Detailed Table of Contents

Preface ...... xvii A Organization ...... xviii B Role of Equilibrium Chemistry ...... xviii C Computational Software ...... xix D How to Use Te Electronic Textbook’s Features...... xix E Acknowledgments ...... xxi F Updates, Ancillary Materials, and Future Editions ...... xxiii G How To Contact the Author ...... xxiii Introduction to Analytical Chemistry ...... 1 1A What is Analytical Chemistry? ...... 2 1B Te Analytical Perspective ...... 5 1C Common Analytical Problems ...... 7 1D Key Terms ...... 8 1E Chapter Summary ...... 8 1F Problems ...... 9 1G Solutions to Practice Exercises ...... 10 Basic Tools of Analytical Chemistry ...... 13 2A Measurements in Analytical Chemistry ...... 14 2A.1 Units of Measurement ...... 14 2A.2 Uncertainty in Measurements ...... 16 2B Concentration ...... 18 2B.1 Molarity and Formality ...... 19 2B.2 Normality ...... 20 2B.3 Molality ...... 20 2B.4 Weight, Volume, and Weight-to-Volume Percents ...... 20 2B.5 Parts Per Million and Parts Per Billion ...... 20 2B.6 Converting Between Concentration Units ...... 21 2B.7 p-Functions ...... 21 2C Stoichiometric Calculations ...... 23 2D Basic Equipment ...... 25 2D.1 Equipment for Measuring Mass ...... 26 2D.2 Equipment for Measuring Volume ...... 26 2D.3 Equipment for Drying Samples ...... 29 2E Preparing Solutions ...... 29 2E.1 Preparing Stock Solutions...... 30 2E.2 Preparing Solutions by Dilution ...... 31 2F Spreadsheets and Computational Software ...... 32 2G Te Laboratory Notebook ...... 33 2H Key Terms ...... 34 2I Chapter Summary...... 34 2J Problems ...... 34 2K Solutions to Practice Exercises ...... 37 The Vocabulary of Analytical Chemistry ...... 41 3A Analysis, Determination and Measurement ...... 42 3B Techniques, Methods, Procedures, and Protocols ...... 43 3C Classifying Analytical Techniques ...... 44 3D Selecting an Analytical Method ...... 45 3D.1 Accuracy ...... 45 3D.2 Precision ...... 46 3D.3 Sensitivity ...... 46 3D.4 Specifcity and Selectivity ...... 47 3D.5 Robustness and Ruggedness...... 50 3D.6 Scale of Operation ...... 50 3D.7 Equipment, Time, and Cost ...... 52 3D.8 Making the Final Choice ...... 52 3E Developing the Procedure ...... 53 3E.1 Compensating for Interferences ...... 53 3E.2 Calibration ...... 54 3E.3 Sampling ...... 54 3E.4 Validation...... 55 3F Protocols ...... 55 3G Te Importance of Analytical Methodology ...... 56 3H Key Terms ...... 57 3I Chapter Summary...... 57 3J Problems ...... 58 3K Solutions to Practice Exercises ...... 61 Evaluating Analytical Data ...... 63 4A Characterizing Measurements and Results ...... 64 4A.1 Measures of Central Tendency ...... 64 4A.2 Measures of Spread ...... 66 4B Characterizing Experimental Errors ...... 68 4B.1 Errors Tat Afect Accuracy ...... 68 4B.2 Errors Tat Afect Precision ...... 73 4B.3 Error and Uncertainty ...... 75 4C Propagation of Uncertainty ...... 76 4C.1 A Few Symbols ...... 77 4C.2 Uncertainty When Adding or Subtracting ...... 77 4C.3 Uncertainty When Multiplying or Dividing ...... 78 4C.4 Uncertainty for Mixed Operations ...... 78 4C.5 Uncertainty for Other Mathematical Functions ...... 79 4C.6 Is Calculating Uncertainty Actually Useful? ...... 81 4D Te Distribution of Measurements and Results ...... 82 4D.1 Populations and Samples ...... 83 4D.2 Probability Distributions for Populations ...... 