and Morgan, 1970) arefundamentally quite similar. Both imply site-limited adsorption processesSoil and Environmental Chemistry392Hydrogen bonding plays an important role in goethite crystal structure,causing Fe OI bonds to be longer than Fe OII bonds: 210.5 pm and193.9 pm (Szytula, Burewicz et al., 1968; Yang, Lu et al., 2006), respecti-vely. The actual bond valence sum z for the two oxygen ions in goethite(Structure 2), based on the empirical bond valence function of Brown andAltermatt (1985) and the goethite crystal data of Yang and colleagues(2006) listed in Table 9C.1 are zI 3 0:61 v:u: 0:02 v:u: 1:85 v:u: andzII 3 0:39 v:u: 0:99 v:u: 2:16 v:u:, respectively (see Table 9.5).At the goethite surface the coordination of most O2 ions decreases dra-involving an adsorbate molecule binding to a site whose defining characteris-tic is the affinity for the site for the adsorbate. Implicit is the notion that eachadsorbate molecule occupies a finite footprint on the adsorbent surface thatdetermines the adsorbate surface density at the adsorption maximum. You canconsider the pH-dependent proton surface charge sH (see Figure 9.12) as aplot of the pH-dependent proton adsorption.If the Parks and de Bruyn pH-dependent surface charge model representedin reactions (9.20) and (9.21) is chemically reasonable, then the limiting pro-ton surface charge sH should approximate the O2 ion surface density typicalof oxide mineral surfaces. The Pauling ionic radius of an O2 ion is 140 pm,which is equivalent to 62,000 pm2 ion1 and a surface density of 24mmol m2 for a plane of close-packed O2 spheres. Schindler and Kamber(1968) estimate the area density of proton adsorption sites on silica gelcol-loidal hydrous SiO2 s to be 4.0 mmol m2. The limiting proton surfacecharge sH of kaolinite (see Figure 9.12) is comparable, reaching 12mmolc m2 at pH 9.9.8. VALENCE BOND MODEL OF PROTON SITESThe crystal structure of goethite contains two distinct O2 ions (Structure 2):OI is four-coordinate (three Fe3 ions and one H ion), and OII is three-coordinate (three Fe3 ions plus a hydrogen bond).Structure 2. Oxygen coordination in goethitematically relative to Structure 2. Russell and colleagues (1974) described aChapter 9 Adsorption and Surface Chemistry 393surface site model (Structure 3) for goethite FeO OH s that identified threedifferent O2 ion sites at the surface. Site A O2 ions are coordinated by asingle Fe3 ion, Site B O2 ions are coordinated by three Fe3 ions, and SiteC O2 ions are coordinated by two Fe3 ions.Structure 3. Oxygen coordination at the surface of goethite. Source: Reproduced with permissionfrom Russell, J.D., Parfitt, R. L., et al., 1974. Surface structures of gibbsite goethite andphosphated goethite. Nature 248, 220221.TABLE 9.5 Bond Lengths and Bond Valences for the Mineral GoethiteBond Bond Length rij Bond ValenceFeOI 210.3 pm 175.9 pm sFeOI 0:61 v :u:FeOII 194.4 pm 175.9 pm sFeOII 0:39 v:u:HOII 88.5 pm 88.2 pm sHOI 0:99 v:u:H OII 231.1 pm 88.2 pm sH OI 0:02 v :u:Note: Brown and Altermatt (1985): sij e r0rij =B ; B 37 pmSource: Based on the refinement by Yang et al., 2006.Site B O2 ions have the same coordination as OII ions in the interior of goe-thite, making these the least likely to undergo hydrolysis reactions (9.20) and(9.21), as suggested by Parks and de Bruyn. Site C O2 ions would tend to binda single proton as a neutral site and release a proton through a reaction similar to(9.21). Russell and colleagues (1974) identify Site A O2 ions as likely to bindtwo protons to form a positively charged site through a reaction similar to (9.20).The model proposed by Russell and colleagues would have one protonbound to all three sites when the goethite surface has a net zero surfacecharge; Site A OH would bear a negative 0.5 charge, Site B OH would beara positive 0.5 charge, and Site C OH would charge neutral.Soil and Environmental Chemistry394Desorption of a proton H from the mineral surface generates a negatively-charged cation exchange site that will attract the coadsorbed cation M.9.8.1. Interpreting pH-Dependent Ion Adsorption ExperimentsFigure 9.10 plots the pH-dependent adsorption of Co II and Cu II by thealuminosilicate imogolite, a tubular mineral similar to kaolinite. The solutionchemistry of these two components is quite different. Component Co II exists predominantly as the divalent cation Co2 aq throughout the entirepH range. The divalent cation Cu2 aq predominates below pH 7.6, andthe divalent cation Cu2 OH 22 aq predominates over a narrow pH rangebefore the neutral species Cu OH 02 aq becomes the major solution speciesat pH 8. Despite the fact that both adsorbates are divalent cations belowzA Xizini 360@1A 110@1A 1:5 v:u:zB Xizini 360@1A 360@1A 360@1A 110@1A 2:5 v:u:zC Xizini 360@1A 360@1A 110@1A 2:0 v:u:This assignment is based on the Pauling (1929) electrostatic valence principle:In a stable coordination structure the electric charge of each anion tends to compen-sate the strength of the electrostatic valence bonds reaching to it from the cations atthe centers of the polyhedra of which it forms a corner.The electrostatic valence sum for Site A OH is 1.5 instead of 2.0, so thissite registers a net 0.5 site charge. The electrostatic valence sum for Site BOH is 2.5 instead of 2.0, making this site a net 0.5 site charge.An alternative model appears in Appendix 9C. This model creates a neu-tral surface by cleaving through the crystal along a specific plane and adsorb-ing water molecules to restore the coordination of structural cations exposedat the surface by cleavage. The model described in Appendix 9C shows thata charged surface site created by the adsorption of a single proton or desorp-tion of a single proton is best seen as a pair of oxygen speciesO2 or OHor H2Othat equally share the positive or negative surface charge.Charge neutrality is maintained by coadsorbing an anion X for each protonH adsorbed by the surface. This makes good sense because the adsorption of aproton H by the mineral surface generates a positively-charged anion exchangesite that will attract the coadsorbed anion X. Charge neutrality is also main-tained by coadsorbing a cationM for each protonH desorbed from the surface.pH 7.6, the imogolite surface has a markedly higher affinity for adsorbingneutral species H2SeO4 aq below pH 3.5, the univalent anion HSeO4 aq Chapter 9 Adsorption and Surface Chemistry 395predominates over the pH range 3.5 to 7.6, and the divalent anionSeO24 aq becomes the major solution species at pH 7.6.While the decrease in selenate adsorption with increasing pH appears tocorrelate with the decrease in negative surface charge (Su and Suarez, 1997),nearly all of the selenite in solution adsorbs to a negatively charged goethitesurface while the dominant solution species is neutral H2SeO04 aq and substan-tial selenite adsorption occurs in the pH range 9 to 11, where the goethitesurface either has a net zero surface charge or is negatively charged andthe dominant selenite solution species is a divalent anion SeO23 . Seleniumoxyanion adsorption behavior cannot be explained by anion valence.Numerous studies report similar results where the adsorption of solutionspecies by mineral surfaces does not correlate with surface charge. This typeof adsorption behavior is clearly not an ion exchange process, though ionexchange and electrostatic forces may contribute to the adsorption process.Apparently the adsorption affinity of a particular mineral surface for a givencomponent is determined by the chemistry of both reactantssurface siteand adsorbate. Surface chemists have yet to develop a predictive model forthe adsorption of inorganic components (neutral or charged species) by mineralsurfaces based on the chemical properties of both reactants.The chemical state and the properties of a mineral surface site are moredifficult to characterize than solution species. Measurements of proton surfacecharge (see Figure 9.12) have proven insufficient to characterize adsorptionaffinity. In the past few decades, most adsorption research by environmentalchemists has focused on characterizing the chemical structure of the adsor-bate-surface site complexthe chemical product that forms when adsorbatebinds to the surface of an adsorbent. Perhaps once chemists have collectedsufficient chemical information about surface complexes, they will understandwhat to measure in order to predict adsorption affinity.9.9. SURFACE COMPLEXESHuang and Stumm (1973), Stumm and colleagues (Stumm, Hohl et al., 1976),and Schindler and colleagues (Schindler, Furst et al., 1976) extended earlierproton adsorption models to include ion adsorption by mineral surfaces.In much the same way that earlier proton adsorption models depict the bind-ing of protons to the surface by forming a complex with a surface site (9.20),Cu2 aq . This difference in adsorption behavior cannot be explained bycation valence.Figure 9.11 plots the pH-dependent adsorption of selenate SeO24 and sel-enite SeO23 by goethite. The solution chemistry of these two components isalso quite different. Selenate exists predominantly as the divalent anionSeO24 throughout the entire pH range. Selenite exists predominantly as the0 ion adsorption binds to sites at the mineral-water interface throughSoil and Environmental Chemistry396electrostatic forces (see Appendix 9C, Structures C4 and C5) and ligand-exchange bonds.Structure 4. Monodentate Complex. Source: Reproduced with permission from Barger, J.R.,Brown, G.E., et al., 1997. Surface complexation of Pb(II) at oxide-water interfaces: I. XAFSand bond-valence determination of mononuclear and polynuclear Pb(II) sorption products onaluminum oxides. Geochim. Cosmochim. Acta 61, 26172637.Structure 5. Bidentate Complex. Source: Reproduced with permission from Barger, J.R., Brown,G.E., et al., 1997. Surface complexation of Pb(II) at oxide-water interfaces: I. XAFS and bond-valence determination of mononuclear and polynuclear Pb(II) sorption products on aluminumoxides. Geochim. Cosmochim. Acta 61, 26172637.A ligand-exchange reaction occurs when an oxygen or hydroxyl ion atthe mineral surface displaces water molecules surrounding a metal cation toform an inner-sphere surface complex. The mono-dentate surface complexin Structure 4 represents the probable structure for about half of the 2.0 mmol m2 Pb II adsorbed to aAl2O3s at pH 7 (Barger, Brown et al., 1997). Thebidentate surface complex (Structure 5) represents the probable structure ofthe remaining half of the Pb II surface complexes under those conditions.Barger and colleagues estimate the bond length dPb O and the nonbondedinternuclear distance dPb Al using scattering data from X-ray absorptionspectroscopy.Barger and colleagues assumed 3-fold coordination for the observeddPb O bond distance of 232 pm. Pb II coordination in the minerallitharge PbO s is 4-fold, and the mean dPb O bond distance is 231 pm,so Structures 4 and 5 were modified to show the most probable Pb II coor-dination environment; the nonbonded internuclear distance dPb Al isnot affected as long as the dPb O bond distance remains the same.X-ray absorption methods offer two independent estimates of coordinationnumber: the number of oxygen atoms directly bonded to Pb II , which is a directestimate based on the intensity of the scattering peak (Figure 9.13) for the first7atomic shell, and an indirect estimate based on the bond valence (Brown andAltermatt, 1985), which is calculated from dPb O bond distance. Bond dis-tance measurements from X-ray absorption methods, based on the position ofthe scattering peaks (Figure 9.13), are consistently more accurate than coordi-nation number measurements, making the latter approach for estimatingcoordination number the most reliable.The X-ray absorption scattering curve (Figure 9.13) is equivalent to a radialdistribution function, showing the intensity of X-ray scattering by atoms sur-rounding the atom that absorbs the X-ray radiation. Since the scattering curvein Figure 9.13 is from X-ray absorption at the Pb L3 absorption edge (i.e.,13,055 eV), the origin is occupied by Pb II . The first scattering peak, labeledO for oxygen atoms in the first atomic shell, is the most intense (the distance Rin the scattering curve is not the actual bond distance because X-ray scatteringintroduces a phase shift f that depends on the scattering atom). Two other scat-tering peaks, labeled Al for aluminum atoms in the second atomic shell, alsoappear in Figure 9.13. The first corresponds to the shorter bi-dentate Structure5 and the second to the longer mono-dentate Structure 4.Anions also form surface complexes by displacing a hydroxyl or watermolecule at the mineral surface and water molecules surrounding the hydratedanion (Structure 6).Structure 6. Phosphate (shaded circles) inner-sphere complex with Site C at the goethite (100) sur-face. Source: Reproduced with permission from Russell, J.D., Parfitt, R.L., et al., 1974. Surfacestructures of gibbsite goethite and phosphated goethite. Nature 248, 220221.FIGURE 9.13 This graph plots the X-ray absorp-tion scattering intensity at the Pb L3 absorptionedge from 2.0 mmol m2 Pb II adsorbed toaAl2O3s at pH 7 Source: Reproduced with per-mission from Barger, J.R., Brown, G.E., et al., 1997.Surface complexation of Pb(II) at oxide-water inter-faces: I. XAFS and bond-valence determination ofmononuclear and polynuclear Pb(II) sorption pro-ducts on aluminum oxides. Geochim. Cosmochim.Acta 61, 2617-2637.Chapter 9 Adsorption and Surface Chemistry 39Structure 7. Outer-sphere complex of Pb(II) adsorbed to aAl2O3(s). Source: Reproduced withpermission from Barger, J.R., Towle, S.N., et al., 1996. Outer-sphere Pb(II) adsorbed at specificsites on single crystal alpha-alumina. Geochim. Cosmochim. Acta 60, 35413547.Soil and Environmental Chemistry398Structure 7 illustrates an outer-sphere complex where the ionPb II inthis caseretains its entire first hydration shell and binds to the mineral sur-face through a combination of electrostatic forces and hydrogen bondsbetween the surface and water molecules hydrating the adsorbed ion.Surface chemists using X-ray absorption spectroscopy and other methodshave also collected evidence of surface precipitates forming at the mineral-water interface under conditions in which water chemistry simulations failto predict precipitation. The X-ray scattering curve in Figure 9.14 representsa surface complex between Dy III , a lanthanide element whose chemistryresembles trivalent actinide elements, and surface sites on the hydrous alumi-num oxide boehmite gAlOOHs.Phosphate ions adsorb to all environmental clay surfaces under acid condi-tions. The presence of the phosphate dramatically increases the affinity of theboehmite surface forDy III , producing a surface complex whose structure is veryFIGURE 9.14 This graph plots theX-ray absorption scattering intensityat the Dy L3 absorption edge from1.0 mmol m2 Dy III adsorbed tog AlOOHs boehmite at pH 7.Source: Reproduced with permissionfrom Yoon, S.J., Helmke, P.A., et al.,2002. X-ray absorption and magneticstudies of trivalent lanthanide ionssorbed on pristine and phosphate-modified boehmite surfaces. Langmuir18, 1012810136.much more readily than compounds that are precipitated as insoluble solids orChapter 9 Adsorption and Surface Chemistry 399adsorbed to the surfaces of environmental colloids. Adsorption processesimmobilize potential toxicants, lowering their uptake by living organismsand their movement with groundwater. Adsorption also ensures that toxicantsadhering to environmental colloids pose a continuing health risk because itrepresents a reservoir that continually releases toxicants into pore water forsimilar to the structure of known dysprosium phosphate crystalline solids (Yoon,Helmke et al., 2002). This is only one example of many where the surface complexformed when inorganic ions adsorbed at mineral surfaces resemble a precipitaterather than the surface complexes illustrated in Structures 47.9.10. SUMMARYThis chapter began with a description of mineral and organic colloidal adsor-bents commonly found in soils, sediments, aquifers, and suspended surfacewaters. These colloidal adsorbents have sufficient capacity, a direct conse-quence of their high surface-to-volume ratio, to adsorb compounds dissolvedin water to significantly alter pore water chemistry.Environmental chemists typically encounter two types of adsorption pro-cesses: site-limited and partitioning. The two processes have distinctly differ-ent adsorption isotherms, L-type and C-type, respectively. L-type adsorptionisotherms characterize the adsorption of most compounds by mineral colloidsor cation adsorption by humic colloids, but C-type isotherms are restrictedto the adsorption of neutral organic compounds by humic colloids and othermolecular-aggregate colloids. Neutral organic compounds partition intononpolar domains within molecular-aggregate colloids, giving rise to theirdistinctive adsorption isotherm.Both the capacity and the affinity of mineral colloids, with the exceptionof layer silicate clays, to adsorb inorganic and organic ions depend on pH.The pH-dependent adsorbing behavior of mineral colloids results from theadsorption and desorption of protons, leading to the development of surfacecharge. The effect of pH-dependent surface charge on the adsorbing behaviorof mineral colloids is well documented but poorly understood.The current state of our understanding comes from studies that determinethe structure and composition of the surface complex that forms when inor-ganic and organic ions bind to mineral surfaces. In some cases the chemicalstructure of the surface complex resembles the simple model similar to themodel for proton binding to oxygen atoms at the mineral surface, but in othercases the chemical structure of the surface complex has a composition that isincompatible with the simple site-binding model.The ultimate significance of surface chemistry and adsorption for environ-mental chemists can be traced back to the larger question of biological avail-ability and toxicity. Plants and animals take up compounds dissolved in waterbiological uptake.APPENDI R RATES IN WATER:STOKESSEnvironmental Chemistry4004p3R3 Dr g 6p R v 9A:5Solving (9A.5) for the sedimentation velocity we have (9A.6), the Stokes sed-imentation velocity expression used to determine particle size.v 29 R2 Dr g 9A:6ExampleThe viscosity of water at 20C is 1.002 103 kg m1 s1. The acceleration dueto gravity g is 9.802 m s2. The densities of water and silicate