1.ChemistryModern Analytical ChemistryDavid Harvey DePauw UniversityBostonBurr Ridge, IL Dubuque, IA Madison, WI New York San Francisco St. Louis Bangkok Bogot Caracas Lisbon London MadridMexico City Milan New Delhi Seoul Singapore Sydney Taipei Toronto

2. McGraw-Hill Higher Education A Division of The McGraw-Hill CompaniesMODERN ANALYTICAL CHEMISTRYCopyright 2000 by The McGraw-Hill Companies, Inc. All rights reserved. Printed inthe United States of America. Except as permitted under the United States Copyright Act of1976, no part of this publication may be reproduced or distributed in any form or by anymeans, or stored in a data base or retrieval system, without the prior written permission of thepublisher.This book is printed on acid-free paper.1 2 3 4 5 6 7 8 9 0 KGP/KGP 0 9 8 7 6 5 4 3 2 1 0ISBN 0072375477Vice president and editorial director: Kevin T. KanePublisher: James M. SmithSponsoring editor: Kent A. PetersonEditorial assistant: Jennifer L. BensinkDevelopmental editor: Shirley R. OberbroecklingSenior marketing manager: Martin J. LangeSenior project manager: Jayne KleinProduction supervisor: Laura FullerCoordinator of freelance design: Michelle D. WhitakerSenior photo research coordinator: Lori HancockSenior supplement coordinator: Audrey A. ReiterCompositor: Shepherd, Inc.Typeface: 10/12 MinionPrinter: Quebecor Printing Book Group/KingsportFreelance cover/interior designer: Elise LansdonCover image: George Diebold/The Stock MarketPhoto research: Roberta Spieckerman AssociatesColorplates: Colorplates 16, 8, 10: David Harvey/Marilyn E. Culler, photographer;Colorplate 7: Richard Megna/Fundamental Photographs; Colorplate 9: Alfred Pasieka/SciencePhoto Library/Photo Researchers, Inc.; Colorplate 11: From H. Black, Environ. Sci. Technol.,1996, 30, 124A. Photos courtesy D. Pesiri and W. Tumas, Los Alamos National Laboratory;Colorplate 12: Courtesy of Hewlett-Packard Company; Colorplate 13: David Harvey.Library of Congress Cataloging-in-Publication DataHarvey, David, 1956Modern analytical chemistry / David Harvey. 1st ed.p. cm.Includes bibliographical references and index.ISBN 00723754771. Chemistry, Analytic. I. Title. QD75.2.H374 2000 543dc21 9915120CIPINTERNATIONAL EDITION ISBN 0071169539Copyright 2000. Exclusive rights by The McGraw-Hill Companies, Inc. for manufactureand export. This book cannot be re-exported from the country to which it is consigned byMcGraw-Hill. The International Edition is not available in North America.www.mhhe.com 3. ContentsContentsPreface xii 2C.5 Conservation of Electrons 232C.6 Using Conservation Principles inChapter 1 Stoichiometry Problems 232D Basic Equipment and Instrumentation 25 Introduction 1 2D.1 Instrumentation for Measuring Mass 251AWhat is Analytical Chemistry? 2 2D.2 Equipment for Measuring Volume 261BThe Analytical Perspective 52D.3 Equipment for Drying Samples 291CCommon Analytical Problems 82E Preparing Solutions 301DKey Terms 9 2E.1 Preparing Stock Solutions 301ESummary 9 2E.2 Preparing Solutions by Dilution 311FProblems 92F The Laboratory Notebook 321GSuggested Readings 10 2G Key Terms 321HReferences 10 2H Summary 332I Problems 33Chapter 2 2J Suggested Readings 342K References 34 Basic Tools of Analytical Chemistry 112A Numbers in Analytical Chemistry 12Chapter 32A.1 Fundamental Units of Measure 122A.2 Significant Figures 13The Language of Analytical Chemistry 352B Units for Expressing Concentration 153A Analysis, Determination, and Measurement362B.1 Molarity and Formality 153B Techniques, Methods, Procedures, and2B.2 Normality 16Protocols 362B.3 Molality 183C Classifying Analytical Techniques 372B.4 Weight, Volume, and Weight-to-Volume 3D Selecting an Analytical Method 38Ratios 18 3D.1 Accuracy 382B.5 Converting Between Concentration Units 183D.2 Precision 392B.6 p-Functions 19 3D.3 Sensitivity 392C Stoichiometric Calculations 20 3D.4 Selectivity 402C.1 Conservation of Mass 223D.5 Robustness and Ruggedness 422C.2 Conservation of Charge 223D.6 Scale of Operation 422C.3 Conservation of Protons 22 3D.7 Equipment, Time, and Cost 442C.4 Conservation of Electron Pairs 233D.8 Making the Final Choice 44iii 4. iv Modern Analytical Chemistry 3E Developing the Procedure 45 4E.4 Errors in Significance Testing 84 3E.1 Compensating for Interferences 45 4F Statistical Methods for Normal Distributions 85 3E.2 Calibration and Standardization 474F.1 Comparing X to 85 3E.3 Sampling 47 4F.2 Comparing s2 to 2 87 3E.4 Validation 47 4F.3 Comparing Two Sample Variances 88 3F Protocols 484F.4 Comparing Two Sample Means 88 3G The Importance of Analytical Methodology484F.5 Outliers 93 3H Key Terms 504G Detection Limits 95 3I Summary 504H Key Terms 96 3J Problems 51 4I Summary 96 3K Suggested Readings 52 4J Suggested Experiments 97 3L References 52 4K Problems 984L Suggested Readings 102Chapter 4 4M References 102 Evaluating Analytical Data 53 4A Characterizing Measurements and Results 54 Chapter 5 4A.1 Measures of Central Tendency 54 Calibrations, Standardizations, 4A.2 Measures of Spread 55 and Blank Corrections 104 4B Characterizing Experimental Errors 57 5A Calibrating Signals 105 4B.1 Accuracy 57 5B Standardizing Methods 106 4B.2 Precision 625B.1 Reagents Used as Standards 106 4B.3 Error and Uncertainty 645B.2 Single-Point versus Multiple-Point 4C Propagation of Uncertainty 64 Standardizations 108 4C.1 A Few Symbols 655B.3 External Standards 109 4C.2 Uncertainty When Adding or Subtracting 65 5B.4 Standard Additions 110 4C.3 Uncertainty When Multiplying or 5B.5 Internal Standards 115Dividing 66 5C Linear Regression and Calibration Curves 117 4C.4 Uncertainty for Mixed Operations 66 5C.1 Linear Regression of Straight-Line Calibration 4C.5 Uncertainty for Other MathematicalCurves 118Functions 675C.2 Unweighted Linear Regression with Errors 4C.6 Is Calculating Uncertainty Actually Useful? 68in y 119 4D The Distribution of Measurements and5C.3 Weighted Linear Regression with Errors Results 70 in y 124 4D.1 Populations and Samples 715C.4 Weighted Linear Regression with Errors 4D.2 Probability Distributions for Populations 71in Both x and y 127 4D.3 Confidence Intervals for Populations 75 5C.5 Curvilinear and Multivariate 4D.4 Probability Distributions for Samples 77Regression 127 4D.5 Confidence Intervals for Samples 80 5D Blank Corrections 128 4D.6 A Cautionary Statement 81 5E Key Terms 130 4E Statistical Analysis of Data 82 5F Summary 130 4E.1 Significance Testing 82 5G Suggested Experiments 130 4E.2 Constructing a Significance Test 83 5H Problems 131 4E.3 One-Tailed and Two-Tailed Significance5I Suggested Readings 133Tests 845J References 134 5. Contents vChapter 6Chapter7 Equilibrium Chemistry 135Obtaining and Preparing Samplesfor Analysis 179 6AReversible Reactions and Chemical Equilibria 136 7A The Importance of Sampling 180 6B Thermodynamics and Equilibrium7B Designing a Sampling Plan 182 Chemistry 1367B.1 Where to Sample the Target 6C Manipulating Equilibrium Constants 138 Population 182 6D Equilibrium Constants for Chemical7B.2 What Type of Sample to Collect 185 Reactions 1397B.3 How Much Sample to Collect 187 6D.1 Precipitation Reactions 139 7B.4 How Many Samples to Collect 191 6D.2 AcidBase Reactions 140 7B.5 Minimizing the Overall Variance 192 6D.3 Complexation Reactions 1447C Implementing the Sampling Plan 193 6D.4 OxidationReduction Reactions 145 7C.1 Solutions 193 6E Le Chteliers Principle 1487C.2 Gases 195 6F Ladder Diagrams 150 7C.3 Solids 196 6F.1 Ladder Diagrams for AcidBase Equilibria 1507D Separating the Analyte from 6F.2 Ladder Diagrams for ComplexationInterferents 201 Equilibria 153 7E General Theory of Separation 6F.3 Ladder Diagrams for OxidationReduction Efficiency 202 Equilibria 155 7F Classifying Separation Techniques 205 6G Solving Equilibrium Problems 1567F.1 Separations Based on Size 205 6G.1 A Simple Problem: Solubility of Pb(IO3)2 in 7F.2 Separations Based on Mass or Density 206 Water 1567F.3 Separations Based on Complexation 6G.2 A More Complex Problem: The Common Ion Reactions (Masking) 207 Effect 157 7F.4 Separations Based on a Change 6G.3 Systematic Approach to Solving Equilibrium of State 209 Problems 159 7F.5 Separations Based on a Partitioning Between 6G.4 pH of a Monoprotic Weak Acid 160 Phases 211 6G.5 pH of a Polyprotic Acid or Base 163 7G LiquidLiquid Extractions 215 6G.6 Effect of Complexation on Solubility 1657G.1 Partition Coefficients and Distribution 6H Buffer Solutions 167 Ratios 216 6H.1 Systematic Solution to Buffer 7G.2 LiquidLiquid Extraction with No Secondary Problems 168Reactions 216 6H.2 Representing Buffer Solutions with7G.3 LiquidLiquid Extractions Involving Ladder Diagrams 170 AcidBase Equilibria 219 6I Activity Effects 1717G.4 LiquidLiquid Extractions Involving Metal 6J Two Final Thoughts About Equilibrium Chelators 221 Chemistry 1757H Separation versus Preconcentration 223 6K Key Terms 175 7I Key Terms 224 6L Summary 175 7J Summary 224 6M Suggested Experiments 176 7K Suggested Experiments 225 6N Problems 1767L Problems 226 6O Suggested Readings 1787M Suggested Readings 230 6P References 1787N References 231 6. viModern Analytical ChemistryChapter 8 9B.7 Characterization Applications 3099B.8 Evaluation of AcidBase Titrimetry 311 Gravimetric Methods of Analysis 2329C Titrations Based on Complexation Reactions 314 8A Overview of Gravimetry 2339C.1 Chemistry and Properties of EDTA 315 8A.1 Using Mass as a Signal 2339C.2 Complexometric EDTA Titration Curves 317 8A.2 Types of Gravimetric Methods 2349C.3 Selecting and Evaluating the End Point 322 8A.3 Conservation of Mass 2349C.4 Representative Method 324 8A.4 Why Gravimetry Is Important 235 9C.5 Quantitative Applications 327 8B Precipitation Gravimetry 2359C.6 Evaluation of Complexation Titrimetry 331 8B.1 Theory and Practice 235 9D Titrations Based on Redox Reactions 331 8B.2 Quantitative Applications 247 9D.1 Redox Titration Curves 332 8B.3 Qualitative Applications 2549D.2 Selecting and Evaluating the End Point 337 8B.4 Evaluating Precipitation Gravimetry 254 9D.3 Representative Method 340 8C Volatilization Gravimetry 255 9D.4 Quantitative Applications 341 8C.1 Theory and Practice 255 9D.5 Evaluation of Redox Titrimetry 350 8C.2 Quantitative Applications 259 9E Precipitation Titrations 350 8C.3 Evaluating Volatilization Gravimetry 2629E.1 Titration Curves 350 8D Particulate Gravimetry 2629E.2 Selecting and Evaluating the End Point 354 8D.1 Theory and Practice 263 9E.3 Quantitative Applications 354 8D.2 Quantitative Applications 264 9E.4 Evaluation of Precipitation Titrimetry 357 8D.3 Evaluating Precipitation Gravimetry 265 9F Key Terms 357 8E Key Terms 265 9G Summary 357 8F Summary 266 9H Suggested Experiments 358 8G Suggested Experiments 266 9I Problems 360 8H Problems 2679J Suggested Readings 366 8I Suggested Readings 2719K References 367 8J References 272 Chapter10Chapter 9 Spectroscopic Methodsof Analysis 368 Titrimetric Methods of Analysis 27310A Overview of Spectroscopy 369 9A Overview of Titrimetry 274 10A.1 What Is Electromagnetic Radiation 369 9A.1 Equivalence Points and End Points 274 10A.2 Measuring Photons as a Signal 372 9A.2 Volume as a Signal 27410B Basic Components of Spectroscopic 9A.3 Titration Curves 275Instrumentation 374 9A.4 The Buret 27710B.1 Sources of Energy 375 9B