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2. Boston Burr Ridge, IL Dubuque, IA Madison, WI New York San Francisco St. LouisBangkok Bogot Caracas Lisbon London MadridMexico City Milan New Delhi Seoul Singapore Sydney Taipei TorontoCChheemmiissttrryyModern Analytical ChemistryDavid HarveyDePauw University1400-Fm 9/9/99 7:37 AM Page i 3. MODERN 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 2000543dc21 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.comMcGraw-Hill Higher EducationA Division of The McGraw-Hill Companies1400-Fm 9/9/99 7:37 AM Page ii 4. iiiContentsContentsPreface xiiChapter 1Introduction 11A What is Analytical Chemistry? 21B The Analytical Perspective 51C Common Analytical Problems 81D Key Terms 91E Summary 91F Problems 91G Suggested Readings 101H References 10Chapter 2Basic Tools of Analytical Chemistry 112A Numbers in Analytical Chemistry 122A.1 Fundamental Units of Measure 122A.2 Significant Figures 132B Units for Expressing Concentration 152B.1 Molarity and Formality 152B.2 Normality 162B.3 Molality 182B.4 Weight, Volume, and Weight-to-VolumeRatios 182B.5 Converting Between Concentration Units 182B.6 p-Functions 192C Stoichiometric Calculations 202C.1 Conservation of Mass 222C.2 Conservation of Charge 222C.3 Conservation of Protons 222C.4 Conservation of Electron Pairs 232C.5 Conservation of Electrons 232C.6 Using Conservation Principles inStoichiometry Problems 232D Basic Equipment and Instrumentation 252D.1 Instrumentation for Measuring Mass 252D.2 Equipment for Measuring Volume 262D.3 Equipment for Drying Samples 292E Preparing Solutions 302E.1 Preparing Stock Solutions 302E.2 Preparing Solutions by Dilution 312F The Laboratory Notebook 322G Key Terms 322H Summary 332I Problems 332J Suggested Readings 342K References 34Chapter 3The Language of Analytical Chemistry 353A Analysis, Determination, and Measurement 363B Techniques, Methods, Procedures, andProtocols 363C Classifying Analytical Techniques 373D Selecting an Analytical Method 383D.1 Accuracy 383D.2 Precision 393D.3 Sensitivity 393D.4 Selectivity 403D.5 Robustness and Ruggedness 423D.6 Scale of Operation 423D.7 Equipment, Time, and Cost 443D.8 Making the Final Choice 441400-Fm 9/9/99 7:37 AM Page iii 5. iv Modern Analytical Chemistry4E.4 Errors in Significance Testing 844F Statistical Methods for Normal Distributions 854F.1 ComparingX to 854F.2 Comparing s2 to 2 874F.3 Comparing Two Sample Variances 884F.4 Comparing Two Sample Means 884F.5 Outliers 934G Detection Limits 954H Key Terms 964I Summary 964J Suggested Experiments 974K Problems 984L Suggested Readings 1024M References 102Chapter 5Calibrations, Standardizations,and Blank Corrections 1045A Calibrating Signals 1055B Standardizing Methods 1065B.1 Reagents Used as Standards 1065B.2 Single-Point versus Multiple-PointStandardizations 1085B.3 External Standards 1095B.4 Standard Additions 1105B.5 Internal Standards 1155C Linear Regression and Calibration Curves 1175C.1 Linear Regression of Straight-Line CalibrationCurves 1185C.2 Unweighted Linear Regression with Errorsin y 1195C.3 Weighted Linear Regression with Errorsin y 1245C.4 Weighted Linear Regression with Errorsin Both x and y 1275C.5 Curvilinear and MultivariateRegression 1275D Blank Corrections 1285E Key Terms 1305F Summary 1305G Suggested Experiments 1305H Problems 1315I Suggested Readings 1335J References 1343E Developing the Procedure 453E.1 Compensating for Interferences 453E.2 Calibration and Standardization 473E.3 Sampling 473E.4 Validation 473F Protocols 483G The Importance of Analytical Methodology 483H Key Terms 503I Summary 503J Problems 513K Suggested Readings 523L References 52Chapter 4Evaluating Analytical Data 534A Characterizing Measurements and Results 544A.1 Measures of Central Tendency 544A.2 Measures of Spread 554B Characterizing Experimental Errors 574B.1 Accuracy 574B.2 Precision 624B.3 Error and Uncertainty 644C Propagation of Uncertainty 644C.1 A Few Symbols 654C.2 Uncertainty When Adding or Subtracting 654C.3 Uncertainty When Multiplying orDividing 664C.4 Uncertainty for Mixed Operations 664C.5 Uncertainty for Other MathematicalFunctions 674C.6 Is Calculating Uncertainty Actually Useful? 684D The Distribution of Measurements andResults 704D.1 Populations and Samples 714D.2 Probability Distributions for Populations 714D.3 Confidence Intervals for Populations 754D.4 Probability Distributions for Samples 774D.5 Confidence Intervals for Samples 804D.6 A Cautionary Statement 814E Statistical Analysis of Data 824E.1 Significance Testing 824E.2 Constructing a Significance Test 834E.3 One-Tailed and Two-Tailed SignificanceTests 841400-Fm 9/9/99 7:37 AM Page iv 6. Contents vChapter 7Obtaining and Preparing Samplesfor Analysis 1797A The Importance of Sampling 1807B Designing a Sampling Plan 1827B.1 Where to Sample the TargetPopulation 1827B.2 What Type of Sample to Collect 1857B.3 How Much Sample to Collect 1877B.4 How Many Samples to Collect 1917B.5 Minimizing the Overall Variance 1927C Implementing the Sampling Plan 1937C.1 Solutions 1937C.2 Gases 1957C.3 Solids 1967D Separating the Analyte fromInterferents 2017E General Theory of SeparationEfficiency 2027F Classifying Separation Techniques 2057F.1 Separations Based on Size 2057F.2 Separations Based on Mass or Density 2067F.3 Separations Based on ComplexationReactions (Masking) 2077F.4 Separations Based on a Changeof State 2097F.5 Separations Based on a Partitioning BetweenPhases 2117G LiquidLiquid Extractions 2157G.1 Partition Coefficients and DistributionRatios 2167G.2 LiquidLiquid Extraction with No SecondaryReactions 2167G.3 LiquidLiquid Extractions InvolvingAcidBase Equilibria 2197G.4 LiquidLiquid Extractions Involving MetalChelators 2217H Separation versus Preconcentration 2237I Key Terms 2247J Summary 2247K Suggested Experiments 2257L Problems 2267M Suggested Readings 2307N References 231Chapter 6Equilibrium Chemistry 1356A Reversible Reactions and ChemicalEquilibria 1366B Thermodynamics and EquilibriumChemistry 1366C Manipulating Equilibrium Constants 1386D Equilibrium Constants for ChemicalReactions 1396D.1 Precipitation Reactions 1396D.2 AcidBase Reactions 1406D.3 Complexation Reactions 1446D.4 OxidationReduction Reactions 1456E Le Chteliers Principle 1486F Ladder Diagrams 1506F.1 Ladder Diagrams for AcidBase Equilibria 1506F.2 Ladder Diagrams for ComplexationEquilibria 1536F.3 Ladder Diagrams for OxidationReductionEquilibria 