1400-Fm 9/9/99 7:37 AM Page i CChheemmiissttrryy Modern Analytical Chemistry David Harvey DePauw University Boston Burr Ridge, IL Dubuque, IA Madison, WI New York San Francisco St. Louis Bangkok Bogotá Caracas Lisbon London Madrid Mexico City Milan New Delhi Seoul Singapore Sydney Taipei Toronto 1400-Fm 9/9/99 7:37 AM Page ii McGraw-Hill Higher Education A Division of The McGraw-Hill Companies MODERN ANALYTICAL CHEMISTRY Copyright © 2000 by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the United States of America. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval system, without the prior written permission of the publisher. 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 0 ISBN 0–07–237547–7 Vice president and editorial director: Kevin T. Kane Publisher: James M. Smith Sponsoring editor: Kent A. Peterson Editorial assistant: Jennifer L. Bensink Developmental editor: Shirley R. Oberbroeckling Senior marketing manager: Martin J. Lange Senior project manager: Jayne Klein Production supervisor: Laura Fuller Coordinator of freelance design: Michelle D. Whitaker Senior photo research coordinator: Lori Hancock Senior supplement coordinator: Audrey A. Reiter Compositor: Shepherd, Inc. Typeface: 10/12 Minion Printer: Quebecor Printing Book Group/Kingsport Freelance cover/interior designer: Elise Lansdon Cover image: © George Diebold/The Stock Market Photo research: Roberta Spieckerman Associates Colorplates: Colorplates 1–6, 8, 10: © David Harvey/Marilyn E. Culler, photographer; Colorplate 7: Richard Megna/Fundamental Photographs; Colorplate 9: © Alfred Pasieka/Science Photo 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 Data Harvey, David, 1956– Modern analytical chemistry / David Harvey. — 1st ed. p. cm. Includes bibliographical references and index. ISBN 0–07–237547–7 1. Chemistry, Analytic. I. Title. QD75.2.H374 2000 543—dc21 99–15120 CIP INTERNATIONAL EDITION ISBN 0–07–116953–9 Copyright © 2000. Exclusive rights by The McGraw-Hill Companies, Inc. for manufacture and export. This book cannot be re-exported from the country to which it is consigned by McGraw-Hill. The International Edition is not available in North America. www.mhhe.com 1400-Fm 9/9/99 7:37 AM Page iii Contents Contents Preface xii 2C.5 Conservation of Electrons 23 1 2C.6 Using Conservation Principles in Chapter Stoichiometry Problems 23 2D Basic Equipment and Instrumentation 25 Introduction 1 2D.1 Instrumentation for Measuring Mass 25 1A What is Analytical Chemistry? 2 2D.2 Equipment for Measuring Volume 26 1B The Analytical Perspective 5 2D.3 Equipment for Drying Samples 29 1C Common Analytical Problems 8 2E Preparing Solutions 30 1D Key Terms 9 2E.1 Preparing Stock Solutions 30 1E Summary 9 2E.2 Preparing Solutions by Dilution 31 1F Problems 9 2F The Laboratory Notebook 32 1G Suggested Readings 10 2G Key Terms 32 1H References 10 2H Summary 33 2 2I Problems 33 Chapter 2J Suggested Readings 34 Basic Tools of Analytical Chemistry 11 2K References 34 3 Chapter 2A Numbers in Analytical Chemistry 12 2A.1 Fundamental Units of Measure 12 The Language of Analytical Chemistry 35 2A.2 Significant Figures 13 2B Units for Expressing Concentration 15 3A Analysis, Determination, and Measurement 36 2B.1 Molarity and Formality 15 3B Techniques, Methods, Procedures, and 2B.2 Normality 16 Protocols 36 2B.3 Molality 18 3C Classifying Analytical Techniques 37 2B.4 Weight, Volume, and Weight-to-Volume 3D Selecting an Analytical Method 38 Ratios 18 3D.1 Accuracy 38 2B.5 Converting Between Concentration Units 18 3D.2 Precision 39 2B.6 p-Functions 19 3D.3 Sensitivity 39 2C Stoichiometric Calculations 20 3D.4 Selectivity 40 2C.1 Conservation of Mass 22 3D.5 Robustness and Ruggedness 42 2C.2 Conservation of Charge 22 3D.6 Scale of Operation 42 2C.3 Conservation of Protons 22 3D.7 Equipment, Time, and Cost 44 2C.4 Conservation of Electron Pairs 23 3D.8 Making the Final Choice 44 iii 1400-Fm 9/9/99 7:37 AM Page iv 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 47 4F.1 Comparing Xto m 85 3E.3 Sampling 47 4F.2 Comparing s2to s 2 87 3E.4 Validation 47 4F.3 Comparing Two