minerals at 20Care 1.00103 kg m3 and 2.65 103 kg m3, respectively. The following table liststhe sedimentation rate of spherical silicate particles in water at 20C.Radius, m Sedimentation Velocity, m s11.0 106 3.59 1061.0 107 3.59 108G. G. Stokes (1851) derived an equation (9A.4) for the frictional force f actingon a spherical particle with radius R. Combining the settling velocity of aspherical particle (9A.3) with the frictional expression (9A.4) yields (9A.5).f 6p R 9A:4 Dr rparticle rfluid 9A:2A frictional force fproportional to the viscosity of the fluidopposes thesettling of the suspended particle (9A.3). The particle will initially accelerateto a terminal velocity v at which point the frictional force equals the netsettling force and the particle begins to settle at a constant velocity v.Vparticle Dr g f v 9A:3difference between the gravitational Fg force and buoyancy Fb force. Thebuoyancy force Fb is a function of: particle volume V, particle density rparticle,and the density rfluid of the suspending fluid.Fg Fb Vparticle Dr g 9A:1Solid particles suspended in a liquid settle under the force of gravity. The rateof sedimentation depends on particle buoyancy (the difference between thedensity of the particles and the density of the liquid), the viscosity of the liq-uid and the size of the particles.The net force (9A.1) causing a particle suspended in a liquid to settle is theLAW1.0 1081.0 109X 9A. PA TICLE SEDIMENTATIONSoil and3.59 10103.59 1012Chapter 9 Adsorption and Surface Chemistry 401The sedimentation rate is on the order of one particle diameter per secondwhen the radius is 1 mm at the upper limit of the colloidal range and hasdecreased to on the order of one-thousandth of a particle diameter when theradius is 1 nm at the lower limit of the colloidal range. In other words, a particlewith a radius of 1 nm would settle 1 mm in 109 seconds or roughly 30 years.Such slow settling rates make colloidal suspensions stable on the timescale ofmost laboratory experiments.APPENDIX 9B. LINEAR LANGMUIR EXPRESSIONThe non-linear L-type adsorption isotherm expression (9B.1) given here isidentical to expression (9.9) given earlier in section 9.5.1.q qmax Kac C1 Kac C 9B:1Non-linear expression (9B.1) is rearranged to yield a linearized expression(9B.2) where the slope qmax 1 and intercept qmax Kac 1 contain the sameparameters appearing in the non-linear expression. This approach was popularat a time when non-linear optimization was not a practical option.1q 1 Kac C qmax Kac C1q 1qmax Kac C Kac Cqmax Kac C 1q 1qmax Kac C 1qmax Cq Cqmax Kac C Cqmax Cq qmax Kac 1 q1max C 9B:2Parameter fitting involves linear regression of a linearized dataset C=q,C followed by extraction of the two L-type isotherm parameters qmax,Kac fromthe slope (9B.3) and intercept (9B.4).qmax 1slope9B:3Kac slopeintercept9B:4Soil and Environmental Chemistry402APPENDIX 9C. HYDROLYSIS MODEL OF PROTON SITESIt is possible to generate a model of any mineral surface by cleaving the crys-tal structure parallel to a specific crystal face. The example here is the same(100) goethite surface described by Russell and colleagues (Russell, Parfittet al., 1974). The goethite crystal structure, viewed along the b crystal axis,appears in Structure C1. Oxygen ions O2 appear as open circles, hydroxylions OH as shaded circles, water molecules H2O as large black-filledcircles, and protons as small filled circles in Structures C1C4.Structure C1. Goethite crystal structure (a- and c-axes are in plane of the page). Source: Repro-duced with permission from Russell, J.D., Parfitt, R.L., et al., 1974. Surface structures of gibbsitegoethite and phosphated goethite. Nature 248, 220221.Structure C2 illustrates the cleavage along the goethite (100) crystal planeto create two identical (100) surfaces. The arrows show the final position ofoxygen ions O2 following cleavage. One quarter of the Fe3 coordinationpolyhedra on each surface is 5-coordinate after this imaginary cleavage.Structure C2. Cleavage along the (100) crystal plane of goethite. Source: Reproduced with per-mission from Russell, J.D., Parfitt, R.L., et al., 1974. Surface structures of gibbsite goethite andphosphated goethite. Nature 248, 220221.Parks and de Bruyn (1962) described the mechanism for the developmentof surface charge as follows:The mechanism by which the surface charge is established may be viewed qualitatively asa two-step process: surface hydration followed by dissociation of the surface hydroxide.The hydration step may be visualized as an attempt by the exposed surface cations toChapter 9 Adsorption and Surface Chemistry 403trostatic valence principle (Pauling, 1929) in equations (9C.1) through (9C.3).za 36 FeO 11 HO 1:5 v:u: 9C:1zb 36 FeO 36 FeO 36 FeO 11 HO 2:5 v:u: 9C:2zw 36 FeO 36 FeO 11 HO 2:0 v:u: 9C:3Structure C3. The neutral (100) surface of goethite with adsorbed water molecules. Source:Reproduced with permission from Russell, J.D., Parfitt, R.L., et al., 1974. Surface structures ofgibbsite goethite and phosphated geothite. Nature 248, 220221.Structure C3the model for a charge neutral goethite surfaceis our point ofreference. Titrating the surface by adding a strong acid HX will increase thetendency for the surface to adsorb protons by Site a (9C.4), as depicted incomplete their coordination shell of nearest neighbors. . . . The net result is that the sur-face now is covered by a hydroxyl layer with the cations buried below the surface.The adsorption of water molecules at the tail of each arrow in structure C2restores all Fe3 coordination polyhedra to 6-coordinate without depositingcharge on the newly formed surface. This is illustrated in Structure C3. Addi-tional water molecules would adsorb to the oxide surface without directlycoordinating Fe3 ions through hydrogen bonding. Water molecules adsorbedby hydrogen bonding represent the first layer of water molecules hydratingthe oxide surface.Structure C3 differs from Structure 4 (Russell, Parfitt et al., 1974) becausea water molecule bridges between the structural water molecule at Site a inStructure C3 and the structural oxygen at Site w. Structure C3 is explicitlycharge neutral because the water molecule a transfers one proton throughthe bridging water molecule to the structural oxygen w.The bond valence sum for each of the three sites is calculated using the elec-Structure C4.Soil and Environmental Chemistry404Proton adsorption, by the structural hydroxyl (Site a in StructureC3) convert-ing it to a water molecule (Site a in Structure C4), generates a positively chargedsurface that will co-adsorb anions X to maintain charge balance.Titrating the surface by adding a strong base MOH will increase the ten-dency for the surface to desorb protons from Site w (9C.5), as depicted inStructure C5. Removing protons from Structure C3 through proton desorption(Structure C5) creates a negatively charged surface that will coadsorb cationsto maintain charge balance.Owzw2:5 v:u:M aq OH aq Ow aq zw1:5 v:u:M aq H2O l 9C:5The state of Site a remains the same as in Structure C3, with a bond valencesum (9C.1) of 1.5 valence units (v.u.). Half of the negative charge acting onthe co-adsorbed cation M aq is on Site w and half of the negative chargeis on Site a even though the proton desorbed from Site w.Structure C5. The proton-deficient (100) surface of goethite. Source: Reproduced with permissionfrom Russell, J.D., Parfitt, R.L., et al., 1974. Surface structures of gibbsite goethite andphosphated goethite. Nature 248, 220221.Oaza1:5 v:u:H aq X aq OaH aq za2:5 v:u:X aq 9C:4The state of Site w remains the same as in Structure C3, with a bond valencesum (9C.3) of 2.5 v.u. Half of the positive charge acting on the co-adsorbedanion X aq is on Site a and half of the negative charge is on Site w eventhough the proton adsorbed at Site a.Structure C4. The proton-rich (100) surface of goethite. Source: Reproduced with permission fromRussell, J.D., Parfitt, R.L., et al., 1974. Surface structures of gibbsite goethite and phosphatedgoethite. Nature 248, 220221.sas -tivwa awa )on -na -sis dthChapter 9 Adsorption and Surface Chemistry 405Estimate the coefficient, KOM, for Supona sorption on the Yolo soil, based on alinear fit of the data. Express KOM in units of milliliters per gram of organic matter.SolutionA linear fit of sorbed activity qSupona as a function of CSupona activity in solu-tion yields a slope of 667: KOM 667 g mL-1.2. The Yolo soil in problem 1from a University of California-Davis experimentstation near Sacramento, Californiacontains 5.3% organic matter on adry-weight basis. Using your results fromproblem 1, determine the KD for Suponasorption on the Yolo soil. ExpressKD in units of milliliters per gram of (whole) soil.CSupona, activity mL-1 qSupona, activity g-10.0182 12.040.0358 26.180.0709 47.120.1406 91.100.2896 194.5A proton-rich (positively charged) oxide surface (Structure C4) developprotons bind to surface oxygen ions. Similarly, a proton-deficient (negaely charged) oxide surface (Structure C5) develops as protons desorb fromter molecules on the surface. The proton surface site is best considered aster-hydroxyl pair (Structure C4) or a hydroxyl-oxygen pair (Structure C5goethite. In a similar analysis of gibbsite surfaces, where the Al3 coordition polyhedra form sheets rather than chains, the proton-rich surface conts of water-water pairs, the neutral surface as water-hydroxyl pairs, ane proton-deficient surface as hydroxyl-hydroxyl pairs.Problems1. A sorption experiment of the organophosphate insecticide Supona by the Yolosoil series yielded the results listed in the following table. (The insecticide waslabeled with radioactive C-14, so the activity is in arbitrary units.)3.Soil and Environmental Chemistry406P P Pslope a of 5.331E-3 and an intercept b of 4.628E-3. The two Langmuir iso-therm parameters qmax and KD are defined using the preceding relations.A linear fit C q1 as a function of the soluble concentration C yields aAn effective way to estimate the two Langmuir adsorption isotherm para-meters (qmax and the affinity parameter KD) is by using a linearized Langmuirequation:Cq0@1A a C ba q1maxb Kac qmax 1Plot the data from the experiment using the preceding linearized Langmuirequation, perform a linear fit of the linearized data, and determine the twoLangmuir adsorption isotherm parameters: qmax and Kac.Solution0.344 62.710.463 75.211.001 92.711.821 108.335.984 146.0411.09 168.7517.26 172.7122.53 187.92P P P P soil0.040 35.620.141 49.38C mg mL1 q mg g1 The following data are from an experiment measuring phosphate adsorptionby a soil. The experimental data consist of the quantity of phosphate remain-ing in solution at steady state, CP mgP mL1 , and the quantity of substancephosphate-phosphorus on the surface at steady state, qP mgP g1soil .SolutionThe relationship between KOM and KD is given following.KD fOM KOMKD 0:053 667 KD 35:44.7yields a slope a of 1.12E6 and an intercept b of 1.51E2. The two Langmuirisotherm parameters q and K are defined using the preceding relations.steady state, CPb2 molPb2 L1 , and the quantity of Pb2 adsorbed by kao-linite at steady state, qPb2 mmolPb2 m2kaolinite .An effective way to estimate the two Langmuir adsorption isotherm parameters(qmax and the affinity parameter KD) is by using a linearized Langmuir equation:Cq0@1A a C ba q1maxb Kac qmax 1Plot the data from the experiment using the preceding linearized Langmuirequation, perform a linear fit of the linearized data, and determine the twoLangmuir adsorption isotherm parameters: qmax and Kac.SolutionA linear fit CPb2 q1Pb2 as a function of the soluble concentration CPb2CPb2 molPb2 L1 qPb2 mmolPb2 m2kaolinite 4.83E-05 2.52E-079.65E-05 3.92E-071.45E-04 4.48E-071.93E-04 5.17E-072.41E-04 5.60E-072.90E-04 5.98E-073.38E-04 6.29E-073.86E-04 6.81E-074.34E-04 6.75E-074.83E-04 7.17E-07ac b 5:331 103The following data (courtesy of T. Ranatunga and R. W. Taylor, Alabama A &M University) are from an experiment measuring Pb2 adsorption at pH 4 bythe nonswelling clay mineral kaolinite with a surface area of 9.6 m2 g1. Theexperimental data consist of the quantity of Pb2 remaining in solution at a q1maxqmax a1 5:331 103 1 187:6 mgP g1soilb KD qmax 1K a 4:628 103 1:152Chapter 9 Adsorption and Surface Chemistry 40max acRisk AssessmentAppendix 10C. Chemical- andSite-Specific FactorsTarget RiskCumulativenoncarcinogenic Risk 444A major impetus for the growth of environmental chemistry dates from thejarring discovery in the 1960s and 1970s of human health hazards causedby environmental pollution. Prior to the modern environmental movement, keyamendments to the Federal Food, Drugs and Cosmetic Act (U.S. Congress,Soil and Environmental Chemistry.# 2012 Elsevier Inc. All rights reserved.10.1. INTRODUCTIONTransport byGroundwater 436Noncarcinogenic Risk 443Appendix 10J. CumulativeChapter Outline10.1 Introduction 40910.2 The Federal RiskAssessment Paradigm 41110.3 Dose-ResponseAssessment 41110.4 Exposure PathwayAssessment 41910.5 Intake Estimates 42510.6 Risk Characterization 42810.7 Exposure Mitigation 43110.8 Summary 434Appendix 10A. Chemical- andSite-Specific Factors thatMay Affect ContaminantTransport by SurfaceWater 435Appendix 10B. Chemical- andSite-Specific Factors thatMay Affect Contaminantthat May AffectContaminant TransportInvolving Soils orSediments 437Appendix 10D. Chemical- andSite-Specific Factors thatMay Affect ContaminantTransport Involving Airand Biota 438Appendix 10E. WaterIngestion Equation 438Appendix 10F. Soil IngestionEquation 441Appendix 10G. Food IngestionEquation 442Appendix 10H. Air InhalationEquation 442Appendix 10I. HazardIndexCumulativeChapter 104091938)the Miller Pesticide Amendments (U.S. Congress, 1954), the FoodAdditives Amendment (U.S. Congress, 1958), and the Color Additives Amend-ment (U.S. Congress, 1960)were enacted to mitigate exposure to potentialcarcinogens in food. This formed a basis for developing the risk assessmentparadigm employed by the U.S. federal government (Figure 10.1) thatexpanded risk assessment beyond food to include air, water, and soil.Chemical pollution of the environment results from the release of com-pounds that are toxic to humans. Chronic human toxicity can take many forms(Table 10.1) that invariably originate with either the impairment of normalTABLE 10.1 A Classification of Chronic Toxicities and their Human HealthEffectsFIGURE 10.1 The Federal Risk Assessment Paradigm. Source: Reproduced with permissionfrom National Research Council, 1983. Risk Assessment in the Federal Government: Managingthe Process. Washington, D.C., National Academies Press.Soil and Environmental Chemistry410Toxicity Adverse Health EffectGerm cell mutagenicity Mutation of adult germ cells resulting in heritable abnormaltraitsCarcinogenicity Chromosomal damage resulting in the development ofmalignant tumors (See Box 10.1)Reproductive toxicity(teratogenicity)Loss of adult fertility and abnormal development of fetus orchildrenSpecific target organtoxicityLoss of organ functionChapter 10 Risk Assessment 41110.3. DOSE-RESPONSE ASSESSMENTFrom the outset, risk assessment follows different routes depending onwhether a chemical compound is identified as a known (or potential) carcino-gen. The assessment of noncarcinogens owes much to basic principlesof pharmacology, while carcinogens owe their unique assessment to earlystudies of radiation-induced cancer. As our understanding of carcinogenesis10.2. THE FEDERAL RISK ASSESSMENT PARADIGM10.2.1. Risk AssessmentScientific research supports human health risk assessment in three ways (seeFigure 10.1): identifying hazardous chemical compounds, developing dose-response functions necessary to predict adverse effects based on low-levelchronic doses delivered by the environment, and estimating uptake from vari-ous routes by representative human populations. Risk assessment draws fromeach of these scientific fields to characterize specific health risks, whether thatis an incremental excess lifetime cancer risk or the probability of an adverseeffect in a particular population.10.2.2. Risk Management and MitigationRisk characterization is essentially a quantitative prediction of the adverseeffect on human health that integrates our scientific understanding of toxicol-ogy and environmental exposure. Federal, state, and local government agenciesassume ultimate responsibility for mitigating health hazards by establishingemission standards or action levels, both designed to reduce contaminantlevels at various exposure points (air, water, and soil). Mitigation may involveremoval and secure disposal of hazardous waste or excessively contaminatedsoil or, in many cases, management of contaminated sites by imposing insti-tutional controls designed to limit human contact with contaminants that areimpractical to remove. As indicated in Figure 10.1, risk management isan endeavor that attempts to balance the risk posed by pollution againstthe economic, social, and political costs of reducing risk. Not surprisingly,marginal costs increase substantially as risk declines.biochemical processes or genetic damage. Genetic damage can result inabnormal development, mutations, or cancer.The following section reviews the paradigm employed by the U.S. federalgovernment to assess human health hazards resulting from chemicalpollution of the environment and to mitigate adverse health effects resultingfrom chemical pollution.improves, there is growing recognition within the scientific community thatearly distinctions between carcinogens and noncarcinogens were unwarranted.The regulatory community, however, has proven unwilling or unable to aban-don practices developed 50 years ago.10.3.1. Dose-Response DistributionsToxicologists fit dose-response data to numerous mathematical response func-tions; some (but not all) are cumulative probability distributions (cdf) derivedfrom processes with specific characteristics (e.g., a Poisson cdf represents theprobability of random independent events such as radioactive decay). The pri-mary distinguishing characteristic of these response functions is the presenceor absence of a response threshold; the more common threshold responsefunctions (Table 10.2) are plotted in Figures 10.2 to 10.4.TABLE 10.2 The Most Common Threshold Response FunctionsModel Cumulative Distribution Function Parameterslogistic P D; m,s 11 e Dm =s location m > 0, scale s > 0PoissonP D; l XDi0li eli! lWeibull P D; l, k 1 e D=l k scale l > 0, shape k > 00.20Soil and Environmental Chemistry412Dose, D0.001.000.800.600.40Probability, P(D)FIGURE 