1556G Solving Equilibrium Problems 1566G.1 A Simple Problem: Solubility of Pb(IO3)2 inWater 1566G.2 A More Complex Problem: The Common IonEffect 1576G.3 Systematic Approach to Solving EquilibriumProblems 1596G.4 pH of a Monoprotic Weak Acid 1606G.5 pH of a Polyprotic Acid or Base 1636G.6 Effect of Complexation on Solubility 1656H Buffer Solutions 1676H.1 Systematic Solution to BufferProblems 1686H.2 Representing Buffer Solutions withLadder Diagrams 1706I Activity Effects 1716J Two Final Thoughts About EquilibriumChemistry 1756K Key Terms 1756L Summary 1756M Suggested Experiments 1766N Problems 1766O Suggested Readings 1786P References 1781400-Fm 9/9/99 7:38 AM Page v 7. vi Modern Analytical ChemistryChapter 8Gravimetric Methods of Analysis 2328A Overview of Gravimetry 2338A.1 Using Mass as a Signal 2338A.2 Types of Gravimetric Methods 2348A.3 Conservation of Mass 2348A.4 Why Gravimetry Is Important 2358B Precipitation Gravimetry 2358B.1 Theory and Practice 2358B.2 Quantitative Applications 2478B.3 Qualitative Applications 2548B.4 Evaluating Precipitation Gravimetry 2548C Volatilization Gravimetry 2558C.1 Theory and Practice 2558C.2 Quantitative Applications 2598C.3 Evaluating Volatilization Gravimetry 2628D Particulate Gravimetry 2628D.1 Theory and Practice 2638D.2 Quantitative Applications 2648D.3 Evaluating Precipitation Gravimetry 2658E Key Terms 2658F Summary 2668G Suggested Experiments 2668H Problems 2678I Suggested Readings 2718J References 272Chapter 9Titrimetric Methods of Analysis 2739A Overview of Titrimetry 2749A.1 Equivalence Points and End Points 2749A.2 Volume as a Signal 2749A.3 Titration Curves 2759A.4 The Buret 2779B Titrations Based on AcidBase Reactions 2789B.1 AcidBase Titration Curves 2799B.2 Selecting and Evaluating theEnd Point 2879B.3 Titrations in Nonaqueous Solvents 2959B.4 Representative Method 2969B.5 Quantitative Applications 2989B.6 Qualitative Applications 3089B.7 Characterization Applications 3099B.8 Evaluation of AcidBase Titrimetry 3119C Titrations Based on Complexation Reactions 3149C.1 Chemistry and Properties of EDTA 3159C.2 Complexometric EDTA Titration Curves 3179C.3 Selecting and Evaluating the End Point 3229C.4 Representative Method 3249C.5 Quantitative Applications 3279C.6 Evaluation of Complexation Titrimetry 3319D Titrations Based on Redox Reactions 3319D.1 Redox Titration Curves 3329D.2 Selecting and Evaluating the End Point 3379D.3 Representative Method 3409D.4 Quantitative Applications 3419D.5 Evaluation of Redox Titrimetry 3509E Precipitation Titrations 3509E.1 Titration Curves 3509E.2 Selecting and Evaluating the End Point 3549E.3 Quantitative Applications 3549E.4 Evaluation of Precipitation Titrimetry 3579F Key Terms 3579G Summary 3579H Suggested Experiments 3589I Problems 3609J Suggested Readings 3669K References 367Chapter 10Spectroscopic Methodsof Analysis 36810A Overview of Spectroscopy 36910A.1 What Is Electromagnetic Radiation 36910A.2 Measuring Photons as a Signal 37210B Basic Components of SpectroscopicInstrumentation 37410B.1 Sources of Energy 37510B.2 Wavelength Selection 37610B.3 Detectors 37910B.4 Signal Processors 38010C Spectroscopy Based on Absorption 38010C.1 Absorbance of Electromagnetic Radiation 38010C.2 Transmittance and Absorbance 38410C.3 Absorbance and Concentration: BeersLaw 3851400-Fm 9/9/99 7:38 AM Page vi 8. Contents vii11B Potentiometric Methods of Analysis 46511B.1 Potentiometric Measurements 46611B.2 Reference Electrodes 47111B.3 Metallic Indicator Electrodes 47311B.4 Membrane Electrodes 47511B.5 Quantitative Applications 48511B.6 Evaluation 49411C Coulometric Methods of Analysis 49611C.1 Controlled-Potential Coulometry 49711C.2 Controlled-Current Coulometry 49911C.3 Quantitative Applications 50111C.4 Characterization Applications 50611C.5 Evaluation 50711D Voltammetric Methods of Analysis 50811D.1 Voltammetric Measurements 50911D.2 Current in Voltammetry 51011D.3 Shape of Voltammograms 51311D.4 Quantitative and Qualitative Aspectsof Voltammetry 51411D.5 Voltammetric Techniques 51511D.6 Quantitative Applications 52011D.7 Characterization Applications 52711D.8 Evaluation 53111E Key Terms 53211F Summary 53211G Suggested Experiments 53311H Problems 53511I Suggested Readings 54011J References 541Chapter 12Chromatographic and ElectrophoreticMethods 54312A Overview of Analytical Separations 54412A.1 The Problem with SimpleSeparations 54412A.2 A Better Way to Separate Mixtures 54412A.3 Classifying Analytical Separations 54612B General Theory of ColumnChromatography 54712B.1 Chromatographic Resolution 54912B.2 Capacity Factor 55012B.3 Column Selectivity 55212B.4 Column Efficiency 55210C.4 Beers Law and MulticomponentSamples 38610C.5 Limitations to Beers Law 38610D Ultraviolet-Visible and InfraredSpectrophotometry 38810D.1 Instrumentation 38810D.2 Quantitative Applications 39410D.3 Qualitative Applications 40210D.4 Characterization Applications 40310D.5 Evaluation 40910E Atomic Absorption Spectroscopy 41210E.1 Instrumentation 41210E.2 Quantitative Applications 41510E.3 Evaluation 42210F Spectroscopy Based on Emission 42310G Molecular PhotoluminescenceSpectroscopy 42310G.1 Molecular Fluorescence andPhosphorescence Spectra 42410G.2 Instrumentation 42710G.3 Quantitative Applications Using MolecularLuminescence 42910G.4 Evaluation 43210H Atomic Emission Spectroscopy 43410H.1 Atomic Emission Spectra 43410H.2 Equipment 43510H.3 Quantitative Applications 43710H.4 Evaluation 44010I Spectroscopy Based on Scattering 44110I.1 Origin of Scattering 44110I.2 Turbidimetry and Nephelometry 44110J Key Terms 44610K Summary 44610L Suggested Experiments 44710M Problems 45010N Suggested Readings 45810O References 459Chapter 11Electrochemical Methods of Analysis 46111A Classification of Electrochemical Methods 46211A.1 Interfacial Electrochemical Methods 46211A.2 Controlling and Measuring Current andPotential 4621400-Fm 9/9/99 7:38 AM Page vii 9. 