Sample Variances 88 3F Protocols 48 4F.4 Comparing Two Sample Means 88 3G The Importance of Analytical Methodology 48 4F.5 Outliers 93 3H Key Terms 50 4G Detection Limits 95 3I Summary 50 4H Key Terms 96 3J Problems 51 4I Summary 96 3K Suggested Readings 52 4J Suggested Experiments 97 3L References 52 4K Problems 98 4 4L Suggested Readings 102 Chapter 4M References 102 Evaluating Analytical Data 53 5 Chapter 4A Characterizing Measurements and Results 54 Calibrations, Standardizations, 4A.1 Measures of Central Tendency 54 and Blank Corrections 104 4A.2 Measures of Spread 55 4B Characterizing Experimental Errors 57 5A Calibrating Signals 105 4B.1 Accuracy 57 5B Standardizing Methods 106 4B.2 Precision 62 5B.1 Reagents Used as Standards 106 4B.3 Error and Uncertainty 64 5B.2 Single-Point versus Multiple-Point 4C Propagation of Uncertainty 64 Standardizations 108 4C.1 A Few Symbols 65 5B.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 115 Dividing 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 Mathematical Curves 118 Functions 67 5C.2 Unweighted Linear Regression with Errors 4C.6 Is Calculating Uncertainty Actually Useful? 68 in y 119 4D The Distribution of Measurements and 5C.3 Weighted Linear Regression with Errors Results 70 in y 124 4D.1 Populations and Samples 71 5C.4 Weighted Linear Regression with Errors 4D.2 Probability Distributions for Populations 71 in Both xand y 127 4D.3 Confidence Intervals for Populations 75 5C.5 Curvilinear and Multivariate 4D.4 Probability Distributions for Samples 77 Regression 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 Significance 5I Suggested Readings 133 Tests 84 5J References 134 1400-Fm 9/9/99 7:38 AM Page v v Contents 6 7 Chapter Chapter Equilibrium Chemistry 135 Obtaining and Preparing Samples for Analysis 179 6A Reversible Reactions and Chemical Equilibria 136 7A The Importance of Sampling 180 6B Thermodynamics and Equilibrium 7B Designing a Sampling Plan 182 Chemistry 136 7B.1 Where to Sample the Target 6C Manipulating Equilibrium Constants 138 Population 182 6D Equilibrium Constants for Chemical 7B.2 What Type of Sample to Collect 185 Reactions 139 7B.3 How Much Sample to Collect 187 6D.1 Precipitation Reactions 139 7B.4 How Many Samples to Collect 191 6D.2 Acid–Base Reactions 140 7B.5 Minimizing the Overall Variance 192 6D.3 Complexation Reactions 144 7C Implementing the Sampling Plan 193 6D.4 Oxidation–Reduction Reactions 145 7C.1 Solutions 193 6E Le Châtelier’s Principle 148 7C.2 Gases 195 6F Ladder Diagrams 150 7C.3 Solids 196 6F.1 Ladder Diagrams for Acid–Base Equilibria 150 7D Separating the Analyte from 6F.2 Ladder Diagrams for Complexation Interferents 201 Equilibria 153 7E General Theory of Separation 6F.3 Ladder Diagrams for Oxidation–Reduction Efficiency 202 Equilibria 155 7F Classifying Separation Techniques 205 6G Solving Equilibrium Problems 156 7F.1 Separations Based on Size 205 6G.1 A Simple Problem: Solubility of Pb(IO3)2in 7F.2 Separations Based on Mass or Density 206 Water 156 7F.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 Liquid–Liquid Extractions 215 6G.6 Effect of Complexation on Solubility 165 7G.1 Partition Coefficients and Distribution 6H Buffer Solutions 167 Ratios 216 6H.1 Systematic Solution to Buffer 7G.2 Liquid–Liquid Extraction with No Secondary Problems 168 Reactions 216 6H.2 Representing Buffer Solutions with 7G.3 Liquid–Liquid Extractions Involving Ladder Diagrams 170 Acid–Base Equilibria 219 6I Activity Effects 171 7G.4 Liquid–Liquid Extractions Involving Metal Chelators 221 6J Two Final Thoughts About Equilibrium Chemistry 175 7H 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 176 7L Problems 226 6O Suggested Readings 178 7M Suggested Readings 230 6P References 178 7N References 231 1400-Fm 9/9/99 7:38 AM Page vi vi Modern Analytical Chemistry 8 Chapter 9B.7 Characterization Applications 309 9B.8 Evaluation of Acid–Base Titrimetry 311 Gravimetric Methods of Analysis 232 9C Titrations Based on Complexation Reactions 314 9C.1 Chemistry and Properties of EDTA 315 8A Overview of Gravimetry 233 9C.2 Complexometric EDTA Titration