10.2 The Poisson cumulative probability distribution is a threshold response function.Chapter 10 Risk Assessment 4130.800.600.40Probability, P(D)0.201.0010.3.2. The No-Threshold One-Hit ModelThe one-hit model has a meaning that extends beyond a specific mathemati-cal expression. The simplest one-hit cdf employs a single dose coefficientparameter l.P D; l 1 el D 10:1The most recognizable attribute of any one-hit model is the absence of a thresh-old dose D (Figure 10.5). Carcinogen risk assessment models have generallybeen based on the premise that risk is proportional to cumulative lifetime dose.For lifetime human exposure scenarios, therefore, the exposure metric usedDose, D0.00FIGURE 10.3 The logistic cumulative probability distribution is a threshold response function.1.00Dose, D0.800.600.40Probability, P(D)0.200.00FIGURE 10.4 The Weibull cumulative probability distribution is a threshold response function.1.00Soil and Environmental Chemistry414for carcinogenic risk assessment has been the lifetime average daily dose(EPA, 2005). The dose D is prorated over a 70-year human lifetime, scalingthe probability of carcinogenesis P D; l by continuous lifetime exposure.The simplest no-threshold response function representative of the one-hitmodel appears in Figure 10.5. While response functions such as those in Fig-Dose, D0.800.600.40Probability, P(D)0.200.00FIGURE 10.5 The cumulative probability distribution for the simplest one-hit model is a non-threshold response function.ures 10.2 to 10.5 are the subject of continuing research and debate by pharma-cologists and toxicologists, they are of little practical consequence becauserisk assessment focuses on low-dose extrapolation methods largely indepen-dent of a particular cdf.110.3.3. Low-Dose Extrapolation of Noncarcinogenic ResponseFunctionsSeveral fundamental assumptions govern low-dose extrapolations when thetoxicant is a noncarcinogen. The first relates to the pharmacokinetics ofnoncarcinogenic chemicals in humans and animals. The adverse effect of atoxicant is a function of the steady-state concentration in the bodythe bodyburden. The steady-state body burden is a function of the intake and elimina-tion rates from the body, quantified by the biological half-life t1/2 of thesubstance.The dose plotted in a noncarcinogenic dose-response curve is the steady-state body burden mg kg1 prorated on a daily basis: the average daily dose1. Low-dose extrapolation using the benchmarkdose method does depend on the choice of cdf.Chapter 10 Risk Assessment 415tration in the food (or water), the relative rates of intake and elimination, andthe biological half-life.CE IR CIER 1 eER=Vd t IR CIER 1 eln2 t=t 1=2 10:4The steady-state concentration, however, is simply the concentration of thecontaminant in the water or food being ingested CI times the ratio of ingestionand elimination rates:CESS IR CIER10:5Figure 10.6 illustrates a low-dose extrapolation method for noncarcinogenicdose-response functions relative to three toxicological end-points: the lowestobservable adverse effect level LOAEL, the no adverse effect level NOAEL,and the reference dose RfD. The error bars in Figure 10.6 illustrate the statis-IR water: L d1, soil or food: kg d1 (i.e., the volume of water ingested orthe mass of a particular food ingested per day) times the concentration ofthe contaminant in the water or food being ingested CI.The elimination rate RE mg d1 is a function of the eliminationrate factorfor example, the volume of urine eliminated per dayER L d1 times the concentration of the contaminant in the urine CE.The elimination rate constant kE, a first-order constant, is a function of thebiological half-life t1/2 of the contaminant in the organism or, alternatively,the effective distribution volume of water in the body Vd:kE ln 2 t1=2 ERVd 10:3In the short term, the concentration being eliminated depends on the concen-the bioconcentration factor BCF).At steady state, the rate of intake equals the rate of elimination:RI REIR CI ER CE 10:2The intake rate RI mg d1 is a function of the ingestion rate factor10.3.4. Estimating the Steady-State Body BurdenThe steady-state body burden of any chemical substance depends on intakeand elimination rates, RI and RE. The elimination rate RE depends on theelimination route, kinetics (typically first-order rate law), and storage (i.e.,ADD mg kg1 d1 . The cumulative dose ingested throughout the exposureduration is considered irrelevant.tical distinction between NOAELthe highest dose whose adverse effect is41involve extrapolation. Relative to these two points is the reference doseRfD, an extrapolated toxicological end-point.10.3.5. Reference Dose RfDThe reference dose RfD mg L1 d1 is a low-dose extrapolated end-pointstrictly limited to noncarcinogenic toxicants. The RfD end-point can bedefined relative to either a NOAEL (10.6) or a LOAEL (10.7).RfD NOAELUF MF NOAEL10n 1 10:6RfD LOAEL10 UF MF LOAEL10 10n 1 10:7The RfD end-point depends on the nature of the dose-response study, whether itinvolves humans or animals or whether it is a long- or short-term study.Uncertainty Factorsstatistically insignificantand LOAELthe lowest dose whose adverse effectis statistically significant. This portion of the dose-response curve does notFIGURE 10.6 Low-dose portion of an adverseeffect dose-response curve for a noncarcinogenshowing three toxicological end-points used inrisk assessment: LOAEL, NOAEL, and RfD.Soil and Environmental Chemistry6UFH 101long-term human studiesUFA 102long-term animal studiesUFS 103short-term animal studiesModifying Factors 0 < MF 1; default MF 1Interspecies extrapolationextrapolating from animal-based dose-response stud-ies to define human toxicological end-pointsis a common practice involvingmuch greater uncertainty than the type of extrapolation illustrated in Figure 10.6.10.3.6. Low-Dose Extrapolation of Carcinogenic ResponseFunctionsThe earliest research on carcinogenesis came from scientists studying thehealth effects of ionizing radiationhigh-energy alpha and beta particles emit-ted by radioactive elements and high-energy photons (gamma- and X-rays).7These studies led to the one-hit theory that postulates that the absorption of asingle high-energy particle or photon by tissue is sufficient to initiate carcino-genesis. A key feature of the one-hit model is the absence of a threshold dose.Scientists established certain polycyclic aromatic compounds (e.g., benzo[a]pyrene, Structure 1, and naphthylamine, Structure 2) as cancer-causingagents as early as 1949 (Goulden and Tipler, 1949; Cooper, 1954; Lefemine,1954; Hoffmann, Masuda et al., 1969). The mechanisms of carcinogenesiswere poorly understood at that time, leading toxicologists to adopt the one-hit theory of radiation-induced carcinogenesis.Structure 1. Benzo[a]pyrene (CAS 50-32-8)Structure 2. 1-Naphthylamine (CAS 134-32-7)Carcinogenesis, regardless of the cause (Box 10.1), has a lengthy latencyperiod where the duration of the latent period decreases as the dose (radiationor chemical) increases. Furthermore, carcinogens and radiation both producemutations. Aside from these similarities, the actual interaction with tissue isprofoundly different for radiation and chemicals.The absorption and retention of any chemical compound, regardless ofits toxicology (see Table 10.1), depend on its molecular properties. The anatomicpath followed by a specific compound, the barriers (gastrointestinal, renal, placen-tal, blood-brain, etc.) it crosses or cannot cross, also depends on their chemicalproperties. Unlike ionizing radiation, there are few universal carcinogens. Mostcarcinogens target specific organisms, a single gender, a particular age group,or individuals experiencing specific physiological stresses.Figure 10.7 illustrates the low-dose extrapolation method for carcinogenicdose-response functions relative to three toxicological end-points: the effec-tive dose resulting in a 10% incremental excess lifetime cancer risk ED10,the lower-limit effective dose (i.e. the lower 95% confidence limit) associatedwith a 10% incremental excess lifetime cancer risk LED10, and the point-of-departure POD. The error bars in Figure 10.7 illustrate the statisticaluncertainty at the lower dose limit of the dose-response curvethe pointwhere low-dose extrapolation begins.The adverse response, given the extended latency of carcinogensis, isscaled as the incremental excess lifetime cancer risk IELCR. Figure 10.7 illus-Chapter 10 Risk Assessment 41trates an assessment based on a 10% IELCR that intersects the dose-responsecurve at a dose designated ED10, although empirical data may extend belowSoil and Environmental Chemistry418Box 10.1 The Knudson Two-Hit ModelOncologists associate two regulatory gene classes with carcinogenesis (Gibbs,2003): oncogenes and tumor suppressor genes. Proto-oncogenes promote cellproliferation in immature or stem cells, while tumor-suppressor genes repress cellED10. The statistical uncertainty associated with the ED10 end-point definesthe LED10 dose associated with a 10% IELCR. The point-of-departure PODis best understood by reference to Figure 10.7.The adverse effect of a carcinogen is assessed as a function of thecumulative lifetime body burden. The dose plotted in a carcinogenicdose-response curve is prorated over a human lifetime of 70 years (EPA,division preparatory to further signals that initiate cell differentiation into maturetissue. Knudson (1971) suggested an alternative to the one-hit model of carcino-genesis that postulated the necessity of two disabling mutations, one for eachallele of a tumor-suppressor gene, to initiate carcinogenesisthe so-calledtwo-hit hypothesis. If the individual inherited a disabling mutation in a singletumor-suppressor allele, then exposure to a carcinogen resulting in a disablingmutation in the second allelea one-hit scenariowould be sufficient toinitiate carcinogenesis. Individuals susceptible to carcinogens presumably carrydisabling mutations to a single tumor-suppressor allele.An enabling mutation of a proton-oncogene, perhaps a mutation to thepromoter region disabling the binding of a repressor protein, is sufficient to initiatecarcinogenesis. Mutant proto-oncogenes, rendering them unresponsive to repres-sion, are known as oncogenes. A one-hit mutation targeting either proto-oncogene allele can result in carcinogenesis, although by a different mechanismthan disabling mutations of tumor-suppressor genes.Chapter 10 Risk Assessment 4192005): the lifetime average daily dose LADD mg kg1 d1. The assumptionis that a high carcinogenic body burden accumulated over a short period oftime is equivalent to a low body burden accumulated over a lifetime. Forinstance, daily consumption of 2 liters of water by an adult results in a averagedaily dose of 15 milligrams per kilogram per day if the exposure duration is1 year and the concentration is 530 ppm but if this same exposure is proratedover 70 years the life time average daily dose is a mere 0.22 milligrams perkilogram per day.The one-hit theory assumes there is no threshold and any dose has a finiteprobability of initiating carcinogenesis; performing a linear extrapolationfrom the POD to zero dose is the proper risk assessment protocol. Notice thatthe slope is steeper and the estimate of risk is more conservative if the extrap-olation is made using a POD defined by LED10 rather than ED10. The slope ofthis extrapolation is known as the cancer slope factor CSF.Figures 10.6 and 10.7 demonstrate the profound significance of the one-hit theory on carcinogenic risk assessment. The one-hit theory determines theFIGURE 10.7 Low-dose portion of anadverse effect dose-response curve for acarcinogen showing three toxicologicalend-points used in risk assessment: ED10,LED10, and POD.metrics used to quantify carcinogenic risk: reliance on cumulative rather thansteady-state body burden and the low-dose extrapolation method (Figure 10.7).None of these explicitly depends on a specific dose-response function.10.4. EXPOSURE PATHWAY ASSESSMENTFigure 10.8 illustrates the elements of exposure pathway assessment. A recep-tor or exposed population receives a contaminant dose, provided that all ele-ments in the exposure pathway are present.10.4.1. ReceptorsThe exposure pathway terminates with a specific human populationthereceptor in risk assessment terminologythat receives a contaminant dosefrom the environment (see Figure 10.8). The exposed or potentially exposedSoil and Environmental Chemistry420population is distinguished from the general population by some characteristicthat brings this subpopulation into contact with contaminated environmentalmedia. For instance, urban air pollution affects ambient air throughout theurban environment, placing the entire residential urban population in contactwith contaminant gases and particulates, while certain manufacturing pro-cesses pollute a work site, exposing only workers at that site. One can furtherdistinguish high-risk populations: a particular age group in a residential urbanpopulation or workers performing specific tasks at a work site.The U.S. EPA Exposure Factors Handbook (Wood, Phillips et al., 1997) pro-vides numerous examples of activity patterns that influence the type and durationof contact experienced by different subpopulations. Day and colleagues (2007),for instance, reported on the exposure pathway assessment at a factory producingcopper-beryllium wire that distinguishes work area subpopulations.10.4.2. Exposure RoutesToxicologists employ pharmacological drug disposition models (Figure 10.9)to represent exposure routes. Contaminants entering the human body ulti-mately elicit an adverse effect by acting on a target organ. The magnitudeFIGURE 10.8 A complete exposure pathway begins with a contamination source and a mode ofenvironmental transport and reaches an exposed population or receptors through some exposurepointcontaminated environmental mediaand an exposure (uptake) route. Source: Reproducedwith permission from U.S. Department of Health and Human Services, 1992. Public HealthAssessment Guidance Manual. Agency for Toxic Substances and Disease Registry. Atlanta, GA.Chapter 10 Risk Assessment 421of the adverse effect is most closely linked to the contaminant concentrationor dose at the target organthe biologically effective dose. A complex inter-nal pathwaythe exposure routeconnects the point where the contaminantenters the bodythe exposure pointand the target organ.The exposure route begins with either oral or dermal intake that delivers apotential dose to the human once the contaminant crosses an intake bound-FIGURE 10.9 The generalized exposure route model is adopted from pharmacology drug dispo-sition models. Source: Reproduced with permission from Wood, P., Phillips, L., et al., 1997.Exposure Factors Handbook. U. S. E. P. Agency. Washington, DC, Office of Research and Devel-opment, National Center for Environmental Assessment, 1193.arythe lining of the sinus passages or lungs, at various points along the gas-trointestinal tract, or the skin.2 The potential dose is typically lower than theconcentration at the exposure point because intake is usually less than 100%efficient. Following intake, the contaminant undergoes distribution throughoutsome portion of the human body. The distribution volume (Eq. (10.3)) and thepossibility for clearance (i.e., elimination) reduce the applied dose that arrivesat the biological barrier (vascular, renal, placental, blood-brain, etc.) that pro-tects the organ from potentially toxic substances. Contaminant uptake is thepassage of the compound across a biological barrier, resulting in an internaldose lowered by the transport properties of the barrier from the applied dose.Finally, metabolism and elimination processes (reverse transport across thebiological barrier) further lower the internal dose to the biologically effectivedose just mentioned.Eukaryotesorganisms whose cells have a nucleusrely on selective iontransporters to regulate uptake across the cell membrane into the cytoplasm.The selectivity of these ion transporters serves as a biological barrier to theuptake of inorganic toxic substances. Zinc homeostasis in mammalian cells2. Skin and mucous membranes are considered nonspecific barriers.Soil and Environmental Chemistry422is maintained by a combination of import and export transporters (Liuzzi andCousins, 2004). There is no evidence that cadmium ions are exported fromFIGURE 10.10 The generalizeduptake and efflux pathways ofarsenic in mammals include boththe electrochemical reduction ofAs(V) to As(III) and transportersthat export either the arsenic(III)-gluthathione complex As GS 3 orarsenous acid. Arsenic uptake isbelieved to occur via phosphateion transporters. Source: Repro-duced with permission fromRosen, B.P. Liu, Z., 2009. Trans-port pathways for arsenic andselenium: A minireview. Environ-ment International 35, 512515.mammalian cells by any of the known ZnT zinc efflux transporters(Martelli, Rousselet et al., 2006), but cadmium export is possible by alterna-tive routes: efflux by transporters of other divalent metal cations (e.g.,Mn2) or export of cadmium complexes with ligands such as cysteine orglutathione. Figure 10.10 illustrates the cytoplasmic processes initiating theelimination of arsenate by mammalian cells; the intracellular reduction ofAs(IV) followed by the methylation and export of As(III).10.4.3. Exposure PointsPotential exposed populations come into contact with media containing con-taminants, known as the exposure point (see Figure 10.9). An exposure pointcan be a wide range of media (Wood, Phillips et al., 1997) ranging fromambient air, water, sediments, and soil to food and consumer products. Ourprimary concern here is with environmental mediaair, water, sediments,and soilthat deliver contaminants to humans by inhalation, ingestion, anddermal contact (see Figure 10.8).Table 10.3 lists possible exposure points. Risk analysts distinguish expo-sure points from environmental media at the source of the exposure pathwayand mobile environmental mediaair and waterthat transport and dispersecontaminants. Each exposure point implies potential exposure routes andexposed populations, the latter depending on specific activities.Chapter 10 Risk Assessment 423TABLE 10.3 Possible Exposure Points for Contaminated EnvironmentalMediaEnvironmentalMediaExposure PointsSoil Surface soil at work sites, residential sites, and parks; subsurfacesoil exposed during excavation or other disturbance