12B.5 Peak Capacity 55412B.6 Nonideal Behavior 55512C Optimizing Chromatographic Separations 55612C.1 Using the Capacity Factor to OptimizeResolution 55612C.2 Using Column Selectivity to OptimizeResolution 55812C.3 Using Column Efficiency to OptimizeResolution 55912D Gas Chromatography 56312D.1 Mobile Phase 56312D.2 Chromatographic Columns 56412D.3 Stationary Phases 56512D.4 Sample Introduction 56712D.5 Temperature Control 56812D.6 Detectors for Gas Chromatography 56912D.7 Quantitative Applications 57112D.8 Qualitative Applications 57512D.9 Representative Method 57612D.10 Evaluation 57712E High-Performance LiquidChromatography 57812E.1 HPLC Columns 57812E.2 Stationary Phases 57912E.3 Mobile Phases 58012E.4 HPLC Plumbing 58312E.5 Sample Introduction 58412E.6 Detectors for HPLC 58412E.7 Quantitative Applications 58612E.8 Representative Method 58812E.9 Evaluation 58912F LiquidSolid Adsorption Chromatography 59012G Ion-Exchange Chromatography 59012H Size-Exclusion Chromatography 59312I Supercritical Fluid Chromatography 59612J Electrophoresis 59712J.1 Theory of Capillary Electrophoresis 59812J.2 Instrumentation 60112J.3 Capillary Electrophoresis Methods 60412J.4 Representative Method 60712J.5 Evaluation 60912K Key Terms 60912L Summary 61012M Suggested Experiments 61012N Problems 615viii Modern Analytical Chemistry12O Suggested Readings 62012P References 620Chapter 13Kinetic Methods of Analysis 62213A Methods Based on Chemical Kinetics 62313A.1 Theory and Practice 62413A.2 Instrumentation 63413A.3 Quantitative Applications 63613A.4 Characterization Applications 63813A.5 Evaluation of Chemical KineticMethods 63913B Radiochemical Methods of Analysis 64213B.1 Theory and Practice 64313B.2 Instrumentation 64313B.3 Quantitative Applications 64413B.4 Characterization Applications 64713B.5 Evaluation 64813C Flow Injection Analysis 64913C.1 Theory and Practice 64913C.2 Instrumentation 65113C.3 Quantitative Applications 65513C.4 Evaluation 65813D Key Terms 65813E Summary 65913F Suggested Experiments 65913G Problems 66113H Suggested Readings 66413I References 665Chapter 14Developing a Standard Method 66614A Optimizing the Experimental Procedure 66714A.1 Response Surfaces 66714A.2 Searching Algorithms for ResponseSurfaces 66814A.3 Mathematical Models of ResponseSurfaces 67414B Verifying the Method 68314B.1 Single-Operator Characteristics 68314B.2 Blind Analysis of Standard Samples 68314B.3 Ruggedness Testing 68414B.4 Equivalency Testing 6871400-Fm 9/9/99 7:38 AM Page viii 10. Contents ix15D Key Terms 72115E Summary 72215F Suggested Experiments 72215G Problems 72215H Suggested Readings 72415I References 724AppendixesAppendix 1A Single-Sided Normal Distribution 725Appendix 1B t-Table 726Appendix 1C F-Table 727Appendix 1D Critical Values for Q-Test 728Appendix 1E Random Number Table 728Appendix 2 Recommended Reagents for Preparing PrimaryStandards 729Appendix 3A Solubility Products 731Appendix 3B Acid Dissociation Constants 732Appendix 3C MetalLigand Formation Constants 739Appendix 3D Standard Reduction Potentials 743Appendix 3E Selected Polarographic Half-Wave Potentials 747Appendix 4 Balancing Redox Reactions 748Appendix 5 Review of Chemical Kinetics 750Appendix 6 Countercurrent Separations 755Appendix 7 Answers to Selected Problems 762Glossary 769Index 78114C Validating the Method as a StandardMethod 68714C.1 Two-Sample Collaborative Testing 68814C.2 Collaborative Testing and Analysis ofVariance 69314C.3 What Is a Reasonable Result for aCollaborative Study? 69814D Key Terms 69914E Summary 69914F Suggested Experiments 69914G Problems 70014H Suggested Readings 70414I References 704Chapter 15Quality Assurance 70515A Quality Control 70615B Quality Assessment 70815B.1 Internal Methods of QualityAssessment 70815B.2 External Methods of QualityAssessment 71115C Evaluating Quality Assurance Data 71215C.1 Prescriptive Approach 71215C.2 Performance-Based Approach 7141400-Fm 9/9/99 7:38 AM Page ix 11. x Modern Analytical ChemistryA Guide to Using This Text. . . in ChapterRepresentative MethodsAnnotated methods of typicalanalytical procedures link theory withpractice. The format encouragesstudents to think about the design ofthe procedure and why it works.246 Modern Analytical ChemistryRepresentativeMethodsAn additional problem is encountered when the isolated solid is non-stoichiometric. For example, precipitating Mn2+ as Mn(OH)2, followed by heatingto 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 resultsfrom 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.6Representative 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.Method 8.1 Determination of Mg2+ in Water and Wastewater7Description of Method. Magnesium is precipitated as MgNH4PO4 6H2O using(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 solublein 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. Afterfiltering, the precipitate is converted to Mg2P2O7 and weighed.Procedure. Transfer a sample containing no more than 60 mg of Mg2+ into a600-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 constantlystirring, 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.Allow the resulting solution and precipitate to stand overnight. Isolate theprecipitate by filtration, rinsing with 5% v/v NH3. Dissolve the precipitate in 50 mLof 10% v/v HCl, and precipitate a second time following the same procedure. Afterfiltering, 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 at1100 C.Questions1. Why does the procedure call for a sample containing no more than 60 mg ofq yThere is a serious limitation, however, to an external standardization. Therelationship between Sstand and CS in equation 5.3 is determined when the ana-lyte is present in the external standards matrix. In using an external standardiza-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. Thisis shown in Figure 5.4, where the relationship between the signal and the amountof analyte is shown for both the samples matrix and the standards matrix. Inthis example, using a normal calibration curve results in a negative determinateerror. 