the four laws of soil chemistry: the leeper lecture 1998

C S I R O P U B L I S H I N G

Australian Journal of Soil Research

Volume 37, 1999© CSIRO Australia 1999

A journal for the publication of original research in all branches of soil science

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Aust. J. Soil Res., 1999, 37, 787–829 .

The four laws of soil chemistry: the Leeper

lecture 1998

N. J. Barrow

22 Townsend Dale, Mt Claremont, WA 6010, Australia

The author

This paper is the written version of the Professor G.W. Leeper Memorial lecture for 1998. Professor Ge-offrey Leeper graduated from Melbourne Universityin 1924 and after brief periods at the Common-wealth Explosives Factory in Maribyrnong, at theUniversity of Adelaide, and at the Rowett ResearchInstitute in Scotland he returned to Melbournein 1930 as a research scholar in chemistry in theFaculty of Agriculture. He progressed throughLecturer and Associate Professor, to a personalchair in Agricultural Chemistry. The followingis taken from his obituary in Chemistry in Aus-tralia, August 1994. ‘Leeper will be rememberedas a scholar, a teacher and as a scientist. Nostudent could pass through Leeper’s care withoutbeing influenced by his insistence that he or she

should write more clearly. His insistence that standards should be maintained at a high leveloften bewildered students but afterwards, it all made sense; he still sits on the shoulder of manya graduate in agricultural science from the University of Melbourne. He will be rememberedwith affection by the large number of people who came under his influence.’ In 1992 theVictorian Branch of the Australian Society of Soil Science initiated an annual memorial publiclecture. The lecturer is asked to present a critical review of an aspect of soil science and ‘isfree to choose the subject of his of her address but is bound to present the lecture in stylewhich can only be described as ‘Leeperian’—that is to say erudite, unashamedly critical, andinteresting’. The seventh lecture in the series was presented by Doctor Jim Barrow (pictured).He is a ‘semi-retired’ soil scientist who spent his research career in CSIRO in the Divisionsof Plant Industry, Land Resources Management, Animal Production, Soils, Land and Water,and Forestry and Forest Products. He retired as a Chief Research Scientist.

Abstract

The proposed 4 laws of soil chemistry are: ions react with charged surfaces; soil surfaces areheterogeneous; an initial adsorption reaction is followed by a penetration of the adsorbed ionsinto the interior of the reacting particles; and it is impossible to re-apply fertiliser to thesame soil because the soil has changed. These laws can explain the observed behaviour of thereactions of cations and anions with soil. These include the effects of the level of application,period of reaction, effects of temperature, interactions between pH and salt concentration,desorption, and the isotopic exchangeability.

Introduction

When I was a undergraduate, way back in the early 1950s, a recurringexamination question required us to discuss the fate of arsenic added to Victoriansoils. This sounds innocent enough. You might presume that the topic had been

q CSIRO 1999 0004-9573/99/050787$15.00

Matthew J Bosworth

10.1071/SR98115

788 N. J. Barrow

covered in lectures and all that was required was to regurgitate the lecture notes.Anyone making such an assumption did not know Professor Leeper! As far as Icould recall, arsenic had never been mentioned in lectures and presumably wewere required to extrapolate from what we knew about other elements, whichwas little enough in those days. Yet here was an interesting idea: if one couldpredict the behaviour of one element from knowledge of others, how far can thisbe taken? Are there underlying principles which describe the behaviour of allreactants? Indeed there are, and this is the subject of this lecture.

But first a little homespun philosophy on the importance of comprehensivenessin theories. Consider the story of the blind men who blundered into an elephant.Each came to a different conclusion about the nature of the beast according towhether he contacted the trunk (a hose), the side (a wall), or a leg (a tree). Alot of soil chemistry has been like that with people looking at a little bit of thebehaviour of one element. We can’t really claim to understand the subject untilwe understand all of the subject. We won’t understand phosphate (or arsenate)unless we know how the behaviour differs from, or is similar to, a host of otheranions and cations.

When we look at the elements of interest, macronutrients, micronutrients,and pollutants, we see a frightening diversity. Yet one thing is common abouttheir soil chemistry, and it should be chiselled above the doorways of every soilsbuilding in every university. It is simply this: ‘Ions react with charged surfaces’.This may seem so obvious as to be insulting. Yet it is surprising how often itis forgotten. A good discipline when considering any article on soil chemistryis to ask yourself whether this ‘First Law’ has been remembered. You may besurprised to find how often it, or its implications, have been forgotten. Thislecture will therefore be concerned with the ions present in solution and thecharged surfaces with which they react.

Terminology

Before we can progress very far, we have to agree on the meaning of the wordswe are using. Let us therefore begin with a short lexicon.

Sorption means the transfer of a material from a liquid phase (such as the soilsolution) to the solid phase, the soil itself. No mechanism is implied; the wordmerely describes an observation. Sorption includes adsorption which means thatthe sorbed material is on the outside of the soil particle.

Specifically sorbed means that the soil shows a preference for the sorbedsubstance. Thus cations such as copper or zinc might be sorbed despite thepresence of much higher concentrations of sodium or calcium. Similarly, anionssuch as selenite or molybdate might be sorbed despite much higher concentrationsof chloride or nitrate. Again, no mechanism is implied by this term. It is simplya description of an observation.

Specificity is not a bifurcating property with just two states, specific andnon-specific. Rather it is a graded property so that one can arrange ions into asequence of specificities: for example, phosphate > selenite > borate > chloride.

Co-ordinately adsorbed and covalently adsorbed are terms which one might usewhen discussing the mechanism of specific sorption. They indicate particularhypotheses about the mechanism. Thus, one should distinguish a description ofwhat was observed, specific sorption, from a hypothesis of a mechanism.

The four laws of soil chemistry 789

Fixation is a term sometimes used to mean sorption, and sometimes to describethe slow changes by which a nutrient becomes less readily taken up by plantsthrough time. Its ambiguity is one reason why I do not use it. There are twofurther reasons. One is that it is used with a quite different meaning in referringto nitrogen fixation. The other is that it implies that the ‘fixed’ nutrient haslost all value and I do not think that this is the case.

Electric potential is a term which frightens many of us. We seem to be readilyable to visualise charge and to talk of positively or negatively charged surfacesbut the idea of potential seems less concrete. Nor do text book definitions help,for they speak of the work done to move a unit charge up to a surface andthis seems too abstract. Yet it is important to become familiar with the idea ofelectric potential if we are to use the First Law. Any charged surface will havea potential field near it. The intensity of the field will change as we move awayfrom the surface into the bulk liquid and the rate of this change will depend onthe electrical properties of the medium. All ions in this field will be affected byit. The electric potential provides a measure of the size of that effect. It too is agraded property. It may range from producing a strong attraction through weakattraction and weak repulsion to a strong repulsion, depending on the sign ofthe charge and the density of charge on the surface.

The ions

Calculating the ions present in solution is simple, provided you know the valuefor the dissociation constants of the acid or base involved. In most cases thereare well-known accepted values. But there are exceptions. For zinc, Baes andMesmer (1976) give the value for pK1 as 8 ·96. A similar value is used by Spositoand Mattigod (1980) in the model Geochem. On the other hand, Lindsay (1979)gives the value as 7 ·69 and this lower value is often used by soil scientists. Thisposes a dilemma: how can we choose the correct value? The ideal recourse toseparate measurement is not available because hydrolysis proceeds to only a smallextent before the onset of precipitation, thus making measurement difficult (Baesand Mesmer 1976). I prefer the Baes and Mesmer value because it is in a workspecifically devoted to evaluating such measurements and because the source ofthe data is given. There are also problems with selenite. The first source usedby most people is the ‘Handbook of Chemistry and Physics’ (Weast 1971). Thisgives a value of 7 ·31 for the pK2 of seleneous acid. Yet the well-documentedvalue in Baes and Mesmer (1976) is 8 ·5. The message is clear: beware!

The anions

The anions of interest can be regarded as deriving from the dissociation ofacids, several of them from weak acids. Perhaps the simplest in some respectsis the monovalent borate ion (B(OH)−4 ), for which the pK is about 9 ·2. Theproportion present as borate ions is given by: K/((H+) + K). When (H+) ismuch bigger than K, at pH 4 it is 10−4 compared to 10−9 ·2, then the expressionapproximates to: K/(H+). In this range, a 10-fold decrease in (H+), that is, unitincrease in pH, causes a 10-fold increase in the proportion present as B(OH)−4 .Rather more complicated is selenium for which both selenate (SeO2−

4 ) and selenite(SeO2−

3 ) may be stable in soils for long periods. Selenate is derived from a fairlystrong acid. It is therefoe virtually completely dissociated at soil pH values and

790 N. J. Barrow

the SeO2−4 ion is the only ion present. Selenite, on the other hand, is derived

from a weaker acid with the pK2 at 8 ·5 and hence the concentration of SeO2−3

ions increases with increasing pH over much of the range of soil pH (Fig. 1a).

1e+0

1e-1

1e-2

1e-3

1e-4

1e-5

1e-6

1e-7

1e+0

1e-1

1e-2

1e-3

1e-4

1e-5

1e-6

1e-7

1e-8

(a) (b)

3 4 5 6 7 8 9 10 3 4 5 6 8 9 107

pH

Fra

ctio

n as

indi

cate

d io

n

MoO42-

HPO42-

SeO32-

B(OH)4

-

HMoO4

-

CuOH+

ZnOH+

CoOH+

NiOH+

CdOH+

MnOH+

Fig. 1. Effect of pH on the fraction present as the indicted species. Thus, the line labelledSeO2−

3 indicates the fraction of the selenite present as this ion. The values for molybdate arefor a total concentration of 1 µM.

Phosphate may seem to be complicated because phosphoric acid can dissociate3 protons with pK values of about 2, 7, and 12. However, in the range of soilpH, only the second of these dissociation steps is important. The first step withits pK of about 2 is virtually complete and the third step with a pK of about12 has little influence. As a result, we see a 10-fold increase in the divalentHPO2−

4 ion with unit increase in pH up to about pH 6. In order to be ableto answer Professor Leeper’s question, we need to know that arsenate behavesvery much like phosphate and has similar values for the pK of its 3 dissociationsteps. Arsenite, on the other hand, has only one dissociation step with a pKnear 9 ·2. Its dissociation behaviour is therefore like that of borate.

The chemistry of molybdate is a little more complicated. Molybdic aciddissociates in 2 steps but both pK1 and pK2 are near 4 so that the MoO2−

4

ion increases in concentration with increasing pH but the HMoO−4 ion reaches amaximum at low pH and then decreases rapidly (Fig. 1a). Molybdate polymerscan be important at low pH but not at the concentrations of molybdate presentin soil solutions.

Fluorine, an essential micronutrient for animals, would seem to be a simplecase in that one might expect F− to be the only ion present in solution. However,in soil solutions, the concentration of aluminium ions increases rapidly as the pHis decreased below about 5 and fluoride and aluminium have a strong affinity foreach other. Barrow and Ellis (1986a) showed that only a small proportion ofthe fluoride in a solution which had been allowed to react with soil was presentas the free fluoride ion between pH 4 and 5.