Titrations Based on AcidBase Reactions 27810B.2 Wavelength Selection 376 9B.1 AcidBase Titration Curves 279 10B.3 Detectors 379 9B.2 Selecting and Evaluating the 10B.4 Signal Processors 380 End Point 28710C Spectroscopy Based on Absorption 380 9B.3 Titrations in Nonaqueous Solvents 295 10C.1 Absorbance of Electromagnetic Radiation 380 9B.4 Representative Method 296 10C.2 Transmittance and Absorbance 384 9B.5 Quantitative Applications 298 10C.3 Absorbance and Concentration: Beers 9B.6 Qualitative Applications 308Law 385 7. Contentsvii10C.4Beers Law and Multicomponent 11B Potentiometric Methods of Analysis 465 Samples 38611B.1 Potentiometric Measurements 46610C.5 Limitations to Beers Law 386 11B.2 Reference Electrodes 471 10D Ultraviolet-Visible and Infrared 11B.3 Metallic Indicator Electrodes 473 Spectrophotometry 38811B.4 Membrane Electrodes 47510D.1 Instrumentation 388 11B.5 Quantitative Applications 48510D.2 Quantitative Applications 394 11B.6 Evaluation 49410D.3 Qualitative Applications 402 11C Coulometric Methods of Analysis 49610D.4 Characterization Applications 403 11C.1 Controlled-Potential Coulometry 49710D.5 Evaluation 40911C.2 Controlled-Current Coulometry 499 10E Atomic Absorption Spectroscopy 412 11C.3 Quantitative Applications 50110E.1 Instrumentation 412 11C.4 Characterization Applications 50610E.2 Quantitative Applications 415 11C.5 Evaluation 50710E.3 Evaluation 422 11D Voltammetric Methods of Analysis 508 10F Spectroscopy Based on Emission 423 11D.1 Voltammetric Measurements 509 10G Molecular Photoluminescence11D.2 Current in Voltammetry 510 Spectroscopy 42311D.3 Shape of Voltammograms 51310G.1 Molecular Fluorescence and11D.4 Quantitative and Qualitative Aspects Phosphorescence Spectra 424of Voltammetry 51410G.2 Instrumentation 42711D.5 Voltammetric Techniques 51510G.3 Quantitative Applications Using Molecular11D.6 Quantitative Applications 520 Luminescence 42911D.7 Characterization Applications 52710G.4 Evaluation 43211D.8 Evaluation 531 10H Atomic Emission Spectroscopy 434 11E Key Terms 53210H.1 Atomic Emission Spectra 434 11F Summary 53210H.2 Equipment 435 11G Suggested Experiments 53310H.3 Quantitative Applications 437 11H Problems 53510H.4 Evaluation 440 11I Suggested Readings 540 10I Spectroscopy Based on Scattering 441 11J References 54110I.1 Origin of Scattering 44110I.2 Turbidimetry and Nephelometry 441 10J Key Terms 446Chapter 12 10K Summary 446 Chromatographic and Electrophoretic 10L Suggested Experiments 447 Methods 543 10M Problems 45012A Overview of Analytical Separations 544 10N Suggested Readings 458 12A.1 The Problem with Simple 10O References 459Separations 54412A.2 A Better Way to Separate Mixtures 544Chapter 1112A.3 Classifying Analytical Separations 546 12B General Theory of Column Electrochemical Methods of Analysis 461 Chromatography 547 11A Classification of Electrochemical Methods 46212B.1 Chromatographic Resolution 54911A.1 Interfacial Electrochemical Methods 462 12B.2 Capacity Factor 55011A.2 Controlling and Measuring Current and 12B.3 Column Selectivity 552 Potential 46212B.4 Column Efficiency 552 8. viii Modern Analytical Chemistry 12B.5 Peak Capacity 55412O Suggested Readings 620 12B.6 Nonideal Behavior 55512P References 620 Chapter 1312C Optimizing Chromatographic Separations 556 12C.1 Using the Capacity Factor to OptimizeResolution 556 12C.2 Using Column Selectivity to OptimizeKinetic Methods of Analysis622Resolution 55813A Methods Based on Chemical Kinetics 623 12C.3 Using Column Efficiency to Optimize 13A.1 Theory and Practice 624Resolution 559 13A.2 Instrumentation 63412D Gas Chromatography 563 13A.3 Quantitative Applications 636 12D.1 Mobile Phase 56313A.4 Characterization Applications 638 12D.2 Chromatographic Columns 564 13A.5 Evaluation of Chemical Kinetic 12D.3 Stationary Phases 565 Methods 639 12D.4 Sample Introduction 56713B Radiochemical Methods of Analysis 642 12D.5 Temperature Control 568 13B.1 Theory and Practice 643 12D.6 Detectors for Gas Chromatography 56913B.2 Instrumentation 643 12D.7 Quantitative Applications 571 13B.3 Quantitative Applications 644 12D.8 Qualitative Applications 57513B.4 Characterization Applications 647 12D.9 Representative Method 576 13B.5 Evaluation 648 12D.10 Evaluation 57713C Flow Injection Analysis 64912E High-Performance Liquid13C.1 Theory and Practice 649 Chromatography 578 13C.2 Instrumentation 651 12E.1 HPLC Columns 578 13C.3 Quantitative Applications 655 12E.2 Stationary Phases 579 13C.4 Evaluation 658 12E.3 Mobile Phases 58013D Key Terms 658 12E.4 HPLC Plumbing 58313E Summary 659 12E.5 Sample Introduction 58413F Suggested Experiments 659 12E.6 Detectors for HPLC 58413G Problems 661 12E.7 Quantitative Applications 58613H Suggested Readings 664 12E.8 Representative Method 58813I References 665 12E.9 Evaluation 58912F LiquidSolid Adsorption Chromatography 59012G Ion-Exchange Chromatography 590 Chapter 1412H Size-Exclusion Chromatography 593 Developing a Standard Method 66612I Supercritical Fluid Chromatography 59614A Optimizing the Experimental Procedure 66712J Electrophoresis 59714A.1 Response Surfaces 667 12J.1 Theory of Capillary Electrophoresis 598 14A.2 Searching Algorithms for Response 12J.2 Instrumentation 601 Surfaces 668 12J.3 Capillary Electrophoresis Methods 604 14A.3 Mathematical Models of Response 12J.4 Representative Method 607 Surfaces 674 12J.5 Evaluation 609 14B Verifying the Method 68312K Key Terms 60914B.1 Single-Operator Characteristics 68312L Summary 61014B.2 Blind Analysis of Standard Samples 68312M Suggested Experiments 61014B.3 Ruggedness Testing 68412N Problems 615 14B.4 Equivalency Testing 687 9. Contentsix 14CValidating the Method as a Standard15D Key Terms 721 Method 68715E Summary 72214C.1 Two-Sample Collaborative Testing 688 15F Suggested Experiments 72214C.2 Collaborative Testing and Analysis of15G Problems 722 Variance 69315H Suggested Readings 72414C.3 What Is a Reasonable Result for a15I References 724 Collaborative Study? 698 14D Key Terms 699 14E Summary 699Appendixes Appendix 1A Single-Sided Normal Distribution 725 14F Suggested Experiments 699 Appendix 1B t-Table 726 14G Problems 700Appendix 1C F-Table 727 14H Suggested Readings 704Appendix 1D Critical Values for Q-Test 728 14I References 704Appendix 1E Random Number Table 728Chapter 15 Appendix 2Recommended Reagents for Preparing Primary Standards 729 Appendix 3A Solubility Products 731 Quality Assurance 705 Appendix 3B Acid Dissociation Constants 732 Appendix 3C MetalLigand Formation Constants 739 15A Quality Control 706 Appendix 3D Standard Reduction Potentials 743 15B Quality Assessment 708Appendix 3E Selected Polarographic Half-Wave Potentials 74715B.1 Internal Methods of QualityAppendix 4Balancing Redox Reactions 748Assessment 708 Appendix 5Review of Chemical Kinetics 75015B.2 External Methods of QualityAppendix 6Countercurrent Separations 755Assessment 711 Appendix 7Answers to Selected Problems 762 15C Evaluating Quality Assurance Data 712 Glossary 76915C.1 Prescriptive Approach 712 Index 78115C.2 Performance-Based Approach 714 10. xModern Analytical ChemistryA Guide to Using This Text. . . in ChapterRepresentative Methods 246Modern Analytical ChemistryAnnotated methods of typicalanalytical procedures link theory with An additional problem is encountered when the isolated solid is non-stoichiometric. For example, precipitating Mn2+ as Mn(OH)2, followed by heatingpractice. The format encourages to produce the oxide, frequently produces a solid with a stoichiometry of MnOx ,where x varies between 1 and 2. In this case the nonstoichiometric product resultsstudents to think about the design of from the formation of a mixture of several oxides that differ in the oxidation stateof manganese. Other nonstoichiometric compounds form as a result of lattice de-fects in the crystal structure.6the procedure and why it works.Representative Method The best way to appreciate the importance of the theoreti-cal and practical details discussed in the previous section is to carefully examine theprocedure for a typical precipitation gravimetric method. Although each methodhas its own unique considerations, the determination of Mg2+ in water and waste-water by precipitating MgNH4PO4 6H2O and isolating Mg2P2O7 provides an in-structive example of a typical procedure.Margin Notes Representative MethodsMethod 8.1Determination of Mg2+ in Water and Wastewater7Margin notes direct studentsDescription of Method. Magnesium is precipitated as MgNH4PO4 6H2O usingto colorplates located toward (NH4)2HPO4 as the precipitant. The precipitates solubility in neutral solutions(0.0065 g/100 mL in pure water at 10 C) is relatively high, but it is much less solublethe middle of the bookin the presence of dilute ammonia (0.0003 g/100 mL in 0.6 M NH3). The precipitant isnot very selective, so a preliminary separation of Mg2+ from potential interferents isnecessary. Calcium, which is the most significant interferent, is usually removed byits prior precipitation as the oxalate. The presence of excess ammonium salts fromthe precipitant or the addition of too much ammonia can lead to the formation ofMg(NH4)4(PO4)2, which is subsequently isolated as Mg(PO3)2 after drying. Theprecipitate is isolated by filtration using a rinse solution of dilute ammonia. After110 Modern Analytical Chemistry filtering, the precipitate is converted to Mg2P2O7 and weighed. either case, the calibration curve provides a means for relating Ssamp to the ana- Procedure. Transfer a sample containing no more than 60 mg of Mg2+ into a lytes concentration.600-mL beaker. Add 23 drops of methyl red indicator, and, if necessary, adjust thevolume to 150 mL. Acidify the solution with 6 M HCl, and add 10 mL of 30% w/v(NH4)2HPO4. After cooling, add concentrated NH3 dropwise, and while constantly EXAMPLE 5.3stirring, until the methyl red indicator turns yellow (pH > 6.3). After stirring for5 min, add 5 mL of concentrated NH3, and continue stirring for an additional 10 min.Color plate 1 shows an example of a set of A second spectrophotometric method for the quantitative determination of Allow the resulting solution and precipitate to stand overnight. Isolate theexternal standards and their corresponding Pb2+ levels in blood gives a linear normal calibration curve for which precipitate by filtration, rinsing with 5% v/v NH3. Dissolve the precipitate in 50 mLnormal calibration curve. of 10% v/v HCl, and precipitate a second time following the same procedure. AfterSstand = (0.296 ppb1) CS + 0.003 filtering, carefully remove the filter paper by charring. Heat the precipitate at 500 Cuntil the residue is white, and then bring the precipitate to constant weight at What is the Pb2+ level (in ppb) in a sample of blood if Ssamp is 0.397?1100 C. SOLUTIONQuestions To determine the concentration of Pb2+ in the sample of blood, we replace 1. Why does the procedure call for a sample containing no more than 60 mg of Sstand in the calibration equation with Ssamp and solve for CA Ssamp 0.003 0.397 0.003CA = = = 1.33 ppb0.296 ppb 10.296 ppb 1 It is worth noting that the calibration equation in this problem includes an extra term that is not in equation 5.3. Ideally, we expect the calibration curve toq y give a signal of zero when CS is zero. This is