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-ble, or an alternative method of standardization must be used. Both approachesare discussed in the following sections.5B.4 Standard AdditionsThe complication of matching the matrix of the standards to that of the samplecan be avoided by conducting the standardization in the sample. This is knownas the method of standard additions. The simplest version of a standard addi-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 ismatrix matchingAdjusting the matrix of an externalstandard so that it is the same as thematrix of the samples to be analyzed.method of standard additionsA standardization in which aliquots of astandard solution are added to thesample.Examples of Typical ProblemsEach example problem includes adetailed solution that helps students inapplying the chapters material topractical problems.Margin NotesMargin notes direct studentsto colorplates located towardthe middle of the bookBold-faced Key Terms with Margin DefinitionsKey words appear in boldface when they are introduced within the text.The term and its definition appear in the margin for quick review by thestudent. All key words are also defined in the glossary.110 Modern Analytical Chemistryeither case, the calibration curve provides a means for relating Ssamp to the ana-lytes concentration.EXAMPLE 5.3A second spectrophotometric method for the quantitative determination ofPb2+ levels in blood gives a linear normal calibration curve for whichSstand = (0.296 ppb1) CS + 0.003What is the Pb2+ level (in ppb) in a sample of blood if Ssamp is 0.397?SOLUTIONTo determine the concentration of Pb2+ in the sample of blood, we replaceSstand in the calibration equation with Ssamp and solve for CAIt is worth noting that the calibration equation in this problem includes anextra term that is not in equation 5.3. Ideally, we expect the calibration curve togive a signal of zero when CS is zero. This is the purpose of using a reagentblank to correct the measured signal. The extra term of +0.003 in ourcalibration equation results from uncertainty in measuring the signal for thereagent blank and the standards.An external standardization allows a related series of samples to be analyzedusing a single calibration curve. This is an important advantage in laboratorieswhere many samples are to be analyzed or when the need for a rapid throughput ofl i iti l t i i l f th t l t dCSAsampppb= = = ... ...0 0030 2960 397 0 0030 2961 331ppbppb1Color plate 1 shows an example of a set ofexternal standards and their correspondingnormal calibration curve.x1400-Fm 9/9/99 7:38 AM Page x 12. List of Key TermsThe key terms introduced within the chapter arelisted at the end of each chapter. Page referencesdirect the student to the definitions in the text.SummaryThe summary provides the student with a briefreview of the important concepts within the chapter.Suggested ExperimentsAn annotated list of representative experiments isprovided from the Journal of Chemical Education.. . . End of Chaptery y5E KEY TERMSaliquot (p. 111)external standard (p. 109)internal standard (p. 116)linear regression (p. 118)matrix matching (p. 110)method of standard additions (p. 110)multiple-point standardization (p. 109)normal calibration curve (p. 109)primary reagent (p. 106)reagent grade (p. 107)residual error (p. 118)secondary reagent (p. 107)single-point standardization (p. 108)standard deviation about theregression (p. 121)total Youden blank (p. 129)In a quantitative analysis, we measure a signal and calculate theamount of analyte using one of the following equations.Smeas = knA + SreagSmeas = kCA + SreagTo obtain accurate results we must eliminate determinate errorsaffecting the measured signal, Smeas, the methods sensitivity, k,and any signal due to the reagents, Sreag.To ensure that Smeas is determined accurately, we calibratethe equipment or instrument used to obtain the signal. Balancesare calibrated using standard weights. When necessary, we canalso correct for the buoyancy of air. Volumetric glassware canbe calibrated by measuring the mass of water contained or de-livered and using the density of water to calculate the true vol-ume. Most instruments have calibration standards suggested bythe manufacturer.An analytical method is standardized by determining its sensi-tivity. There are several approaches to standardization, includingthe use of external standards, the method of standard addition,and the use of an internal standard. The most desirable standard-ization strategy is an external standardization. The method ofstandard additions, in which known amounts of analyte are addedto the sample, is used when the samples matrix complicates theanalysis. An internal standard, which is a species (not analyte)added to all samples and standards, is used when the proceduredoes not allow for the reproducible handling of samples andstandards.Standardizations using a single standard are common, but alsoare subject to greater uncertainty. Whenever possible, a multiple-point standardization is preferred. The results of a multiple-pointstandardization are graphed as a calibration curve. A linear regres-sion analysis can provide an equation for the standardization.A reagent blank corrects the measured signal for signals due toreagents other than the sample that are used in an analysis. Themost common reagent blank is prepared by omitting the sample.When a simple reagent blank does not compensate for all constantsources of determinate error, other types of blanks, such as thetotal Youden blank, can be used.5F SUMMARYCalibrationVolumetric glassware (burets, pipets, andvolumetric flasks) can be calibrated in the manner describedin Example 5.1. Most instruments have a calibration samplethat can be prepared to verify the instruments accuracy andprecision. For example, as described in this chapter, asolution of 60.06 ppm K2Cr2O7 in 0.0050 M H2SO4 shouldgive an absorbance of 0.640 0.010 at a wavelength of350.0 nm when using 0.0050 M H2SO4 as a reagentblank. These exercises also provide practice with usingvolumetric glassware, weighing samples, and preparingsolutions.StandardizationExternal standards, standard additions,and internal standards are a common feature of manyquantitative analyses. Suggested experiments using thesestandardization methods are found in later chapters. A goodproject experiment for introducing external standardization,standard additions, and the importance of the samplesmatrix is to explore the effect of pH on the quantitativeanalysis of an acidbase indicator. Using bromothymol blueas an example, external standards can be prepared in a pH 9buffer and used to analyze samples buffered to different pHsin the range of 610. Results can be compared with thoseobtained using a standard addition.5G Suggested EXPERIMENTSThe following exercises and experiments help connect the material in this chapter to the analytical laboratory.Experiments1. When working with a solid sample, it often is necessary tobring the analyte into solution by dissolving the sample in asuitable solvent. Any solid impurities that remain areremoved by filtration before continuing with the analysis.In a typical total analysis method, the procedure mightreadAfter dissolving the sample in a beaker, remove anysolid