83 4D.3 Confdence Intervals for Populations ...... 89 4D.4 Probability Distributions for Samples ...... 91 4D.5 Confdence Intervals for Samples ...... 95 4D.6 A Cautionary Statement ...... 96 4E Statistical Analysis of Data ...... 97 4E.1 Signifcance Testing ...... 97 4E.2 Constructing a Signifcance Test ...... 98 4E.3 One-Tailed and Two-Tailed Signifcance Tests ...... 99 4E.4 Errors in Signifcance Testing ...... 100 4F Statistical Methods for Normal Distributions ...... 101 4F.1 Comparing X to n ...... 101 4F.2 Comparing s2 to v2 ...... 103 4F.3 Comparing Two Sample Variances ...... 104 4F.4 Comparing Two Sample Means ...... 105 4F.5 Outliers ...... 112 4G Detection Limits ...... 115 4H Using Excel and R to Analyze Data ...... 117 4H.1 Excel ...... 117 4H.2 R ...... 120 4I Key Terms ...... 128 4J Chapter Summary ...... 129 4K Problems ...... 129 4L Solutions to Practice Exercises ...... 139 Standardizing Analytical Methods ...... 147 5A Analytical Standards...... 148 5A.1 Primary and Secondary Standards ...... 148 5A.2 Other Reagents ...... 148 5A.3 Preparing a Standard Solution ...... 149

5B Calibrating the Signal (Stotal) ...... 150 5C Determining the Sensitivity (kA) ...... 150 5C.1 Single-Point versus Multiple-Point Standardizations ...... 151 5C.2 External Standards ...... 152 5C.3 Standard Additions ...... 155 5C.4 Internal Standards ...... 161 5D Linear Regression and Calibration Curves ...... 163 5D.1 Linear Regression of Straight Line Calibration Curves ...... 164 5D.2 Unweighted Linear Regression with Errors in y ...... 164 5D.3 Weighted Linear Regression with Errors in y ...... 174 5D.4 Weighted Linear Regression with Errors in Both x and y ...... 177 5D.5 Curvilinear and Multivariate Regression ...... 177

5E Compensating for the Reagent Blank (Sreag) ...... 178 5F Using Excel and R for a Regression Analysis ...... 180 5F.1 Excel ...... 180 5F.2 R ...... 184 5G Key Terms ...... 189 5H Chapter Summary ...... 189 5I Problems ...... 190 5J Solutions to Practice Exercises ...... 194 Equilibrium Chemistry ...... 201 6A Reversible Reactions and Chemical Equilibria ...... 202 6B Termodynamics and Equilibrium Chemistry ...... 203 6C Manipulating Equilibrium Constants ...... 205 6D Equilibrium Constants for Chemical Reactions ...... 206 6D.1 Precipitation Reactions ...... 206 6D.2 Acid–Base Reactions ...... 206 6D.3 Complexation Reactions ...... 211 6D.4 Oxidation–Reduction (Redox) Reactions ...... 213 6E Le Châtelier’s Principle ...... 216 6F Ladder Diagrams ...... 218 6F.1 Ladder Diagrams for Acid–Base Equilibria ...... 219 6F.2 Ladder Diagrams for Complexation Equilibria ...... 222 6F.3 Ladder Diagram for Oxidation/Reduction Equilibria ...... 224 6G Solving Equilibrium Problems ...... 225 6G.1 A Simple Problem—Solubility of Pb(IO3)2 ...... 226 6G.2 A More Complex Problem—Te Common Ion Efect ...... 227 6G.3 A Systematic Approach to Solving Equilibrium Problems ...... 229 6G.4 pH of a Monoprotic Weak Acid ...... 231 6G.5 pH of a Polyprotic Acid or Base ...... 233 6G.6 Efect of Complexation on Solubility ...... 235 6H Bufer Solutions ...... 237 6H.1 Systematic Solution to Bufer Problems ...... 238 6H.2 Representing Bufer Solutions with Ladder Diagrams ...... 240 6H.3 Preparing a Bufer ...... 241 6I Activity Efects ...... 242 6J Using Excel and R to Solve Equilibrium Problems ...... 247 6J.1 Excel ...... 