of the surface;excavated and transported soil used as fillSediment Submerged or exposed stream and lake sediment, sandbars,Establishing exposure points requires detailed knowledge of both thenature and extent of contamination through environmental testing andbiological monitoring. Environmental testing analyzes all of the environmen-tal media listed in Table 10.3 to identify and quantify potential contaminants.Biological monitoring collects and analyzes biological fluid and tissuesamples from potential exposed populations to confirm and quantify exposure.10.4.4. Fate and TransportContinuing to work our way toward the contaminant source, the next compo-nent in the exposure pathway (see Figure 10.8) is contaminant fate andoverbank flood deposits, and drainage ditches; excavated andtransported sediments used as fill or the result of ditch, drainagechannel, canal, and watercourses maintenanceGroundwater Wells and springs supplying water for municipal, domestic,industrial, agricultural, and recreational purposesSurface Water Lakes, ponds, streams, and storm drainage supplying water formunicipal, domestic, industrial, agricultural, and recreationalpurposesAir Ambient air downwind of a contaminated site, indoor aircontaining migrating soil gasese.g., flammable (methane) andasphyxiating (carbon dioxide) gas entering buildings on or adjacentto landfillsBiota Plants (cultivated and gathered fruits and vegetables, plants usedfor medicinal purposes), animals (livestock, game, and otherterrestrial or aquatic organisms), or other natural products that havecontacted contaminated soil, sediment, waste materials,groundwater, surface water, or airOther Contaminated materials at commercial or industrial sites (e.g., rawmaterials, sludge from treatment processes, waste piles, radiation-laden metals) may provide a direct point of contact for on-siteworkers, visitors, or trespassersSource: DHHS, 1992.biological conditions change over time and location.Soil and Environmental Chemistry424Adsorption lowers toxicity by reducing biological availability (i.e., watersolubility) and, in the process, leads to a substances accumulation in soils,sediments, and aquifers. Contaminant storage and buildup in environmentalsolids contributes to legacy pollution, whose long-term risk is often difficultto assess.Mobile environmental mediawater (above- or belowground), solvents,and gases (above- and belowground)disperse contaminants from their pri-mary and secondary sources, expanding the area and volume of contaminatedenvironmental media and increasing the opportunity for human exposure.Water percolating through soil, sediments, and aquifers transports contami-nants slowly and over rather short distances belowground. Surface water flowand atmospheric currents disperse suspended particles rapidly and, in somecases, over considerable distances. The cost of environmental mitigation andthe scope of the exposed population can increase dramatically with environ-mental transport.Appendixes 10A10D list chemical-specific and site-specific factors thatinfluence the fate and transport of contaminants in the environment. Thoughlacking chemical and mechanistic detail, the tables in Appendixes 10A10Dgive a broad perspective of the way risk analysts understand fate and transportprocesses.10.4.5. Primary and Secondary SourcesEvery hazardous substance that contaminates the environment has a history.The history begins with a production process that utilizes the compound ofconcern or that generates the compound as either a primary product or by-product. The history terminates with the compound of concern entering awaste stream that may or may not involve recovery or recycling. The agricul-ture, mining, manufacturing, and chemical industries in the United Statesare undergoing a transformation designed to minimize the use and productionof hazardous substances, but this transformation will not entirely eliminatethe release of hazardous substances into the environment at production andtransport in environmental media. This is environmental chemistrys primaryfocus and the principal topic of this book. Most hazardous substances undergoprofound biological and chemical transformation upon entering soils or aqui-fers, the atmosphere, or water; often the transformations are quite complexand depend on prevailing conditions.Biological and chemical transformations acting in concert may degrade ahazardous substance, eliminating or reducing toxicity, or they can activate asubstance, substantially enhancing toxicity. Examples of both are well known.Often biological and chemical transformations of inorganic substances thatlower toxicity under prevailing conditions are reversed when chemical andstorage facilities.dle products that are hazardous. Waste management, especially when recov-in this process is exposure pathway elimination. If all components of an expo-Chapter 10 Risk Assessment 425sure pathway are present, then risk analysts identify this as a completed exposurepathwaya pathway of concern because a specific population is exposed viathe pathway to a contamination source. If one or more elements of an exposurepathway are absent, then risk analysts identify this as an eliminated exposurepathway. A potential exposure pathway would be one where the presence orabsence of one or more pathway elements is unverified. The Exposure PathwayElimination (Box 10.2) illustrates this process with a real case.10.5. INTAKE ESTIMATESThe general exposure route model (see Figure 10.9) begins with intake ofcontaminated media. This section discusses intake estimates for specificexposure routes. Intake equations (see Appendixes 10E10H) estimate thedose delivered to an exposed population, specifically the body burdenmg kg1 d1 . Intake dose estimates for carcinogens must compute a cumu-lative body burden, while a steady-state body burden is computed for noncar-cinogens. Intake dose estimates also depend on different criteria for setting theingestion (or inhalation) rate IR, broadly known as exposure factors. Once weclearly understand the role of averaging time in computing body burdenmg kg1 d1 and the statistical significance of exposure factors, we canfully comprehend and apply the various intake equations.10.5.1. Averaging TimeOSWER Directive 9285.6-03 (EPA, 1991) provides the following guidanceery and recycling are costly or inefficient, creates further opportunities forenvironmental contamination during waste storage, transport, and disposal.Hazardous substances released into the environment from any of the pri-mary sources just mentioned will contaminate soils, surface water bodies,groundwater, sediments, and aquifers. Contaminated environmental mediabecome secondary sources upon the removal of the primary sourcedismantling production, storage or distribution facilities, termination of end-point use, or closing of waste disposal sitesoften leaving secondary sourcesas a continuing pollution legacy.10.4.6. Exposure AssessmentThe ultimate goal of exposure pathway assessment is identifying pathways ofconcern linking a contaminant source to an exposed population. A key factorOpportunities for environmental pollution occur during the distributionand end-point use. Often distributors or end-users fail to properly store or han-for setting the averaging time for intake equations:Box 10.2 Exposure Pathway EliminationIn 1974, over opposition by surrounding landowners, the Dane County ZoningBoard granted John DeBeck permission to open and operate a landfill in an aban-doned limestone quarry near Black Earth Creek. The Board did not requireDeBeck to install a secure liner or monitoring wells. DeBeck operated the RefuseHideaway landfill from 1974 through 1987 in the face of continued opposition bylandowners whose properties bordered the landfill. At one point homeownersfiled a lawsuit that temporarily closed the landfill for 15 months.In March 1988, the Wisconsin Department of Natural Resources (WDNR)detected cleaning solvents from the landfill in two domestic wells and contaminatedrunoff in a drainage ditch that emptied into Black Earth Creek. TheWDNR asked theDane County Zoning Board to rescind the landfill permit issued to DeBeck. Afterthreatening to file a lawsuit, theWisconsin attorney general, Don Hanaway, reachedan agreement with DeBeck to stop accepting waste byMay 16, 1988, and to install aclay cap and methane vents at the landfill. DeBeck filed for bankruptcy a year later,and inOctober 1992, the U.S. Environmental Protection Agency added Refuse Hide-away to the National Priorities List, designating it a Superfund site.The following table lists the exposure pathway components and the exposure timeframe for Refuse Hideaway. The exposure point (drinking water from private wells),the exposure route (ingestion of drinkingwater), and a potentially exposed population(landowners relying onprivatewells for drinkingwater) existed prior to the opening ofRefuse Hideaway, but the exposure pathway is eliminated because a contaminantsource and transport did not exist during that time frame.The presence of a potential exposure pathway linking Refuse Hideaway todomestic drinking water wells motivated the 53 landowners in the vicinity tooppose the opening and operation of the landfill. It provided a basis for the courtjudgment temporarily closing the landfill and for early efforts by the Wisconsinattorney general and the WDNR to terminate operations. Legal efforts to closethe landfill were unsuccessful until the detection of solvents in domestic wellscompleted the exposure pathway.Exposure PathwayComponentTime Frame of ExposureBefore 1974 19741987 1988PresentContaminant Source No Yes YesFate and Transport No Unknown YesExposure Point Yes Yes YesExposure Route Yes Yes YesPotentially ExposedPopulationsYes Yes YesConclusion EliminatedPathwayPotentialPathwayCompletedPathwaySoil and Environmental Chemistry426Chapter 10 Risk Assessment 427Averaging time (AT) for exposure to noncarcinogenic compounds is always equal toED [exposure duration], whereas, for carcinogens, a 70-year AT is still used in orderto compare to [USEPA] Agency slope factors typically based on that value.By specifying a human lifetime (70 years) as the averaging time, the car-cinogen body burden mg kg1 d1 becomes effectively the cumulativebody burden, scaled to a daily intake mg kg1 d1 . Noncarcinogen bodyburden, which is also scaled to a daily intake mg kg1 d1 , is averagedover a much shorter time scalethe exposure duration ED. Equating averag-ing time AT to exposure duration ED for noncarcinogens implicitly assumesany deviation from steady state can be neglected.For noncarcinogens, the steady-state body burden mg kg1 d1 iscalled the Average Daily Dose (ADD). For carcinogens, the cumulative bodyburden mg kg1 d1 is known as the Lifetime Average Daily Dose(LADD), scaled using an averaging time AT equal to the mean lifetime:70 y 365 d y1 .10.5.2. Exposure FactorsKey parameters influencing body burden estimates relate to the behavior andphysical characteristics of each potential exposed population: the ingestion rateIR associated with a particular exposure route and the exposure duration ED.Earlier we discussed the importance of probability distributions on statisticalestimates of central tendency and variation in any population. Toxicologistsstudying exposure factors rely on statistical methods to estimate the most likelyexposureMLE and the reasonable maximum exposure RME, based on the modeand the 95th percentile for the potential exposed population, respectively.For example, the Exposure Factors Handbook (Wood, Phillips et al.,1997) distinguishes several potential exposed populations, each with distinc-tive water ingestion rates: adults and children in the general population, lactat-ing and pregnant females, and highly active individuals. Population studiesalso distinguish ingestion rates IR and exposure durations ED for residential,industrial, commercial, agricultural, and recreational activity.Table 10.4 lists standard inhalation rates that distinguish ambient fromindoor air, where the key variable is not the breathing rate but exposure dura-tion ED, a behavioral characteristic. The residential RME total inhalation rateof 20 m3 d1 is less than the total RME for the general population becausethe typical residential population is general population subgroups who wouldbe expected to spend the majority of their time at home: housewives; service andhousehold workers; retired people; and unemployed workers (EPA, 1991).The potable water ingestion rate in Table 10.4 corresponds to the 90th per-centile for the general population and assumes that the general population isabsent from their residential water supply about 15 days per year. Potablewater ingestion in the workplace is assumed to be 50% of the total wateringestion rate IR, a population behavior characteristic.Soil and Environmental Chemistry428Soil ingestion includes actual outdoor soil and indoor dust. Soil inges-tion covers both purposeful soil consumption (a behavior known as pica)and incidental ingestion through hand-to-mouth contact or particulates enter-ing the mouth or nostrils while breathing. Children younger than 6 years oldingest significantly more soil than other age groups, yet another populationbehavior characteristic.Ingestion rates for certain foods identify subpopulations or food sourcesassociated with exposure pathways of concern: homegrown fruits and vegeta-bles grown in contaminated soil, a subpopulation that subsists on fish caughtin contaminated lakes or streams, or nursing infants subsisting on breast milk.TABLE 10.4 Residential Exposure Factors for Selected Exposure RoutesIntake Route Standard U.S. EPA Exposure FactorWater Ingestion Rate 2 L d1Soil Ingestion Rate Child (age 16 years): 200 mg d1Adult (age > 6 years): 100 mg d1Air Inhalation Rate Total: 20 m3 d1Indoor: 15 m3 d1Homegrown Produce Ingestion Rate Fruit: 42 g d1Vegetables: 80 g d1Subsistence Fish Ingestion Rate 132 g d1Source: EPA, 1991.Intake equations for water, soil, and food ingestion and air inhalation, alongwith examples of each, appear in Appendixes 10E10H.10.6. RISK CHARACTERIZATIONArmed with equations for estimating contaminant intake based on concentrationsat the exposure point (Appendixes 10E10H), we are now prepared to quantifyrisk. Risk is a function of intake and toxicity. Quantifying risk from exposure toa carcinogen is based on a definite statistical probability: the incremental excesslifetime cancer risk IELCR. The risk factor for a noncarcinogen, on the other hand,is not directly linked to the probability of an adverse effect on a population.10.6.1. The Incremental Excess Lifetime Cancer RiskThe incremental excess lifetime cancer risk IELCR is the probability of devel-oping cancer as the result of exposure to a specific carcinogen and appearsas an incremental increase in cancer cases in the exposed population overwhat would occur in the absence of exposure. An acceptable IELCR can varybut is often 1 to 10%, depending on variability in the population study.3 Theprobability of developing cancer, based on the number of cancer cases in thepopulationregardless of ageis the lifetime cancer risk. Carcinogen toxic-ity is quantified by the cancer slope factor SF mg1toxicant kgtoxicant d of eachsubstance (10.9), whose units are the inverse of the Lifetime Average DailyDose LADD because the ratio is a probability (i.e., unitless).Chapter 10 Risk Assessment 429ExampleA child (15 kg) ingests soil 200 mg d1 containing 1 mg kg1 benzene. Theoral slope factor SF for the carcinogen benzene is 0.029 mg1 kg d .Soil Intake 1:14 106 mgbenzene kg1 d1IELCR LADD SFIELCR 1:14 106 mgbenzene kg1 d1 2:9 102 mg1benzene kg d IELCR 3 108Cumulative risk resulting from simultaneous exposure to several carci-nogens is found by adding the IELCR values for each carcinogen and apply-ing a cumulative IELCR to the total (see Appendix 10I). Generally, the3. Variability in any population study of carcinogenesis ultimately determines the minimalIELCR detectable with statistical confidence. A population study with low variability permitsIELCR detection as low as 1% with reasonable statistical confidence. Inherent variability typicallylimits IELCR detection with reasonable statistical confidence to 5% or 10%. The correspondingExampleAn adult (70 kg) drinks water 2 L d1 containing 0.05 mg L1 benzene (seeAppendix 10E, first example). The oral slope factor SF for the carcinogen benzeneis 0.029 mg1 kg d .Water Intake 5:9 104 mgbenzene kg1 d1IELCR LADD SFIELCR 5:9 104 mgbenzene kg1 d1 2:9 102 mg1benzene kg d IELCR 2 105Risk Dose Toxicity 10:8IELCR LADD SF 10:9LADD is a toxicological end-point dose symbolized, respectively, as ED01, ED05, or ED10.1:33 104 mgtoluene kg1 d1Soil and Environmental Chemistry430HQ 0:2 mgtoluene kg1 d1HQ 6:7 104 < 1oral, tolueneHQ 1:4 102 mgtoluene kg1 d10:2 mgtoluene kg1 d1HQ 7 102 < 1ExampleA child (15 kg) ingests soil (200 mg d1) containing 10 mg kg1 toluene. Thereference dose for toluene is RfD 0:2 mgtoluene kg1 d1.Soil ADD 1:33 104 mgtoluene kg1 d1HQ ADDtolueneRfDoral, tolueneHQ ADDRfD10:10ExampleAn adult (70 kg) drinks water 2 L d1 containing 0.5 mg L1 toluene(see Appendix 10E, second example). The reference dose for toluene isRfD 0:2 mgtoluene kg1 d1.Water ADD 1:4 102 mgtoluene kg1 d1HQ ADDtolueneRfDacceptable cumulative IELCR should be no larger than the acceptable IELCRfor exposure to a single carcinogen.10.6.2. The Hazard QuotientThe hazard quotientHQ (the risk factor applied to noncarcinogens) relates the dosedelivered at the exposure point (the Average Daily Dose ADD) to a toxicologicalend-point: the reference dose RfD (10.10). Earlier we described how the referencedose RfD is a low-dose end-point, extrapolated from either a NOAEL (Eq. (10.6))or LOAEL (Eq. (10.7)). An acceptable hazard quotient HQ is less than 1.Risk DoseToxicityChapter 10 Risk Assessment 431Cumulative risk resulting from simultaneous exposure to several noncarci-nogens is found by adding the HQ values to obtain a Hazard Index HI (seeAppendix 10J). An acceptable HI for cumulative exposure is the same asthe acceptable HQ for exposure to a single noncarcinogen: HI < 1.10.7. EXPOSURE MITIGATIONFederal and state agencies employ several practices to mitigate exposure.Mitigation typically involves specific actions taken to eliminate exposurepathways and to reduce risk to acceptable levels at exposure points. The fol-lowing example illustrates actions taken by the Wisconsin DNR to mitigateexposure from contamination at