impurities by passing the solution containingthe analyte through filter paper, collecting thesolution in a clean Erlenmeyer flask. Rinse the beakerwith several small portions of solvent, passing theserinsings through the filter paper, and collecting themin the same Erlenmeyer flask. Finally, rinse the filterpaper with several portions of solvent, collecting therinsings in the same Erlenmeyer flask.For a typical concentration method, however, the proceduremight state4. A sample was analyzed to determine the concentration of ananalyte. Under the conditions of the analysis, the sensitivity is17.2 ppm1. What is the analytes concentration if Smeas is 35.2and Sreag is 0.6?5. A method for the analysis of Ca2+ in water suffers from aninterference in the presence of Zn2+. When the concentrationof Ca2+ is 50 times greater than that of Zn2+, an analysis forCa2+ gives a relative error of 2.0%. What is the value of theselectivity coefficient for this method?6. The quantitative analysis for reduced glutathione in blood iscomplicated by the presence of many potential interferents.In one study, when analyzing a solution of 10-ppbglutathione and 1.5-ppb ascorbic acid, the signal was 5.43times greater than that obtained for the analysis of 10-ppbglutathione.12 What is the selectivity coefficient for thisanalysis? The same study found that when analyzing asolution of 350-ppb methionine and 10-ppb glutathione thesignal was 0 906 times less than that obtained for the analysis3J PROBLEMSy yThe role of analytical chemistry within the broader discipline ofchemistry has been discussed by many prominent analyticalchemists. Several notable examples follow.Baiulescu, G. E.; Patroescu, C.; Chalmers, R. A. Education andTeaching in Analytical Chemistry. Ellis Horwood: Chichester,1982.Hieftje, G. M. The Two Sides of Analytical Chemistry, Anal.Chem. 1985, 57, 256A267A.Kissinger, P. T. Analytical ChemistryWhat is It? Who Needs It?Why Teach It? Trends Anal. Chem. 1992, 11, 5457.Laitinen, H. A. Analytical Chemistry in a Changing World,Anal. Chem. 1980, 52, 605A609A.Laitinen, H. A. History of Analytical Chemistry in the U.S.A.,Talanta 1989, 36, 19.Laitinen, H. A.; Ewing, G. (eds). A History of AnalyticalChemistry. The Division of Analytical Chemistry ofthe American Chemical Society: Washington, D.C.,1972.McLafferty, F. W. Analytical Chemistry: Historic and Modern,Acc. Chem. Res. 1990, 23, 6364.1G SUGGESTED READINGS1. Ravey, M. Spectroscopy 1990, 5(7), 11.2. de Haseth, J. Spectroscopy 1990, 5(7), 11.3. Fresenius, C. R. A System of Instruction in Quantitative ChemicalAnalysis. John Wiley and Sons: New York, 1881.4. Hillebrand, W. F.; Lundell, G. E. F. Applied Inorganic Analysis, JohnWiley and Sons: New York, 1953.5. Van Loon, J. C. Analytical Atomic Absorption Spectroscopy. AcademicPress: New York, 1980.6. Murray, R. W. Anal. Chem. 1991, 63, 271A.7. For several different viewpoints see (a) Beilby, A. L. J. Chem. Educ.1970, 47, 237238; (b) Lucchesi, C. A. Am. Lab. 1980, October,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.Spectroscopy 1990, 5, 2021; (g) Strobel, H. A. Am. Lab. 1990,October, 1724.8. Hieftje, G. M. Am. Lab. 1993, October, 5361.9. See, for example, the following laboratory texts: (a) Sorum, C. H.;Lagowski, J. J. Introduction to Semimicro Qualitative Analysis, 5th ed.Prentice-Hall: Englewood Cliffs, NJ, 1977.; (b) Shriner, R. L.; Fuson,R. C.; Curtin, D. Y. The Systematic Identification of OrganicCompounds, 5th ed. John Wiley and Sons: New York, 1964.1H REFERENCESProblemsA variety of problems, many basedon data from the analytical literature,provide the student with practicalexamples of current research.Suggested ReadingsSuggested readings give the studentaccess to more comprehensivediscussion of the topics introducedwithin the chapter.ReferencesThe references cited in thechapter are provided so thestudent can access them forfurther information.xi1400-Fm 9/9/99 7:38 AM Page xi 13. As 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.xiiPreface Preface1400-Fm 9/9/99 7:38 AM Page xii 14. 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.1400-Fm 9/9/99 7:38 AM Page xiii 15. 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 topicsxiv Preface1400-Fm 9/9/99 7:38 AM Page xiv 16. 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 BallantineNorthern Illinois UniversityJohn E. BauerIllinois State UniversityAli BazziUniversity of MichiganDearbornSteven D. BrownUniversity of DelawareWendy ClevengerUniversity of TennesseeChattanoogaCathy CobbAugusta State UniversityPaul FlowersUniversity of North CarolinaPembrokeNancy GordonUniversity of Southern Maine1400-Fm 9/9/99 7:38 AM Page xv 17. Virginia M. IndiveroSwarthmore CollegeMichael JanusaNicholls State UniversityJ. David JenkinsGeorgia Southern UniversityRichard S. MitchellArkansas State UniversityGeorge A. Pearse, Jr.Le Moyne CollegeGary RaysonNew Mexico State UniversityDavid RedfieldNW Nazarene 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.xvi PrefaceVincent RemchoWest Virginia UniversityJeanette K. RiceGeorgia Southern UniversityMartin W. RoweTexas A&M UniversityAlexander ScheelineUniversity of IllinoisJames D. StuartUniversity of ConnecticutThomas J. WenzelBates CollegeDavid ZaxCornell University1400-Fm 9/9/99 7:38 AM Page xvi 18. CChhaapptteerr 11IntroductionChemistry 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.1400-CH01 9/9/99 2:20 PM Page 1 19. 2 Modern Analytical Chemistry*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.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.2Heres 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.