248 6J.2 R ...... 251 6K Some Final Toughts on Equilibrium Calculations ...... 254 6L Key Terms ...... 255 6M Chapter Summary ...... 255 6N Problems ...... 257 6O Solutions to Practice Exercises ...... 260 Collecting and Preparing Samples ...... 271 7A Te Importance of Sampling ...... 272 7B Designing A Sampling Plan ...... 275 7B.1 Where to Sample the Target Population ...... 275 7B.2 What Type of Sample to Collect ...... 279 7B.3 How Much Sample to Collect ...... 281 7B.4 How Many Samples to Collect ...... 283 7B.5 Minimizing the Overall Variance ...... 285 7C Implementing the Sampling Plan ...... 287 7C.1 Solutions ...... 287 7C.2 Gases ...... 289 7C.3 Solids ...... 291 7D Separating the Analyte from Interferents ...... 297 7E General Teory of Separation Efciency ...... 297 7F Classifying Separation Techniques ...... 300 7F.1 Separations Based on Size ...... 300 7F.2 Separations Based on Mass or Density ...... 302 7F.3 Separations Based on Complexation Reactions (Masking) ...... 304 7F.4 Separations Based on a Change of State ...... 306 7F.5 Separations Based on a Partitioning Between Phases ...... 309 7G Liquid–Liquid Extractions ...... 314 7G.1 Partition Coefcients and Distribution Ratios ...... 314 7G.2 Liquid–Liquid Extraction With No Secondary Reactions ...... 315 7G.3 Liquid–Liquid Extractions Involving Acid–Base Equilibria ...... 318 7G.4 Liquid–Liquid Extraction of a Metal–Ligand Complex ...... 320 7H Separation Versus Preconcentration ...... 323 7I Key Terms ...... 323 7K Problems ...... 324 Gravimetric Methods ...... 337 8A Overview of Gravimetric Methods ...... 338 8A.1 Using Mass as an Analytical Signal ...... 338 8A.2 Types of Gravimetric Methods ...... 339 8A.3 Conservation of Mass ...... 339 8A.4 Why Gravimetry is Important ...... 340 8B Precipitation Gravimetry ...... 340 8B.1 Teory and Practice ...... 340 8B.2 Quantitative Applications ...... 354 8B.2 Qualitative Applications ...... 361 8B.3 Evaluating Precipitation Gravimetry...... 361 8C Volatilization Gravimetry ...... 362 8C.1 Teory and Practice ...... 362 Termogravimetry ...... 363 8C.2 Quantitative Applications ...... 367 8C.3 Evaluating Volatilization Gravimetry ...... 370 8D Particulate Gravimetry ...... 371 8D.1 Teory and Practice ...... 371 8D.2 Quantitative Applications ...... 373 8D.3 Evaluating Particulate Gravimetry ...... 374 8E Key Terms ...... 375 8F Chapter Summary ...... 375 8G Problems ...... 375 8H Solutions to Practice Exercises ...... 385 Titrimetric Methods ...... 391 9A Overview of Titrimetry ...... 392 9A.1 Equivalence Points and End points ...... 392 9A.2 Volume as a Signal ...... 392 9A.3 Titration Curves ...... 394 9A.4 Te Buret ...... 395 9B Acid–Base Titrations ...... 396 9B.1 Acid–Base Titration Curves ...... 398 9B.2 Selecting and Evaluating the End Point ...... 406 9B.3 Titrations in Nonaqueous Solvents ...... 414 9B.5 Qualitative Applications ...... 428 9B.6 Characterization Applications ...... 429 9B.7 Evaluation of Acid–Base Titrimetry ...... 432 9C Complexation Titrations ...... 437 9C.1 Chemistry and Properties of EDTA ...... 437 9C.2 Complexometric EDTA Titration Curves ...... 440 9C.3 Selecting and Evaluating the End point ...... 445 9C.4 Quantitative Applications ...... 450 9C.5 Evaluation of Complexation Titrimetry ...... 454 9D Redox Titrations ...... 455 9D.1 Redox Titration Curves ...... 