the purpose of using a reagent There is a serious limitation, however, to an external standardization. The blank to correct the measured signal. The extra term of +0.003 in ourrelationship between Sstand and CS in equation 5.3 is determined when the ana- calibration equation results from uncertainty in measuring the signal for thelyte is present in the external standards matrix. In using an external standardiza- reagent blank and the standards. tion, we assume that any difference between the matrix of the standards and thesamples matrix has no effect on the value of k. A proportional determinate erroris introduced when differences between the two matrices cannot be ignored. This An external standardization allows a related series of samples to be analyzedis shown in Figure 5.4, where the relationship between the signal and the amount using a single calibration curve. This is an important advantage in laboratories of analyte is shown for both the samples matrix and the standards matrix. In where many samples are to be analyzed or when the need for a rapid throughput of this example, using a normal calibration curve results in a negative determinatel i iti lt ii lf tht l t derror. When matrix problems are expected, an effort is made to match the matrixof the standards to that of the sample. This is known as matrix matching. Whenthe samples matrix is unknown, the matrix effect must be shown to be negligi-Examples of Typical Problemsble, or an alternative method of standardization must be used. Both approachesare discussed in the following sections.Each example problem includes a matrix matchingAdjusting the matrix of an externalstandard so that it is the same as the5B.4 Standard Additionsdetailed solution that helps students inmatrix of the samples to be analyzed.The complication of matching the matrix of the standards to that of the sampleapplying the chapters material tomethod of standard additionscan be avoided by conducting the standardization in the sample. This is knownas the method of standard additions. The simplest version of a standard addi-A standardization in which aliquots of apractical problems. standard solution are added to thesample.tion is shown in Figure 5.5. A volume, Vo, of sample is diluted to a final volume,Vf, and the signal, Ssamp is measured. A second identical aliquot of sample is Bold-faced Key Terms with Margin Definitions Key words appear in boldface when they are introduced within the text. The term and its definition appear in the margin for quick review by the student. All key words are also defined in the glossary.x 11. . . . End of Chapteryy 5E KEY TERMSList of Key TermsThe key terms introduced within the chapter are aliquot (p. 111) multiple-point standardization (p. 109)secondary reagent (p. 107) external standard (p. 109) normal calibration curve (p. 109)single-point standardization (p. 108)listed at the end of each chapter. Page references internal standard (p. 116) primary reagent (p. 106) standard deviation about the linear regression (p. 118) reagent grade (p. 107) regression (p. 121)direct the student to the definitions in the text. matrix matching (p. 110) residual error (p. 118)total Youden blank (p. 129) method of standard additions (p. 110) 5F SUMMARYSummary In a quantitative analysis, we measure a signal and calculate theand the use of an internal standard. The most desirable standard-The summary provides the student with a brief amount of analyte using one of the following equations.ization strategy is an external standardization. The method ofstandard additions, in which known amounts of analyte are addedreview of the important concepts within the chapter. Smeas = knA + Sreagto the sample, is used when the samples matrix complicates theanalysis. An internal standard, which is a species (not analyte) Smeas = kCA + Sreagadded to all samples and standards, is used when the procedure To obtain accurate results we must eliminate determinate errors affecting the measured signal, Smeas, the methods sensitivity, k,does not allow for the reproducible handling of samples andstandards.Suggested Experiments and any signal due to the reagents, Sreag. To ensure that Smeas is determined accurately, we calibrateStandardizations using a single standard are common, but alsoare subject to greater uncertainty. Whenever possible, a multiple-An annotated list of representative experiments ispoint standardization is preferred. The results of a multiple-point the equipment or instrument used to obtain the signal. Balances are calibrated using standard weights. When necessary, we canstandardization are graphed as a calibration curve. A linear regres-provided from the Journal of Chemical Education. also correct for the buoyancy of air. Volumetric glassware can sion analysis can provide an equation for the standardization. be calibrated by measuring the mass of water contained or de-A reagent blank corrects the measured signal for signals due to livered and using the density of water to calculate the true vol-reagents other than the sample that are used in an analysis. The ume. Most instruments have calibration standards suggested bymost common reagent blank is prepared by omitting the sample. the manufacturer.When a simple reagent blank does not compensate for all constant An analytical method is standardized by determining its sensi- sources of determinate error, other types of blanks, such as the tivity. There are several approaches to standardization, including total Youden blank, can be used. the use of external standards, the method of standard addition,5G Suggested EXPERIMENTSSuggested ReadingsSuggested readings give the studentExperimentsThe following exercises and experiments help connect the material in this chapter to the analytical laboratory.access to more comprehensiveCalibrationVolumetric glassware (burets, pipets, and StandardizationExternal standards, standard additions,volumetric flasks) can be calibrated in the manner describedand internal standards are a common feature of many discussion of the topics introducedin Example 5.1. Most instruments have a calibration samplequantitative analyses. Suggested experiments using thesethat can be prepared to verify the instruments accuracy andstandardization methods are found in later chapters. A good within the chapter.precision. For example, as described in this chapter, a project experiment for introducing external standardization,solution of 60.06 ppm K2Cr2O7 in 0.0050 M H2SO4 shouldstandard additions, and the importance of the samples yygive an absorbance of 0.640 0.010 at a wavelength ofmatrix is to explore the effect of pH on the quantitative350.0 nm when using 0.0050 M H2SO4 as a reagent analysis of an acidbase indicator. Using bromothymol blueblank. These exercises also provide practice with using1G SUGGESTED READINGSas an example, external standards can be prepared in a pH 9volumetric glassware, weighing samples, and preparing buffer and used to analyze samples buffered to different pHssolutions.in the range of 610. Results can be compared with those The role of analytical chemistry within the broader discipline ofLaitinen, H. A. Analytical Chemistry in a Changing World,obtained using a standard addition.chemistry has been discussed by many prominent analyticalAnal. Chem. 1980, 52, 605A609A.chemists. Several notable examples follow.Laitinen, H. A. History of Analytical Chemistry in the U.S.A., Baiulescu, G. E.; Patroescu, C.; Chalmers, R. A. Education andTalanta 1989, 36, 19.Teaching in Analytical Chemistry. Ellis Horwood: Chichester,Laitinen, H. A.; Ewing, G. (eds). A History of Analytical1982.Chemistry. The Division of Analytical Chemistry ofReferences Hieftje, G. M. The Two Sides of Analytical Chemistry, Anal.Chem. 1985, 57, 256A267A. the American Chemical Society: Washington, D.C., 1972. Kissinger, P. T. Analytical ChemistryWhat is It? Who Needs It? McLafferty, F. W. Analytical Chemistry: Historic and Modern,The references cited in the Why Teach It? Trends Anal. Chem. 1992, 11, 5457. Acc. Chem. Res. 1990, 23, 6364.chapter are provided so thestudent can access them for 1H REFERENCESfurther information. 1. Ravey, M. Spectroscopy 1990, 5(7), 11. 2. de Haseth, J. Spectroscopy 1990, 5(7), 11. 113119; (c) Atkinson, G. F. J. Chem. Educ. 1982, 59, 201202; (d) Pardue, H. L.; Woo, J. J. Chem. Educ. 1984, 61, 409412; (e) Guarnieri, M. J. Chem. Educ. 1988, 65, 201203; (f) de Haseth, J. 3. Fresenius, C. R. A System of Instruction in Quantitative Chemical Spectroscopy 1990, 5, 2021; (g) Strobel, H. A. Am. Lab. 1990,Analysis. John Wiley and Sons: New York, 1881. October, 1724. 4. Hillebrand, W. F.; Lundell, G. E. F. Applied Inorganic Analysis, John8. Hieftje, G. M. Am. Lab. 1993, October, 5361.Wiley and Sons: New York, 1953.9. See, for example, the following laboratory texts: (a) Sorum, C. H.; 5. Van Loon, J. C. Analytical Atomic Absorption Spectroscopy. Academic Lagowski, J. J. Introduction to Semimicro Qualitative Analysis, 5th ed.Press: New York, 1980. Prentice-Hall: Englewood Cliffs, NJ, 1977.; (b) Shriner, R. L.; Fuson, 6. Murray, R. W. Anal. Chem. 1991, 63, 271A.3J PROBLEMS7. For several different viewpoints see (a) Beilby, A. L. J. Chem. Educ. R. C.; Curtin, D. Y. The Systematic Identification of Organic Compounds, 5th ed. John Wiley and Sons: New York, 1964.1970, 47, 237238; (b) Lucchesi, C. A. Am. Lab. 1980, October, 1. When working with a solid sample, it often is necessary to 4. A sample was analyzed to determine the concentration of anbring the analyte into solution by dissolving the sample in a analyte. Under the conditions of the analysis, the sensitivity issuitable solvent. Any solid impurities that remain are17.2 ppm1. What is the analytes concentration if Smeas is 35.2removed by filtration before continuing with the analysis.and Sreag is 0.6?In a typical total analysis method, the procedure mightread 5. A method for the analysis of Ca2+ in water suffers from an Problemsinterference in the presence of Zn2+. When the concentration After dissolving the sample in a beaker, remove anyof Ca2+ is 50 times greater than that of Zn2+, an analysis forCa2+ gives a relative error of 2.0%. What is the value of the A variety of problems, many based solid impurities by passing the solution containing the analyte through filter paper, collecting the solution in a clean Erlenmeyer flask. Rinse the beakerselectivity coefficient for this method? on data from the analytical literature, 6. The quantitative analysis for reduced glutathione in blood is with several small portions of solvent, passing these rinsings through the filter paper, and collecting themcomplicated by the presence of many potential interferents.In one study, when analyzing a solution of 10-ppb provide the student with practical in the same Erlenmeyer flask. Finally, rinse the filter paper with several portions of solvent, collecting theglutathione and 1.5-ppb ascorbic acid, the signal was 5.43times greater than that obtained for the analysis of 10-ppb examples of current research. rinsings in the same Erlenmeyer flask. glutathione.12 What is the selectivity coefficient for thisFor a typical concentration method, however, the procedureanalysis? The same study found that when analyzing