%Ni =mass point A mass point Bmass sample 1001400-CH01 9/9/99 2:20 PM Page 2 20. Chapter 1 Introduction 3Original SamplePbSO4SandBasicferricacetateCuS1:3 H2SO4/HNO3 100C (810 h)dilute w/H2O, digest 24 hCu2+, Fe3+Co2+, Ni2+Fe3+, Co2+, Ni2+Fe(OH)3CoS, NiSCuS, PbSCo(OH)2, Ni(OH)2CoO, NiOcool, add NH3digest 5070, 30 minCo2+, Ni2+Fe3+WasteWasteCo2+, Ni2+aqua regiaheat, add HCl untilstrongly acidicbubble H2S (g)WasteCo2+SolidKeySolutionH2O, HClheatadd Na2CO3 until alkalineNaOHK3Co(NO3)5Ni2+neutralize w/ NH3Na2CO3, CH3COOHslightly acidify w/ HClheat, bubble H2S (g)HClheatCoas aboveCo, Niheat, H2 (g)HNO3K2CO3, KNO3CH3COOHdigest 24 hdilutebubble H2S(g)ABFigure 1.1Analytical scheme outlined by Fresenius3 for the gravimetric analysis of Ni in ores.1400-CH01 9/9/99 2:20 PM Page 3 21. The combination of determining the mass of Ni2+ by difference, coupled with theneed for many reactions and filtrations makes this procedure both time-consumingand 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 forthe analysis of Ni2+ in ores progressed from precipitating Ni(DMG)2 to flameatomic 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 . . . thescience of inventing and applying the concepts, principles, and . . . strategies formeasuring the characteristics of chemical systems and species.6 Analytical chemiststypically operate at the extreme edges of analysis, extending and improving the abil-ity of all chemists to make meaningful measurements on smaller samples, on morecomplex samples, on shorter time scales, and on species present at lower concentra-tions. Throughout its history, analytical chemistry has provided many of the toolsand 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.4 Modern Analytical ChemistryOriginal sampleResidueNi(DMG)2(s)HNO3, HCl, heatSolutionSolidKeySolution20% NH4Cl10% tartaric acidtake alkaline with 1:1 NH3YesNoAtake acid with HCl1% alcoholic DMGtake alkaline with 1:1 NH3take acid with HCl10% tartaric acidtake alkaline with 1:1 NH3 Issolidpresent?%Ni = 100mass A 0.2031g sampleFigure 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 forthe difference in the formula weights ofNi(DMG)2 and Ni; see Chapter 8 for moredetails.1400-CH01 9/9/99 2:20 PM Page 4 22. Chapter 1 Introduction 5You 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 1974.1400-CH01 9/9/99 2:20 PM Page 5 23. Figure 1.3Flow diagram for the analytical approach tosolving problems; modified after Atkinson.7canalysis. Finding an appropriate balance between these parameters is frequentlycomplicated by their interdependence. For example, improving the precision of ananalysis may require a larger sample. Consideration is also given to collecting, stor-ing, and preparing samples, and to whether chemical or physical interferences willaffect 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. Aspart of the validation process, appropriate chemical or physical standards are usedto calibrate any equipment being used and any solutions whose concentrationsmust be known. The selected samples are then analyzed and the raw data recorded.The raw data collected during the experiment are then analyzed. Frequently thedata must be reduced or transformed to a more readily analyzable form. A statisticaltreatment of the data is used to evaluate the accuracy and precision of the analysisand 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. Whena 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.6 Modern Analytical Chemistry1. Identify the problemDetermine type of information needed(qualitative, quantitative,characterization, or fundamental)Identify context of the problem2. Design the experimental procedureEstablish design criteria (accuracy, precision,scale of operation, sensitivity, selectivity,cost, speed)Identify interferentsSelect methodEstablish validation criteriaEstablish sampling strategy Feedbackloop3. Conduct an experimentCalibrate instruments and equipmentStandardize reagentsGather data4. Analyze the experimental dataReduce or transform dataAnalyze statisticsVerify resultsInterpret results5. Propose a solutionConduct external evaluation1400-CH01 9/9/99 2:20 PM Page 6 24. As 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 ofChapter 1 Introduction 71400-CH01 9/9/99 2:20 PM Page 7 25. 8 Modern Analytical Chemistryqualitative analysisAn analysis in which we determine theidentity of the constituent species in asample.Nd in samples. Unfortunately, mass spectrometry is not a selective technique. Amass spectrum provides information about the abundance of ions with a givenmass. It cannot distinguish, however, between different ions with the same mass.Consequently, the choice of TIMS required developing a procedure for separatingthe tracer from the aerosol particulates.Validating the final experimental protocol was accomplished by running amodel study in which 148Nd was released into the atmosphere from a 100-MW coalutility boiler. Samples were collected at 13 locations, all of which were 20 km fromthe source. Experimental results were compared with predictions determined by therate 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 passthrough the analytical approach. As research progressed, problems were encoun-tered and modifications made, representing a cycle through steps 2, 3, and 4 of theanalytical 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 chemicalanalysis and analytical chemistry. For other analytically oriented scientists, such asphysical chemists and physical organic chemists, the primary emphasis is on theproblem, with the results of an analysis supporting larger research goals involvingfundamental studies of chemical or physical processes. The essence of analyticalchemistry, 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 informationavailable to other research scientists. In some cases, the success of an analyticalmethod may even suggest new research problems.1C Common Analytical ProblemsIn Section 1A we indicated that analytical chemistry is more than a collection ofqualitative and quantitative methods of analysis. Nevertheless, many problems onwhich analytical chemists work ultimately involve either a qualitative or quantita-tive measurement. Other problems may involve characterizing a samples chemicalor physical properties. Finally, many analytical chemists engage in fundamentalstudies of analytical methods. In this section we briefly discuss each of these fourareas of analysis.Many problems in analytical chemistry begin with the need to identify what ispresent in a sample. This is the scope of a qualitative analysis, examples of whichinclude identifying the products of a chemical reaction, screening an athletes urinefor the presence of a performance-enhancing drug, or determining the spatial dis-tribution of Pb on the surface of an airborne particulate. Much of the early work inanalytical chemistry involved the development of simple chemical tests to identifythe presence of inorganic ions and organic functional groups. The classical labora-tory courses in inorganic and organic qualitative analysis,9 still taught at someschools, are based on this work. Currently, most qualitative analyses use methodssuch as infrared spectroscopy, nuclear magnetic resonance, and mass spectrometry.These