Refuse Hideaway. The actions represent theselected remedy announced in the official Record of Decision (EPA, 1995)for Refuse Hideaway landfill.The Source Control actions in Table 10.5 address contamination at thesource of the exposure pathway and are designed to restrict access, eliminateprimary and secondary contamination sources at the site, and restrict contam-inant transport offsite. The Groundwater Treatment actions focus on off-sitemitigation, primarily treating the groundwater plume to prevent furthercontaminant migration offsite. The Water Supply actions address the exposurepoint: domestic wells.Mitigation also relies on setting and enforcing standards designed to limitrisk in the exposed population. The selected remedies at Refuse Hideawaylandfill refer to standards twice: extraction of groundwater when volatileorganic compounds are greater than 200 ppb and installation of treatmentsystems for any private well with concentrations exceeding NR 140 Enforce-ment Standards. The role of risk assessment in setting enforcement standardsis the topic of this section.You will encounter numerous acronyms used to identify risk-based stan-dards; a few appear in Table 10.6. A RBCL, associated with a particularHQ or IELCR, or a MOE, are not enforceable standards but merely guidelinesfor setting enforceable standards. They would appear in the box labeled Reg-ulatory Options in the Federal Risk Assessment Paradigm (see Figure 10.1).The setting of MCLs and MCLGs occurs at the level of Agency Action, repre-senting a regulatory consensus designed to provide acceptable protection ofpublic health while taking into account attendant economic, social, and polit-ical constraints.An RBCL always relates to a particular exposure route because it esti-mates the contaminant concentration at the exposure point associated witha quantifiable risk. The following example estimates the RBCL for a carcino-gen dissolved in water, the exposure point being ground or surface water andthe exposure route water ingestion. Expression (10.11) is the LADD equationTABLE 10.5 Selected Remedies for Risk Mitigation at Refuse HideawayLandfillSource Control Deed restrictions and zoning modificationsWarning signs posted around the perimeter of the propertyMaintenance of the existing single barrier (clay) cap, vegetation,and surface runoff controlsOperation and maintenance of the existing landfill gas extractionand destruction system and leachate extraction and off-sitetreatment and disposal systemGroundwater monitoring of selected monitoring wells and privatehome wellsGroundwaterTreatmentExtraction of the most highly contaminated groundwater (greaterthan 200 ppb total [volatile organic compounds]) in the vicinity ofthe landfill and treatment of groundwater to meet applicablegroundwater discharge standardsInjection of the treated water into the aquifer upgradient of thelandfill to stimulate in situ biodegradation of degradablecomponents of the contaminationMonitoring and evaluating the effectiveness of the groundwaterextraction, treatment, and reinjection system in achieving progresstoward cleanup standardsWater Supply Supply a point-of-entry treatment system for any private wellexhibiting contaminants originating at the Refuse Hideawaylandfill with concentrations exceeding NR 140 EnforcementStandards (federal MCLs) or that are believed by the WDNR andEPA to be imminently at risk for exceeding those standardsConstruct a community water supply well if the number of homesrequiring replacement water supplies makes [construction of acommunity well] cost effectiveTABLE 10.6 Acronyms Used to Identify Air, Water, Soil, and Food StandardsAcronym DefinitionRBCL A risk-based concentration level that meets an acceptable risk standard:HQ < 1 or IELCR in the range 105 to 103MCL A maximum contaminant level subject to enforcementMCLG A maximum contaminant level goal that serves as a nonenforceable targetfor remediationMOE A margin of exposure (NOAEL ADD) related to HQ (Eq. (10.10))Soil and Environmental Chemistry432Chapter 10 Risk Assessment 433ExampleCompute the RBCL for the water ingestion of toluene by adults, assumingthe acceptable risk is HQ 1. The reference dose RfD for toluene is0:2 mg kg1 d1. We will assume that the exposed population consists ofadults who will drink contaminated water for 30 years.ADD CW IR EF EDBM AT CW IRBMADDRB HQ RfDoral RfDoralAdult RBCL 29 ppbfor water ingestion. Expression (10.12) quantifies LADD using the targetIELCR.Intake Equation : LADD CW IR EF EDBM AT 10:11Risk Quantification : LADD Target IELCRSF10:12The RBCL for a carcinogen in water is found by equating the two precedingexpressions and solving for the concentration in water CW:CW,RBCL Target IELCRSF BM ATIR EF ED 10:13ExampleCompute the RBCL for the water ingestion of benzene by adults, assuming a veryconservative target IELCR of 105. The cancer slope factor SF for benzene is0:029 mg1 kg d. We will assume that the exposed population consists ofadults who will drink contaminated water for 30 years.RBCL 1050:029 mg1benzene kg d0@1A BM ATIR EF ED0@1AAdult RBCL 105 mgbenzene0:029 kg d0@1A 70 kg 70 y 365 d y1 2 Lwater d1 350 d y1 30 y Adult RBCL 17:96090@1A mgbenzeneL2435 0:029 mgbenzeneL2435Soil and Environmental Chemistry434assessment. Exposure pathway assessment establishes links between the con-tamination source and potential exposed populations, evaluating all potentialtransport pathways, exposure points, and exposure routes that could connecta potential exposed population to a contamination source.Risk characterization quantifies risk in exposed populations where anexposure pathway is completed. Risk characterization employs intake equa-tions for each potential exposure route to estimate the potential dose. Riskcharacterization allows the setting of risk-based contaminant levels for eachcontaminant and exposure route. The enforcement standardsmaximum con-taminant levels MCLsadopted by federal and state environmental agenciesderive from risk-based contaminant levels RBCLs. The environmental chem-ist is a key participant in the risk assessment process, whether throughCW ,RBCL RfDoral BMIR RBCL 0:2 mgtoluene kg1 d1 BMIR0@1AAdult RBCL 0:2 mgtoluenekg d0@1A 70 kg2 Lwater d10@1AAdult RBCL 1420@1Amgtoluene L1Adult RBCL 7 ppm10.8. SUMMARYChemical contaminant risk assessment in the United States follows a para-digm (see Figure 10.1) that begins with hazard identification and dose-response assessment and reaches its completion with exposure assessmentand risk characterization. Risk assessment results provide a scientific basisfor risk management and mitigation. Dose-response assessment follows sepa-rate tracks for carcinogens and noncarcinogens, the principal difference beingthe absence of a threshold dose and response based on cumulative ratherthan steady-state dose when predicting carcinogenesis. Distinctions betweencarcinogens and noncarcinogens also determine the method for low-doseextrapolation and, ultimately, risk characterization.A key element in all risk assessment studies of contaminants in theenvironment is exposure assessment, more specifically exposure pathwayresearch studies of fate and transport or collecting field data during environ-mental monitoring studies.APPENDIX 10A. CHEMICAL- AND SITE-SPECIFIC FACTORSTHAT MAY AFFECT CONTAMINANT TRANSPORT BY SURFACEWATERTable 10A.1 lists the transport mechanisms and the chemical-specific andsite-specific factors affecting contaminant fate and transport by surface water.It is excerpted from Appendix E of the Public Health Assessment GuidanceManual (EPA, 1992).TABLE 10A.1 Chemical- and Site-Specific Factors Affecting ContaminantTransport: Surface WaterTransport Mechanism Factors Affecting TransportChemical-SpecificConsiderationsSite-Specific ConsiderationsSurface WaterOverland flow (via naturaldrainage or man-madechannels)l Watersolubilityl KOCl Precipitation (amount, frequency,duration)l Infiltration ratel Topography (especially gradientsand sink holes)l Vegetative cover and land usel Soil/sediment type and chemistryl Use as water supply intake areasl Location, width, and depth ofchannel; velocity; dilution factors;direction of flowl Floodplainsl Point and nonpoint sourcedischarge areasVolatilization l Watersolubilityl Vapor pressurel Henrys Lawconstantl Climatic conditionsl Surface areal Contaminant concentrationChapter 10 Risk Assessment 435Hydrologic connectionbetween surface waterand groundwaterl Henrys Lawconstantl Groundwater/surface waterrecharge and dischargel Stream bed permeabilityl Soil type and chemistryl Geology (especially Karstconditions)Adsorption to soil particlesand particle sedimentationl Watersolubilityl Kl Particle size and densityl Geochemistry of soils/sedimentsOWContinuedTABLE 10A.1 Chemical- and Site-Specific Factors Affecting ContaminantTransport: Surface WaterContdTransport Mechanism Factors Affecting TransportChemical-SpecificConsiderationsSite-Specific Considerationsl KOCl Densityl Organic carbon content of soils/sedimentBiologic uptake l KOWl BCFl Chemical concentrationl Presence of fish, plants, and otheranimalsSource: Reproduced with permission from United States Department of Health and HumanServices, 1992. Public Health Assessment Guidance Manual. Agency for Toxic Substances andDisease Registry. Atlanta, GA.Soil and Environmental Chemistry436APPENDIX 10B. CHEMICAL- AND SITE-SPECIFIC FACTORSTHAT MAY AFFECT CONTAMINANT TRANSPORT BYGROUNDWATERTable 10B.1 lists the transport mechanisms and the chemical-specific and site-specific factors affecting contaminant fate and transport by groundwater.It is excerpted from Appendix E of the Public Health Assessment GuidanceManual (EPA, 1992).TABLE 10B.1 Chemical- and Site-Specific Factors Affecting ContaminantTransport: GroundwaterTransport Mechanism Factors Affecting TransportChemical-SpecificConsiderationsSite-Specific ConsiderationsGroundwaterMovement within and acrossaquifers or discharge tosurface waterl Density (moreor less densethan water)l Water solubilityl KOCl Site hydrogeologyl Precipitationl Infiltration ratel Porosityl Hydraulic conductivityl Groundwater flow directionl Depth to aquiferl Groundwater/surface waterrecharge and discharge zonesContinuedChapter 10 Risk Assessment 437TABLE 10B.1 Chemical- and Site-Specific Factors Affecting ContaminantTransport: GroundwaterContdTransport Mechanism Factors Affecting TransportChemical-SpecificConsiderationsSite-Specific ConsiderationsAPPENDIX 10C. CHEMICAL- AND SITE-SPECIFIC FACTORSTHAT MAY AFFECT CONTAMINANT TRANSPORT INVOLVINGSOILS OR SEDIMENTSTable 10C.1 lists the transport mechanisms and the chemical-specific and site-specific factors affecting contaminant fate and transport from contaminatedsoils and sediments, including both particulate transport by erosion and mobi-lization of contaminants from soil by water. It is excerpted from Appendix Eof the Public Health Assessment Guidance Manual (EPA, 1992).l Presence of other compoundsl Soil typel Geochemistry of site soils andaquifersl Presence and condition ofwells (well location, depth,and use; casing material andconstruction; pumping rate)l Conduits, sewersVolatilization (to soil gas,ambient air, and indoor air)l Water solubilityl Vapor pressurel Henrys Lawconstantl Diffusivityl Depth to water tablel Soil type and coverl Climatologic conditionsl Contaminant concentrationsl Properties of buildingsl Porosity and permeability ofsoils and shallow geologicmaterialsAdsorption to soil particlesor precipitation out ofsolutionl Water solubilityl KOWl KOCl Presence of natural carboncompoundsl Soil type, temperature, andchemistryl Presence of other compoundsBiologic uptake l KOW l Groundwater use for irrigationand livestock wateringSource: Reproduced with permission from United States Department of Health and HumanServices, 1992. Public Health Assessment Guidance Manual. Agency for Toxic Substances andDisease Registry. Atlanta, GA.Soil and Environmental Chemistry438TABLE 10C.1 Chemical- and Site-Specific Factors Affecting ContaminantTransport: Soil and SedimentsTransportMechanismFactors Affecting TransportChemical-SpecificConsiderationsSite-Specific ConsiderationsSoil (Surface and Subsurface) and SedimentSoil Erosion l Particle densityl Runoff velocityl Plant coverl Soil erodibilityl Rainfall intensityAPPENDIX 10D. CHEMICAL- AND SITE-SPECIFIC FACTORSTHAT MAY AFFECT CONTAMINANT TRANSPORT INVOLVINGAIR AND BIOTATable 10D.1 lists the transport mechanisms and the chemical-specific andsite-specific factors affecting contaminant fate and transport by the atmo-sphere and biota. It is excerpted from Appendix E of the Public HealthAssessment Guidance Manual (EPA, 1992).APPENDIX 10E. WATER INGESTION EQUATIONThe water ingestion equation (10E.1) is a function of six variables listedin Table 10E.1. One parameter is the contaminant water concentration CWl Slope and slope lengthSurface WaterRunoffl Water solubilityl KOCl Plant coverl Infiltration rate and hydraulicconductivity of soill Precipitation ratel Slope and slope lengthLeaching l Water solubilityl KOCl Soil profile characteristics(e.g., impermeable horizons)l Soil porosity and permeabilityl Soil chemistry (especially acid/base)l Cation exchange capacityl Organic carbon contentVolatilization l Vapor pressurel Henrys Law constantl Physical properties of soill Chemical properties of soill Climatologic conditionsBiologic uptake l BCFl Bioavailabilityl Soil propertiesl Contaminant concentrationSource: Reproduced with permission from United States Department of Health and HumanServices, 1992. Public Health Assessment Guidance Manual. Agency for Toxic Substances andDisease Registry. Atlanta, GA.TABLE 10D.1 Chemical- and Site-Specific Factors Affecting ContaminantTransport: Air and BiotaTransportMechanismFactors Affecting TransportChemical-SpecificConsiderationsSite-Specific ConsiderationsAirAerosolization l Water solubility l Chemicals stored under pressureAtmosphericdepositionl Particle size l Rainfall intensity and frequencyl Wind speed and directionVolatilization l Henrys Lawconstantl Presence of open containers, exposedsurfaces, or leaking equipmentWind l NA l Speed, direction, atmospheric stabilityBiotaBioaccumulation l KOWl Biological half-lifel Presence of plants and animalsl Consumption rateMigration NA l Commercial activities (farming,aquaculture, livestock, dairies)l Sport activities (hunting, fishing)l Migratory speciesVapor sorption NA l Soil typel Plant speciesRoot uptake NA l Contaminant depthl Soil moisturel Plant speciesSource: Reproduced with permission from United States Department of Health and HumanServices, 1992. Public Health Assessment Guidance Manual. Agency for Toxic Substances andDisease Registry. Atlanta, GA.TABLE 10E.1 Water Ingestion Equation ParametersParameter and Units SymbolWater Concentration mg L1 CWIngestion Rate L d1 IRExposure Duration y EDExposure Frequency d y1 EFBody Mass kg BMAveraging Time d ATChapter 10 Risk Assessment 43944ADDtoluene CW IR EF ED BM@ A 1EF ED@ A CW IRBM@ AADDtoluene0:5mgtolueneL0@1A 2 Ld0@1A70 kg 0BBBBBB@1CCCCCCA10 1Life time Average Daily Dosebenzene CW IR EF ED BM@ A 1ATcarcinogen@ ALADDbenzene 0:05mg L1 2 L d1 350 d y1 30 y 70 kg 0@1A 170 y 365 d y1 mean life time0B@1CALADDbenzene 1:095 103 mg1:79 106 kg d0@1ALADDbenzene 5:9 104 mg kg1 d1ExampleAn adult (70 kg) drinks water (2 L d1) containing 0.5 mg L1 toluene. Estimatethe toluene dose. Toluene is classified as a noncarcinogen.Average Daily Dosetoluene CW IR EF ED BM0@1A 1ATnoncarcinogen0@1A0 1 0 1 0 10 1 0 1at the exposure point. The averaging time AT depends on the nature of thecontaminantcarcinogen or noncarcinogen. The remaining parameters dependon the physical and behavioral characteristics of the potential exposed population.Water Ingestion CW IR ED EF BM 1AT 10E:1The following two examples illustrate estimates of the body burden dose for acarcinogenthe lifetime average daily dose LADDand a noncarcinogenthe average daily dose ADD. Notice that the product of exposure durationand exposure frequency EF ED equals the averaging time AT for non-carcinogens.ExampleAn adult (70 kg) drinks water (2 L d1) containing 0.05 mg L1 benzene. Esti-mate the benzene dose. Benzene is a known carcinogen.Soil and Environmental Chemistry0ADDtoluene 1:0 mg d70 kg@ AADDtoluene 1:4 102 mg kg1 d1APPENDIX 10F. SOIL INGESTION EQUATIONThe soil ingestion equation (10F.1) is a function of six variables and a conversionfactor listed in Table 10F.1. One parameter is the contaminant soil concentrationCS at the exposure point. The averaging timeAT, as always, depends on the natureof the contaminantcarcinogen or noncarcinogen. The remaining parametersdepend on the physical and behavioral characteristics of the potential exposedpopulation.Soil Ingestion CS CF IR ED EF BM 1AT 10F:1Chapter 10 Risk Assessment 441ADDarsenic 2:45 104 mgarsenic kg1 d1TABLE 10F.1 Soil Ingestion Equation ParametersParameter and Units SymbolSoil Concentration mg kg1 CSConversion Factor 106 kg mg1 CFIngestion Rate mg d1 IRExposure Duration y EDExposure Frequency d y1 EFThe following example estimates the body burden dose for a noncarcinogen.ExampleA child (15 kg) ingests soil (200 mg d1) containing 18.4 mg kg1 arsenic(Arain, Kazi et al., 2009). Estimate the arsenic dose using the averaging time fora noncarcinogen.Average Daily Dosearsenic CS CF IR EF ED BM0@1A 1ATnoncarcinogen0@1AADDarsenic CS CF IR EF ED BM0@1A 1EF ED0@1AADDarsenic18:4mgarsenickgsoil0@1A 106 kgmg0@1A0@1A 200 mgsoild0@1A15kg ADDarsenic 3:68 103 mgarsenic15 kg d0@1ABody Mass kg BMAveraging Time d ATAPPENDIX 10G. FOOD INGESTION EQUATIONThe food ingestion equation is similar to the soil ingestion equation (10F.1),substituting food concentration CF for soil concentration. The followingexample estimates the body burden dose for a noncarcinogen in food.ExampleAn adult (60 kg) living in Bengal ingests spinach (100 mg d1) containing0.9 mg kg1 arsenic (Arain, Kazi et al., 2009). Estimate the arsenic dose.Average Daily Dosearsenic CF CF IR EF ED BM0@1A 1ATnoncarcinogen0@1AADD foodSoil and Environmental Chemistry442ADDarsenic 9:0 105 mgarsenic60 kg d0@1AADDarsenic 1:5 106 mgarsenic kg1 d1APPENDIX 10H. AIR INHALATION EQUATIONThe air ingestion equation (10H.1) is a function of six variables listed inTable 10H.1. One parameter is the contaminant air concentration CA at theexposure point. The averaging time AT, as always, depends on the nature ofTABLE 10H.1 Air Inhalation Equation ParametersParameter and Units SymbolAir Concentration mg m3 CAInhalation Rate m3 d1 IRExposure Duration y