amight state solution of 350-ppb methionine and 10-ppb glutathione thesignal was 0 906 times less than that obtained for the analysis xi 12. Preface PrefaceA s currently taught, the introductory course in analytical chemistry emphasizesquantitative (and sometimes qualitative) methods of analysis coupled with a heavydose of equilibrium chemistry. Analytical chemistry, however, is more than equilib-rium chemistry and a collection of analytical methods; it is an approach to solvingchemical problems. Although discussing different methods is important, that dis-cussion should not come at the expense of other equally important topics. The intro-ductory analytical course is the ideal place in the chemistry curriculum to exploretopics such as experimental design, sampling, calibration strategies, standardization,optimization, statistics, and the validation of experimental results. These topics areimportant in developing good experimental protocols, and in interpreting experi-mental results. If chemistry is truly an experimental science, then it is essential thatall chemistry students understand how these topics relate to the experiments theyconduct in other chemistry courses.Currently available textbooks do a good job of covering the diverse range of wetand instrumental analysis techniques available to chemists. Although there is somedisagreement about the proper balance between wet analytical techniques, such asgravimetry and titrimetry, and instrumental analysis techniques, such as spec-trophotometry, all currently available textbooks cover a reasonable variety of tech-niques. These textbooks, however, neglect, or give only brief consideration to,obtaining representative samples, handling interferents, optimizing methods, ana-lyzing data, validating data, and ensuring that data are collected under a state of sta-tistical control.In preparing this textbook, I have tried to find a more appropriate balancebetween theory and practice, between classical and modern methods of analysis,between analyzing samples and collecting and preparing samples for analysis, andbetween analytical methods and data analysis. Clearly, the amount of material in thistextbook exceeds what can be covered in a single semester; its my hope, however,that the diversity of topics will meet the needs of different instructors, while, per-haps, suggesting some new topics to cover.The anticipated audience for this textbook includes students majoring in chem-istry, and students majoring in other science disciplines (biology, biochemistry,environmental science, engineering, and geology, to name a few), interested inobtaining a stronger background in chemical analysis. It is particularly appropriatefor chemistry majors who are not planning to attend graduate school, and who oftendo not enroll in those advanced courses in analytical chemistry that require physicalchemistry as a pre-requisite. Prior coursework of a year of general chemistry isassumed. Competence in algebra is essential; calculus is used on occasion, however,its presence is not essential to the materials treatment.xii 13. Preface xiiiKey Features of This TextbookKey features set this textbook apart from others currently available. A stronger emphasis on the evaluation of data. Methods for characterizingchemical measurements, results, and errors (including the propagation oferrors) are included. Both the binomial distribution and normal distributionare presented, and the idea of a confidence interval is developed. Statisticalmethods for evaluating data include the t-test (both for paired and unpaireddata), the F-test, and the treatment of outliers. Detection limits also arediscussed from a statistical perspective. Other statistical methods, such asANOVA and ruggedness testing, are presented in later chapters. Standardizations and calibrations are treated in a single chapter. Selecting themost appropriate calibration method is important and, for this reason, themethods of external standards, standard additions, and internal standards aregathered together in a single chapter. A discussion of curve-fitting, includingthe statistical basis for linear regression (with and without weighting) also isincluded in this chapter. More attention to selecting and obtaining a representative sample. The design of astatistically based sampling plan and its implementation are discussed earlier,and in more detail than in other textbooks. Topics that are covered includehow to obtain a representative sample, how much sample to collect, how manysamples to collect, how to minimize the overall variance for an analyticalmethod, tools for collecting samples, and sample preservation. The importance of minimizing interferents is emphasized. Commonly usedmethods for separating interferents from analytes, such as distillation, masking,and solvent extraction, are gathered together in a single chapter. Balanced coverage of analytical techniques. The six areas of analyticaltechniquesgravimetry, titrimetry, spectroscopy, electrochemistry,chromatography, and kineticsreceive roughly equivalent coverage, meetingthe needs of instructors wishing to emphasize wet methods and thoseemphasizing instrumental methods. Related methods are gathered together in asingle chapter encouraging students to see the similarities between methods,rather than focusing on their differences. An emphasis on practical applications. Throughout the text applications fromorganic chemistry, inorganic chemistry, environmental chemistry, clinicalchemistry, and biochemistry are used in worked examples, representativemethods, and end-of-chapter problems. Representative methods link theory with practice. An important feature of thistext is the presentation of representative methods. These boxed features presenttypical analytical procedures in a format that encourages students to thinkabout why the procedure is designed as it is. Separate chapters on developing a standard method and quality assurance. Twochapters provide coverage of methods used in developing a standard methodof analysis, and quality assurance. The chapter on developing a standardmethod includes topics such as optimizing experimental conditions usingresponse surfaces, verifying the method through the blind analysis ofstandard samples and ruggedness testing, and collaborative testing usingYoudens two-sample approach and ANOVA. The chapter on qualityassurance covers quality control and internal and external techniques forquality assessment, including the use of duplicate samples, blanks, spikerecoveries, and control charts. 14. xiv Preface Problems adapted from the literature. Many of the in-chapter examples and end-of-chapter problems are based on data from the analytical literature, providingstudents with practical examples of current research in analytical chemistry. An emphasis on critical thinking. Critical thinking is encouraged throughproblems in which students are asked to explain why certain steps in ananalytical procedure are included, or to determine the effect of an experimentalerror on the results of an analysis. Suggested experiments from the Journal of Chemical Education. Rather thanincluding a short collection of experiments emphasizing the analysis ofstandard unknowns, an annotated list of representative experiments from theJournal of Chemical Education is included at the conclusion of most chapters.These experiments may serve as stand alone experiments, or as starting pointsfor individual or group projects.The Role of Equilibrium Chemistry in Analytical ChemistryEquilibrium chemistry often receives a significant emphasis in the introductory ana-lytical chemistry course. While an important topic, its overemphasis can cause stu-dents to confuse analytical chemistry with equilibrium chemistry. Although atten-tion to solving equilibrium problems is important, it is equally important for stu-dents to recognize when such calculations are impractical, or when a simpler, morequalitative approach is all that is needed. For example, in discussing the gravimetricanalysis of Ag+ as AgCl, there is little point in calculating the equilibrium solubilityof AgCl since the concentration of Cl at equilibrium is rarely known. It is impor-tant, however, to qualitatively understand that a large excess of Cl increases the sol-ubility of AgCl due to the formation of soluble silver-chloro complexes. Balancingthe presentation of a rigorous approach to solving equilibrium problems, this textalso introduces the use of ladder diagrams as a means for providing a qualitative pic-ture of a system at equilibrium. Students are encouraged to use the approach bestsuited to the problem at hand.Computer SoftwareMany of the topics covered in analytical chemistry benefit from the availability ofappropriate computer software. In preparing this text, however, I made a consciousdecision to avoid a presentation tied to a single computer platform or software pack-age. Students and faculty are increasingly experienced in the use of computers,spreadsheets, and data analysis software; their use is, I think, best left to the person-al choice of each student and instructor.OrganizationThe textbooks organization can be divided into four parts. Chapters 13 serve as anintroduction, providing an overview of analytical chemistry (Chapter 1); a review ofthe basic tools of analytical chemistry, including significant figures, units, and stoi-chiometry (Chapter 2); and an introduction to the terminology used by analyticalchemists (Chapter 3). Familiarity with the material in these chapters is assumedthroughout the remainder of the text. Chapters 47 cover a number of topics that are important in understanding howa particular analytical method works. Later chapters are mostly independent of thematerial in these chapters. Instructors may pick and choose from among the topics 15. Preface xvof these chapters, as needed, to support individual course goals. The statistical analy-sis of data is covered in Chapter 4 at a level that is more complete than that found inother introductory analytical textbooks. Methods for calibrating equipment, stan-dardizing methods, and linear regression are gathered together in Chapter 5. Chapter6 provides an introduction to equilibrium chemistry, stressing both the rigoroussolution to equilibrium problems, and the use of semi-quantitative approaches, suchas ladder diagrams. The importance of collecting the right sample, and methods forseparating analytes and interferents are covered in Chapter 7.Chapters 813 cover the major areas of analysis, including gravimetry(Chapter 8), titrimetry (Chapter 9), spectroscopy (Chapter 10), electrochemistry(Chapter 11), chromatography and electrophoresis (Chapter 12), and kinetic meth-ods (Chapter 13). Related techniques, such as acidbase titrimetry and redoxtitrimetry, or potentiometry and voltammetry, are gathered together in single chap-ters. Combining related techniques together encourages students to see the similar-ities between methods, rather than focusing on their differences. The first techniquepresented in each chapter is generally that which is most commonly covered in theintroductory course.Finally, the textbook concludes with two chapters discussing the design andmaintenance of analytical