qualitative applications of identifying organic and inorganic compounds arecovered adequately elsewhere in the undergraduate curriculum and, so, will receiveno further consideration in this text.1400-CH01 9/9/99 2:20 PM Page 8 26. Perhaps the most common type of problem encountered in the analytical lab isa quantitative analysis. Examples of typical quantitative analyses include the ele-mental analysis of a newly synthesized compound, measuring the concentration ofglucose in blood, or determining the difference between the bulk and surface con-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.The purpose of a qualitative, quantitative, and characterization analysis is tosolve a problem associated with a sample. A fundamental analysis, on the otherhand, is directed toward improving the experimental methods used in the otherareas of analytical chemistry. Extending and improving the theory on which amethod is based, studying a methods limitations, and designing new and modify-ing old methods are examples of fundamental studies in analytical chemistry.Chapter 1 Introduction 9characterization analysisAn analysis in which we evaluate asamples chemical or physical properties.fundamental analysisAn analysis whose purpose is to improvean analytical methods capabilities.quantitative analysisAn analysis in which we determine howmuch of a constituent species is presentin a sample.1D KEY TERMScharacterization analysis (p. 9)fundamental analysis (p. 9)qualitative analysis (p. 8) quantitative analysis (p. 9)Analytical chemists work to improve the ability of all chemists tomake meaningful measurements. Chemists working in medicinalchemistry, clinical chemistry, forensic chemistry, and environ-mental chemistry, as well as the more traditional areas of chem-istry, need better tools for analyzing materials. The need to workwith smaller quantities of material, with more complex materi-als, with processes occurring on shorter time scales, and withspecies present at lower concentrations challenges analyticalchemists to improve existing analytical methods and to developnew analytical techniques.Typical problems on which analytical chemists work includequalitative analyses (what is present?), quantitative analyses(how much is present?), characterization analyses (what arethe materials chemical and physical properties?), and funda-mental analyses (how does this method work and how can it beimproved?).1E SUMMARY1. For each of the following problems indicate whether itssolution requires a qualitative, quantitative, characterization,or fundamental study. More than one type of analysis may beappropriate for some problems.a. A hazardous-waste disposal site is believed to be leakingcontaminants into the local groundwater.b. An art museum is concerned that a recent acquisition is aforgery.c. A more reliable method is needed by airport security fordetecting the presence of explosive materials in luggage.d. The structure of a newly discovered virus needs to bedetermined.e. A new visual indicator is needed for an acidbase titration.f. A new law requires a method for evaluating whetherautomobiles are emitting too much carbon monoxide.2. Read a recent article from the column Analytical Approach,published in Analytical Chemistry, or an article assigned byyour instructor, and write an essay summarizing the nature ofthe problem and how it was solved. As a guide, refer back toFigure 1.3 for one model of the analytical approach.1F PROBLEMS1400-CH01 9/9/99 2:20 PM Page 9 27. 10 Modern Analytical ChemistryThe role of analytical chemistry within the broader discipline ofchemistry has been discussed by many prominent analyticalchemists. Several notable examples follow.Baiulescu, G. E.; Patroescu, C.; Chalmers, R. A. Education andTeaching in Analytical Chemistry. Ellis Horwood: Chichester,1982.Hieftje, G. M. The Two Sides of Analytical Chemistry, Anal.Chem. 1985, 57, 256A267A.Kissinger, P. T. Analytical ChemistryWhat is It? Who Needs It?Why Teach It? Trends Anal. Chem. 1992, 11, 5457.Laitinen, H. A. Analytical Chemistry in a Changing World,Anal. Chem. 1980, 52, 605A609A.Laitinen, H. A. History of Analytical Chemistry in the U.S.A.,Talanta 1989, 36, 19.Laitinen, H. A.; Ewing, G. (eds). A History of AnalyticalChemistry. The Division of Analytical Chemistry of theAmerican Chemical Society: Washington, D.C., 1972.McLafferty, F. W. Analytical Chemistry: Historic and Modern,Acc. Chem. Res. 1990, 23, 6364.Mottola, H. A. The Interdisciplinary and MultidisciplinaryNature of Contemporary Analytical Chemistry and Its CoreComponents, Anal. Chim. Acta 1991, 242, 13.Tyson, J. Analysis: What Analytical Chemists Do. Royal Society ofChemistry: Cambridge, England, 1988.Several journals are dedicated to publishing broadly in thefield of analytical chemistry, including Analytical Chemistry,Analytica Chimica Acta, Analyst, and Talanta. Other journals, toonumerous to list, are dedicated to single areas of analyticalchemistry.Current research in the areas of quantitative analysis, qualitativeanalysis, and characterization analysis are reviewed biannually(odd-numbered years) in Analytical Chemistrys ApplicationReviews.Current research on fundamental developments in analyticalchemistry are reviewed biannually (even-numbered years) inAnalytical Chemistrys Fundamental Reviews.1G SUGGESTED READINGS1. Ravey, M. Spectroscopy 1990, 5(7), 11.2. de Haseth, J. Spectroscopy 1990, 5(7), 11.3. Fresenius, C. R. A System of Instruction in Quantitative ChemicalAnalysis. John Wiley and Sons: New York, 1881.4. Hillebrand, W. F.; Lundell, G. E. F. Applied Inorganic Analysis, JohnWiley and Sons: New York, 1953.5. Van Loon, J. C. Analytical Atomic Absorption Spectroscopy. AcademicPress: New York, 1980.6. Murray, R. W. Anal. Chem. 1991, 63, 271A.7. For several different viewpoints see (a) Beilby, A. L. J. Chem. Educ.1970, 47, 237238; (b) Lucchesi, C. A. Am. Lab. 1980, October,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.Spectroscopy 1990, 5, 2021; (g) Strobel, H. A. Am. Lab. 1990,October, 1724.8. Hieftje, G. M. Am. Lab. 1993, October, 5361.9. See, for example, the following laboratory texts: (a) Sorum, C. H.;Lagowski, J. J. Introduction to Semimicro Qualitative Analysis, 5th ed.Prentice-Hall: Englewood Cliffs, NJ, 1977.; (b) Shriner, R. L.; Fuson,R. C.; Curtin, D. Y. The Systematic Identification of OrganicCompounds, 5th ed. John Wiley and Sons: New York, 1964.1H REFERENCES1400-CH01 9/9/99 2:20 PM Page 10 28. CChhaapptteerr 211Basic Tools of Analytical ChemistryIn 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.1400-CH02 9/8/99 3:47 PM Page 11 29. 