The cations

In solution, the micronutrient metal ions tend to be surrounded by 6 watermolecules arranged in an octahedron. We might write such an ion as, for example,Zn(H2O)2+

6 . Such ions are multiprotic acids because the water molecules maylose protons. The first step gives ZnOH(H2O)+

5 , the monovalent cation, moresimply written ZnOH+. Further steps give the uncharged species, Zn(OH)2, andlater the monovalent anion. In the case of zinc the acid is very weak; the pKfor the first dissociation step is large.

Calculation of the proportion of the zinc ions present as ZnOH+ is importantbecause it has been suggested that these ions play a role in the reaction of zincwith soil (Tiller et al . 1972). Neglecting for the moment further dissociation, andalso the formation of complexes, the proportion present as ZnOH+ ions is givenby: K1/((H+) + K1). As was the case with borate, when (H+) is much biggerthan K1, say 10−4 compared to 10−8 ·96, then the expression approximates to:K1/(H+). Again, unit increase in pH causes a 10-fold increase in the proportionpresent as ZnOH+. The value assigned to K1 is therefore important not onlyfor determining the value for the proportion present as ZnOH+ but also fordetermining the range over which the ‘10-fold’ relation with pH holds.

The simple pattern for the proportions of zinc ions present is shown in Fig. 1b.The other micronutrient cations follow a similar pattern but displaced to the leftor the right. Thus, copper is thought to have a pK1 value of about 8 (Baes andMesmer 1976) compared to zinc at 8 ·96, and is therefore displaced to the left.To the right we have, in sequence, cobalt at 9 ·65, nickel at 9 ·87, cadmium at10 ·08, and manganese at 10 ·59. This similar behaviour is mirrored by, but isnot necessarily the direct cause of, similar behaviour for these ions in soil. Bythe way, mercury is rather different. It is a stronger acid with both pK1 andpK2 near 3 (Baes and Mesmer 1976). Because of this second dissociation, theproportions present as Hg2+ and HgOH+ decrease with increasing pH within thenormal range of soil pH (Barrow and Cox 1992a).

Soil solutions contain many molecules and some of these may complex withthe metal cations. Chloride, and to some extent, nitrate can complex the metals.The magnitude of the association constants can be obtained from compilations,but the precision of the values may be low. However, this uncertainty is smallcompared to that for organic complexes. Especially at the metal concentrationspresent in ordinary, uncontaminated soils, a large proportion of metals such ascopper in solution might be present as organic complexes (Jarvis 1981).

The effect of metal complexes on the extent of sorption reactions is difficultto predict. It depends on affinity of the surface for the complexed and theuncomplexed metal. Even in the apparently simple case of zinc-chloride complexes,it can be difficult to extrapolate from one sorbing material to another. Thus, forgoethite, zinc sorption was greater from chloride solutions than from perchlorate(Bolland 1970), and greater from chloride than from nitrate (Forbes 1973; Forbeset al . 1974; Padmanabham 1983). This would suggest that chloride complexes,such as ZnCl+, had some affinity for the reacting surface and this assumptionwas successfully included in models to describe the reaction (Barrow et al . 1981).For soil, however, the opposite result was obtained: at the same pH, sorptionwas smaller from a chloride solution than from nitrate (Barrow and Ellis 1986b).This suggests that ZnCl+ had little affinity for the reacting surface in the soil.

792 N. J. Barrow

Such apparently conflicting results are not infeasible. Experience with mercuryis similar. Mercury forms very strong complexes with chloride and, in mostcases, the presence of chloride decreases mercury sorption (Forbes et al . 1974;Kinniburgh and Jackson 1978; Barrow and Cox 1992a, 1992b). Even so, Barrowand Cox (1992a) had to assume that the HgCl+ ions also participated in thereaction in order to model the data. This is consistent with reports that, undersome conditions, chloride increased sorption of mercury by clays (Farrah andPickering 1978).

An interesting effect of metal complexes with organic matter in the soil solutionis that sigmoid sorption curves may be produced. For example, Neal and Sposito(1986) obtained sigmoid sorption curves for cadmium in the presence of sewagesludge, and Barrow and Cox (1992b) found that, especially in the absence ofchloride, sorption curves for mercury were sigmoid. The explanation seems to bethat complexes with soluble organic matter keep the metal ions in solution untilsome threshold is exceeded. Only when the capacity of the organic matter tocomplex the metal is exceeded can reaction with the soil occur. Consequentlythe sorption curves have a sigmoid shape.

The materials with which nutrients react

It is generally accepted that nutrients react with clay minerals, with metaloxides, and with organic matter. This view is, of course, very simplistic if onlyfor the reason that each of these categories react with the others so that pureexamples of them in soil may be rare. Nevertheless, there have been many studiesof the reactions between nutrients and each of these categories of materials andthese have helped to understand the reactions involved even though they havesometimes caused misunderstandings because of differences between the purecompounds and those in soils.

The clay minerals.

Clay minerals are the ‘classic’ materials in soil chemistry because their structurewas elucidated very early in the development of the science, and similarly, theirrole in ion exchange was also realised very early. The role of ion exchange in thereactions of K+, Na+, Ca2+, and Mg2+ with clay minerals is perhaps the bestunderstood aspect of soil chemistry and need not be considered further here.

It was natural to consider ion exchange as an important mechanism for reactionof metal cations such as copper and zinc with soils. However, the concentrationof these micronutrient metal ions in soil solutions is much lower than that ofthe major cations and especially lower than that of calcium. Because of theimportance of valency in ion exchange, of the ions normally present in soilsolution, calcium is of the greatest importance in considering competition forexchange sites. Ion exchange could only be an important mechanism for themicronutrient metals if the selectivity for say copper was much higher than thatof calcium. This does not seem to be the case (el-Sayed et al . 1970).

This makes it unlikely that ion exchange is an important mechanism for themicronutrient metals. Furthermore, other sinks for the these ions are ‘deeper’ andthere are therefore few ions remaining to participate in ion exchange. Nevertheless,attempts to measure exchangeable metal cations are often made. Sometimes thisinvolves an initial extraction of a soil with water to remove the ‘soluble’ metal


but the main step is extraction with a salt solution to remove the ‘exchangeable’metal.

Interpretation of the results obtained is contentious for two reasons. The first,and most obvious, is concerned with the effects of pH. If the pH is not controlled,for most soils, the salt solution will decrease the pH and, because of the largeeffects of pH on sorption (see later), this will release some of the sorbed metal.If the pH is controlled at say 7 (Shuman 1985), in most soils this will be achange in pH and this change will affect the strength of sorption and thereforethe apparent value of exchangeable cation. To explain the second reason, wehave to anticipate some of the information on the effects of salt on covalentsorption. The general rule is that increasing the salt concentration decreases theabsolute value of the electric potential near a charged surface. If the potentialis negative, as it usually is for sorption of metal ions by soil, it becomes lessnegative. This decreases the sorption of the metals. Examples are: for sorptionof nickel on kaolinite (Mattigod et al . 1979); for zinc on soil (Barrow and Ellis1986b); for copper, cadmium, and lead on kaolinite (Schindler et al . 1987); andfor cadmium on soil (Naidu et al . 1994). Thus, increasing the salt concentrationto remove supposedly exchangeable ions will also remove some of the metal ionswhich are covalently adsorbed.

This is a case in which studies of pure substances may have caused aproblem. Many studies of covalent sorption have involved iron oxides. Thelaboratory-prepared oxides usually have a point of zero charge >8; the exact valuedepends on the extent of contamination mainly with carbonate. Metal sorptionis usually at a pH <8 and therefore on positive surfaces. One effect of increasingionic strength is therefore to increase sorption by the rule indicated above.However, the increasing ionic strength also decreases the activity coefficient andthis component decreases sorption so the net effect is small. Thus, Okazaki et al .(1986) reported no effect of electrolyte concentration on adsorption of copper andzinc by iron and aluminium oxides. Similarly, from their own work, and from asurvey of the literature, Hayes and Leckie (1987) concluded that there was littleeffect of electrolyte concentration on metal adsorption. This is one example inwhich results obtained with pure substances cannot be simply extended to soil.

Variable-charge mineral surfaces.

Despite their familiarity to soil scientists, the clay minerals are rather unusualcrystals. This is because, for most of their surface, the bonds of the surfaceatoms are fully satisfied. This is not the case for most crystals. The ‘classic’case is that of silver chloride which takes up an excess of silver or of chlorideions depending on whether the medium contains more silver or more chloride.Consequently the particles carry a charge which depends on the compositionof the medium. It is a variable charge. The oxides of metals such as iron,aluminium, and manganese also have unsatisfied bonds on the outside of eachcrystal. So also do the edges of clay minerals as distinct from the plane faces.These surfaces take up water molecules in attempting to satisfy those bonds.Depending on the pH, these water molecules may gain or lose protons (H+) andso acquire a charge. They are therefore variable charge surfaces with the chargedepending on the pH.

794 N. J. Barrow

There are many oxides present in soils. Taylor et al . (1983) list 6 iron oxides,5 aluminium oxides, and 13 manganese oxides. (The term ‘oxide’ is used looselyhere to include oxyhydroxides.) Of the iron oxides, goethite is most commonlyfound in soils of many climatic regions (Sposito 1984). The presence of oxides isapparent simply from observing one of the most obvious properties of soils: theircolour. Soil colour is partly related to the amounts of organic matter in the soilsbut also to the amount and particle size of the oxides present. Iron oxides areespecially important, with goethite giving the yellow-browns and haematite thereds. The names red earth, terra rossa, terre rosse, and kraznozem, which havebeen applied to soils in various languages, all show the effectiveness of rednessin catching peoples’ attention.

There have been very many studies of the sorption of ions by variable chargeminerals, including micronutrients, macronutrients, and pollutants. Dzombak andMorel (1990) list >50 studies of reactions of inorganic cations and anions withhydrous ferric oxides. The cations studied include Mg, Ba, Ca, Sr, Ag, Cu, Zn,Cd, Co, Ni, Mn, Pb, and Hg; the anions, PO4, AsO4, SO4, SeO3, SeO4, VO4,CrO4, and B(OH)3. This list makes it clear that such reactions could be veryimportant in controlling the supply of both essential nutrients and toxic ions toplants.

Of the several iron oxides present in soil, goethite is the most widely studied.To understand the implications and the limitations of these studies, we need todescribe some of the properties of goethite. It is designated α-FeOOH where theα denotes hexagonal close packing. However, the goethite which occurs in soilsis rather different from the material used in many laboratory experiments. It isfar from pure. It may contain manganese and other trace metals (Stiers andSchwertmann 1986; Hiller et al . 1989), various anions (Kuhnel et al . 1975; Hilleret al . 1989), and, especially, aluminium (Norrish and Rosser 1983; Lewis andSchwertmann 1980; Fey and Dixon 1981; Schulze 1982; Schulze and Schwertmann1984).