methods, two topics of importance to analytical chemists.Chapter 14 considers the development of an analytical method, including its opti-mization, verification, and validation. Quality control and quality assessment arediscussed in Chapter 15.AcknowledgmentsBefore beginning an academic career I was, of course, a student. My interest inchemistry and teaching was nurtured by many fine teachers at Westtown FriendsSchool, Knox College, and the University of North Carolina at Chapel Hill; their col-lective influence continues to bear fruit. In particular, I wish to recognize DavidMacInnes, Alan Hiebert, Robert Kooser, and Richard Linton. I have been fortunate to work with many fine colleagues during my nearly 17years of teaching undergraduate chemistry at Stockton State College and DePauwUniversity. I am particularly grateful for the friendship and guidance provided byJon Griffiths and Ed Paul during my four years at Stockton State College. At DePauwUniversity, Jim George and Bryan Hanson have willingly shared their ideas aboutteaching, while patiently listening to mine. Approximately 300 students have joined me in thinking and learning about ana-lytical chemistry; their questions and comments helped guide the development ofthis textbook. I realize that working without a formal textbook has been frustratingand awkward; all the more reason why I appreciate their effort and hard work. The following individuals reviewed portions of this textbook at various stagesduring its development.David Ballantine Wendy ClevengerNorthern Illinois University University of TennesseeChattanoogaJohn E. BauerCathy CobbIllinois State UniversityAugusta State UniversityAli BazziPaul FlowersUniversity of MichiganDearbornUniversity of North CarolinaPembrokeSteven D. BrownNancy GordonUniversity of Delaware University of Southern Maine 16. xvi PrefaceVirginia M. Indivero Vincent RemchoSwarthmore College West Virginia UniversityMichael Janusa Jeanette K. RiceNicholls State UniversityGeorgia Southern UniversityJ. David Jenkins Martin W. RoweGeorgia Southern UniversityTexas A&M UniversityRichard S. MitchellAlexander ScheelineArkansas State UniversityUniversity of IllinoisGeorge A. Pearse, Jr.James D. StuartLe Moyne College University of ConnecticutGary RaysonThomas J. WenzelNew Mexico State UniversityBates CollegeDavid Redfield David ZaxNW Nazarene University Cornell UniversityI am particularly grateful for their detailed written comments and suggestions forimproving the manuscript. Much of what is good in the final manuscript is the resultof their interest and ideas. George Foy (York College of Pennsylvania), John McBride(Hofstra University), and David Karpovich (Saginaw Valley State University) checkedthe accuracy of problems in the textbook. Gary Kinsel (University of Texas atArlington) reviewed the page proofs and provided additional suggestions. This project began in the summer of 1992 with the support of a course develop-ment grant from DePauw Universitys Faculty Development Fund. Additional finan-cial support from DePauw Universitys Presidential Discretionary Fund also isacknowledged. Portions of the first draft were written during a sabbatical leave in theFall semester of the 1993/94 academic year. A Fisher Fellowship provided releasetime during the Fall 1995 semester to complete the manuscripts second draft. Alltech and Associates (Deerfield, IL) graciously provided permission to use thechromatograms in Chapter 12; the assistance of Jim Anderson, Vice-President,and Julia Poncher, Publications Director, is greatly appreciated. Fred Soster andMarilyn Culler, both of DePauw University, provided assistance with some of thephotographs. The editorial staff at McGraw-Hill has helped guide a novice through theprocess of developing this text. I am particularly thankful for the encouragement andconfidence shown by Jim Smith, Publisher for Chemistry, and Kent Peterson,Sponsoring Editor for Chemistry. Shirley Oberbroeckling, Developmental Editor forChemistry, and Jayne Klein, Senior Project Manager, patiently answered my ques-tions and successfully guided me through the publishing process. Finally, I would be remiss if I did not recognize the importance of my familyssupport and encouragement, particularly that of my parents. A very special thanks tomy daughter, Devon, for gifts too numerous to detail.How to Contact the AuthorWriting this textbook has been an interesting (and exhausting) challenge. Despitemy efforts, I am sure there are a few glitches, better examples, more interesting end-of-chapter problems, and better ways to think about some of the topics. I welcomeyour comments, suggestions, and data for interesting problems, which may beaddressed to me at DePauw University, 602 S. College St., Greencastle, IN 46135, orelectronically at harvey@depauw.edu. 17. Chapter 1IntroductionC hemistry is the study of matter, including its composition,structure, physical properties, and reactivity. There are manyapproaches to studying chemistry, but, for convenience, wetraditionally divide it into five fields: organic, inorganic, physical,biochemical, and analytical. Although this division is historical andarbitrary, as witnessed by the current interest in interdisciplinary areassuch as bioanalytical and organometallic chemistry, these five fieldsremain the simplest division spanning the discipline of chemistry.Training in each of these fields provides a unique perspective to thestudy of chemistry. Undergraduate chemistry courses and textbooksare more than a collection of facts; they are a kind of apprenticeship. Inkeeping with this spirit, this text introduces the field of analyticalchemistry and the unique perspectives that analytical chemists bring tothe study of chemistry. 1 18. 2 Modern Analytical Chemistry 1A What Is Analytical Chemistry?Analytical chemistry is what analytical chemists do.*We begin this section with a deceptively simple question. What is analytical chem-istry? Like all fields of chemistry, analytical chemistry is too broad and active a disci-pline for us to easily or completely define in an introductory textbook. Instead, wewill try to say a little about what analytical chemistry is, as well as a little about whatanalytical chemistry is not. Analytical chemistry is often described as the area of chemistry responsible forcharacterizing the composition of matter, both qualitatively (what is present) andquantitatively (how much is present). This description is misleading. After all, al-most all chemists routinely make qualitative or quantitative measurements. The ar-gument has been made that analytical chemistry is not a separate branch of chem-istry, but simply the application of chemical knowledge.1 In fact, you probably haveperformed quantitative and qualitative analyses in other chemistry courses. For ex-ample, many introductory courses in chemistry include qualitative schemes foridentifying inorganic ions and quantitative analyses involving titrations. Unfortunately, this description ignores the unique perspective that analyticalchemists bring to the study of chemistry. The craft of analytical chemistry is not inperforming a routine analysis on a routine sample (which is more appropriatelycalled chemical analysis), but in improving established methods, extending existingmethods to new types of samples, and developing new methods for measuringchemical phenomena.2 Heres one example of this distinction between analytical chemistry and chemi-cal analysis. Mining engineers evaluate the economic feasibility of extracting an oreby comparing the cost of removing the ore with the value of its contents. To esti-mate its value they analyze a sample of the ore. The challenge of developing and val-idating the method providing this information is the analytical chemists responsi-bility. Once developed, the routine, daily application of the method becomes thejob of the chemical analyst. Another distinction between analytical chemistry and chemical analysis isthat analytical chemists work to improve established methods. For example, sev-eral factors complicate the quantitative analysis of Ni2+ in ores, including thepresence of a complex heterogeneous mixture of silicates and oxides, the low con-centration of Ni2+ in ores, and the presence of other metals that may interfere inthe analysis. Figure 1.1 is a schematic outline of one standard method in use dur-ing the late nineteenth century.3 After dissolving a sample of the ore in a mixtureof H2SO4 and HNO3, trace metals that interfere with the analysis, such as Pb2+,Cu2+ and Fe3+, are removed by precipitation. Any cobalt and nickel in the sampleare reduced to Co and Ni, isolated by filtration and weighed (point A). Afterdissolving the mixed solid, Co is isolated and weighed (point B). The amountof nickel in the ore sample is determined from the difference in the masses atpoints A and B.mass point A mass point B%Ni = 100 mass sample*Attributed to C. N. Reilley (19251981) on receipt of the 1965 Fisher Award in Analytical Chemistry. Reilley, who wasa professor of chemistry at the University of North Carolina at Chapel Hill, was one of the most influential analyticalchemists of the last half of the twentieth century. 19. Chapter 1 Introduction3 Original Sample1:3 H2SO4/HNO3 100C (810 h)dilute w/H2O, digest 24 h PbSO4Cu2+, Fe3+SandCo2+, Ni2+ dilute bubble H2S(g) Fe3+, Co2+, Ni2+ CuScool, add NH3digest 5070, 30 minFe(OH)3 Co2+, Ni2+HClslightly acidify w/ HCl heat, bubble H2S (g) Fe3+neutralize w/ NH3 WasteCoS, NiSNa2CO3, CH3COOH aqua regia heat, add HCl until Basic strongly acidic bubble H2S (g) ferric acetate Co2+, Ni2+CuS, PbS heat add Na2CO3 until alkaline NaOH Co(OH)2, Ni(OH)2WasteheatCoO, NiO Solidheat, H2 (g) Key Solution Co, Ni AHNO3K2CO3, KNO3CH3COOHdigest 24 h Ni2+ K3Co(NO3)5 H2O, HClCo2+ Wasteas above CoBFigure 1.1Analytical scheme outlined by Fresenius3 for the gravimetric analysis of Ni in ores. 20. 4Modern Analytical Chemistry Original sample HNO3, HCl, heatResidue Solution 20% NH4Cl 10% tartaric acid take alkaline with 1:1 NH3take acid with HCl10% tartaric acidtake alkaline with 1:1 NH3 Is Yessolidpresent? SolidKey No take acid with HClSolution 1% alcoholic DMG take alkaline with 1:1 NH3ANi(DMG)2(s)Figure 1.2Analytical scheme outlined by Hillebrand andLundell4 for the gravimetric analysis of Ni inores (DMG = dimethylgloxime). The factor of0.2031 in the equation for %Ni accounts formass A 0.2031the difference in the formula weights of %Ni = 100Ni(DMG)2 and Ni; see Chapter 8 for moreg sampledetails. The combination of determining the mass of Ni2+ by difference, coupled with the need for many reactions and filtrations makes this procedure both time-consuming and difficult to perform accurately.The development, in 1905, of dimethylgloxime (DMG), a reagent that selec- tively precipitates Ni2+ and Pd2+, led to an improved analytical method for deter- mining Ni2+ in ores.4 As shown in Figure 1.2, the mass of Ni2+ is measured directly, requiring fewer manipulations and less time. By the 1970s, the standard method for the analysis of Ni 2+ in ores progressed from precipitating Ni(DMG) 2 to flame atomic absorption spectrophotometry,5 resulting in an even more rapid analysis. Current interest is directed toward using inductively coupled plasmas for determin- ing trace metals in ores.In summary, a more appropriate description of analytical chemistry is . . . the science of inventing and applying the concepts, principles, and . . . strategies for measuring the characteristics of chemical systems and species.6 Analytical chemists typically operate at the extreme edges of analysis, extending and improving the abil- ity of all chemists to make meaningful measurements on smaller samples, on more complex samples, on shorter time scales, and on species present at lower concentra- tions. Throughout its history, analytical chemistry has provided many of the tools and methods necessary for research in the other four traditional areas of chemistry, as well as fostering multidisciplinary research in, to name a few, medicinal chem- istry, clinical chemistry, toxicology, forensic chemistry, material science, geochem- istry, and environmental chemistry. 