12 Modern Analytical Chemistry2A 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 Table2.1. These units are called SI units after the Systme International dUnits. Othermeasurements are defined using these fundamental SI units. For example, we mea-sure the quantity of heat produced during a chemical reaction in joules, (J), whereTable 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.For simplicity, we express these measurements using scientific notation; thus, amole contains 6.0221367 1023 particles, and the stated mass is 1 1015 g. Some-times it is preferable to express measurements without the exponential term, replac-ing it with a prefix. A mass of 1 1015 g is the same as 1 femtogram. Table 2.3 listsother common prefixes.1 J = 1m kg2s2Table 2.1 Fundamental SI UnitsMeasurement Unit Symbolmass kilogram kgvolume liter Ldistance meter mtemperature kelvin Ktime second scurrent ampere Aamount of substance mole molscientific notationA shorthand method for expressing verylarge or very small numbers byindicating powers of ten; for example,1000 is 1 103.SI unitsStands for Systme International dUnits.These are the internationally agreed onunits for measurements.1400-CH02 9/8/99 3:47 PM Page 12 30. 2A.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 leastSignificant figures are a reflection of a measurements uncertainty. The num-ber of significant figures is equal to the number of digits in the measurement, withthe exception that a zero (0) used to fix the location of a decimal point is not con-sidered significant. This definition can be ambiguous. For example, how many sig-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 = 0 00011 2637100 0 0079... %ggChapter 2 Basic Tools of Analytical Chemistry 13Table 2.2 Other SI and Non-SI UnitsMeasurement Unit Symbol Equivalent SI unitslength angstrom 1 = 1 1010 mforce newton N 1 N = 1 m kg/s2pressure pascal Pa 1 Pa = 1 N/m2 = 1 kg/(m s2)atmosphere atm 1 atm = 101,325 Paenergy, work, heat joule J 1 J = 1 N m = 1 m2kg/s2power watt W 1 W = 1 J/s = 1 m2kg/s3charge coulomb C 1 C = 1 A spotential volt V 1 V = 1 W/A = 1 m2kg/(s3A)temperature degree Celsius C C = K 273.15degree Fahrenheit F F = 1.8(K 273.15) + 32Table 2.3 Common Prefixes for ExponentialNotationExponential Prefix Symbol1012 tera T109 giga G106 mega M103 kilo k101 deci d102 centi c103 milli m106 micro 109 nano n1012 pico p1015 femto f1018 atto asignificant figuresThe digits in a measured quantity,including all digits known exactly andone digit (the last) whose quantity isuncertain.1400-CH02 9/8/99 3:47 PM Page 13 31. 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 significantfigures is equal to the number of digits to the right of the decimal, including allzeros. Digits to the left of the decimal are not included as significant figures sincethey 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 orreaction, 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 moleof calcium. In the equality1000 mL = 1 Lboth 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 measuringmass 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 toothers that the mass was determined using a balance capable of weighing to onlythe nearest 1 mg. Similarly, a buret with scale markings every 0.1 mL can beread 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 12.241mL 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 thatcalculation can never be more certain than that measurements uncertainty. Simplyput, 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 subtractionare 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 digitthat is significant for all three numbers is in the hundredths place.135.621 + 0.33 + 21.2163 = 157.1673 = 157.17When multiplying and dividing, the general rule is that the answer contains thesame number of significant figures as that number in the calculation having thefewest significant figures. Thus,It is important to remember, however, that these rules are generalizations.What is conserved is not the number of significant figures, but absolute uncertaintywhen adding or subtracting, and relative uncertainty when multiplying or dividing.For example, the following calculation reports the answer to the correct number ofsignificant figures, even though it violates the general rules outlined earlier.101991 02= .22 91 015216 3020 21361 0 214. ... .= =14 Modern Analytical Chemistry1400-CH02 9/8/99 3:48 PM Page 14 32. Chapter 2 Basic Tools of Analytical Chemistry 15Since 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 presentin a known amount of solution2.1Although 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. Molarityis the concentration of a particular chemical species in solution. Formality, on theother hand, is a substances total concentration in solution without regard to its spe-cific chemical form. There is no difference between a substances molarity and for-mality if it dissolves without dissociating into ions. The molar concentration of a so-lution of glucose, for example, is the same as its formality.For substances that ionize in solution, such as NaCl, molarity and formality aredifferent. 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,Concentrationamount of soluteamount of solution=molarityThe number of moles of solute per literof solution (M).formalityThe number of moles of solute,regardless of chemical form, per liter ofsolution (F).concentrationAn expression stating the relativeamount of solute per unit volume orunit mass of solution.1400-CH02 9/8/99 3:48 PM Page 15 33. instead, is 0.1 M in Na+ and 0.1 M in Cl. The formality of NaCl, however, is 0.1 Fbecause it represents the total amount of NaCl in solution. The rigorous definitionof molarity, for better or worse, is largely ignored in the current literature, as it is inthis text. When we state that a solution is 0.1 M NaCl we understand it to consist ofNa+ 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 oftenused to simplify its expression in equations and writing. The use of square bracketsaround 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 NormalityNormality is an older unit of concentration that, although once commonly used, isfrequently ignored in todays laboratories. Normality is still used in som