Curves 317 8A.1 Using Mass as a Signal 233 9C.3 Selecting and Evaluating the End Point 322 8A.2 Types of Gravimetric Methods 234 9C.4 Representative Method 324 8A.3 Conservation of Mass 234 9C.5 Quantitative Applications 327 8A.4 Why Gravimetry Is Important 235 9C.6 Evaluation of Complexation Titrimetry 331 8B Precipitation Gravimetry 235 9D Titrations Based on Redox Reactions 331 8B.1 Theory and Practice 235 9D.1 Redox Titration Curves 332 8B.2 Quantitative Applications 247 9D.2 Selecting and Evaluating the End Point 337 8B.3 Qualitative Applications 254 9D.3 Representative Method 340 8B.4 Evaluating Precipitation Gravimetry 254 9D.4 Quantitative Applications 341 8C Volatilization Gravimetry 255 9D.5 Evaluation of Redox Titrimetry 350 8C.1 Theory and Practice 255 9E Precipitation Titrations 350 8C.2 Quantitative Applications 259 9E.1 Titration Curves 350 8C.3 Evaluating Volatilization Gravimetry 262 9E.2 Selecting and Evaluating the End Point 354 8D Particulate Gravimetry 262 9E.3 Quantitative Applications 354 8D.1 Theory and Practice 263 9E.4 Evaluation of Precipitation Titrimetry 357 8D.2 Quantitative Applications 264 9F Key Terms 357 8D.3 Evaluating Precipitation Gravimetry 265 9G Summary 357 8E Key Terms 265 9H Suggested Experiments 358 8F Summary 266 9I Problems 360 8G Suggested Experiments 266 9J Suggested Readings 366 8H Problems 267 9K References 367 8I Suggested Readings 271 10 8J References 272 Chapter 9 Chapter Spectroscopic Methods of Analysis 368 Titrimetric Methods of Analysis 273 10A 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 274 10B Basic Components of Spectroscopic 9A.3 Titration Curves 275 Instrumentation 374 9A.4 The Buret 277 10B.1 Sources of Energy 375 9B Titrations Based on Acid–Base Reactions 278 10B.2 Wavelength Selection 376 9B.1 Acid–Base Titration Curves 279 10B.3 Detectors 379 9B.2 Selecting and Evaluating the 10B.4 Signal Processors 380 End Point 287 10C 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: Beer’s 9B.6 Qualitative Applications 308 Law 385 1400-Fm 9/9/99 7:38 AM Page vii vii Contents 10C.4 Beer’s Law and Multicomponent 11B Potentiometric Methods of Analysis 465 Samples 386 11B.1 Potentiometric Measurements 466 10C.5 Limitations to Beer’s Law 386 11B.2 Reference Electrodes 471 10D Ultraviolet-Visible and Infrared 11B.3 Metallic Indicator Electrodes 473 Spectrophotometry 388 11B.4 Membrane Electrodes 475 10D.1 Instrumentation 388 11B.5 Quantitative Applications 485 10D.2 Quantitative Applications 394 11B.6 Evaluation 494 10D.3 Qualitative Applications 402 11C Coulometric Methods of Analysis 496 10D.4 Characterization Applications 403 11C.1 Controlled-Potential Coulometry 497 10D.5 Evaluation 409 11C.2 Controlled-Current Coulometry 499 10E Atomic Absorption Spectroscopy 412 11C.3 Quantitative Applications 501 10E.1 Instrumentation 412 11C.4 Characterization Applications 506 10E.2 Quantitative Applications 415 11C.5 Evaluation 507 10E.3 Evaluation 422 11D Voltammetric Methods of Analysis 508 10F Spectroscopy Based on Emission 423 11D.1 Voltammetric Measurements 509 10G Molecular Photoluminescence 11D.2 Current in Voltammetry 510 Spectroscopy 423 11D.3 Shape of Voltammograms 513 10G.1 Molecular Fluorescence and 11D.4 Quantitative and Qualitative Aspects Phosphorescence Spectra 424 of Voltammetry 514 10G.2 Instrumentation 427 11D.5 Voltammetric Techniques 515 10G.3 Quantitative Applications Using Molecular 11D.6 Quantitative Applications 520 Luminescence 429 11D.7 Characterization Applications 527 10G.4 Evaluation 432 11D.8 Evaluation 531 10H Atomic Emission Spectroscopy 434 11E Key Terms 532 10H.1 Atomic Emission Spectra 434 11F Summary 532 10H.2 Equipment 435 11G Suggested Experiments 533 10H.3 Quantitative Applications 437 11H Problems 535 10H.4 Evaluation 440 11I Suggested Readings 540 10I Spectroscopy Based on Scattering 441 11J References 541 10I.1 Origin of Scattering 441 12 10I.2 Turbidimetry and Nephelometry 441 Chapter 10J Key Terms 446 Chromatographic and Electrophoretic 10K Summary 446 Methods 543 10L Suggested Experiments 447 10M Problems 450 12A Overview of Analytical