21. Chapter 1 Introduction 5 You will come across numerous examples of qualitative and quantitative meth-ods in this text, most of which are routine examples of chemical analysis. It is im-portant to remember, however, that nonroutine problems prompted analyticalchemists to develop these methods. Whenever possible, we will try to place thesemethods in their appropriate historical context. In addition, examples of current re-search problems in analytical chemistry are scattered throughout the text. The next time you are in the library, look through a recent issue of an analyti-cally oriented journal, such as Analytical Chemistry. Focus on the titles and abstractsof the research articles. Although you will not recognize all the terms and methods,you will begin to answer for yourself the question What is analytical chemistry? 1B The Analytical PerspectiveHaving noted that each field of chemistry brings a unique perspective to the studyof chemistry, we now ask a second deceptively simple question. What is the analyt-ical perspective? Many analytical chemists describe this perspective as an analyticalapproach to solving problems.7 Although there are probably as many descriptionsof the analytical approach as there are analytical chemists, it is convenient for ourpurposes to treat it as a five-step process: 1. Identify and define the problem. 2. Design the experimental procedure. 3. Conduct an experiment, and gather data. 4. Analyze the experimental data. 5. Propose a solution to the problem.Figure 1.3 shows an outline of the analytical approach along with some im-portant considerations at each step. Three general features of this approach de-serve attention. First, steps 1 and 5 provide opportunities for analytical chemiststo collaborate with individuals outside the realm of analytical chemistry. In fact,many problems on which analytical chemists work originate in other fields. Sec-ond, the analytical approach is not linear, but incorporates a feedback loopconsisting of steps 2, 3, and 4, in which the outcome of one step may cause areevaluation of the other two steps. Finally, the solution to one problem oftensuggests a new problem.Analytical chemistry begins with a problem, examples of which include evalu-ating the amount of dust and soil ingested by children as an indicator of environ-mental exposure to particulate based pollutants, resolving contradictory evidenceregarding the toxicity of perfluoro polymers during combustion, or developingrapid and sensitive detectors for chemical warfare agents.* At this point the analyti-cal approach involves a collaboration between the analytical chemist and the indi-viduals responsible for the problem. Together they decide what information isneeded. It is also necessary for the analytical chemist to understand how the prob-lem relates to broader research goals. The type of information needed and the prob-lems context are essential to designing an appropriate experimental procedure.Designing an experimental procedure involves selecting an appropriate methodof analysis based on established criteria, such as accuracy, precision, sensitivity, anddetection limit; the urgency with which results are needed; the cost of a single analy-sis; the number of samples to be analyzed; and the amount of sample available for*These examples are taken from a series of articles, entitled the Analytical Approach, which has appeared as a regularfeature in the journal Analytical Chemistry since 1974. 22. 6Modern Analytical Chemistry1. Identify the problem Determine type of information needed 5. Propose a solution(qualitative, quantitative,Conduct external evaluationcharacterization, or fundamental) Identify context of the problem2. Design the experimental procedure Establish design criteria (accuracy, precision,4. Analyze the experimental datascale of operation, sensitivity, selectivity,cost, speed) Reduce or transform data Identify interferents Analyze statistics Select method Verify results Establish validation criteria Interpret results Establish sampling strategyFeedbackloop 3. Conduct an experimentCalibrate instruments and equipmentStandardize reagentsFigure 1.3Gather dataFlow diagram for the analytical approach tosolving problems; modified after Atkinson.7c analysis. Finding an appropriate balance between these parameters is frequently complicated by their interdependence. For example, improving the precision of an analysis may require a larger sample. Consideration is also given to collecting, stor- ing, and preparing samples, and to whether chemical or physical interferences will affect the analysis. Finally, a good experimental procedure may still yield useless in- formation if there is no method for validating the results.The most visible part of the analytical approach occurs in the laboratory. As part of the validation process, appropriate chemical or physical standards are used to calibrate any equipment being used and any solutions whose concentrations must be known. The selected samples are then analyzed and the raw data recorded.The raw data collected during the experiment are then analyzed. Frequently the data must be reduced or transformed to a more readily analyzable form. A statistical treatment of the data is used to evaluate the accuracy and precision of the analysis and to validate the procedure. These results are compared with the criteria estab- lished during the design of the experiment, and then the design is reconsidered, ad- ditional experimental trials are run, or a solution to the problem is proposed. When a solution is proposed, the results are subject to an external evaluation that may re- sult in a new problem and the beginning of a new analytical cycle. 23. Chapter 1 Introduction 7As an exercise, lets adapt this model of the analytical approach to a real prob-lem. For our example, we will use the determination of the sources of airborne pol-lutant particles. A description of the problem can be found in the following article:Tracing Aerosol Pollutants with Rare Earth Isotopes byOndov, J. M.; Kelly, W. R. Anal. Chem. 1991, 63, 691A697A.Before continuing, take some time to read the article, locating the discussions per-taining to each of the five steps outlined in Figure 1.3. In addition, consider the fol-lowing questions: 1. What is the analytical problem? 2. What type of information is needed to solve the problem? 3. How will the solution to this problem be used? 4. What criteria were considered in designing the experimental procedure? 5. Were there any potential interferences that had to be eliminated? If so, howwere they treated? 6. Is there a plan for validating the experimental method? 7. How were the samples collected? 8. Is there evidence that steps 2, 3, and 4 of the analytical approach are repeatedmore than once? 9. Was there a successful conclusion to the problem? According to our model, the analytical approach begins with a problem. Themotivation for this research was to develop a method for monitoring the transportof solid aerosol particulates following their release from a high-temperature com-bustion source. Because these particulates contain significant concentrations oftoxic heavy metals and carcinogenic organic compounds, they represent a signifi-cant environmental hazard. An aerosol is a suspension of either a solid or a liquid in a gas. Fog, for exam-ple, is a suspension of small liquid water droplets in air, and smoke is a suspensionof small solid particulates in combustion gases. In both cases the liquid or solid par-ticulates must be small enough to remain suspended in the gas for an extendedtime. Solid aerosol particulates, which are the focus of this problem, usually havemicrometer or submicrometer diameters. Over time, solid particulates settle outfrom the gas, falling to the Earths surface as dry deposition. Existing methods for monitoring the transport of gases were inadequate forstudying aerosols. To solve the problem, qualitative and quantitative informationwere needed to determine the sources of pollutants and their net contribution tothe total dry deposition at a given location. Eventually the methods developed inthis study could be used to evaluate models that estimate the contributions of pointsources of pollution to the level of pollution at designated locations. Following the movement of airborne pollutants requires a natural or artificialtracer (a species specific to the source of the airborne pollutants) that can be exper-imentally measured at sites distant from the source. Limitations placed on thetracer, therefore, governed the design of the experimental procedure. These limita-tions included cost, the need to detect small quantities of the tracer, and the ab-sence of the tracer from other natural sources. In addition, aerosols are emittedfrom high-temperature combustion sources that produce an abundance of very re-active species. The tracer, therefore, had to be both thermally and chemically stable.On the basis of these criteria, rare earth isotopes, such as those of Nd, were selectedas tracers. The choice of tracer, in turn, dictated the analytical method (thermalionization mass spectrometry, or TIMS) for measuring the isotopic abundances of 24. 