EDExposure Frequency d y1 EFBody Mass kg BMAveraging Time d ATarsenic 60kg ADDarsenic CF CF IR EF ED BM0@1A 1EF ED0@1A0:90mgarsenickg0@1A 106 kgmg0@1A0@1A 100 mgfoodd0@1AChapter 10 Risk Assessment 443Simultaneous exposure at subthreshold levels to several toxicants can result inadverse health effects. The Hazard Index HI (10I.1) estimates the cumulativerisk from exposure to multiple noncarcinogens. Acceptable risk is defined asHI < 1.HI XiHQi 10I:1The following example lists three noncarcinogenic elements, each with a dif-ferent average daily dose ADD based on typical groundwater concentrationsindoor air (15 m3 d1) containing radon-222. Dane County (EPA, 1993) ismapped as Zone 1 (predicted average indoor level > 0.148 Bq L1 indoor air).Estimate the radon-222 dose.We can estimate the absorbed dose using the conventional air intakeequation, assuming that the body absorbs all radioactive decays from inhaledradon-222.LifetimeAverageDailyDoseradon222 CAIR EF ED BM0@1A 1ATcarcinogen0@1ALADDradon222 0:0148BqL1 103Lm3 15m3d1 350d y1 30y 70kg 0@1A 1ATcarcinogen0@1ALADDradon222 2:331106Bq70 kg 2:45104d 0@1ALADDradon2221:30 Bqkg1d1APPENDIX 10I. HAZARD INDEXCUMULATIVENONCARCINOGENIC RISKthe contaminantcarcinogen or noncarcinogen. The remaining parametersdepend on the physical and behavioral characteristics of the potential exposedpopulation.Air Inhalation CA IR ED EF BM 1AT 10H:1The following example illustrates estimates of the body burden dose forradon-222, a carcinogenthe lifetime average daily dose.ExampleAn adult (70 kg) living in Dane County, Wisconsin (Radon Zone 1), inhalesin the United States (Newcomb and Rimstidt, 2002). The exposure route isdrinking water consumption. The following table lists the hazard quotient HQfor each substance and the cumulative HI.the cumulative target risk CTR both appear in the table. The excess cancerrisk resulting from vinyl chloride exposure is predicted to be 180 casesper million, while 13 excess cases result from benzene exposure in drinkingwater contaminated by Refuse Hideaway landfill, resulting in a CTR of abou193 excess cancer cases in the exposed population.Toxicant ADD mgtoxicantkgbodymass dh iRfD mgtoxicantkgbodymass dh iHQCd 0.0003 0.001 0.30Toxicant LADD mgtoxicantkgbodymass dh iSFkgbodymass dmgtoxicanth iIELCRSoil and Environmental Chemistry444Benzene 2:3 104 0.029 1:3 105Vinyl chloride 2:5 104 0.72 1:8 104CTR 1:9 104tSimultaneous exposure at subthreshold levels to several toxicants can resultin adverse health effects. The cumulative target risk CTR (10J.1) estimatesthe IELCR resulting from exposure to two or more carcinogens. Acceptablerisk is variable, depending on the acceptable number of excess lifetime cancercases in the exposed population: 104 < CTR < 106.CTR XiIELCRi 10J:1The following example lists two known carcinogens, each with a differentlifetime average daily dose LADD based on exposure to untreated wellwater samples taken near the Refuse Hideaway landfill in 1987 (benzene 24 mg L1; vinyl chloride 20 mg L1). The exposure duration is calculatedbased on continuous exposure from 1987 to 2010. The cancer slope factor SFapplies to all forms of cancer. The IELCR for each substance andAPPENDIX 10J. CUMULATIVE TARGET RISKCUMULATIVECARCINOGENIC RISKZn 0.0076 0.3 0.03As 0.0004 0.0003 1.33HI 1.665SolutionThe NOAEL is the highest experimental measurement on the dose-responsecurve that is not statistically different from zero (the error bars for theresponse to this dose level overlap with no response). The LOAEL is thelowest experimental measurement on the dose-response curve that is statisti-cally different from zero (the error bars for the response to this dose level donot span no response).3. A 15 kg child has been drinking water (0.6 L d1 containing 0.05 mg L1 ben-zene, a known carcinogen), for 6 years. Estimate the Lifetime Average Daily0.80.70.60.50.40.30.20.10.00.01 0.1DoseResponse12. The single-hit dose-response curve plotted above represents the probabilityof a toxic response from the ingestion of a contaminant. NOTE: The error bars(plotted above) represent uncertainty in the observation of the response. Takinginto account the uncertainty represented on the plot, determine a reasonableno observable adverse effect level (NOAEL) for this dose-response curve.Problems1. The following single-hit model represents the probability of a toxic responsefrom the ingestion of a contaminant. The probability of a toxic responseP D; r is plotted below the model using a logarithmic scale for dose D andprobability r of damage to a single cell.P D; r 1 er DAssume that the toxic response represented by the dose-response curveplotted below is the probability of a fatality caused by exposure to thecontaminant. Draw on the graph (below) the lethal dose that represents a50% fatality probability in the population: LD50.1.00.9Chapter 10 Risk Assessment 44Dose LADD for this case.Lifetime Average Daily Dose CW IR EF EDBM AT44Adult ADDtoluene 4:7 105 mg kg1 d15. What is the average daily dose ADD of methylmercury CH3Hg in a 70 kgadult who eats 500 g of tuna daily containing 0.2 ppm CH3Hg? The half-lifeof CH3Hg in humans is 70 days.Adult ADDmethylHg 0:2mgmethylHgkgfish 103 kgg 500 gfishd 70 kg 1:4 103mg kg1 d16. Suppose a 70 kg adult consumes 100 micrograms a day of a substance xwhose steady-state level in the body is later established to be 0.1 ppm. Whatis the half-life for elimination of this substance from the body?SolutionBM Cbody ln2 70 kg 0:1 mg kg1 ln2LADDbenzene 1:71 104 mg kg1 d14. A 70 kg adult construction worker, age 50 years, ingests 330 mg d1 of soilcontaining 10 mg kg1 toluene (toluene has not been identified as a carcino-gen). Work-related exposure frequency is 200 days per year. Assume that atypical construction worker has 30 years of work exposure. Average DailyDose ADD of toluene in this case.Average Daily Dose CS CF IR EF EDBM ATSolutionToluene is not a carcinogen, so the Averaging Time AT is the duration ofexposure, or 30 years.Adult ADDtoluene 10mgtoluenekgsoil0@1A 106 kgmg0@1A0@1A 330 mgsoild0@1A 200 dy0@1A 30 y 70 kg 30 y 200 dy0@1ALifetime Average Daily Dose CW IR EF EDBM ATLADDbenzene 0:05 mg L1 0:6 L d1 365 d y1 6 y 15 kg 70 y 365 d y1 LADDbenzene 65:7 mg3:83 105 kg d0@1ASolutionBenzene is a carcinogen, so the averaging time AT is a lifetime, or 70 years,while the exposure duration ED is the length of time this adult consumed con-taminated water, or 6 years.Soil and Environmental Chemistry6t1=2 IR CF 100 mg d1 103 mg mg1 50 dOnce consumption of food containing this substance stops, how long does ittake for the level of this substance to reach 0.025 mg kg1?SolutionA steady-state body concentration of 0.025 mg kg1 is one-fourth of the orig-inal steady state, equivalent to 2 half-lives or 100 days.7. 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382383Indexes, f indicate figures and t indicate tables.Activity index, 285286Activity product validation, simulations, 192Adhesion, 371372Adsorbents, 371colloids as, 372374, 387388, 399Alcohol fermentation, 354355463Index464Alkalinitycarbonate, 281definition, 282283exchangeable calcium and, 298extreme, pH>8.4, 293296methyl orange end-point, 282283reference point defining, 257258, 262silicate, 281282Alumina, 391Aluminosilicate minerals, 89Aluminosilicate tetrahedral sheets, 91, 92f,93fAmino acids, dissolved in soil pore water,224Ammonia, 118Ammonia-based fertilizers, 276277, 280Amphiphilic molecules, 228229, 253254, 379Anaerobic bacteriafacultative and obligate, 353354fermentative, 354355Anaerobiosis, 322, 349Anion exchange, 277Anion surface complexes, 397398Anoxia, 322, 360Apatite, 166Apatite solubilityeffect of the citrate on, 201202as a function of pH, 200Aqueous carbon dioxide reference level,262263, 280Aqueous electrolyte solutions, 153154Aqueous silica conjugate acid-base pairs,281282Aqueous solubilitygases, 162, 174175ionic compounds, 160162two ionic solids, 166167,175176Aquicludes, 4748Aquifer formations, 4748, 47fAquiferssulfide in, 164water flow in, 4954Aquifuges, 4748Aquitards, 4748Aridic soil moisture regime, 292Arithmetic mean, 1920calculating, 8Arithmetic standard deviation, 1920Arsenic, 2, 1416Astatine, 12, 31Atmophilic elements, 10Biological activity zone, 321Biological residue, 212, 213, 217Atmospheric gasescarbon dioxideabove ground, 269270below ground, 271most abundant, 270tnitrogen oxides, 273275nitrogen-to-sulfur emissions ratio, 274, 276fpresent day composition, 345primordial gas cloud, 2, 8, 345saturation effect, 305306sulfur oxides, 271273sulfur trioxide conversion to sulfuric acid,305306Atom mole fraction, 4Atomic number, 6Atomic weight, 6Atterberg Limits, 285Auto emissions, 273274Auto-ignition temperature, 216217Average, 8, 20BBacteriaanaerobic respiration of, 174175methanogenic, 360chemolithotrophic, 347, 351353, 353tClostridium, 164165denitrifying, 273facultative and obligate, 353354fermentative, 354355iron-reducing, 347fmetal-reducing, 356358nitrate reducing, 273, 277, 355356, 356f,357fsulfate-reducing, 164, 358360, 359tBacterial siderophores, 225227, 226tBall-and-stick models, 90, 91fBase, defined, 258, 259Base strength, defining, 260261BasicitySee acididy and basicityBernoulli equation, 4950Beta decay reaction, 29Bicarbonate reference levels, 306308Big Bang, 4Bilayers, 253254Bioaccumulation, 386bBioamphiphiles, 379Biogenic emissions, 274Biologically fixed carbon, 220221Index 465Biomagnification, 386bBiomass, 1416, 213, 217Biomass harvesting, 276277, 280Biosurfactantsdissolved in soil pore water, 228229surface microlayers, 250252Biota, chemical- and site-specific factorsaffecting contaminant transport, 438Biotite, 91, 9495Bioturbation, 287Bismuth, 31Body burden estimation, 415416, 427Borate minerals, 269Boron, 2, 1416Bottled water, contaminants in, 2Braggs Law, 109Brnsted-Lowery model of acid-basereaction, 259Buffer index, 303304Bulk density, 4546, 46bBulk silicate Earth, 6fCCadmium, 164165Calcite solubility, 169170Calcite-apatite-pyromorphite simultaneoussolubility, 199200Calcium, 166Calvin cycle, 210Capillary forces, vadose zone, 5860,7576Capillary fringe zone, 6061Carbon cyclechemical stability in the, 213global, 209210See also soil organic carbon cycleCarbon dioxideabove ground, 269270below ground, 271Carbon dioxide fixation, 346Carbon dioxide partial pressure,causes of, 271Carbon fixation, 210212, 217, 345346Carbon mineralization, 212213Carbon turnover models, 217221Carbonate alkalinity, 281Carbonate reference levels, 306308Carbonate rocks, 267268Carbon-based compounds, tetrahedral bondgeometry, 90Carboxylates, 225227Carcinogenesis, 416Cations, 90Central Limit Theorem, 35Central tendency, 8, 16, 3740Chalcophilic elements, 10f, 11Charge balance validation in simulations, 189,193. See also Water chemistrysimulations, using ChemEQLCharge balancingcarbonate alkalinity, 281methyl orange end-point, 282283mineral acidity, 283plant tissue and the rhizosphere, 280silicate alkalinity, 281282water alkalinity, 280Chemical groups and periods, 4Chemical hydrology, focus of, 41Chemical pollution, 410411Chemical reactions, thermodynamic functionsfor, 151152See also Gibbs free energyChemical sedimentary rocks, 265Chemical weatheringacid-base implicationscarbonate rocks, 267268evaporite rocks, 269silicate rocks, 265267soil acidification, 276sulfide minerals, 268summary overview, 269global impact, 265Jackson clay mineral weathering sequence,8688, 266Chemolithotrophic bacteria, 347, 351353, 353tChlorfenvinphos, 376377, 377f, 378fChlorite layer structure, 9697, 96fCinnabar solubility in an open systemcontaining the dihydrogen sulfide,Carcinogenic exposureexposure metric, 413414low-dose extrapolation of responsefunctions, 416419quantifying risk, 428430regulating, 409410risk assessment, historically, 411412Catabolism, 212, 347349Catecholamide, 225227, 247250Cation exchange capacitymeasuring, 120, 120fsaturation process, 119Cation exchange isotherm, measuring,120122, 120f, 122t, 123f, 123t196199Index466Clastic sedimentary rocks, 265Clayformation of, 85plasticity, 284286Clay colloid chemistry, impact of Na ions,287, 288289Clay colloids, 103sodium-ion accumulation on the clayexchange complex, ESP, 289292Clay mineralogy, introduction, 85Clay mineralsdefined, 85formation of, 85Jackson weathering sequence, 8688, 266swelling predictors, 292See also kaolinite; smectite; vermiculiteClay swelling, 98See also swelling clay mineralsClay-size mineral particlesadsorption by, 373374granular-size particles vs., 284particle sedimentation rates in water, 374,400401Closed-shell compounds, 214Close-packed ionic solids, 90Clostridium bacteria, 164165Clostridium thernoacetium, 164165CNO cycle, 3233Coal combustion emissions, 271, 273274Cobalt, 11Colloids, 399as adsorbents, 372374, 387388, 399clay minerals, 103humic, 245246hydrophobic and hydrophilic, 252256, 379Color Additives Amendment, 409410Compoundsbioorganic, dissolved in soil pore water, 224carbon-based, 90chemical reactions of, 152closed-shell, 214constituent elements of, 152ionic, aqueous solubility of, 160162Compressive force, 59Conditional selectivity coefficients, 142143Conductivityelectrical, 289t, 292hydraulic, 4849, 54, 62, 7984, 287, 288289Congruent dissolution reactions, 269Conjugate acid-base pairs, 259260aqueous carbon dioxide reference level,262, 262taqueous silica solutions, 281282bicarbonate and carbonate reference levels,306308water reference level, 261262, 261tContaminant exposure. See exposure routepathway; risk assessmentContaminant intake, equations for estimating,425428air inhalation equation, 442443averaging time, 425427exposure factors, 427428food ingestion equation, 442soil ingestion equation, 441Coordinate-covalent bonds, 372Coordination polyhedra, 90Core-collapse, 28Cosmic ray spallation, 30Cosmological imprint, 4C-type adsorption isotherm, 376377, 377f,378f, 379, 383DDarcy, Henry, 4849Darcys Law, 4849, 71Database equilibrium constants, 172Database validation in simulations, 192193See also water chemistry simulations, usingChemEQLDatum, 4849Debye, Peter, 153154Debye-Huckel limiting law, 154155Decomposable plant material (DPM),220Degree of saturation, 47Denitrification, 273, 277Denitrification reaction, 277Detergents, 253254Dialysis cell, 375Diatomite rock mineralogy, 265Differentiation, 8Dioctrahedral octahedral sheet, 93fDispersive soils, 278Disproportionation reaction, 274Dissociation of water, 280Dissolved organic carbon (DOC)amino acids, 224bioorganic compounds characteristics,223229biosurfactants, 228229defined, 221222extracellular enzymes, 224organic acids, 223224siderophores, 224228See also soil organic carbonmenitsulElectrElectrElectrIndex 467Electrical conductivity, 289t, 292Electrochemical cells, reduction half reactions,326327Electrolyte solutions, 153154Electron transport chainsaerobic, 350353, 351t, 352tDissolved organic nitrogen (DON), 224Distribution coefficient, 383Dose-response distributions, 412Dose-response risk assessmentdose-response distributions, 412low-dose extrapolationof carcinogenic response functions,416419of noncarcinogenic response functions,414415one-hit model, no-threshold,413414reference dose RfD, 416steady-state body burden estimation,415416two-hit model, Knudsens, 418bDPMSee decomposable plant material (DPM)EEarthbasic silicate, 1011a brief history of the, 23density, 910metallic core, 11percent as water, 42porosity of, 4546segregation of layers, 1011, 22Earths crustacid-base chemistry, impact of weatheringon, 263269composition of, 3, 305tcosmological imprint, 4dissolution by reaction, 294, 295felemental abundance in, 34, 345,346tlayers, composition and density, 1011,10f, 12oxide mole-per-mass composition, 265tplate tectonics, 12primary elements of, 89Earths silicate crustchemical weathering, 8688, 266, 269,293294layers, composition and density, 1011facultative and obligate anaerobes, 353354fermentative anaerobic bacteria, 354355Elements, enrichment and depletionduring planetary formation, 8, 14, 15fduring rock cycle and soil development,14, 15fduring segregation, 14, 15fstatistical analysis to determine variabilitycentral tendency and variation of a log-normal distribution, estimate, 3740concentration frequency distributions,1618concentrations and concentration range,estimating using the log-normaldistribution, 1821Elliott Soil Standard Humic Acid (1S102H),238, 252Endocellular enzymes, 224Electrostatic, 372Elementsavailability for living organisms, 3existence of, 12existence on Earth, 12formal oxidation numbersassigning, 323t, 362363calculating for minerals, 104105mean estimation for carbon in humicfractions, 231overview, 322323redox principles, 322323, 323t,362363organization in the Periodic Table, 46origin and abundance ofbulk silicate Earth, 6fEarths crust, 34, 15fplanetary accretion, 912the rock cycle, 1213soil formation, 1316soils, 34Solar System, 34summary overview, 2122stable, existence of, 12unstable, existence of, 12Envirotal-reducing bacteria, 356358rate reducing bacteria, 355356, 356ffate-reducing bacteria, 358360, 359tonic shells, 2223ons, mass of, 78on-transfer reactions, 321, 322,328Gibbs free energy, 350introduction, 349360methanogenic anaerobic archae, 358360nmental redox conditions, 331333,332fEquiliErosioEthanEukarEuropIndex468Evaporite rocks, 269Evaporite sedimentary rocks, 265Even-odd effect, 4, 6Exchange complex, 124Exchangeable acidity, 298302gibbsite solubility, 298300ion exchange isotherm for asymmetric(AI3, Ca2) exchange, 310313neutralizing, 301302role of asymmetric (AI3, Ca2) exchange,300301, 308309, 310313Exchangeable calcium, 298Exchangeable sodiumpercentage (ESP), 288292Exchangeable sodium ratio (ESR), 289292Exchanger-bound ions, 121Exothermic fusion as energy source, 8Exposure mitigation, 431434Exposure pathway assessmentchemical- and site-specific factors affectingtransporta mineral, 168169brium table, 156n/erodibility, 287289ol fermentation, 354355yotes, 421422ean Union drinking water standard, 2Environmental reduction potentials,measuring, 333, 363370Environmental Working Group, 2Enzymes, dissolved, 224Equilibrium constantactivity and concentrations, 153154Gibbs energy of reaction and, 152153thermodynamic functions for chemicalreactions, 151152Equilibrium dialysis, 375Equilibrium systems, modelingaqueous solubility of an ionic compound,160162Henrys Law, aqueous solubility of gases,162hydrolysis of a weak diprotic base,163166hydrolysis of a weak monoprotic acid,156160simultaneous equilibriumaqueous solubility of two ionic solids,166167the effect of ion complexes on thesolubility of a mineral, 169170the effect of pH on the solubility ofair and