Fordham et al . (1984) described an unusual fibrous goethite for which theatomic ratios were 4 : 2 : 1 for Fe : Al : Si. This corresponds to about 5% Si byweight. Fordham and Norrish (1979) found silicon contents of iron oxide pelletsfrom a variety of soils to range between 1% and 4%. It is of course difficult tobe sure that samples are uncontaminated but these values were believed to befree of this problem. If we are to understand the behaviour of soil goethites, weneed to know how these silicon atoms are arranged. It seems unlikely that theyare scattered at random through the crystal but this is difficult to investigate forthe minute particles of soil goethite. Fordham et al . (1984) pointed out that thesilicon apparently occupied a stable position because it was resistant to extractionwith oxalate. They speculated that the silicon was adsorbed on the surface ofmicrocrystals. This suggestion is consistent with the work of Smith and Eggleton(1983) who examined 4 samples of botryoidal goethite which varied in silicacontent from zero to 1 ·25%. The samples which contained silica were composedof fine needle-like grains with diameters as small as 30 µm. They suggested thatthe gaps between the grains could consist of a monolayer of silica. The sampleof goethite that did not contain silica did not have this structure. Thus, thesilica in soil goethites might exist as a sort of mortar between microcrystals ofthe oxide.


Because of the presence of these contaminants in natural goethites, theirbehaviour may differ from that of the pure goethite most often studied. Forexample, the presence of the silica means that the change in charge and ofpotential with change in pH will be different from that of pure goethite.

The water content of goethite is commonly greater than that calculated fromthe formula FeOOH. This is true for both synthetic goethites (Thiel 1963; Feyand Dixon 1981) and natural goethites (Kuhnel et al . 1975; Murad 1979). Oneexplanation is that the extra water could be H2O molecules enclosed in thestructure as suggested by Fey and Dixon (1981). In this case, the extra watercould be bound in micro-pores between domain boundaries. Another explanationis that some of the Fe atoms of the structure are missing and the charge isbalanced by extra protonation of adjacent oxygen atoms as suggested by Schulze(1982). The formula would then be written: Fe1−xO1−3x(OH)1+3x, where x isthe proportion of the iron atoms that are missing.

Organic matter

Reactions with organic matter have been frequently studied for copper andzinc. One stimulus for such studies is the common occurrence of deficiencies onorganic soils. Of the micronutrient metals, copper has the greatest affinity fororganic matter and some studies have found up to half of the copper presentas organically bound (reviewed by Stevenson and Fitch 1981). Nevertheless, itis difficult to make any simple statement about the sequence of preference formetals. A typical affinity sequence (quoted by McBride 1989) is Cu > Ni > Pb> Co > Ca > Zn > Mn > Mg. However, he points out that such sequencesare commonly inconsistent and depend on the nature of the organic matter, themethods used, and the pH of measurement. An important factor is the degreeof loading. Thus, at low loadings, Cd is strongly preferred to Ca yet at highloadings the affinity is similar. Nor is it easy to make firm statements about thekind of bond involved, for McBride (1989) concludes that whether researchersobserve chelates, inner sphere complexes or outer sphere complexes depends tosome degree on the experimental conditions. Nevertheless he concludes thatCu2+ mostly forms inner sphere complexes, whereas most of the other first-rowtransition metals (Mn2+, Fe2+, and Co2+) form outer sphere complexes. For adetailed review of the bonding of other metals, see McBride (1989).

An important characteristic of the reaction between metal ions and soil organicmater is that the apparent affinity decreases as the amount of metal increases.That is, the reaction behaves as if there are a few sites of very high affinity,slightly more sites of somewhat lower affinity, rather more sites of moderateaffinity, and so on. McBride (1989) has suggested that some of the sites of highaffinity might involve sulfhydryl groups in soil organic matter. The effect of thedistribution of sites is that, in describing the reaction, it may be necessary touse an affinity term which decreases as the amount of loading increases, ratherthan an affinity constant. This approach was used by Cheam (1973) and byBresnahan et al . (1978) for the reaction between copper and fulvic acids andby Barrow and Cox (1992b) in describing the reaction of mercury with a soil.It is worth mentioning in passing that this behaviour introduces a ‘chicken andegg’ problem. By this I mean that one needs to know the amount of loadingbefore one can calculate the mean affinity constant. Yet one needs the affinity

796 N. J. Barrow

constant to calculate the loading. This problem can be solved by making aseries of guesses of, say, the affinity constant, calculating the loading which thisvalue would give, and then checking whether this loading will give the assumedaffinity constant. Computers can be programmed to cycle through a sequenceof repeated guesses very quickly until the initial guessed value agrees with thecalculated value so that this is no longer a difficulty.

There is one final point to make in considering the reaction of nutrients withorganic matter. It is that organic matter is also a variable charge substance: itscharge varies with pH. We may think of the various functional groups as havinga range of values for their pK so that they dissociate at different pH values.The overall effect is that the surface is positive at low pH and negative at highpH. Equations developed to describe reactions with ‘variable charge surfaces’ insoil are meant to be general and to apply to oxides, the edges of clay minerals,and to organic matter.

The three laws of soil reaction with plant nutrients

The first law

We have already met the first law: ions react with charged surfaces. We nowconsider how to apply it. First we consider the still frequently used approach inwhich it is ignored. Imagine a simple adsorption reaction in which sites on thesurface of particles adsorb a reactant, x . The equilibrium equation could thenbe represented:

Site+ x−→←−Site-x (1)

If the initial concentration of sites is m, the equilibrium concentration of x isc, and of the product Site-x is S (all in convenient units), then the equilibriumconstant K is given by:

K =S

(m− S)c(2)

Re-arranging gives:

S =mKc

1 +Kc(3)

This is the Langmuir adsorption equation. It may be derived in other ways(Elprince and Sposito 1981) but this simple derivation shows that it is compatiblewith adsorption on one uniform surface on which all sites are equal and whichare not changed by reaction. As we shall see later, it fails for reactions ofnutrients with soils because it does not meet either of these requirements. Forthe moment, we shall consider how we can modify it to encompass the first law.

Several models have been developed to describe the reaction of both cationsand anions with variable charge oxides such as goethite. The models differ intheir complexity and in their aims. Some, for example, are concerned with thedetailed modelling of the bonds formed at the surface. However, all modelsinclude terms such that the amount of reaction depends not only on the solution


concentration of the reacting ion but also on the electric potential in the planeof adsorption, although the derivation of this relationship and the way that isspecified differs between models. The model of Bowden et al . (1977) is veryuseful in that it can be adapted to apply not only to the model substances forwhich it was developed but also to soils. This model uses the surface activityfunction (ais):

ais = αγcKi exp (−ziFΨ/RT ) (4)

where α is the proportion of the reactant present as the reacting species, γ isthe activity coefficient, c is the total concentration, K i is the binding constantof the reacting species i , z i is the charge (including sign) on the reacting ion, Fis the Faraday constant, Ψ is the electrical potential, and R is the gas constant.The surface activity function is then used instead of the terms for concentrationand equilibrium constant in Eqn 3.

Consider now the individual components of the surface activity function. Theconstants R and F are needed to convert to the appropriate units. The Tterm describes the effects of temperature on the adsorption reaction itself. Thisshould not be confused with the effects of temperature on reactions which mayfollow adsorption (see later). The effects of temperature on adsorption have beendiscussed by Barrow (1992a). The effects are complex because, in addition tothe effects of the T term of Eqn 4, there are effects on the ions in solution andon the charge on the surface. It was concluded that, on balance, adsorptionof anions should decrease with increasing temperature and adsorption of cationsshould increase.

The α term is included because it is found that reaction is not related to thetotal concentration in solution but to the concentration of specific ions. As wehave seen earlier, the value of α changes with pH and we shall later see howthese changes are important in determining the effects of pH on sorption. Theγ term is included to enable extension to cases in which the ionic strength ofthe background electrolyte, and hence the activity coefficient, are varied.

The term for the binding constant K i carries the subscript ‘i ’ to indicate thatit refers to particular ions, not the total concentration. It replaces the K termof Eqn 3.

The −z i term adjusts for the sign of the charge. For example, if the ionis negatively charged, the value of −z i is positive. Hence, when the potentialis positive, the exponential term is large; when the potential is negative theexponential term is less than unity. This means that reaction of ions withopposite-charged sites is increased and reaction with like-charged sites is decreased.Reaction is not, however, prevented by like charge. It can occur if the productof the K i term and the exponential term is large enough, that is, if the chemicalaffinity is large enough.

The Ψ term plays a pivotal role in describing the influence of the electricalcharge on the surface. For variable charge surfaces, its value varies with theconcentration of the ions that determine the charge, the ‘potential determiningions’. As explained earlier, protons are important potential determining ions foroxide surfaces. That is, the value of Ψ depends partly on pH. However, this isnot the only effect. Imagine a positively charged surface. As we move from that

798 N. J. Barrow

surface into the bulk solution the potential will decrease, reaching, by convention,zero in the bulk solution. The rate of decrease with distance will partly dependon the electrical properties of the interfacial region and partly on the propertiesand concentration of the electrolyte. The more concentrated the electrolyte, themore its ions crowd near the surface and the more rapidly the potential fallswith increasing distance. Thus the rule is that increasing the concentration ofthe electrolyte decreases the absolute value of the potential of ions reacting withthe surface: positive values become less positive; negative values less negative.

Consider now differences between adsorbed ions. An ion which has its meancentre of charge very close to the oxide surface will experience a higher potentialthan an ion with its mean centre of charge further away. Thus, fluoride ionsmight be expected to occupy a position similar to that of hydroxyl ions andto experience a much higher potential than selenate ions for which the oxygenatoms would draw the mean centre of charge further from the surface.

Protons are not the only potential determining ion. To understand why otherions affect the potential we need to consider the fate of the charge carried byreacting ions

The problem of charge

In simple ion exchange, there is no change in surface charge or in the pHof the solution. One ion simply replaces an equivalent amount of another ion.When there is some specific affinity for the surface, this is not the case. Itis obvious that the charge on reacting ions cannot simply disappear. We maythink of two alternatives: either it may affect the surface or it may affect thesolution. That is, a reacting anion may make the surface more negative or itmay displace hyroxyl ions from the surface and raise the pH of the solution.Similarly, a reacting cation might make the surface more positive or it mightdisplace a proton and decrease the pH of the solution. In practice, the division isnever sharp. Both effects always occur, although in specific cases one effect maybe larger than the other. For a particular reactant, the split between the twoalternatives depends on the pH, on the amount of sorption which has alreadyoccurred, and on the ionic strength (Bolan and Barrow 1984). As an example,reaction with phosphate increased the pH when the initial pH was about 5 ·8,but decreased it when the initial pH was about 7 (Barrow 1987). It is thereforepointless to try to write simple equations to describe the reaction. But thereactions, and the balance between the options, can be modelled using rathercomplex sets of equations.

For different reactants, the way the charge is allocated depends on the meanposition of the charge on the adsorbed ion. For an ion such as fluoride, thecharge is close to that of the hyroxyl ions and there is a strong tendency todisplace hyroxyls into the solution, that is, the charge is mainly balanced bychanges in the solution. For larger ions, and especially for oxyanions, rather lessof the charge is balanced by displaced hydroxyls into the solution and rathermore by a decrease in surface charge. Depending on the ion size, specificallyadsorbed cations may reside very close to the surface hydroxyls and protons.Therefore, much of the charge balance is often made by displaced protons intothe solution. To give an artificial numerical example, imagine that 10 zinc atomsreact with a patch of surface carrying a net charge of −100 at a pH of 6. We


are not concerned here with the mechanism of the reaction but only with thecharge balance. As most of the zinc ions in solution are Zn2+, the total chargeof the 10 atoms is close to 20. The outcome might be that the surface charge isincreased to −97 and there are 17 protons released. This example is chosen toillustrate 2 points. One is that, since the charges must balance, one can expressthe outcome either in terms of the change in surface charge or in terms of theprotons released. The other is that simple ratios do not necessarily occur.