Separations 544 10N Suggested Readings 458 12A.1 The Problem with Simple 10O References 459 Separations 544 12A.2 A Better Way to Separate Mixtures 544 11 Chapter 12A.3 Classifying Analytical Separations 546 12B General Theory of Column Electrochemical Methods of Analysis 461 Chromatography 547 11A Classification of Electrochemical Methods 462 12B.1 Chromatographic Resolution 549 11A.1 Interfacial Electrochemical Methods 462 12B.2 Capacity Factor 550 11A.2 Controlling and Measuring Current and 12B.3 Column Selectivity 552 Potential 462 12B.4 Column Efficiency 552 1400-Fm 9/9/99 7:38 AM Page viii viii Modern Analytical Chemistry 12B.5 Peak Capacity 554 12O Suggested Readings 620 12B.6 Nonideal Behavior 555 12P References 620 12C Optimizing Chromatographic Separations 556 13 Chapter 12C.1 Using the Capacity Factor to Optimize Resolution 556 Kinetic Methods of Analysis 622 12C.2 Using Column Selectivity to Optimize Resolution 558 13A Methods Based on Chemical Kinetics 623 12C.3 Using Column Efficiency to Optimize 13A.1 Theory and Practice 624 Resolution 559 13A.2 Instrumentation 634 12D Gas Chromatography 563 13A.3 Quantitative Applications 636 12D.1 Mobile Phase 563 13A.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 567 13B Radiochemical Methods of Analysis 642 12D.5 Temperature Control 568 13B.1 Theory and Practice 643 12D.6 Detectors for Gas Chromatography 569 13B.2 Instrumentation 643 12D.7 Quantitative Applications 571 13B.3 Quantitative Applications 644 12D.8 Qualitative Applications 575 13B.4 Characterization Applications 647 12D.9 Representative Method 576 13B.5 Evaluation 648 12D.10 Evaluation 577 13C Flow Injection Analysis 649 12E High-Performance Liquid 13C.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 580 13D Key Terms 658 12E.4 HPLC Plumbing 583 13E Summary 659 12E.5 Sample Introduction 584 13F Suggested Experiments 659 12E.6 Detectors for HPLC 584 13G Problems 661 12E.7 Quantitative Applications 586 13H Suggested Readings 664 12E.8 Representative Method 588 13I References 665 12E.9 Evaluation 589 4 1 12F Liquid–Solid Adsorption Chromatography 590 Chapter 12G Ion-Exchange Chromatography 590 Developing a Standard Method 666 12H Size-Exclusion Chromatography 593 12I Supercritical Fluid Chromatography 596 14A Optimizing the Experimental Procedure 667 12J Electrophoresis 597 14A.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 683 12K Key Terms 609 14B.1 Single-Operator Characteristics 683 12L Summary 610 14B.2 Blind Analysis of Standard Samples 683 12M Suggested Experiments 610 14B.3 Ruggedness Testing 684 12N Problems 615 14B.4 Equivalency Testing 687 1400-Fm 9/9/99 7:38 AM Page ix ix Contents 14C Validating the Method as a Standard 15D Key Terms 721 Method 687 15E Summary 722 14C.1 Two-Sample Collaborative Testing 688 15F Suggested Experiments 722 14C.2 Collaborative Testing and Analysis of 15G Problems 722 Variance 693 15H Suggested Readings 724 14C.3 What Is a Reasonable Result for a 15I References 724 Collaborative Study? 698 14D Key Terms 699 Appendixes 14E Summary 699 Appendix 1A Single-Sided Normal Distribution 725 14F Suggested Experiments 699 Appendix 1B t-Table 726 14G Problems 700 Appendix 1C F-Table 727 14H Suggested Readings 704 Appendix 1D Critical Values for Q-Test 728 14I References 704 Appendix 1E Random Number Table 728 15 Appendix 2 Recommended Reagents for Preparing Primary Chapter Standards 729 Appendix 3A Solubility Products 731 Quality Assurance 705 Appendix 3B Acid Dissociation Constants 732 Appendix 3C Metal–Ligand Formation Constants 739 15A Quality Control 706 Appendix 3D Standard Reduction Potentials 743 15B Quality Assessment 708 Appendix 3E Selected Polarographic Half-Wave Potentials 747 15B.1 Internal Methods of Quality Appendix 4 Balancing Redox Reactions 748 Assessment 708 Appendix 5 Review of Chemical Kinetics 750 15B.2 External Methods of Quality Appendix 6 Countercurrent Separations 755 Assessment 711 Appendix 7 Answers to Selected Problems 762 15C Evaluating Quality Assurance Data 712 Glossary 769 15C.1 Prescriptive Approach 712 Index 781 15C.2 Performance-Based Approach 714