biota, 438by groundwater, 436soils/sediments, 437by surface water, 435overview, 419Exposure routeexposure points, 422423, 423tfate and transport, 423424general model, 420422primary and secondary sources, 424425receptors (human population), 419420Exposure pathway elimination, 425, 426bExtracellular enzymes, 224FFacultative anaerobes, 353354Federal risk assessment paradigm, 411Fermentation, 354Fermentative anaerobic bacteria, 354355Ferric iron respiratory chain of metal-reducingbacteria, 356358Ferromagnetic elements, 1011, 10fField capacity, 61Fire, auto-ignition temperature, 216217Fluoridation, 166Fluorite, 269Food, Drugs and Cosmetic Act, 409410Food Additives Amendment, 409410Food ingestion equation, 442Formal oxidation numbersassigning, 323t, 362363balancing redox reactions, 324mean estimation for carbon in humicfractions, 231overview, 322323redox principles, 322323, 323t,362363Francium, 12, 31Fungal siderophores, 225227, 226tFusion reactions, 2526GGaines-Thomas selectivity coefficient,124125, 124t, 291292Galvanic cell, 326, 326fGapon selectivity coefficient, 124125, 124t,291292Gasesaqueous solubility of, 162, 174175primordial gas cloud, 2, 8, 345Geometric mean, 1920Geometric mean concentration, 1617Geometric standard deviation, 1617, 1920Index 469contaminant transport, 435Darcys Law, 4849flow nets, 5658flow paths, 42, 55bflow rates, 43, 44t, 4849pore water velocity, 4849, 71hydrologic units, 4748hydrostatic heads and hydrostatic gradients,4954intrinsic permeability, 5456residence time and runoff ratios, 41, 4345,45fwater in the porosphere, 4547See also hydrologyGypsum, 118Gypsum dissolutioncongruent, in sedimentary rocks, 269in evaporite sedimentary rocks, 268Gypsum solubility, modeling, 173,193194HHalite, 269Hazard index, 443444Hazard quotient, 430431Health hazards, humanchronic toxicities and health effects, 410tlegislation mitigating toxic exposure,Geotechnical properties of soil, 284Gibbs free energyequilibrium constant and, 152153of ion exchange, 134135, 136tunder nonstandard conditions, 327328Gibbs free energy of reaction, 125126,151152Gibbs phase rule, 179180Gibbsite solubility, modeling, 176178,194196Gibbsite-variscite simultaneoussolubility, 200Global carbon cycle, 209210Goethite, 105, 392, 393tGoethite solubility, 203208Gold, 11Gramineae, 225227Granite, 91, 9495Gravimetric water content, 46Greenockite, 164165Groundwater divide, 5758Groundwater hydrologychemical- and site-specific factors affecting409410Hydraulic head, 49Hydrogen bonds, 372Hydrogen ion activity, ChemEQL treatmentof, 174Hydrogen-1 and carbon-13 nuclear magneticresonance spectroscopy, 244245Hydrologic cycledefined, 42flow rates, 43global flow rates, 44tintroduction, 23Hydrologic units, 4748HydrologySee also exposure pathway assessment;risk assessmentHedenbergite (pyroxene), 104105Helium burning, 3334Hematite, 372fHenrys Law, 162, 174175Huckel, Erich, 153154Humic, 379Humic amphiphiles, 379Humic colloids, 245246Humic substancesadsorption behavior vs. clays, 374chemical analysisacidometric titration, 234235hydrogen-1 and carbon-13 NMR,244245nitrogen-15 NMR, 235238oxygen content and titratable weakacids, 252phosphorus-31 NMR, 239240sulfur K-edge x-ray absorptionspectroscopy, 240243chemical composition, 231245defined, 229elemental composition, 230231, 230t,231textraction and fractionation, 229230summary overview, 247Humic substances chemical moietiescarboxyl moieties, quantifying, 245nitrogen-containing, 239phosphorus-containing, 240sulfur-containing, 244Hydrated smectite layer structure, 99f, 100f,101f, 102fHydraulic conductivity, 4849, 54, 62, 7984clay colloid chemistry, impact of Na ions,287, 288289solute transport modelsIndex470preparing clay saturated with a singleHydrology (Continued)plate theory model, 6570, 7778the retardation coefficient model,6265, 7677water budgets, 43water resources, 4345See also groundwater hydrology;vadose zone hydrologyHydrolysis model of proton sites, 402408Hydrolysis of a weak diprotic base, 163166Hydrolysis of weak monoprotic acids or basescomputer-based modeling, 171172modeling, 156160Hydrophilic colloids, 252256, 379Hydrophobic colloids, 252256, 379Hydrostatic gradients, 4954Hydrostatic heads, 4954Hydrostatic pressure, 49, 5859Hydroxamate, 225227, 247250Hydroxy-interlayered smectite, 9697, 96fHypolentic zone, 277Hyporheic zone, 277IIgneous rocks, 12, 265Illite layer structure, 95, 95fIncremental excess lifetime cancer risk(IELCR), 428430Industrial emissions, 274Intake, 428See also contaminant intakeInternational Humic Substance Society (IHSS),229International System of Units (SI), 60Interstellar medium, 30Intrinsic permeability, 5456Ion activity coefficient expressions, 154156Ion adsorption experiments, pH-dependentexperimental design, 388392interpreting, 394395Ion exchange, 372discovery of, 118119introduction, 117Ion exchange adsorption isotherm, 382383Ion exchange complex, 124Ion exchange experimentscation exchange capacity, measuring, 120,120fcation exchange isotherm, measuring,120122, 120f, 122t, 123f, 123tcation, 119Jackson weathering sequence, 8688, 266Jenny, Hans, 217Jenny soil organic carbon turnover model, 217Jupiter, 910KKaolinite, 372f, 391ion exchange capacity, 118119selectivity coefficients and the exchangeisotherm, 122125, 124tIon exchange isothermfor asymmetric exchange, 127129, 143derivations from a single-value selectivitycoefficient, 138interpreting, 125140ion selectivityeffect on the, 123f, 130f, 131138, 133f,134fphysical basis for, 134138ionic strength, effect on the, 129130, 130fLibby vermiculite, 144150nonlinear least square fitting ofasymmetric exchange, 143symmetric exchange, 143selectivity coefficients and the, 122125, 124tsummary overview, 140141for symmetric exchange, 126127, 143,144150Ion exchange process, 371Ion exchange selectivity coefficients, 122125,124t, 142143Ion exchanger-bound ions, 121Ionic compounds, aqueous solubility, 160162Ionic solids, aqueous solubility, 166167, 175176Ionic strength I, 292activity and, 154Ionic strength validation in simulations, 191, 193Iridium, 11Iron, 11Iron, biological availability of, 247Isohumic coefficient, 218Isotope formation, 8, 2532Isotope mass, 78Isotopesabundance of, 46, 2325, 24fmass number, 78nuclear binding energy, 68transuranium elements, 3032JJackson, M. L, 8687Kaolinite layer structure, 93, 94f, 391Index 471Kerr selectivity coefficient, 124, 124tKindling point, 216217Knudson two-hit model, 418bLLabile carbon, 222Labile carbon pool, 222, 223, 247Lambert hypothesis, 378Langmuir, Irving, 380Langmuir adsorption model, 380382Law of proportionate effect, 33Layer silicates, structure ofBraggs Law and x-ray diffraction, 109chlorites, 9697, 96fcoordination polyhedra, 90diversity in, causes of, 89hydrated vermiculite, 98103hydroxy- interlayered smectite, 9697kaolinite, 93, 94fmica-illite, 9495, 95fphyllosilicate octahedral sheet, 92phyllosilicate tetrahedral sheet, 9192talc, 93, 94ftetrahedral geometry, 90vermiculite, 97103, 100fx-ray diffraction in, 109smectites; swelling clay mineralsLead in soils, 166Lead phosphate, 166Lewis acid, 372Lewis base, 372Libby vermiculite, 140, 144150Ligand, 372Ligand-exchange reaction, 396Linear Langmuir expression, 401Lipid bilayer, 253254Liquidity index, 285Lithophilic elements, 10f, 11Living organisms classification, 347tLizardite, 93Logarithm of sample concentrations,1617Logarithmic-transformed normal distribution,1617Log-normal distributionscentral tendency statistic, 1617, 3740concentration and concentration range,estimating using, 1821example, 1920Low-dose extrapolationof carcinogenic response functions,416419of noncarcinogenic response functions,414415L-type adsorption isotherm, 375, 376f, 381f,383386Lupines, 169170MMagma, 12Manganese, 11Manure, 118Marcasite, 268Mars, 910Mass balance validation in simulations,189190, 193194Mass defect, 78Mass number, 78Maximum contaminant level (MCL), 2Meanarithmetic, 8, 16geometric, 1920Mechanical properties of soilassessing limits, 285clay-size mineral particles relative to, 284erodibility, 287289hydraulic conductivity, 7984, 287, 288289plasticity, 284286sodicity, 288289Mercury, 910Metal-reducing bacteria, 356358Metamorphic rocks, 13, 265Metamorphism, 13Methanogenic anaerobic archae, 358360Methanogenic bacteria, 360Methyl orange end-point, 282283Mica, 95Mica group minerals, 91Mica layer structure, 9495, 95fMica-illite layer structure, 9495Micelles, 253254, 379Microbial biomass, 220221Microbial respirationaerobic, 349anaerobic, 322, 349catabolism and, 347349environmental redox conditions and,360361introduction, 345361See also electron transport chainsMiller Pesticide Amendments, 409410Mine drainage water, acidic, 283Mineral acidity, 283Mineral classes, major, 86tOIndex472347348Nicotinamide adenine dinucleotide phosphate(NADPH), 212, 213, 348, 351Nitrate leaching, 277Nitrate reducing bacteria, 273, 277, 355356,356f, 357fNitrificationdefined, 277soil acidification and, 280Nitrification reaction, 277Nitrogen cycling in natural landscapes,Mineral colloids, 399as adsorbents, 372374, 387388, 399Mineral density, 46Mineral solubility, modeling, 173Mineral weatheringchemical weathering reactions, 8889Jackson weathering sequence, 8688,266Mineralization, 118Mineralsclay-size particlesgranular-size particles vs., 284surface area of surficial material,importance to, 373converting mass fraction to sum-of-oxidescomposition, 305formal oxidation numbers of elements in,calculating, 104105molecular structure models, 90, 91fprimary and secondary, 13, 87Radius Ratio rule for stable coordinationin, 105108surface area of spherical particles, 373tvariable-charge surfaces, 387388Molecular orbital theory, 213Molecular structure models, minerals,90, 91fMontmorillonite, 121, 316320Muscovite, 91, 9495NNeptune, 910Nernst equation, 327331Net primary production, 217, 220221Network solids, 90Neutron capture, 2122, 2830Neutron-capture reactions, 2526Neutrons, 78Nickel, 11Nicotinamide adenine dinucleotide (NADH),276277Nitrogen fixation, 277Obligate anaerobes, 353354Octanol-water partition coefficient KOW,386Octet rule, 2223, 90Office of Pollution Prevention and Toxics(USEPA), 386bOlivine, 104One-hit model, 413414Organic acids, dissolved in soil pore water,223224Organic carbon accumulation zone, 321Organic colloidal fraction, 373Organic matter, natural, 209, 246247.OrganNitrogen oxides, 273275Nitrogen sources, 118Nitrogen-15 nuclear magnetic resonancespectroscopy, 235238Noble gases, 10Noble metals, 10f, 11Noncarcinogenic toxinscumulative target risk, 444447hazard index, 443444low-dose extrapolation of responsefunctions, 414415reference dose RfD, 416risk assessmenthazard quotient, 430431historically, 411412Normal distribution, 20logarithmic-transformed, 1617sample population, 8No-threshold one-hit model, 413414Nuclear binding energy, 68Nuclear fusion, 2628Nuclear magic numbers, 2225Nuclear magnetic resonance spectroscopyhydrogen-1 and carbon-13, 244245nitrogen-15, 235238phosphorus-31, 239240Nuclear reactions, 2526Nuclear shells, 22, 23Nuclear stability, 6Nucleosynthesis, 8cosmic ray spallation, 30defined, 22neutron capture, 2830nuclear fusion, 2628nuclear reactions, 2526transuranium elements, 3032See also humus; soil organic carbonotrophic organisms, 347Index 473Osmium, 11Osmotic clay swelling, 98Osmotic model of interlayer swelling pressure,109111Oxidation agents, 322Oxidation numbers, formalassigning, 323t, 362363balancing redox reactions, 324mean estimation for carbon in humicfractions, 231overview, 322323redox principles, 322323, 323t, 362363Oxidation-reduction electrodes, 333, 333fOxidation-reduction reactions, 321Oxidative metabolism, 209210Oxides, sum of, 265Oxygen anions, 90PPalladium, 11Particle-size classes, 373tparticle sedimentation rates in water, 374,400401Particulate organic carbon (POM), 223Partition coefficient, 383Pascal, 60Pauling, Linus, 105108, 118119Pauling electrostatic valence principle, 394PBT Profiler Center Internet site, 386bPeninsula of stability, 22Periodic Table of the Elements, 12organization of, 4, 6fperiodicity of, 2223Table of Isotopes compared, 22Periplasm, 355Permeability, intrinsic, 5456Petroleum combustion emissions, 271, 273274pH buffer index, 258, 303304pH-dependent ion adsorption experimentsexperimental design, 388392interpreting, 394395pH-dependent surface charge experiment,390391Phosphorus, 1416Phosphorus-31 nuclear magnetic resonancespectroscopy, 239240Photolithotrophs, 347Photosynthetic carbon fixation, 210, 217, 345346Phreatic zone, 4748Phyllosicate tetrahedral sheet, 9192, 92fPhyllosilicate octahedral sheet, 91f, 92, 93fPhyllosilicates, 91, 92fPierre-Banwart EB/N ratio, 280extracellular enzymes, 224organic acids, 223224siderophores, 224228electrical conductivity, 292Pore water chemistryfocus of, 41SAR, predicting changes in, 296297sodicity and, 293Pore water velocity, 4849, 71Porosity, 4546Porosphere, 4547Pourbaix stability diagrams, features, 334tPourbaix stability diagrams, interpretingessential features needed for, 334precipitate-precipitate reductionequilibrium boundary, 341343simple rules for, 343345solute-precipitate equilibrium boundary,339340solute-precipitate reduction equilibriumboundary, 340341solute-solute hydrolysis equilibriumboundary, 338solute-solute reduction equilibriumPiezometers, 53, 56Planetary accretion, 912Planetary formation, 22Plant biomass carbon mineralization, 212Plant rootsrhizosphere, 223weak acids excreted to increase nutrientavailability, 223water alkalinity, 280Plasticity, 284286Plasticity index, 285286Plate tectonics, 23, 12Plate theory model for solute transport, 6570,7778Platinum, 11Platinum ORP electrodes, 333, 333f,365370Poaceae, 225227Pollution, chemical, 410411Polonium, 31Polyhedral models, 91fPOM. See particulate organic carbon (POM)Pore waterbioorganic compounds dissolved inamino acids, 224biosurfactants, 228229characteristics, 223boundary, 336338water stability limits, 334336PrimaPrimoR-procRubiscIndex474Primordial nucleosynthesis, 26Promethium, 12Protactinium, 12Proton balance, 261Proton siteshydrolysis model, 402408valence bond model, 392395Proton surface charge, 390Proton surface charge sites, 391392Proton surface complexes, 395396Proton-proton I cycle, 27, 33Protons, 78Proton-surface charge experiment, 390Pyridine, 273274Pyrite, 268Pyromorphite, 166Pyrophyllite, 93, 9495Pyroxene (hedenbergite), 104105Pyrrole, 273274Pyruvate decarboxylase, 355Pyruvic acid, 355QQuick clays, 287288RRadioactive decay, 25Radium, 2Radius Ratio rule, 105108Radon, 12, 31Random sequential dilutions, 3537Range, upper and lower limits calculations,2021Redox cascadeaerobic electron transport chains, 352fanaerobic electron transport chainsiron-reducing bacteria, 347fnitrate reducing bacteria, 357fRedox chemistry, 321322Redox principlesformal oxidation numbers, 322323, 323t,362363Nernst equation, 327331redry minerals, 13, 87rdial gas cloud, 2, 8, 345Power plant emissions, 273274Precipitate sedimentary rocks, 265Precipitate-precipitate reduction equilibriumboundary, 341343Pressure-volume work, 49uction half reactions RuBPess neutron capture, 2122, 2930, 32o, 346balancing, 324326, 324telectrochemical cells and, 326327, 327tRedox stability diagrams, interpretingenvironmental redox conditions, 331333environmental reduction potentials usingORP, 333, 363370introduction, 331345See also Pourbaix stability diagrams,interpretingReduced nicotinamide adenine dinucleotide(NADH), 348, 350Reducing agents, 322Reduction half reactionsbalancing, 324326, 324telectrochemical cells and, 326327, 327tpotential, Nernst equation in calculating,327331Reference dose RfD, 416Residence time, groundwater, 41, 4345, 45fResistant carbon, 222Resistant plant material (RPM), 220Respiration, 346Retardation coefficient model for solutetransport, 6265, 7677RfD reference dose, 416Rhenium, 11Rhizosphere, 223Rhodium, 11Ribbon test, 284285, 284bRisk assessmentdose-response assessment, 411419exposure pathway assessment, 419425federal risk assessment paradigm, 411intake estimates for specific exposureroutes, 425428introduction, 409411quantifying risk, 428431summary overview, 434Risk characterization, 411, 428431Risk management and mitigation, 411,431434Rock classification, 265Rock composition, 265converting mass fraction to sum-of-oxides,305dominant mineralogy, 3Rock cycle, 23, 1213Rothamsted turnover model, 16, 219220,221f, 238239(ribulose bisphosphate), 346RuRuSIndex 475Salt formation, 258259Saprolite, 91Saturated zonebelowground carbon in, 217biological activity, 248Saturation, 61degree of, 47Saturation effect, 305306Saturn, 910Seawater, 293294, 293t, 294tcation and anon origins, 293294Secondary minerals, 13, 87Sedimentary rocks, 265Sedimentation rates in water, 374, 400401Segmented amphiphile, 246Selenium, 1416Sequential random dilution model,3537SISee International System of Units (SI)Siderophilic elements, 10fSiderophilic metals, 11Siderophores, 170, 226t, 247250dissolved in soil pore water, 224228Silica, 391Silicate alkalinity, 281282Silicate minerals, 89103See also layer silicates, structure ofSilicate rockschemical weathering, 265267classification, 265Silver, 11Smectitescommon, 97teffect of (Na, Ca2) exchange on thecritical coagulation concentration of,313316hydroxy- interlayered, 9697, 96fion exchange capacity, 118119Smectites, hydratedinterlayer swelling pressureexperimental estimates, 111116osmotic model, 109111osmotic vs. crystalline, 283layer structure, 98103, 99f, 100f, 101f,102fnoff ratios, groundwater, 4345, 45fglobal, 44tthenium, 11molecular dynamic simulations, 135fSodicity, 288289, 289tSodicity risk, 293electrical conductivity criterion, 289t, 292pH criterion, 293296Sodification, factors contributing to, 292Sodium adsorption ratio (SARp)ESP relation, 288289, 289tpore water, predicting changes in,296297simulation to predict changes in, 316320Sodium carbonate solutions, calculating pH,308309Soilabsorbtive power, 118chemical- and site-specific factors affectingcontaminant transport, 437contaminated by lead, remediationtechnology, 166cosmological imprint, 4defined, 86, 217elemental abundance in, 34moisture control section, 292particle-size classes, 373ttexture classes, 373tSoil acidification, 276agricultural impact on, 280Soil carbon pools, 220222Soil composition, 3, 1416Soil fertility, 118Soil formation, 1316Soil horizons, 14, 16organic, 217Soil ingestion equation, 441Soil moisturedefined, 45moisture control section, 292recharge and loss, 7172water-holding capacity of a soil profile,7275Soil moisture zones, 6062Soil organic carboncontent, steady-state convergency, 219distribution, 217222mineralization rate constant,219220turnover