Thus, specifically adsorbing ions are also potential determining ions. Theeffect may be direct in that they directly affect the charge and potential onthe surface. It may be indirect in that they also affect the pH and thereforeaffect the potential via the effects of pH. The important point is that this is onereason why the Langmuir equation is not appropriate for describing reactionsinvolving specific adsorption. These effects on electrical potential are analogousto effects known as ‘lateral interactions’ in studies on adsorption of unchargedions (Barrow et al. 1993).

The second law

The second law is: soil surfaces are heterogeneous. This might be consideredself evident. Yet we still see many attempts to fit the Langmuir equation todescribe specific sorption of ions by soil. As this equation requires uniformreaction sites it follows that those who use it not only fail to see the effects ofspecific sorption on potential but also do not accept the idea that soil surfacesare heterogenous. Direct evidence of heterogeneity comes from studies which haveshown the presence of both positive and negative charges in the same soil. Themagnitude of the charges varies with pH but both can be present, presumablyon separate particles or possibly on separate ‘patches’ of the same particle.

This is another aspect in which soils differ from the oxides which are oftenstudied as models for soils. The oxides may be heterogenous with respect toreaction with cations but not with anions. It has been suggested (Barrow et al .1993) that this arises because some of the missing Fe atoms are incompletelyreplaced by protons thus giving sites of negative potential which would be detectedby adsorbing cations but not by anions. However, subject to this qualification,cations and anions react with the same sites. This may not be the case forsoil. Cations will react with the most negative end of the spectrum of potentialsand anions with the most positive end. Consequently, zinc and phosphate mayinteract strongly with each other when both react with goethite but when theyreact with soil, most of the effects of phosphate on zinc sorption are indirect andcaused by effects on pH. Direct effects are small at low levels of zinc becausethe two ions react with opposite ends of the spectrum of charged sites (Barrow1987).

The question to consider now is how do we use the idea of heterogeneity. Threedifferent approaches have been used. Perhaps the simplest is to postulate thatthe surface is made up of two, or more, uniform ‘sub’-surfaces. Ten publicationswhich used this approach for describing sorption of phosphate appeared between1966 and 1977 (Barrow 1978). Similarly, for reaction with cations, Dzombakand Morel (1990) divided the surface of hydrous ferric oxides into high andlow affinity surfaces and this has been praised as ‘pragmatic, utilitarian andOckhamian’ (Morgan 1991). This seems to be another case in which the surface

800 N. J. Barrow

science and the soils literature have failed to overlap as this approach has beencriticised extensively in the soils literature. On theoretical grounds, it has beenpointed out that fitting of such equations does not show that separate surfacesreally exist (Sposito 1982). On statistical grounds, it has been shown that theequations have poor statistical properties so that estimates of the parametersmay be far from their true value (Ratkowsky 1986). And on practical grounds,equations with fewer parameters and better properties can describe sorption moreefficiently (Barrow 1978). Yet simple ideas die hard and 2-surface Langmuirequations are still being used (Ajwe and Tabatabai 1997).

The other 2 ways of dealing with heterogeneity both postulate that there isa distribution of sites with a few sites of high affinity, rather more of slightlylower affinity, yet more with even lower affinity, and so on. One possibility isto then assume that the mean equilibrium constant decreases as the amountof sorption increases. This is analogous to assuming that the affinity term forreaction with organic matter decreases as the amount of reaction increases andinvolves a similar ‘chicken and egg’ problem which can be overcome using acomputer program to make repeated estimates. This approach has been used todescribe sorption of metals by iron oxides (Benjamin and Leckie 1981; Barrow etal . 1989; Barrow and Cox 1992a). If the mean equilibrium constant is assumedto decrease as log sorption increases, a Freundlich sorption is produced.

The other possibility is to use a distribution function to describe the rangeof site affinities. The outcome may be calculated using a computer programwhich divides the distribution into a number of slices. Within each slice, alocal equation is assumed to describe adsorption within that slice and the totalsorption is summed over the slices. A convenient local equation is Eqn 3 withthe terms for concentration and binding constant replaced by the surface activityfunction (Eqn 4) and with a function to account for the change in potentialas sorption proceeds. A distribution function similar to the normal distributionwas derived by Sposito (1980) and I have used a normal distribution (Barrow1987).

For soils, site affinity could vary in 2 ways. Both the equilibrium constantK i and the electric potential term Ψ of Eqn 4 would be expected to vary fromparticle to particle or from patch to patch. Expansion of the K i term to give theheat of adsorption will show that variations in heat of adsorption or variationsin Ψ will have the same effect. For many purposes it is inefficient to let bothvary. In the examples discussed later, all of the heterogeneity was allocated tothe Ψ term. There are 2 major arguments for this. One is pragmatic: becauseboth positive and negative charges can co-exist in soil, there must be patchyheterogeneity in Ψ. The other is more direct, yet also more abstruse. It arisesbecause we observe that the point of zero salt effect for sorption of anions is ata higher pH than the point of zero charge of the soil. This can be explained ifit is assumed that there is a distribution of potentials and that anions prefer toreact with the most-positive tail of the distribution. It is not until a pH higherthan the point of zero charge is reached that the mean electric potential of thistail is zero. Nevertheless, the allocation of all the heterogeneity to the electricpotential should be seen as a modeling convention. Because it is a convention,it may be abandoned when it is inappropriate and heterogeneity split betweenK i and Ψ.


The third law

The third law is: an initial adsorption reaction is followed by a penetration ofthe adsorbed ions into the interior of the reacting particles. Perhaps the clearestevidence for this law in model systems was provided by Brummer et al . (1988)who showed that sorption of nickel, zinc, and cadmium by goethite continued formany weeks. Dissolution studies and detailed modeling all showed that this wasconsistent with an initial adsorption reaction followed by a diffusive penetrationof the surface (Brummer et al . 1988; Barrow et al . 1989). More recent work(Fischer et al . 1997) has shown that the pathway for this diffusion differs fordifferent metals. Copper, lead, cadmium, and manganese seem to diffuse mainlyvia pores. On the other hand, nickel and chromium were little affected by thepresence of pores and may diffuse via smaller defects such as crystal vacancies.All such processes are fairly slow and, because they require atoms to jump fairlyhigh energy barriers, have a large activation energy. There is therefore a largeeffect of temperature.

For anions, the picture has also recently become more clear. Strauss et al .(1997a, 1997b) have shown that the extent of the slow reaction between phosphateand goethite depended on the crystallinity of the goethite. For samples whichwere well crystallised, there was no slow reaction but for poorly crystallisedsamples the reaction continued for weeks. Strong evidence was provided that themechanism was slow penetration of the spaces between the crystal domains.

In the work of Strauss et al . (1997a, 1997b), diffusion stopped after (at most)3 weeks. This suggested that the penetrating ions had reached the ends of theirpathways. However, in most other cases, diffusion seems to be so slow thatthe depth of penetration is small compared to the size of the reacting particle.Hence the amount penetrated might be expected to be proportional to the squareroot of time. However, this relation can only follow if the source concentrationis constant. As the diffusion proceeds, the concentration in solution decreases.Consequently the concentration of adsorbed reactant decreases and as this is thedriving concentration for the diffusion step, diffusion slows. There are furtherreasons why the observed reaction does not follow the square root rule and thesewill be discussed when we discuss the actual observed rates.

The characteristics of the reactions

The best way to understand the characteristics of the reactions between ionsand soil is to study the way they are affected by important variables such as: theamount added, the period of the reaction, the temperature, pH, ionic strength,competition and co-operation between ions, and desorption. In each case, we willindicate how the 3 laws help explain the observations.

The effects of the amount added

Soil scientists are very interested in the partition of a reactant between thesolution phase and the solid phase, that is the amount sorbed and the amount leftin solution. This partition is very important in controlling the rate of movementof the reactant both to plant roots and in leachate. Much effort has thereforebeen devoted to describing it, conveniently by plotting the amount sorbed by thesoil against the concentration in solution. Such plots are often called ‘adsorption

802 N. J. Barrow

isotherms’. This is unfortunate; a case of false immodesty. First, as indicatedabove, we can seldom be sure that the process involved really is adsorption.Second, the word ‘isotherm’ is borrowed from chemistry where it is used forreactions which depend solely on temperature and pressure (or for reactions insolution, concentration). Hence, if we have fixed the temperature, ‘isotherm’, wedefine the equilibrium fully by specifying concentration. This is not the casefor soil reactions. A somewhat better term is ‘Q/I’ curves: quantity/intensity.However I prefer the term ‘sorption curves’.

In almost all cases, sorption is described by simple curves with the proportionin the soil solution increasing as the amount added increases. There are, however,some exceptions. As indicated earlier, sorption of metals can sometimes givesigmoid curves such that there is an initial increase in concentration withoutmuch increase in sorption (Neal and Sposito 1986; Barrow and Cox 1992b). Thisseems to arise when substances in solution get first call on the metal ions so thatlittle sorption occurs until these reactions have been satisfied. Another exceptionsometimes occurs at very low concentrations; a linear relation between sorptionand concentration may be observed (Jarvis 1981; McLaren et al . 1981). For traceelements in many soils the concentrations may be so low that this is a commonsituation. Nevertheless this straight initial section is the bottom part of a curveand this should be kept in mind when describing (and explaining) the curve.

In considering the equations commonly tested, a limitation has been that theeffective range of the analytical method used (and the interests of the researcher)have usually confined the available data to little more than a 100-fold range ofsolution concentrations. Within such a range, the Freundlich equation usuallydescribes the data well. This equation is:

S = a cb (5)

where a and b are coefficients. When this equation holds, plots of log S againstlog c are straight lines. However, when a large range of values are available, suchlog–log plots are slightly curved. An example of a curved log plot for phosphatesorption over a 104 range of P concentrations was given by Barrow (1985). Forphosphate a complication is that curvature in log–log plots can be caused by thepresence of desorbable phosphate in the soil (Barrow 1978). This is, however,seldom the case for virgin Western Australian soils which therefore may indicatethe ‘true’ shape of sorption curves. Furthermore, plots for weakly sorbed anionssuch as sulfate and selenate and, to a lesser extent, selenite, usually have steeperlog plots than strongly sorbed anions such as phosphate. This is illustrated inFig. 2 in which selenate, selenite, and phosphate are plotted on the same graphby adjusting the solution concentration of selenite and selenate to allow for theirweaker affinity for the surface. Thus, because selenate has a much lower affinitythan phosphate, its concentration in solution was multiplied by 0 ·0014 at pH5 (Fig. 2). This gives a relation extending over about a 106 range in effectivesolution concentration. The figure shows the gentle curvature of the compositelog–log plots. This curvature is reproduced in the figure by a model (Barrow 1987)based on the 3 laws. In this particular application, the second law is important,that is, the shape of the sorption curves is strongly affected by heterogeneity.The way it explains the steeper curves for selenate and selenite is illuminating.