8Modern Analytical Chemistry Nd in samples. Unfortunately, mass spectrometry is not a selective technique. A mass spectrum provides information about the abundance of ions with a given mass. It cannot distinguish, however, between different ions with the same mass. Consequently, the choice of TIMS required developing a procedure for separating the tracer from the aerosol particulates. Validating the final experimental protocol was accomplished by running a model study in which 148Nd was released into the atmosphere from a 100-MW coal utility boiler. Samples were collected at 13 locations, all of which were 20 km from the source. Experimental results were compared with predictions determined by the rate at which the tracer was released and the known dispersion of the emissions. Finally, the development of this procedure did not occur in a single, linear pass through the analytical approach. As research progressed, problems were encoun- tered and modifications made, representing a cycle through steps 2, 3, and 4 of the analytical approach. Others have pointed out, with justification, that the analytical approach out- lined here is not unique to analytical chemistry, but is common to any aspect of sci- ence involving analysis.8 Here, again, it helps to distinguish between a chemical analysis and analytical chemistry. For other analytically oriented scientists, such as physical chemists and physical organic chemists, the primary emphasis is on the problem, with the results of an analysis supporting larger research goals involving fundamental studies of chemical or physical processes. The essence of analytical chemistry, however, is in the second, third, and fourth steps of the analytical ap- proach. Besides supporting broader research goals by developing and validating an- alytical methods, these methods also define the type and quality of information available to other research scientists. In some cases, the success of an analytical method may even suggest new research problems.1C Common Analytical Problems In Section 1A we indicated that analytical chemistry is more than a collection of qualitative and quantitative methods of analysis. Nevertheless, many problems on which analytical chemists work ultimately involve either a qualitative or quantita- tive measurement. Other problems may involve characterizing a samples chemical or physical properties. Finally, many analytical chemists engage in fundamental studies of analytical methods. In this section we briefly discuss each of these four areas of analysis.Many problems in analytical chemistry begin with the need to identify what isqualitative analysis present in a sample. This is the scope of a qualitative analysis, examples of whichAn analysis in which we determine theinclude identifying the products of a chemical reaction, screening an athletes urineidentity of the constituent species in a for the presence of a performance-enhancing drug, or determining the spatial dis-sample. tribution of Pb on the surface of an airborne particulate. Much of the early work in analytical chemistry involved the development of simple chemical tests to identify the presence of inorganic ions and organic functional groups. The classical labora- tory courses in inorganic and organic qualitative analysis,9 still taught at some schools, are based on this work. Currently, most qualitative analyses use methods such as infrared spectroscopy, nuclear magnetic resonance, and mass spectrometry. These qualitative applications of identifying organic and inorganic compounds are covered adequately elsewhere in the undergraduate curriculum and, so, will receive no further consideration in this text. 25. Chapter 1 Introduction9 Perhaps the most common type of problem encountered in the analytical lab isa quantitative analysis. Examples of typical quantitative analyses include the ele- quantitative analysismental analysis of a newly synthesized compound, measuring the concentration of An analysis in which we determine howmuch of a constituent species is presentglucose in blood, or determining the difference between the bulk and surface con-in a sample.centrations of Cr in steel. Much of the analytical work in clinical, pharmaceutical,environmental, and industrial labs involves developing new methods for determin-ing the concentration of targeted species in complex samples. Most of the examplesin this text come from the area of quantitative analysis. Another important area of analytical chemistry, which receives some attentionin this text, is the development of new methods for characterizing physical andchemical properties. Determinations of chemical structure, equilibrium constants,particle size, and surface structure are examples of a characterization analysis. characterization analysis The purpose of a qualitative, quantitative, and characterization analysis is toAn analysis in which we evaluate asolve a problem associated with a sample. A fundamental analysis, on the othersamples chemical or physical properties.hand, is directed toward improving the experimental methods used in the otherareas of analytical chemistry. Extending and improving the theory on which afundamental analysisAn analysis whose purpose is to improvemethod is based, studying a methods limitations, and designing new and modify- an analytical methods capabilities.ing old methods are examples of fundamental studies in analytical chemistry.1D KEY TERMScharacterization analysis (p. 9)qualitative analysis (p. 8)quantitative analysis(p. 9)fundamental analysis (p. 9)1E SUMMARYAnalytical chemists work to improve the ability of all chemists to chemists to improve existing analytical methods and to developmake meaningful measurements. Chemists working in medicinalnew analytical techniques.chemistry, clinical chemistry, forensic chemistry, and environ- Typical problems on which analytical chemists work includemental chemistry, as well as the more traditional areas of chem- qualitative analyses (what is present?), quantitative analysesistry, need better tools for analyzing materials. The need to work (how much is present?), characterization analyses (what arewith smaller quantities of material, with more complex materi- the materials chemical and physical properties?), and funda-als, with processes occurring on shorter time scales, and with mental analyses (how does this method work and how can it bespecies present at lower concentrations challenges analyticalimproved?).1F PROBLEMS1. For each of the following problems indicate whether itsd. The structure of a newly discovered virus needs to be solution requires a qualitative, quantitative, characterization,determined. or fundamental study. More than one type of analysis may bee. A new visual indicator is needed for an acidbase titration. appropriate for some problems. f. A new law requires a method for evaluating whether a. A hazardous-waste disposal site is believed to be leakingautomobiles are emitting too much carbon monoxide. contaminants into the local groundwater. 2. Read a recent article from the column Analytical Approach, b. An art museum is concerned that a recent acquisition is apublished in Analytical Chemistry, or an article assigned by forgery.your instructor, and write an essay summarizing the nature of c. A more reliable method is needed by airport security for the problem and how it was solved. As a guide, refer back to detecting the presence of explosive materials in luggage. Figure 1.3 for one model of the analytical approach. 26. 10Modern Analytical Chemistry 1G SUGGESTED READINGSThe role of analytical chemistry within the broader discipline ofMottola, H. A. The Interdisciplinary and Multidisciplinarychemistry has been discussed by many prominent analyticalNature of Contemporary Analytical Chemistry and Its Corechemists. Several notable examples follow. Components, Anal. Chim. Acta 1991, 242, 13.Baiulescu, G. E.; Patroescu, C.; Chalmers, R. A. Education and Tyson, J. Analysis: What Analytical Chemists Do. Royal Society of Teaching in Analytical Chemistry. Ellis Horwood: Chichester,Chemistry: Cambridge, England, 1988. 1982. Several journals are dedicated to publishing broadly in theHieftje, G. M. The Two Sides of Analytical Chemistry, Anal.field of analytical chemistry, including Analytical Chemistry, Chem. 1985, 57, 256A267A.Analytica Chimica Acta, Analyst, and Talanta. Other journals, tooKissinger, P. T. Analytical ChemistryWhat is It? Who Needs It? numerous to list, are dedicated to single areas of analytical Why Teach It? Trends Anal. Chem. 1992, 11, 5457.chemistry.Laitinen, H. A. Analytical Chemistry in a Changing World,Current research in the areas of quantitative analysis, qualitative Anal. Chem. 1980, 52, 605A609A.analysis, and characterization analysis are reviewed biannuallyLaitinen, H. A. History of Analytical Chemistry in the U.S.A., (odd-numbered years) in Analytical Chemistrys Application Talanta 1989, 36, 19.Reviews.Laitinen, H. A.; Ewing, G. (eds). A History of AnalyticalCurrent research on fundamental developments in analytical Chemistry. The Division of Analytical Chemistry of thechemistry are reviewed biannually (even-numbered years) in American Chemical Society: Washington, D.C., 1972.Analytical Chemistrys Fundamental Reviews.McLafferty, F. W. Analytical Chemistry: Historic and Modern, Acc. Chem. Res. 1990, 23, 6364. 1H REFERENCES1. Ravey, M. Spectroscopy 1990, 5(7), 11. 113119; (c) Atkinson, G. F. J. Chem. Educ. 1982, 59, 201202;2. de Haseth, J. Spectroscopy 1990, 5(7), 11. (d) Pardue, H. L.; Woo, J. J. Chem. Educ. 1984, 61, 409412;(e) Guarnieri, M. J. Chem. Educ. 1988, 65, 201203; (f) de Haseth, J.3. Fresenius, C. R. A System of Instruction in Quantitative ChemicalSpectroscopy 1990, 5, 2021; (g) Strobel, H. A. Am. Lab. 1990, Analysis. John Wiley and Sons: New York, 1881.October, 1724.4. Hillebrand, W. F.; Lundell, G. E. F. Applied Inorganic Analysis, John 8. Hieftje, G. M. Am. Lab. 1993, October, 5361. Wiley and Sons: New York, 1953. 9. See, for example, the following laboratory texts: (a) Sorum, C. H.;5. Van Loon, J. C. Analytical Atomic Absorption Spectroscopy. AcademicLagowski, J. J. Introduction to Semimicro Qualitative Analysis, 5th ed. Press: New York, 1980.Prentice-Hall: Englewood Cliffs, NJ, 1977.; (b) Shriner, R. L.; Fuson,6. Murray, R. W. Anal. Chem. 1991, 63, 271A.R. C.; Curtin, D. Y. The Systematic Identification of Organic7. For several different viewpoints see (a) Beilby, A. L. J. Chem. Educ.Compounds, 5th ed. John Wiley and Sons: New York, 1964. 1970, 47, 237238; (b) Lucchesi, C. A. Am. Lab. 1980, October, 27. Chapter 2Basic Tools of Analytical ChemistryI n the chapters that follow we will learn about the specifics ofanalytical chemistry. In the process we will ask and answer questionssuch as How do we treat experimental data? How do we ensure thatour results are accurate? How do we obtain a representativesample? and How do we select an appropriate analytical technique?Before we look more closely at these and other questions, we will firstreview some basic numerical and experimental tools of importance toanalytical chemists.11 28. 