models, 217221See also dissolved organic carbon(DOC)Soil organic carbon cyclecarbon fixation, 210212carbon mineralization, 212213overview, 209217Index476339340Solute-precipitate reduction equilibriumboundary, 340341Solute-solute hydrolysis equilibrium boundary,338Solute-solute reduction equilibrium boundary,336338S-process neutron capture, 29, 3435Stabilized carbon, 222Standard deviation, geometric, 1617,1920Standard galvanic cell, 326, 326fStandard reduction potentials, 327, 327tStandard state convention, 152Starsenergy output from, 8formation of, 27fusion reactions, 28Steady-state body burden estimation,415416Stimulated nuclear fission, 32Stokes Law, 400401Soil organic carbon cycle (Continued)oxidation of organic compounds bydioxygen, 213217Soil organic carbon pools,220222Soil profile, 14belowground carbon in, 217water-holding capacity, 7275Soil-water zone, 6061Solar Systemformation of, 23, 8, 9statistics, 910Solar System compositiondeterminants of, 4elemental abundance in, 34Solar System segregation, 22Solubility, mineralion complexes effect on, 169170pH effect on, 168169, 176178Solubility determinants, 385Solute transport modelsplate theory modelmultiple sequential partitioning, 6570symbols and units in the derivation of,7778, 78tthe retardation coefficient model, 6265symbols and units in the derivation of,7677, 76tSolute-precipitate equilibrium boundary,Strontium-90, 2Sulfate in natural waters, sources of, 268Sulfate-reducing bacteria (SRB), 164,358360, 359tSulfide minerals, 268Sulfidesin groundwater aquifers, 164production by SRB, 164Sulfur, 1416Sulfur dioxide, 271Sulfur K-edge x-ray absorption spectroscopy,240243Sulfur oxides, 271273, 274Sulfur trioxide, 271Sum of oxides, 265Sunenergy output from, 27formation of, 9rotation of, 2Supernova, 28, 29Superoxide anion radical, 353Superoxide dismutase, 353354Surface charge measurement, pH-dependent,390391Surface chemistry, 399introduction, 371372variable-charge mineral surfaces, 387388Surface complexes, 395399Surface microlayers, 250252Surfactants, 253254See also biosurfactantsSwelling, 97Swelling clay mineralselectrical conductivity as predictor of,289t, 292interlayer swelling pressure, experimentalestimates, 111116osmotic model of interlayer swellingpressure, 109111plasticity, 285smectite and vermiculite layer structure,96f, 97103, 97t, 99f, 100f, 101f, 102fSylvite, 269Synthetic elements, 30TTable of Isotopes, 22, 24f, 25Talc layer structure, 93, 9495, 94fTechnetium, 31Tectosilicates, 91, 92fTensional force, 5960Terrestrial carbon cycleSee soil organic carbon cycleVeVeVolumVolumWWaterbodisIndex 477Texture classes, 373tThermodynamic equilibrium, 125Thermodynamic functions for chemicalreactions, 151152See also Gibbs free energyThermodynamic selectivity coefficientexpressions, 142143Thermonuclear fission cyclescarbon burning, 34the CNO cycle, 3233the triple-alpha process, 3334Thompson, H. S, 118Total apparent acidity, 298Toxicity, 428Transition metal, 372Transuranium elements, 3032Trioctahedral octahedral sheet, 93fTriple-alpha process, 28, 3334Triplet oxygen, 214215Troilite, 268Troilite solubility, effect of pH on, 168169Turnover rate laws, 218219Type II supernova, 28UUbisemiquinone radical, 353United States Environmental ProtectionAgency (USEPA), 2Unsaturated hydraulic conductivity, 7984Uranium, 12Uranium isotopes, 31Uranus, 910VVadose zone, 4748Vadose zone, below ground carbon, 217Vadose zone hydrologycapillary forces, 5860, 7576empirical functions estimating hydrolicproperties, 7984hydraulic conductivity, 62soil moisture zones, 6062water characteristic curve, 62Valence, 4Valence bond model of proton sites, 392395Valence electron configuration, 4Valence shell electron-pair repulsion chemicalbonding model, 90Van der Waals forces, 372Vanselow selectivity coefficient, 124, 124tVenus, 910for drinking, MCL for, 2fluoridating, reasons for, 166particle sedimentation rates in, 374, 400401Water alkalinity, 280Water budgets, 43globally, 44tWater characteristic curve, 62Water chemistryactivity and the equilibrium constant,153156the equilibrium constant,151153summary overview, 187Water chemistry modeling, simple equilibriumsystemsaqueous solubility of an ionic compound,160162in general chemistry, 156170Henrys Law, aqueous solubility of gases,162hydrolysis of a weak diprotic base,163166hydrolysis of a weak monoprotic acid,156160simultaneous equilibriumaqueous solubility of two ionic solids,166167the effect of ion complexes on thesolubility of a mineral,169170the effect of pH on the solubility of amineral, 168169Water chemistry simulations, using ChemEQLapatite solubilityeffect of the citrate on, 201202as a function of pH, 200benefits of, 170calcite-apatite-pyromorphite simultaneouse-energy concept, 385etric water content, 4647ttled, contaminants in, 2sociation of, 280Volcanic activity and rock formation, 12Volcanic eruptions, 271rmiculite, symmetric exchange reactions,144150rmiculite layer structure, 97103hydrated vermiculite, 98103solubility, 199200Water chemistry simulations, using ChemEQL(Continued)cinnabar solubility in an open systemcontaining the dihydrogen sulfide,196199data file format, 187of environmental samplesthe Gibbs Phase rule, 179180logarithmic activity diagrams, 183187reaction quotients and saturationindices, 181183generating new equilibrium expressions,196gibbsite solubility, 194196gibbsite-variscite simultaneous solubility,200goethite solubility, effect ofdesferrioxamine B on, 203208gypsum solubility, 193194Henrys Law, aqueous solubility of gases,174175calcite-apatite-pyromorphite solubility,199200the effect of pH on the solubility of amineral, 176178gibbsite-variscite solubility, 200validating, 170171, 188193Water contaminantsbottled water, 2estimating movement of, 65bWater ingestion equation, 438440Water reference level, 261262Water resourcesglobally, 42, 42thydrologic cycle, 44tresidence time and runoff ratios, 41, 4345,45fWater stability limits, 334336Water table aquifer, 4748Way, J. T, 118White dwarfs, 28Index478hydrogen ion activity, treatment of, 174hydrolysis of weak monoprotic acids orbases, 171172manual and website, 171172mineral solubility, 173predicting water changes in SAR, 316320simultaneous equilibriumaqueous solubility of two ionic solids,175176Wilting point, 6162World Health Organization (WHO), 2XX-ray absorption, 396397X-ray absorption spectroscopy, 240243ZZones of enrichment/depletion, 16preface3-s2.0-B9780124157972000157-mainFront matter3-s2.0-B9780124157972000121-mainCopyright3-s2.0-B9780124157972000133-mainDedication3-s2.0-B9780124157972000145-mainPreface3-s2.0-B9780124157972000017-mainElements: Their Originand AbundanceIntroductionA Brief History of the Solar System and Planet EarthThe Composition of Earth's Crust and SoilsThe Abundance of Elements in the Solar System, Earth's Crust, and SoilsElements and IsotopesNuclear Binding EnergyEnrichment and Depletion during Planetary FormationPlanetary AccretionThe Rock CycleSoil FormationConcentration Frequency Distributions of the ElementsEstimating the Most Probable Concentration and Concentration Range Using the LOGARITHMIC TRANSFORMATIONSummaryFactors Governing Nuclear Stability and Isotope AbundanceThe Table of Isotopes and Nuclear Magic NumbersNuclear Magic NumbersNucleosynthesisNuclear ReactionsNuclear FusionNeutron CaptureCosmic Ray SpallationTransuranium ElementsThermonuclear FUSION CyclesThe CNO CycleThe Triple-Alpha ProcessCarbon BurningNeutron-Emitting Reactions that Sustain the S-ProcessRandom Sequential Dilutions and the Law of Proportionate EffectThe Estimate of Central Tendency and Variation of a Log-Normal Distribution3-s2.0-B9780124157972000029-mainSoil Moisture and HydrologyIntroductionWater Resources and the Hydrologic CycleWater BudgetsResidence Time and Runoff RatiosGroundwater HydrologyWater in the PorosphereHydrologic UnitsDarcy's LawHydrostatic Heads and Hydrostatic GradientsIntrinsic PermeabilityGroundwater Flow NetsVadose Zone HydrologyCapillary ForcesSoil Moisture ZonesThe Water Characteristic Curve and Vadose Zone Hydraulic ConductivityElementary Solute Transport ModelsThe Retardation Coefficient ModelPlate Theory: Multiple Sequential PartitioningSummarySoil Moisture Recharge and LossThe Water-Holding Capacity of a Soil ProfilePredicting Capillary RiseSymbols and Units in the Derivation of the Retardation Coefficient Model of Solute TransportSymbols and Units in the Derivation of the Plate Theory Model of Solute TransportEmpirical Water Characteristic Function and Unsaturated Hydraulic Conductivity3-s2.0-B9780124157972000030-mainClay Mineralogy and Clay ChemistryIntroductionMineral WeatheringMineralogyThe Jackson Weathering SequenceChemical Weathering ReactionsThe Structure of Layer SilicatesCoordination PolyhedraThe Phyllosilicate Tetrahedral SheetThe Phyllosilicate Octahedral SheetKaolinite Layer StructureTalc Layer StructureMica-Illite Layer StructureChlorite and Hydroxy-Interlayered Smectite Layer StructureLayer Structure of the Swelling Clay Minerals: Smectite and VermiculiteThe Swelling of Smectite and Vermiculite Clay MineralsStructure of the Hydrated Clay Mineral InterlayerClay ColloidsFormal Oxidation NumbersOutline placeholderOlivineHedenbergite (Pyroxene)GoethiteThe Geometry of Pauling's Radius Ratio RuleOutline placeholderTrigonalTetrahedronOctahedronBragg's Law and X-Ray Diffraction in Layer SilicatesOsmotic Model of Interlayer Swelling PressureExperimental Estimates of Interlayer Swelling Pressure3-s2.0-B9780124157972000042-mainIon ExchangeIntroductionThe Discovery of Ion ExchangeIon Exchange ExperimentsPreparing Clay Saturated with a Single CationMeasuring Cation Exchange CapacityMeasuring the Cation Exchange IsothermSelectivity Coefficients and the Exchange IsothermInterpreting the Ion Exchange IsothermThe Ion Exchange Isotherm for Symmetric ExchangeThe Ion Exchange Isotherm for Asymmetric ExchangeEffect of Ionic Strength on the Ion Exchange IsothermEffect of Ion Selectivity on the Ion Exchange IsothermPhysical Basis for Ion SelectivityOther Influences on the Ion Exchange IsothermSummaryThermodynamic and Conditional Selectivity CoefficientsNonlinear Least Square Fitting of Exchange IsothermsEquivalent Fraction-Dependent Selectivity Coefficient for (Mg2+, Ca2+) Exchange on the Libby Vermiculite3-s2.0-B9780124157972000054-mainWater ChemistryThe Equilibrium ConstantThermodynamic Functions for Chemical ReactionsGibbs Energy of Reaction and the Equilibrium ConstantActivity and the Equilibrium ConstantConcentrations and ActivityIonic Strength IEmpirical Ion Activity Coefficient ExpressionsModeling Water ChemistrySimple Equilibrium SystemsHydrolysis of a Weak Monoprotic AcidAqueous Solubility of an Ionic CompoundHenry's Law: Aqueous Solubility of GasesHydrolysis of a Weak Diprotic BaseSimultaneous Equilibrium: Aqueous Solubility of Two Ionic SolidsSimultaneous Equilibrium: The Effect of pH on the Solubility of a MineralSimultaneous Equilibrium: The Effect of Ion Complexes on the Solubility of a MineralWater Chemistry SimulationsThe Importance of Validating Water Chemistry SimulationsModeling the Hydrolysis of Weak Monoprotic Acids or BasesModeling Mineral SolubilityChemEQL Treatment of Hydrogen Ion ActivityHenry's Law: Aqueous Solubility of GasesModeling Simultaneous Equilibrium: Aqueous Solubility of Two Ionic SolidsModeling Simultaneous Equilibrium: the Effect of pH on the Solubility of a MineralModeling the Chemistry of Environmental Samples: Groundwater, Soil Pore Water, and Surface WaterThe Gibbs Phase RulePhase Rule ExamplesReaction Quotients and Saturation IndicesLogarithmic Activity DiagramsSummaryChemEQL Result Data File FormatValidating Water Chemistry SimulationsValidation Assessment for Examples 5.13 and 5.16Example 5.13: Gypsum SolubilityExample 5.16: Gibbsite SolubilityCinnabar Solubility in an Open System Containing the Gas Dihydrogen SulfideSimultaneous Calcite-Apatite-Pyromorphite SolubilitySimultaneous Gibbsite-Variscite SolubilityApatite Solubility as a Function of pHEffect of the Citrate on the Solubility of the Calcium Phosphate Mineral ApatiteEffect of the Bacterial Siderophore Desferrioxamine B on the Solubility of the Iron Oxyhydroxide Goethite3-s2.0-B9780124157972000066-mainNatural Organic Matter and Humic ColloidsIntroductionSoil Carbon CycleCarbon FixationCarbon MineralizationOxidation of Organic Compounds by DioxygenSoil CarbonCarbon Turnover ModelsSoil Carbon PoolsDissolved Organic CarbonOrganic AcidsAmino AcidsExtracellular EnzymesSiderophoresBiosurfactantsHumic SubstancesExtraction and FractionationElemental CompositionChemical CompositionAcidometric TitrationNitrogen-15 Nuclear Magnetic Resonance SpectroscopyNitrogen-Containing Chemical Moieties in Humic SubstancesPhosphorus-31 Nuclear Magnetic Resonance SpectroscopyPhosphorus-Containing Chemical Moieties in Humic SubstancesSulfur K-edge X-Ray Absorption SpectroscopySulfur-Containing Chemical Moieties in Humic SubstancesHydrogen-1 and Carbon-13 Nuclear Magnetic Resonance SpectroscopyQuantifying Carboxyl Moieties in Humic SubstancesHumic ColloidsSummaryHydroxamate and Catecholamide Siderophore MoietiesSurface MicrolayersHumic Oxygen Content and Titratable Weak AcidsHydrophobic and Hydrophilic Colloids3-s2.0-B9780124157972000078-mainAcid-Base ChemistryIntroductionPrinciples of Acid-Base ChemistryDissociation: The Arrhenius Model of Acid-Base ReactionsHydrogen Ion Transfer: the Brnsted-Lowery Model of Acid-Base ReactionsConjugate Acids and BasesDefining Acid and Base StrengthAcidity and BasicityWater Reference LevelThe Aqueous Carbon Dioxide Reference LevelSources of Environmental Acidity and BasicityChemical Weathering of Rocks and MineralsSilicate RocksCarbonate RocksSulfide MineralsEvaporite RocksAtmospheric GasesCarbon Dioxide: Above GroundCarbon Dioxide: Below GroundSulfur OxidesNitrogen OxidesAmmonia-Based Fertilizers and Biomass HarvestingOutline placeholderNitrogen Cycling in Natural LandscapesCharge Balancing in Plant Tissue and the RhizosphereWater AlkalinityCarbonate AlkalinitySilicate AlkalinityThe Methyl Orange End-PointMineral AcidityMechanical Properties of Clay Colloids and Soil SodicityClay Plasticity and Soil Mechanical PropertiesClay Content and Granular Particle ContactsSodicitySodium-Ion Accumulation on the Clay Exchange Complex: ESPPore Water Electrical Conductivity ECWExtreme Alkalinity: Soil pH>8.4Predicting Changes in Pore Water SARExchangeable AcidityExchangeable Calcium and Soil AlkalinityGibbsite SolubilityThe Role of Asymmetric (Al3+,Ca2+) ExchangeNeutralizing Exchangeable Soil AciditySummaryBuffer IndexConverting Mass Fraction to Sum-of-Oxides CompositionSaturation Effect: Atmospheric Conversion of Sulfur Trioxide to Sulfuric AcidBicarbonate and Carbonate Reference LevelsCalculating the pH of a Sodium Carbonate SolutionCalculating the Aqueous Carbon Dioxide Concentration in a Weak Base SolutionIon Exchange Isotherm for Asymmetric (Ca2+, Al3+) ExchangeThe Effect of (Na+, Ca2+) Exchange on the Critical Coagulation Concentration of MontmorillonitePredicting Changes in SAR by Water Chemistry Simulation3-s2.0-B978012415797200008X-mainRedox ChemistryIntroductionRedox PrinciplesFormal Oxidation NumbersBalancing Reduction Half ReactionsReduction Half Reactions and Electrochemical CellsThe Nernst EquationInterpreting Redox Stability DiagramsEnvironmental Redox ConditionsMeasuring Environmental Reduction Potentials Using Platinum Oxidation-Reduction ElectrodesPourbaix Stability Diagrams: Preparation and InterpretationWater Stability LimitsThe Solute-Solute Reduction BoundaryThe Solute-Solute Hydrolysis BoundaryThe Solute-Precipitate BoundaryThe Solute-Precipitate Reduction BoundaryThe Precipitate-Precipitate Reduction BoundarySimple Rules for Interpreting Pourbaix DiagramsMicrobial Respiration and Electron Transport ChainsCatabolism and RespirationElectron Transport ChainsAerobic Electron Transport ChainsFacultative and Obligate AnaerobesFermentative Anaerobic BacteriaNitrate Respiratory Chain of Nitrate-Reducing BacteriaFerric Iron Respiratory Chain of Metal-Reducing BacteriaSulfate Respiratory Chain of Sulfate-Reducing BacteriaMethanogenic Anaerobic ArchaeaEnvironmental Redox Conditions and Microbial RespirationSummaryAssigning Formal Oxidation NumbersConverting (pe, pH) Redox Coordinates into (EH, pH) CoordinatesLimitations in the Measurement of the Environmental Reduction Potential Using Platinum ORP Electrodes3-s2.0-B9780124157972000091-mainAdsorption and Surface ChemistryIntroductionMineral and Organic Colloids as Environmental AdsorbentsThe Adsorption Isotherm ExperimentHydrophobic and Hydrophilic ColloidsInterpreting the Adsorption Isotherm ExperimentThe Langmuir Adsorption ModelIon Exchange Adsorption IsothermsLinear Adsorption or Partitioning ModelVariable-Charge Mineral SurfacesThe Adsorption Envelope Experiment: Measuring pH-Dependent Ion AdsorptionAdsorption EdgesMeasuring pH-Dependent Surface ChargeProton Surface Charge SitesValence Bond Model of Proton SitesInterpreting pH-Dependent Ion Adsorption ExperimentsSurface ComplexesSummaryParticle Sedimentation Rates in Water: Stokes's LawLinear Langmuir ExpressionHydrolysis Model of Proton Sites3-s2.0-B9780124157972000108-mainRisk AssessmentIntroductionThe Federal Risk Assessment ParadigmRisk AssessmentRisk Management and MitigationDose-Response AssessmentDose-Response DistributionsThe No-Threshold One-Hit ModelLow-Dose Extrapolation of Noncarcinogenic Response FunctionsEstimating the Steady-State Body BurdenReference Dose RfDLow-Dose Extrapolation of Carcinogenic Response FunctionsExposure Pathway AssessmentReceptorsExposure RoutesExposure PointsFate and TransportPrimary and Secondary SourcesExposure AssessmentIntake EstimatesAveraging TimeExposure FactorsRisk CharacterizationThe Incremental Excess Lifetime Cancer RiskThe Hazard QuotientExposure MitigationSummaryChemical- and Site-Specific Factors that May Affect Contaminant Transport by Surface WaterChemical- and Site-Specific Factors that May Affect Contaminant Transport by GroundwaterChemical- and Site-Specific Factors that May Affect Contaminant Transport Involving Soils or SedimentsChemical- and Site-Specific Factors that May Affect Contaminant Transport Involving Air and BiotaWater Ingestion EquationSoil Ingestion EquationFood Ingestion EquationAir Inhalation EquationHazard Index-Cumulative Noncarcinogenic RiskCumulative Target Risk-Cumulative carcinogenic Risk3-s2.0-B978012415797200011X-mainReferences3-s2.0-B9780124157972000170-mainIndex

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