They occur because the affinity for adsorption is low and only a small part ofthe distribution of sites is occupied. As the amount of sorption becomes verysmall, the Langmuir requirements are approached: the occupied sites are closeto uniform and the change in electric potential with increasing sorption is small.Furthermore, when the product of the affinity term and the concentration issmall, the denominator of Eqn 2 approaches unity. Hence, adsorption is close tolinearly related to concentration at low amounts of sorption. Thus the modelencompasses the whole range of observations.

10

1

0.1

0.01

Ani

on s

orbe

d (µ

mol

/g s

oil)

1

1

1

0.049

0.046

0.059

0.0014

0.00076

0.0012

5

6

7

pH Se (IV) Se (VI)P

0.001 0.01 0.1 1 10 100

'Equivalent' concentration (µmol/L)

Fig. 2. Sorption of phosphate, selenite (Se(IV)), and selenate (Se(VI)) at pH 5, 6, and 7plotted on common axes. The concentrations have been multiplied by the values in the tableto give ‘equivalent’ concentrations. Thus, at pH 5, the value for phosphate is 1, for selenite0 ·049, and for selenate 0 ·0014. (From Barrow and Whelan 1989a).

As the figure shows, the assumption of heterogeneity also reproduces the gentlecurvature of the remainder of the very large range of effective concentrations.Thus the assumption of heterogeneity can explain important aspects of thereaction of ions with soil.

The effects of period of reaction on sorption.

Much chemical thinking is dominated by equilibria and there is a desire tomeasure sorption at equilibrium, so much so that the word ‘equilibrate’ is widelyused to describe mixing of soil with a reactant. However, it is wiser to takeit as a general rule that reactions with soil continue for a very long time sothat a measure of sorption after a given period is merely one possible measure.Rather than thinking of a sorption curve, we should think of a sorption ‘surface’with time as the extra dimension. A sorption curve measured at a given time ismerely one of many possible curves which together make the surface.

804 N. J. Barrow

Farmers have, of course, been aware of the continuing reaction for a verylong time. It is one of the important reasons why they re-apply fertilisers.Because the rate of the reaction affects the need to re-fertilise, it is important tocharacterise it. The rate of any reaction may be followed by measuring eitherthe disappearance of the reactants or the accumulation of the products. Forreactions with soil, it is obviously easier to measure the rate of disappearance ofthe reactant. Two kinds of methods are possible.

In one method, a small amount of soil is mixed with a large volume of solutioncontaining the reactant and, at various times, the concentration remaining insolution is measured. The advantages are that good mixing is obtained and itis easy to separate soil and solution to measure the solution concentration. Thedisadvantages are that too vigorous mixing can cause breakdown of soil particlesand give spurious results (Barrow and Shaw 1979), and it is often inconvenientto continue for periods of months, or years, that are relevant to agriculture.

In the other kind of method, soil is mixed with just sufficient solutioncontaining the reactant to bring the moisture content to near the field watercontent and the mixture is incubated for various periods. The advantages arethat conditions are closer to those of agriculture; little space is required and soincubation can continue for as long as desired; and it is easy to incubate at arange of temperatures. Like most reactions, the rate is increased by increasingthe temperature and, by using moderate temperatures, the equivalent of ratherlong periods at lower temperature can be achieved. The disadvantages are thatthe rate may be limited by lack of mixing and it is more difficult to measurethe remaining concentration in solution. Extraction procedures are undesirablebecause they involve desorption. We have used a ‘null-point’ method. Thisinvolves briefly mixing the soil with a series of solutions containing a range ofconcentrations of the reactant. Some will be too dilute and so desorption willoccur. Some will be too concentrated and so further sorption will occur. Thenull-point is the interpolated intermediate value at which neither sorption nordesorption occurs. For a fuller discussion of these points, see Barrow (1983b).

For many reactants, the rate of reaction can be described by including a termfor time in the Freundlich equation:

S = a1cb1tb2 (6)

The 3-dimensional surface described by this equation is a plane on a log scale.Like the Freundlich equation itself, it is a convenient summary of a set of datasince only 3 parameters are needed. While it has been frequently used to describereaction of phosphate with soil, it also applies to reaction of molybdate (Barrowand Shaw 1975a), fluoride (Barrow and Shaw 1977), selenite and selenate (Barrowand Whelan 1989b), and the cations zinc, cobalt, cadmium, and nickel (Barrow1998) with soils. It therefore describes a widespread phenomenon which occurswith both cations and anions. Indeed, Fig. 3 shows that results for zinc andfor selenite are quite similar. Nevertheless, there are important differences inrate between ions. For cations reacting with soil, the relative rates of reactionwere: cobalt, nickel > zinc À cadmium (Barrow 1998). It is inconvenient thatcadmium, which is unfortunately added as a contaminant of phosphate fertiliser,had little continuing reaction as it indicates that its residual effect would be


high. Presumably its behaviour is associated with its larger ion size. For anionsreacting with soil, the relative rates were: phosphate > selenite > molybdate >fluoride > selenate (Barrow and Whelan 1989b). As is shown in Fig. 4, theserates are correlated with a measure of the affinity of the ions for the surface.This suggests that ions which have a high affinity for the surface sites are ableto penetrate pores and so continue to react.

10

1.0

0.1

0.1 1.0 10 100

Sel

enite

sor

bed

(µm

ol/g

)

Selenite concentration (µM)

300

100

30

10

0.1 1 10

Zinc concentration (µg/mL))

0.01

Zin

c so

rbed

(µg

/g s

oil)

1 day

3 days

10 days

38 days

1 day

3 days

10 days

30 days

Fig. 3. Comparison of the effect of period of incubation at 25◦C for selenite andfor zinc on the relation between solution concentration and amount of sorption.The lines were obtained by fitting the model described in the text to this and toother data. (From Barrow and Whelan 1989b and Barrow 1986b.)

The continuing reaction also occurs with H+ ions. If acid or alkali are addedto a soil the pH does not instantly change to a new value. If alkali is added,the pH is initially raised but slowly decreases from its early high value. At the

806 N. J. Barrow

same time, the negative charge on the soil increases (Mora and Barrow 1996).This occurs because protons slowly move from the interior of the particles to thesurface and thence to the solution. Similarly, if acid is added the pH decreasesbut then slowly increases as protons move into the particles and the positivecharge increases. It should not surprise us that protons can move into or out ofsoil particles just as other ions can.

1

10-2

10-4

2 4 6Log of binding constant

Diff

usio

n te

rm D

(pe

r da

y)~

HPO42-

SeO42-

HMO4-

SeO32-

F-

Fig. 4. Relation between the diffusion term D which measures the relative rateof penetration of the adsorbed ion into the reacting particle and the bindingconstant which measures the relative chemical affinity for the surface. (FromBarrow and Whelan 1989b.)

The continuing reaction is the main reason for the use of the term ‘sorption’.There is much evidence that there is an initial adsorption reaction on the surfaceof the soil particles and that this is relatively rapid and reaches equilibriumwithin, at most, a matter of hours. This is then followed by a much slowerreaction, and hence the term sorption to encompass both reactions.

It should be fairly obvious that the third law is introduced to account forthe phenomenon of the continuing reaction. The law is framed in general termsso that the pathway for the continuing penetration is not specified and indeed,it is possible that it is different for different ions. As is shown in Fig. 3,and in several publications, a model built to include the third law describesthe observations well. Yet how can this be so if diffusion is assumed to beso slow so that the depth of penetration is small compared to the reactingarea? Under these conditions, the amount penetrated might be expected to beproportional to the square root of time, that is, time raised to the power 0 ·5.One reason why this is not the case is that the square root relation should only beexpected if the source concentration were constant. As the diffusion proceeds, theconcentration in solution decreases. Consequently the concentration of adsorbedreactant decreases and as this is the driving concentration for the diffusion step,


diffusion slows. Nevertheless, Eqn 6 shows that, when the concentration is heldconstant, sorption is proportional to time raised to the power b2. The value ofthis term is always observed to be smaller than 0 ·5. There are 3 reasons for this.One is the assumption of heterogeneity of the second law. This gives rise to arange of surface concentrations and so to a range of rates which together sumto give a rate proportional to a lower power of time. A second reason might becalled ‘electrostatic drag’. As shown in the discussion of the first law, sorptionchanges the charge and therefore the value of Ψ. This, in turn, decreases theconcentration of adsorbed reactant and thus the rate of diffusion. The thirdreason is that we do not see the pure kinetics of diffusion. Diffusion is precededby an adsorption reaction. This takes the locus of the point describing theprogress of sorption to a particular position on a plot of log sorption versus logtime and subsequent movement cannot possibly show a slope of 0 ·5.

The effects of temperature on sorption.

If we accept that there is a relatively rapid adsorption reaction followed by aslower reaction, temperature can have separate effects on the separate reactions.As the adsorption reaction is fairly rapid, the effects of temperature are mainlyseen on the position of its equilibrium, rather than on its rate. The adsorptionreaction involves ions reacting with charged surfaces. There can be effects oftemperature on the electric potential of the surface; on the ions in solution; andon the constant describing the affinity of the ions for the surface. The magnitude,and even the direction of the effects, can vary according to the reactants. Thisis discussed further by Barrow (1992a).

In contrast, the effects of temperature on the slow reaction are mainly on itsrate. They are much simpler: increasing temperature increases the rate. TheArrhenius equation may be used to relate the rate coefficient (k) of a reactionto temperature:

k = A exp(−E/RT ) (7)

where E is the activation energy and A is a constant. Modifying Eqn 6 toinclude this gives:

S = a2cb1 (exp(−E/RT )t)b2 (8)

The exponential term is included in the bracket raised to the power b2 becausethe rate is thought to be limited by a diffusion process. With this formulation,the value of the activation energy appropriate to the pragmatic description asin Eqn 8 is the same as that for the mechanistic model built on the three laws.The value of the activation energy E can be an important clue to the mechanismof a reaction. For most reactants with soil it has been found to be about 80–100kJ/mol (Barrow and Whelan 1989b; Barrow 1998). This is a measure of theheight of the energy barrier involved in each ion movement. Its magnitude isconsistent with the energy required for an ion to jump from one sorption sitein a pore to an adjacent site. It is also an indication of the acceleration to beachieved by increasing the temperature. If E is 80 kJ/mol, the rate at 60◦C is91 times that at 15◦C and 4 days at 60◦C is equivalent to a year at 15◦C. By

808 N. J. Barrow

using moderate temperatures it is therefore possible to simulate in the laboratorythe equivalent of much longer periods at field temperature. This is an importanttool for studies on the long-term availability of nutrients.

The interaction between pH and salt concentration.

It is impractical to discuss the effects of pH on reaction without initiallydiscussing the interactions between pH and the concentration of the solution inwhich measurements are made. These interactions are caused by the first law,and are strong evidence for that law. The interactions between pH and saltoccur because there is an initial adsorption reaction of ions on a variable chargesurface. An increase in salt concentration increases the number of counter ionsclose to the surface and therefore changes the way that electric potential changesas we move away from the surface. At any particular distance, that is, for agiven plane of adsorption, it decreases the absolute value of the electric potential.For example, when reaction is with a negatively charged surface, the potentialbecomes less negative and sorption of anions increases. A convenient, though lessprecise, way of thinking about this is that an increase in the cation concentrationnear a negatively charged surface makes it easier for anions to react with thesurface. The corollary is, when increasing salt concentration increases sorptionof anions, the reacting surface must be negatively charged.