12Modern Analytical Chemistry 2A Numbers in Analytical ChemistryAnalytical chemistry is inherently a quantitative science. Whether determining theconcentration of a species in a solution, evaluating an equilibrium constant, mea-suring a reaction rate, or drawing a correlation between a compounds structureand its reactivity, analytical chemists make measurements and perform calculations.In this section we briefly review several important topics involving the use of num-bers in analytical chemistry.2A.1 Fundamental Units of MeasureImagine that you find the following instructions in a laboratory procedure: Trans-fer 1.5 of your sample to a 100 volumetric flask, and dilute to volume. How do youdo this? Clearly these instructions are incomplete since the units of measurementare not stated. Compare this with a complete instruction: Transfer 1.5 g of yoursample to a 100-mL volumetric flask, and dilute to volume. This is an instructionthat you can easily follow. Measurements usually consist of a unit and a number expressing the quantityof that unit. Unfortunately, many different units may be used to express the samephysical measurement. For example, the mass of a sample weighing 1.5 g also maybe expressed as 0.0033 lb or 0.053 oz. For consistency, and to avoid confusion, sci-entists use a common set of fundamental units, several of which are listed in Table SI units 2.1. These units are called SI units after the Systme International dUnits. Other Stands for Systme International dUnits. measurements are defined using these fundamental SI units. For example, we mea- These are the internationally agreed on units for measurements.sure the quantity of heat produced during a chemical reaction in joules, (J), wherem2 kg1J =1 s2Table 2.2 provides a list of other important derived SI units, as well as a few com-monly used non-SI units. Chemists frequently work with measurements that are very large or very small.A mole, for example, contains 602,213,670,000,000,000,000,000 particles, and someanalytical techniques can detect as little as 0.000000000000001 g of a compound. scientific notationFor simplicity, we express these measurements using scientific notation; thus, a A shorthand method for expressing verymole contains 6.0221367 1023 particles, and the stated mass is 1 1015 g. Some- large or very small numbers by indicating powers of ten; for example, times it is preferable to express measurements without the exponential term, replac- 1000 is 1 103. ing it with a prefix. A mass of 1 1015 g is the same as 1 femtogram. Table 2.3 listsother common prefixes. Table 2.1 Fundamental SI UnitsMeasurementUnit Symbolmass kilogram kgvolume literLdistance metermtemperaturekelvin Ktime second scurrentampere Aamount of substancemole mol 29. Chapter 2 Basic Tools of Analytical Chemistry13 Table 2.2 Other SI and Non-SI Units MeasurementUnitSymbolEquivalent SI units1 = 1 1010 m lengthangstrom 1 N = 1 m kg/s2force newton Npressurepascal Pa 1 Pa = 1 N/m2 = 1 kg/(m s2)1 atm = 101,325 Pa atmosphere atm1 J = 1 N m = 1 m2 kg/s2energy, work, heatjouleJ1 W = 1 J/s = 1 m2 kg/s3power watt W1C=1A s chargecoulombCpotential volt V1 V = 1 W/A = 1 m2 kg/(s3 A)temperature degree Celsius C C = K 273.15degree FahrenheitF F = 1.8(K 273.15) + 32 Table 2.3 Common Prefixes for Exponential NotationExponentialPrefix Symbol1012teraT109 gigaG106 megaM103 kilok101decid102centi c103milli m106micro 109nanon1012 picop1015 femto f1018 attoa2A.2 Significant FiguresRecording a measurement provides information about both its magnitude and un-certainty. For example, if we weigh a sample on a balance and record its mass as1.2637 g, we assume that all digits, except the last, are known exactly. We assumethat the last digit has an uncertainty of at least 1, giving an absolute uncertainty ofat least 0.0001 g, or a relative uncertainty of at least0.0001 g 100 = 0.0079%1.2637 g Significant figures are a reflection of a measurements uncertainty. The num- significant figuresber of significant figures is equal to the number of digits in the measurement, with The digits in a measured quantity, including all digits known exactly andthe exception that a zero (0) used to fix the location of a decimal point is not con- one digit (the last) whose quantity issidered significant. This definition can be ambiguous. For example, how many sig-uncertain.nificant figures are in the number 100? If measured to the nearest hundred, thenthere is one significant figure. If measured to the nearest ten, however, then two 30. 14 Modern Analytical Chemistry significant figures are included. To avoid ambiguity we use scientific notation. Thus, 1 102 has one significant figure, whereas 1.0 102 has two significant figures.For measurements using logarithms, such as pH, the number of significant figures is equal to the number of digits to the right of the decimal, including all zeros. Digits to the left of the decimal are not included as significant figures since they only indicate the power of 10. A pH of 2.45, therefore, contains two signifi- cant figures.Exact numbers, such as the stoichiometric coefficients in a chemical formula or reaction, and unit conversion factors, have an infinite number of significant figures. A mole of CaCl2, for example, contains exactly two moles of chloride and one mole of calcium. In the equality1000 mL = 1 L both numbers have an infinite number of significant figures.Recording a measurement to the correct number of significant figures is im- portant because it tells others about how precisely you made your measurement. For example, suppose you weigh an object on a balance capable of measuring mass to the nearest 0.1 mg, but record its mass as 1.762 g instead of 1.7620 g. By failing to record the trailing zero, which is a significant figure, you suggest to others that the mass was determined using a balance capable of weighing to only the nearest 1 mg. Similarly, a buret with scale markings every 0.1 mL can be read to the nearest 0.01 mL. The digit in the hundredths place is the least sig- nificant figure since we must estimate its value. Reporting a volume of 12.241 mL implies that your burets scale is more precise than it actually is, with divi- sions every 0.01 mL.Significant figures are also important because they guide us in reporting the re- sult of an analysis. When using a measurement in a calculation, the result of that calculation can never be more certain than that measurements uncertainty. Simply put, the result of an analysis can never be more certain than the least certain mea- surement included in the analysis.As a general rule, mathematical operations involving addition and subtraction are carried out to the last digit that is significant for all numbers included in the cal- culation. Thus, the sum of 135.621, 0.33, and 21.2163 is 157.17 since the last digit that is significant for all three numbers is in the hundredths place. 135.621 + 0.33 + 21.2163 = 157.1673 = 157.17 When multiplying and dividing, the general rule is that the answer contains the same number of significant figures as that number in the calculation having the fewest significant figures. Thus,22.91 0.152= 0.21361 = 0.214 16.302It is important to remember, however, that these rules are generalizations. What is conserved is not the number of significant figures, but absolute uncertainty when adding or subtracting, and relative uncertainty when multiplying or dividing. For example, the following calculation reports the answer to the correct number of significant figures, even though it violates the general rules outlined earlier.101= 1.02 99 31. Chapter 2 Basic Tools of Analytical Chemistry15Since the relative uncertainty in both measurements is roughly 1% (101 1, 99 1),the relative uncertainty in the final answer also must be roughly 1%. Reporting theanswer to only two significant figures (1.0), as required by the general rules, impliesa relative uncertainty of 10%. The correct answer, with three significant figures,yields the expected relative uncertainty. Chapter 4 presents a more thorough treat-ment of uncertainty and its importance in reporting the results of an analysis. Finally, to avoid round-off errors in calculations, it is a good idea to retain atleast one extra significant figure throughout the calculation. This is the practiceadopted in this textbook. Better yet, invest in a good scientific calculator that allowsyou to perform lengthy calculations without recording intermediate values. Whenthe calculation is complete, the final answer can be rounded to the correct numberof significant figures using the following simple rules. 1. Retain the least significant figure if it and the digits that follow are less thanhalfway to the next higher digit; thus, rounding 12.442 to the nearest tenthgives 12.4 since 0.442 is less than halfway between 0.400 and 0.500. 2. Increase the least significant figure by 1 if it and the digits that follow are morethan halfway to the next higher digit; thus, rounding 12.476 to the nearest tenthgives 12.5 since 0.476 is more than halfway between 0.400 and 0.500. 3. If the least significant figure and the digits that follow are exactly halfway to thenext higher digit, then round the least significant figure to the nearest evennumber; thus, rounding 12.450 to the nearest tenth gives 12.4, but rounding12.550 to the nearest tenth gives 12.6. Rounding in this manner prevents usfrom introducing a bias by always rounding up or down. 2B Units for Expressing ConcentrationConcentration is a general measurement unit stating the amount of solute present concentrationin a known amount of solutionAn expression stating the relative amount of solute per unit volume or amount of soluteunit mass of solution.Concentration = 2.1amount of solutionAlthough the terms solute and solution are often associated with liquid sam-ples, they can be extended to gas-phase and solid-phase samples as well. The actualunits for reporting concentration depend on how the amounts of solute and solu-tion are measured. Table 2.4 lists the most common units of concentration.2B.1 Molarity and FormalityBoth molarity and formality express concentration as moles of solute per liter of solu-tion. There is, however, a subtle difference between molarity and formality. Molaritymolarityis the concentration of a particular chemical species in solution. Formality, on the The number of moles of solute per literother hand, is a substances total concentration in solution without regard to its spe-of solution (M).cific chemical form. There is no difference between a substances molarity and for- formalitymality if it dissolves without dissociating into ions. The molar concentration of a so- The number of moles of solute,lution of glucose, for example, is the same as its formality.regardless of chemical form, per liter ofFor substances that ionize in solution, such as NaCl, molarity and formality are solution (F).different. For example, dissolving 0.1 mol of NaCl in 1 L of water gives a solutioncontaining 0.1 mol of Na+ and 0.1 mol of Cl. The molarity of NaCl, therefore,is zero since there is essentially no undissociated NaCl in solution. The solution, 32. 16Modern Analytical ChemistryTable 2.4 Common Units for ReportingConcentration NameUnitsa Symbol molaritymoles solute Mliters solution formality number FWs solute F liters solution normality number EWs soluteN liters solution molality moles solutem kg solvent weight % g solute% w/w 100 g solution volume %mL solute% v/v100 mL solution weight-to-volume % g solute% w/v100 mL solution parts per million g soluteppm 10 6 g solution parts per billion g soluteppb 10 9 g solution aFW = formula weight; EW = equivalent weight. instead, is 0.1 M in Na+ and 0.1 M in Cl. The formality of NaCl, however, is 0.1 F because it represents the total amount of NaCl in solution. The rigorous definition of molarity, for better or worse, is largely ignored in the current literature, as it is in this text. When we state that a solution is 0.1 M NaCl we understand it to consist of Na+ and Cl ions. The unit of formality is used only when it provides a clearer de- scription of solution chemistry.Molar concentrations are used so frequently that a symbolic notation is often used to simplify its expression in equations and writing. The use of square brackets around a species indicates that we are referring to that species molar concentration. Thus, [Na+] is read as the molar concentration of sodium ions. 2B.2 Normality