An extension of this argument is involved when we compare salts of differentcations, say sodium chloride versus calcium chloride. It is often found thatsorption of anions such as phosphate or sulfate is greater from solutions of calciumsalts. There are probably two effects involved. One is the apparent preference ofnegatively charged sites for cations of higher valency. The other is the smallertendency for calcium ions to retain their hydration shell and therefore for alarger portion to reside closer to the surface. Both effects would be importantwhen sorption of phosphate is onto negatively charged sites. However, sorptionof sulfate was found to be greater from solutions of a calcium salt than from asodium salt at low pH and under conditions for which the reacting surfaces werepositively charged (Courchesne 1991). This suggests that the lower tendency toretain their hydration shell permits calcium ions to approach the sites of sulfateadsorption and so confers some specificity.

By a similar argument, when sorption of anions is decreased by an increasein salt concentration, the reacting surface is positively charged. The results inFig. 5 therefore show that reaction of borate, selenite, and phosphate was witha negative surface at medium to high pH and with a positive surface at low pH,that is, all three nutrients reacted with a variable charge surface.

If the surface is positively charged at low pH and negatively charged atmedium to high pH, it follows that there must be a point of zero charge. It isreasonable to associate this with the observed points of zero salt effect (Fig. 5).However, it is more appropriate to speak of a point of zero mean potential inthe adsorption plane. This is the mean potential of the occupied sites not of thewhole soil. Close inspection of Fig. 5 will show that this point occurred at adifferent pH for each reactant. Furthermore, the smaller the amount of sorption,the higher the pH at which it occurs. This is true for different reactants withdiffering affinities for the surface and therefore different amounts of sorption atthe same solution concentration (Fig. 5) and for the one reactant at different


concentrations (Fig. 6). All of these values for the point of zero salt effect arehigher than the value for the point of zero salt effect on the charge on the soil.For the soil represented in Figs 5 and 6, this was at about pH 4 ·2. Similarresults have been obtained for other soils by Bolan et al . (1986).

1.0 M NaCl

0.1 M NaCl

0.01 M NaCl

10

1.0

0.1

Sor

ptio

n (µ

mol

/g s

oil)

4 6 8pH

Phosphate

Selenite

Borate

Fig. 5. Comparison of the effects of pH and of background electrolyte concentration on thesorption of phosphate, selenite, and borate by a soil. In each case, sorption was measured ata solution concentration of 100 µM. The lines were fitted to the data using the mechanisticmodel described in the text. (From Barrow 1989a).

These observations are crucial evidence for the second law. Imagine that asoil is exposed to a very low concentration of phosphate or a slightly higherconcentration of selenite. The concentrations we are imagining are so low thatonly a small amount of sorption can occur. The adsorbed ions, having ‘firstchoice’, will choose the most favourable sites. If we accept heterogeneity of

810 N. J. Barrow

1.0 M NaCl

0.1 M NaCl

0.01 M NaCl

10

1.0

0.1

Sel

enite

sor

bed

(µm

ol/g

soi

l)

0.1

1

100

0.01

Sol

utio

n co

ncen

trat

ion

of S

e (µ

mol

/L)

4 6 8

pH

Fig. 6. Effect of pH and of concentration of sodium chloride on the sorption of seleniteat the indicated solution concentrations. The lines were fitted to the data using themechanistic model described in the text. (From Barrow and Whelan 1989a.)

electric potential, these are the sites from the most-positive (or least negative)tail of the distribution. The mean potential of these occupied sites will only bezero if the pH is raised to a fairly high value and certainly to a higher value thanthat required for all of the sites to have zero mean potential. That is, the pointof zero salt effect on sorption is higher than the point of zero charge. Imaginenow that the concentration of the reactants is increased. The most positive tailis already occupied so reaction has to spread to less favourable sites with less


positive potential. Furthermore, sorption itself will decrease the potential. Wedo not need to raise the pH quite as far for the mean potential of the occupiedsites to be zero. The argument can be continued to increasing concentrations.The effects are not linear (Fig. 7). They decrease as the amount of sorptionincreases. This is because, as we increase the amount of sorption, we move tofatter parts of the distribution curve and so more reaction is required to producea given effect. Thus, these observations provide strong support for the idea thatthe heterogeneity encapsulated in the second law involves heterogeneity of electricpotential. To summarise, the smaller the amount of sorption, whether caused byvery low solution concentrations or by low affinity of the ion for the adsorbingsurfaces, the higher will be the point of zero salt effect on sorption.

6.5

6.0

5.5

5.0

App

roxi

mat

e po

int o

f zer

o sa

lt ef

fect

0 1 32

Anion sorbed (µmol/g soil)

Selenite

Phosphate

Fig. 7. Relation between the amount of sorbed selenate or phosphate and the approximatepoint of zero salt effect. The point of zero salt effect on pH was about pH 4 ·2. (From Barrowand Whelan 1989a.)

As indicated earlier, for soils, increasing the salt concentration decreases thesorption of cations. Fig. 8 shows this effect when perchlorate was used asthe background electrolyte thus decreasing problems of interpretation caused byformation of complexes such as occur when chloride salts are used. In contrastto the results with anions, no point of zero salt effect was observed. This is tobe expected from an extension of the heterogeneity argument. If such a pointdid exist, it would be at a pH below the point of zero salt effect on pH, that is,for this soil, below pH 4 ·2. At such a low pH there is little metal adsorptionand therefore any such point of zero salt effect cannot be observed.

Explaining the effects of pH on sorption: anions

The effects of pH on sorption of the different nutrients may seem bewilderingin their diversity. Yet all can be consistently explained by the first law. Again,

812 N. J. Barrow

the factors which matter are the ions present in the solution phase and thechange in the potential of the surface with changes in pH. The change in potentialwith change in pH is affected by the size of the ions, or, more precisely, by themean position of the charge on the adsorbed ions. The ions of concern rangefrom small ions such as F− to larger oxy-anions such as selenate. We couldsimply assume that the charge on such ions might be sited at different meandistances from the surface. That is, we could allocate a mean position to thischarge. Or we could follow the more sophisticated arguments of Hiemstra andVan Riemsdijk (1996) who have proposed that the charge on the adsorbed ionis distributed between two planes, one close to the surface, one a little furtheraway. The presence of the O atoms in ions such as selenate means that a largerproportion of the charge is allocated to the outer plane and hence the meanposition of the charge is further from the surface than that for fluoride. Theoutcome is thus similar in that the mean position of the charge differs.

10

1

0.1

10

1

0.1

10

1

0.1

10

1

0.10.01 M0.1 M

Cd Zn

Ni Co

4 5 76 4 5 76

pH

Met

al s

orbe

d (µ

mol

/g)

4 5 76 4 5 76

Fig. 8. Effect of pH and the indicated concentrations of sodium perchlorate on the sorptionof four cations at a solution concentration of 20 µM. (From Barrow and Whelan 1998.)

Before considering the ions in detail, we need to note that Manceau andCharlet (1994) concluded that selenate, sulfate, phosphate, selenite, and arsenateall formed bidentate, inner-sphere complexes with the surface. That is, therewere direct chemical links to the surface atoms via two of the oxygen atoms.Consider now the most controversial of all reactants, phosphate, and supposethat the reaction pathway for phosphate is an initial dissociation of monovalentions to give divalent ones and H+, with the dissociation constant k2, and thatthe divalent ions then react with the surface to give a bidentate linkage. It can


be shown that α2 = α1k2/H+ where the subscripts to α refer to divalent andmonovalent ions. Then the use of the divalent ion in Eqn 4, that is, K 2 α2 hasthe same effect as using K 2 k2 α1/H+ and thus of describing both steps. Nowsuppose the reaction path is different, say reaction of monovalent ions with thesurface followed by dissociation of the adsorbed phosphate and formation of abidentate link. There will then be a different set of reaction constants to describethe position of the equilibrium. However, no matter which pathway we postulate,as long as the reactants and result of the reaction remain the same, the productsof the reaction constants must be equal to K 2 α2 and to K 2 k2 α1/H+. Thus,when a reactant forms a bidentate link to the surface, it is appropriate to referto the divalent ion in solution.

1000

300

100

30

10

Flu

orid

e re

tain

ed (

µg/g

soi

l)

4 5 6 7 5 6 7

1000

300

100

30

3000

pH

(a)(b)

Fig. 9. Effect of pH on the sorption of fluoride by a soil. In the left hand graph, fluoridesorption by a soil is plotted at the following total concentrations (µg/mL) of fluoride insolution: m, 10; ▲, 1; v, 0 ·1. In the right hand graph sorption is plotted at the followingconcentration (µg/mL) of the free fluoride ion: m, 10; ▲, 1; v, 0 ·1. (From Barrow and Ellis1986a.)

Consider now some important anions starting with fluoride. As indicatedearlier, the pK1 of hydrofluoric acid is below the range of soil pH and it might beexpected that the main fluoride species present would be F−. However, fluorideforms strong bonds with aluminium. In the presence of an aluminium oxide,or of soil, below about pH 5 ·5 most of the fluoride in solution is present ascomplexes with aluminium. The other important property of the fluoride ionis that it is about the same size as an hydroxyl ion. It can therefore replacea surface hydroxyl so that its adsorption plane is very close to the surface.Consequently it experiences a marked change in electric potential with changein pH. Thus, in the presence of a source of aluminium, fluoride sorption at agiven total concentration of F in solution increases up to about pH 5 ·5 and thendecreases (Fig. 9a). In the absence of a source of aluminium, or if one calculatesit in terms of free fluoride ions, fluoride sorption decreases with increasing pH(Fig. 9b).

814 N. J. Barrow

Selenate (and sulfate) are also fully dissociated at soil pH values. There istherefore little change in the ion species present in solution with change of pH.However, both differ from fluoride in that the mean adsorption plane is somewhatfurther from the surface. Using the terminology of Hiemstra and Van Riemsdijk(1996), the oxygen atoms cause a large proportion of the charge to be distributedto a plane some distance from the surface. Hence they do not experience sucha large change in electric potential with increasing pH. Further, complexes withaluminium are not as strong. The net effect is a fairly steep decrease in sorptionwith increasing pH (Fig. 10).

0.01 M CaCl20.01 M NaCl

10

1.0

0.1

Sel

enat

e so

rbed

(µm

ol/g

soi

l)

1

100

0.01

Sol

utio

n co

ncen

trat

ion

of S

e (µ

mol

/L)

4 6 8

pH

Fig. 10. Effect of pH and of background electrolyte concentration on sorption of selenate bya soil. The lines were fitted to the data using the model described in the text. (From Barrowand Whelan 1989a.)

Boric acid is fairly weak with its pK1 at about 9. Therefore, in the normalrange of soil pH, the proportion present as the monovalent borate ion (the αterm of Eqn 4) increases 10-fold for a unit increase in pH. The effects of pH on


electric potential and on dissociation therefore oppose each other: the increasinglynegative electric potential favours decreasing adsorption, the increasing α termfavours increased adsorption. Because the ion is monovalent and z i is thereforeunity, the effects of the product z i Ψ within the exponential term of Eqn 4 arenot quite large enough to exceed the effects of the increasing value of the αterm. Sorption therefore increases with increasing pH (Fig. 5).

Selenious acid is a diprotic acid with pK1 at 2 ·7 and pK2 at 8 ·5 in verydilute solution. Hence, in the range of soil pH values, there are two main speciespresent: HSeO−3 and SeO2−

3 (Fig. 1). As is consistent with the formation ofbidentate links to the surface, the effects of pH can be explained by consideringthe divalent ion. We can argue that, because the selenite ion is smaller thanselenate, the mean position of the charge is closer to the surface; or we can arguethat, because it has one fewer O atom, rather more of the charge is distributedto the surface. The outcome is the same: a large decrease in potential withincreasing pH. Furthermore, because the ion is divalent, −z i is 2. The effects ofthe product z i Ψ within the exponential term of Eqn 4 are therefore greater thanfor borate. Like the borate ion, the proportion of the selenite present as SeO2−

3

increases 10-fold for each unit increase in pH, up to about pH 7 ·5. However,this is not sufficient to overcome the effects of the change in electric potentialand sorption decreases (Fig. 5).

The pK1 and pK2 for molybdic acid are close together and below the normalrange of soil pH. Above about pH 5, the concentration of HMoO−4 thereforedecreases 10-fold with a unit increase in pH whereas the concentration of MoO2−

4

increases to be the dominant ion. Interpretation of experiments on molybdatesorption are complicated by the probability that surface polymers form at low pHand moderate molybdate concentration. Nevertheless, it was shown by Barrow(1989b) that competition between molybdate and either arsenate or phosphatecould be described by assuming that the HMoO−4 ion was important in sorption atleast at low concentrations of molybdate. Furthermore, McKenzie (1983) showedthat molybdate sorption by goethite was, on a molar basis, more than twice aslarge as that of phosphate and this would indicate that a monodentate link tothe surface is formed. The more rapid decline in sorption with increasing pHthan occurs for sulfate (Barrow 1970) also suggests that it is necessary to invokethe decreasing concentration of the HMoO−4 ion with increasing pH. Thus, formolybdate, the effects of electric potential and the effects of dissociation workin the same direction, rather than opposing each other. The result is a largedecease in sorption with increasing pH.

The behaviour of phosphate has been delayed because it is important to seeit in the context of the other reactants, rather than to invent special theoriesfor it. Phosphoric acid is triprotic but the third dissociation is well beyond therange of soil pH. The species present in soil solutions are therefore H2PO−4 andHPO2−

4 . Because phosphate forms bidentate links to the surface, the divalention appears to dominate sorption. Its proportion in solution increases 10-foldfor each unit increase in pH up to just below the pK2, which is about 7in a soil solution. Fig. 5 shows that the behaviour of phosphate is similarto that of selenite, and the explanation is analogous. Thus, when phosphatesorption is seen in the context of the other reactants, its behaviour is easy tocomprehend.

816 N. J. Barrow

At last we are in a position to answer at least part of Professor Leeper’s questionabout arsenic. We would expect arsenate sorption to behave like phosphate andthus to decrease gently with increasing pH and arsenite sorption to behave likeborate and to increase gently. This is just what has been observed by Manningand Goldberg (1997).

Explaining the effects of pH on sorption: cations

As indicated earlier, the divalent ions of copper, zinc, cobalt, nickel, cadmium,manganese, and mercury hydrolyse to varying extents. It has been found that,the greater the tendency to hydrolyse, the greater the affinity for the surfacesites on oxides (Dzombak and Morel 1990). We can view this in two ways. Wecan argue that disturbance caused by hydrolysis of the octahedral group of watermolecules surrounding the ions increases the probability that a collision with asurface site will result in a reaction product. That is, ions which are prone tohydrolyse have a large value for the binding constant. Alternatively, we can viewthe hydrolysis as an association with hydroxyl ions:

M2+ + OH−−→←−MOH+

As the link to the surface site is also via an O atom, molecules with a large affinityfor hydroxyl would be expected to have a large affinity for the surface sites.These two views are thus merely two ways of describing the same phenomenon.

Similarly, there are two ways of looking at the effects of pH on individual ions.These hinge on whether the adsorbed ion is considered to be present as bound toone or to two surface sites. If it is bound to one site, the mean centre of chargeis not very close to that of the surface and so the change of electrical potentialwith changing pH is not very great. However, the concentration of the reactingmonovalent ion increases 10-fold per unit increase in pH. These effects are in thesame direction and so there is a large increase in sorption with increasing pH.If, on the other hand, the reacting ion is bound to two surface sites, the meancentre of charge is closer to the surface. There is therefore a greater change inelectric potential with increasing pH and, because the adsorbed ion is divalent,this effect is sufficient to explain the increase in sorption with increasing pH. Formuch sorption data it is difficult to discriminate between these two explanations.However, if it is observed that the effects of changing pH are <10-fold for unitchange in pH, the explanation involving monovalent sorption is excluded.

When sorption of cations on metal oxides is measured, the effects are usuallygreater than 10-fold. Barrow and Whelan (1998) recently measured the effects ofpH on the concentration of metal ions required to produce equal sorption on ironoxides. The effects of a unit increase in pH ranged from 35-fold for zinc to 11-foldfor cadmium. The effects for soil were much smaller: about 10-fold for zinc,about 7-fold for nickel, about 6-fold for cobalt, and about 4-fold for cadmium.These results are important in that they show that conclusions about the effectsof pH on sorption obtained from studies on pure substances may not be directlyapplicable to soil. They can be explained by assuming that divalent ions reactwith variable charge surfaces but that the change in electric potential of thereacting surfaces with change in pH is smaller for soil than for goethite. This isquite feasible. If the reacting surfaces were on oxides, one merely has to assume


that they are ‘contaminated’ to some extent with silicate or even phosphate.This will produce a smaller change in electric potential with change in pH.

The smaller effect of pH on cadmium is consistent with its larger ion size.This would mean that its mean plane of adsorption was slightly further fromthe surface and therefore experienced a smaller change in electric potential withchange in pK than the other cations.

Laboratory measurements of the effects of pH on sorption are far from thecomplete story. Greater interest is in the effects of pH on uptake by plants,which appears to be smaller still. Increasing the pH by one unit caused onlya 1 ·4-fold increase in the of amount zinc or cobalt fertiliser required for equaluptake, that is, a 1 ·4-fold decrease in fertiliser effectiveness (Barrow and Whelan1998). The small effect occurs because increasing pH increases the uptake ofmetals by plants. This has been shown in solution culture for zinc by Chaudhryand Loneragan (1972), for manganese by Robson and Loneragan (1970), and forcadmium by Hatch et al . (1988). It has been considered as an effect of hydrogenions competing with metal ions for uptake, but it may be profitable to considerit as an effect of pH on the electric potential of the surface of the root. In thiscase, it is apparent that the effects of pH on sorption and the effects on uptakemust tend to counterbalance each other.

Because the chemistry of mercury differs from the micronutrient metals, itprovides an informative contrast. As indicated earlier, it is a somewhat strongeracid with pK1 and pK2 both near 3. Because the two pKs are so close, theconcentration of divalent Hg2+ ions decreases almost 100-fold for a unit increasein pH. Similarly, this is opposed by the decrease in electric potential which, ofcourse, favours adsorption of cations. The outcome of these opposing influencesis a slight decrease in sorption with increasing pH. Chloride ions have a strongaffinity for mercury and form complexes especially at low pH. As a result, inthe presence of chloride, the concentration of the free mercury ions, and theamount of mercury sorption, often increase with increasing pH. In soil, sorptionof mercury is even more complicated because mercury forms complexes withsubstances in solution giving sigmoid sorption curves (Barrow and Cox 1992a).

The interaction between the first and third laws, the fourth law

If charged particles react with charged surfaces and this is followed by diffusivepenetration into the particle, an important question is: what happens to thecharge and what are the consequent effects on the potential of the surface? Theanswer is, the electric potential of the surface is changed. This must affectany new adsorption reaction, and indeed any desorption. This leads us to thefourth law which may be expressed in ‘poetic’ terms as: it is impossible to applyfertiliser to the same soil twice. It is impossible because the soil is now different.(By a similar argument, it is impossible to take two fish from the same river.)

Direct evidence for the fourth law comes from studies on macronutrientsbecause they are applied in sufficient quantities to have detectable effects. Theevidence comes from studies in which phosphate was added to soils and reactionwas permitted to continue for a long time. When sorption curves were thenobtained on the samples of reacted soil, the curves were of course displacedbecause of the extra phosphate present. But the slope of the curves at specificconcentrations was also decreased (Fig. 11). That is, the buffering capacity

818 N. J. Barrow

for new phosphate was decreased. These changes are followed through time inFig. 12. In this figure, sorption is plotted against solution concentration raisedto the power 0 ·4. This plot was chosen because a Freundlich equation (Eqn 5)with a power term of 0 ·4 described the results. Plotting on this scale thereforelinearised the equation. Furthermore, in this method of plotting, the slope ofthe lines gives an visual indication of the value of the linear term, a in Eqn5, whereas an extrapolation of the plot gives an indication of the amount ofphosphate which could be desorbed if the concentration were decreased to zero.Fig. 12 thus shows that, after brief incubation with phosphate, a large proportionof the added phosphate was desorbable and the slope of the line was relativelysteep. As the period of incubation (or the temperature) increased, the amountof desorbable phosphate decreased and the slope of the lines also decreased. Iinterpret this as showing that, as phosphate penetrated the particles, it becameincreasingly difficult to desorb it because it was more deeply buried. At the same

1000

500

0

Cha

nge

in s

orbe

d ph

osph

ate

(µg/

g so

il)

0 2.0 4.0 6.0Phosphate concentration in solution (µg P/mL)

Phosphate addedbefore incubation

(µg P/g soil)

0

300

400

600

800

1200

Fig. 11. Effect of prior incubation of a soil at 25◦C for a year with the indicated levels ofaddition of phosphate on the subsequent sorption of phosphate. (From Barrow 1974.)


time, the electric potential of the surface became more negative thus decreasingthe slope of the line and so decreasing the ability to sorb more phosphate.

Further evidence for the fourth law comes from studies of competition forsorption between ions. The ‘standard’ or ‘pre fourth law’ way of describingcompetition was to postulate that two ions merely compete for the same sites.

2500

2000

1500

1000

Pho

spha

te r

etai

ned

(µg

P/g

soi

l)

0 1.0 5.0 10.0 15.0

Phosphate concentration in solution (µg P/mL)

39 days, 42oC

22 days, 25oC

1 day, 25oC

1 h, 25oC

Fig. 12. Values for phosphate sorption and desorption after a soil of high phosphate bufferinghad been incubated with 1500 µg P/g for the indicated periods and temperatures. Thehorizontal scale is concentration raised to the power 0 ·4 (From Barrow 1983a.)

This is described by a form of the Langmuir equation modified to accountfor the decrease in the number of available sites caused by reaction with thecompeting ion. If this mode of competition were important, its effects should beprominent in the early stages of the process when the two ions were competingfor adsorption sites and before much penetration of the particle has occurred.However, as Fig. 13 shows, competition between selenite and phosphate wasleast marked at this stage. Competition became more marked as the reactionproceeded, that is, as both ions penetrated the particles and thereby changed

820 N. J. Barrow

the surface electric potential. As this was more marked for phosphate than forselenite, the competitive advantage was increasingly to phosphate. This meansthat ‘electrical’ competition, competition via the changes in electric potential,was more important than the standard competition for adsorption sites.

1.0

0.8

0.6

0.4

0.2

0

Sub

sequ

ent m

olar

rat

io, P

/(P

+ S

e)

0.2 0.4 0.6 0.8 1.0

Initial molar ratio, P/(P + Se)

0

Fig. 13. Observed and modelled changes through time in the competitionbetween phosphate and selenite for sorption by a soil. If the anions wereequally effective competitors, the points would fall along the diagonal line.The further the points fall below the diagonal line, the more effectivephosphate was as a competitor. The times (h) were as follows: V, 0 ·25;v, 4; 4, 24; ▲, 96; M, 720. (From Barrow 1992b.)

Such results call into question simplistic contrasts between permanent chargeand variable charge in soils. Permanent charge is commonly associated with thepresence of the ‘wrong’ ions in the lattice of clay minerals; variable charge withchanges in charge on the surface caused by the presence of potential-determiningions such as H+ or phosphate. However, changes in the surface concentrationof specifically adsorbed ions induce slow penetration of the ions and consequentchanges in the surface electric potential. The penetration can be reversed (seelater) but this is also a slow process. Hence, rather than two kinds of charge,there is a continuum from charge which can be rapidly changed to charge whichcan be only very slowly changed.


Practical importance of the fourth law

The fourth law seems esoteric: surely of no practical importance? Yet it isimportant in at least two contexts. One is in the residual value of phosphatefertiliser. Bolland and Baker (1998) reapplied phosphate to soil samples thathad received heavy applications 20 years earlier. The projection of the responsecurves (Fig. 14) back to the horizontal axis showed that there was little phosphatecoming from the original application. However, the response to newly appliedphosphate was much steeper where phosphate had previously been applied. Inother words, the period of reaction was so large that the previously appliedphosphate was no longer available yet its reaction with the soil had increasedthe effectiveness of newly applied phosphate. This is an effect that must occurwith all applications of phosphate but which has not previously been recognised.

6

5

4

3

2

1

0

Yie

ld (

g/po

t)

0 0.05 0.1 0.2 0.4 1.0 2.0Fresh phosphorus applied (g P/pot)

Fig. 14. Effect of phosphate applied 20 years earlier on the response of wheatshoots to newly applied phosphate. The original rates were: v, 20 kg/ha; ▼,86 kg/ha; and ▲, 599 kg/ha. Lines are fits to the Mitscherlich equation and areextended to the horizontal axis to indicate the amounts of P available from theoriginal application. (From Bolland and Baker 1998.)

The other practical application of the fourth law is in assessing the storagecapacity of a soil for phosphate. In such usages, phosphate is not added in onelarge dose, but rather as a continuing supply. It is not the ability of the soil tosorb phosphate in the short term that matters but its ability to continue to sorbphosphate. A simple way to measure this would be to incubate soil with several levelsof phosphate at a high temperature for a period of several days thereby simulatingseveral years of reaction. The criterion is then, at what level of added phosphatedoes the soil’s ability to sorb further additions of phosphate become inadequate.

The problems of isotopically exchangeable nutrient

A simple and attractive idea is that the availability of a nutrient can bemeasured by equilibrating the soil with a solution containing a radioactive isotopeof the ion and then measuring the amount of soil nutrient which is exchangeablewith the isotope. That may be so, but there are two problems in interpretingthe results of such a study.

822 N. J. Barrow

One is connected with the assumption that exchange has occurred, that isthat the labelled ions have indeed exchanged with ions sorbed onto sites on thesoil surface. Why should they not react more rapidly with vacant sites andthen continue to react by penetrating the surface? This assumption was foundto closely describe the reaction of labelled P with a soil (Barrow 1991). Thiswork also explored the conditions under which the labelled ions might react morerapidly with occupied sites than with vacant ones and so true exchange mightoccur. These details will not be presented here.

The other problem is tied in with the use of the word ‘equilibrating’. In thestrict sense, it is impossible to measure an amount of isotopically exchangeablesubstance unless equilibrium has indeed been reached. As was indicated earlier,this is seldom achieved and certainly not within the relatively short periods usedin most experiments. The way this problem is usually circumvented is to assumethat the added isotope has come to equilibrium with part of the nutrient andso the measurement is of the amount of nutrient which is exchangeable withinthe chosen period. In reality, the labelled ions may have reacted in parallel withthe ions already present in the soil and one measures the proportion which havecome to a similar stage of penetration. The effect is, of course, similar. However,the problem with this approach is that it involves imposing arbitrary divisionsaccording to the period required for a supposed ‘fraction’ to exchange, divisionswhich are not really there.

To visualise the problem, imagine that we are standing at the top of a verylong shallow slope which becomes less steep but which never has zero slope. Atsome given time, we start a ball rolling down this slope, that is, we apply somefertiliser. At some subsequent time, we start another identical ball down thesame slope. Soon after the second ball is started, the distance between the twowill be relatively large. With increasing time the distance will become relativelysmall, but the second ball will never quite catch the first. The relative distancescovered by the two balls gives a mental picture of the exchangeability of thenutrient. This picture is somewhat different from that obtained by imaginingthat part of the nutrient is isotopically exchangeable. Exchangeability will onlybe high when the second ball has had the opportunity to progress almost as faras the first ball.

The ‘problem’ of desorption

The purpose of measuring sorption of nutrients by soils is often to estimatethe effects on availability to plants or the possibility of leaching losses. However,both these processes involve desorption. The relevance of sorption measurementsto desorption came into question when it was reported that desorption did notseem to follow the same track as ‘ad’-sorption (Kafkafi et al . 1967; Nagarajahet al . 1968). Consequently, it was often said that ‘adsorption was irreversible’.This is nonsense, an oxymoron. The usual meaning of the term irreversible isthat a reaction goes to completion and that there is virtually no back reaction.The classical example of an irreversible reaction is the oxidation of hydrogen towater. Fortunately, there is little spontaneous decomposition of water into itselements! In contrast, the essence of adsorption is that the reaction does not goto completion; there is a back reaction. If this were not so, there could not beany material left in solution and sorption curves could not be drawn. Hence,


if the desorption curves do not follow the same track as sorption curves, thenthe reaction was not limited to adsorption. Something else must have occurred.This is why I prefer to use ‘sorption’ to describe the process.

2000

1500

1000

500

0

Pho

spha

te r

etai

ned

(µg

P/g

soi

l)

0 2 4 6 8 10

Phosphate concentration in solution (µg P/mL)

2000

1000

0 0 2 4 6

10 days 3 days 1 day

1 h

Fig. 15. Desorption and further sorption of phosphate by a soil. Phosphate had beenincubated with the soil at 500, 1000, 1500, and 2000 µg P/g for 7 days at 60◦C. Desorptionwas measured on subsamples of the treated soil using a range of solution : soil ratios, andfurther sorption was measured at a constant ratio using differing initial concentrations of P.Periods involved in this measurement were 1 h, 1 day, 3 days, and 10 days. The main graphshows results after 10 days. Open symbols indicate sorption, closed symbols desorption. Thebroken line joins interpolated points at which neither sorption nor desorption occurred. Theinset shows the position of these ‘null-points’ at other times. (From Barrow 1983c.)

We now know that the ‘something else’ is the slow diffusive penetration whichfollows adsorption: the third law. Let us now explore some of the consequences.As indicated earlier, rather than measuring sorption curves, we could measuresorption surfaces, with period of reaction as the third dimension. A particularpoint on that surface may be reached by some particular combination of amountof reactant added and period of reaction. If the concentration of reactant ischanged, the point will then move across the surface. If the concentration isincreased, the point will move in one direction; if it is decreased it will movein the opposite direction. Fig. 15 shows that these movements are symmetrical:desorption and new sorption follow a common line. This is also shown by Fig. 12.Thus, if the correct comparison is made, the ‘problem’ of desorption disappears.In other words, the amount of desorption follows from and is determined by the

824 N. J. Barrow

prior sorption reaction. Indeed, it was reported as early as 1975 that indexes ofdesorption on a range of soils were highly correlated with indexes of sorption(Barrow and Shaw 1975b). And this is why measurements of sorption, whenproperly used, are indications of the supply to plants and of the possibility ofleaching losses.

600

400

200

0

Flu

orid

e re

tain

ed (

µg F

/g s

oil)

Fluoride concentration in solution (µg F/mL)

0.5 1.0 1.5

100

020 40 60

Time (h)

Flu

orid

e de

sorb

ed

300/1

60/1

Fig. 16. Desorption of fluoride. Fluoride had been incubated with the soil for 4 days at 80◦Cand desorption was then induced at a range of solution : soil ratios. Open circles indicatevalues for the null point concentration, closed circles the observed desorption after 40 h. Linesshow the outputs of a model which had been fitted to observations of the rate of the forwardsorption reaction (data not shown) and are therefore a prediction of the desorption reaction.The inset shows the modelled and observed rates of desorption at solution : soil ratios of 300 : 1and 60 : 1 for a 700 µg F/g level of addition. (From Barrow 1986a).

If the continuing reaction is caused by diffusive penetration into the surfaces,then for a given reactant, the longer the sorption reaction proceeds the slowerwill be the subsequent desorption reaction and the smaller the amount desorbedafter a given period. This is shown to be the case in Fig. 12. If the diffusivepenetration is modelled and then, within the model, the solution concentrationis changed, the observed desorption can be closely reproduced. This is shown forfluoride in Fig. 16. As a final test of these ideas, compare selenite and selenate.Selenite has a fairly well-marked continuing reaction and when desorption ismeasured, the desorption curve does not follow the sorption curve. In contrast,selenate has little continuing reaction and the desorption curve is much closer to


the sorption curve (Fig. 17). In both cases the observed desorption was closelypredicted by a model which incorporated diffusive penetration and which wasfitted to the effects of time on the sorption reaction.

3

2

1

00 5 10 15 0 5 10 15

0.075

0.05

0.025

0

Selenium concentration in solution (µM)

Sel

eniu

m s

orbe

d (µ

mol

/g)

(a) Selenite (b) Selenate

Fig. 17. Desorption and sorption of further (a) selenite and (b) selenate after incubationwith selenite or selenate respectively at the levels indicated by the arrows on the verticalaxes. The lines were derived from the model fitted to observations on the rate of sorption(data not shown) and are therefore a prediction of the desorption reaction. The broken linesindicate the modelled null-point concentration. (From Barrow and Whelan 1989b.)

Conclusions

The essence of this lecture is that there is indeed a diversity in the behaviourof the several reactants. Rather than be frightened by this diversity, we shouldbe challenged by it. This challenge can be met by the four laws of soil chemistrywhich are outlined here. The result is a very parsimonious description of thebehaviour which meets the criterion of William of Occham: it is futile to do withmore what could be done with less. This is an important criterion, but it isnot a sufficient one. A theory should also closely match observations, be basedon concepts of the mechanisms involved, be able to explain a wide diversity ofobservations, and be able to predict behaviour as yet unmeasured. In sum, itshould be efficient, effective, realistic, comprehensive, and predictive. I submitthat the theory outlined here meets these criteria.

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Manuscript received 30 November 1998, accepted 15 April 1999

the four laws of soil chemistry: the leeper lecture 1998

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