456 9D.2 Selecting and Evaluating the End point ...... 461 9D.3 Quantitative Applications ...... 467 9D.4 Evaluation of Redox Titrimetry ...... 477 9E Precipitation Titrations ...... 478 9E.1 Titration Curves ...... 478 9E.2 Selecting and Evaluating the End point ...... 480 9E.3 Quantitative Applications...... 482 9E.4 Evaluation of Precipitation Titrimetry ...... 485 9F Key Terms ...... 486 9G Chapter Summary ...... 486 9H Problems ...... 487 9I Solutions to Practice Exercises ...... 502 Spectroscopic Methods ...... 517 10A Overview of Spectroscopy ...... 518 10A.1 What is Electromagnetic Radiation ...... 518 10A.2 Photons as a Signal Source ...... 521 10A.3 Basic Components of Spectroscopic Instruments ...... 523 Signal Processors ...... 530 10B Spectroscopy Based on Absorption ...... 530 10B.1 Absorbance Spectra ...... 530 10B.2 Transmittance and Absorbance ...... 535 10B.3 Absorbance and Concentration: Beer’s Law ...... 537 10B.4 Beer’s Law and Multicomponent Samples ...... 538 10B.5 Limitations to Beer’s Law ...... 538 10C UV/Vis and IR Spectroscopy ...... 540 10C.1 Instrumentation ...... 540 10C.2 Quantitative Applications ...... 548 10C.3 Qualitative Applications ...... 560 10C.4 Characterization Applications ...... 562 10C.5 Evaluation of UV/Vis and IR Spectroscopy ...... 568 10D Atomic Absorption Spectroscopy ...... 572 10D.1 Instrumentation ...... 572 10D.2 Quantitative Applications ...... 576 10D.3 - Evaluation of Atomic Absorption Spectroscopy ...... 583 10E Emission Spectroscopy ...... 585 10F Photoluminescence Spectroscopy ...... 585 10F.1 Fluorescence and Phosphorescence Spectra ...... 586 10F.2 Instrumentation ...... 590 10F.3 Quantitative Applications ...... 593 10F.4 Evaluation of Photoluminescence Spectroscopy ...... 597 10G Atomic Emission Spectroscopy ...... 599 10G.1 Atomic Emission Spectra ...... 599 10G.2 Equipment ...... 600 10G.3 Quantitative Applications ...... 601 10G.4 Evaluation of Atomic Emission Spectroscopy ...... 607 10H Spectroscopy Based on Scattering ...... 608 10H.1 Origin of Scattering...... 608 10H.2 Turbidimetry and Nephelometry ...... 609 10I Key Terms ...... 615 10J Chapter Summary ...... 616 10K Problems ...... 617 10L Solutions to Practice Exercises ...... 634 Electrochemical Methods ...... 637 11A Overview of Electrochemistry ...... 638 11A.2 Five Important Concepts ...... 638 11A.2 Controlling and Measuring Current and Potential ...... 640 11A.3 Interfacial Electrochemical Techniques ...... 643 11B Potentiometric Methods ...... 644 11B.1 Potentiometric Measurements ...... 645 11B.2 Reference Electrodes ...... 651 11B.3 Metallic Indicator Electrodes ...... 655 11B.4 Membrane Electrodes ...... 656 11B.5 Quantitative Applications ...... 669 11B.6 Evaluation ...... 678 11C Coulometric Methods ...... 681 11C.1 Controlled-Potential Coulometry ...... 681 11C.2 Controlled-Current Coulometry ...... 684 11C.3 Quantitative Applications ...... 687 11C.4 Characterization Applications ...... 693 11C.5 - Evaluation ...... 694 11D Voltammetric Methods ...... 696 11D.1 Voltammetric Measurements ...... 696 11D.2 Current in Voltammetry ...... 698 11D.3 Shape of Voltammograms ...... 703 11D.4 Quantitative and Qualitative Aspects of Voltammetry ...... 703 11D.5 Voltammetric Techniques ...... 705 11D.6 Quantitative Applications ...... 714 11D.7 Characterization Applications ...... 722 11D.8 Evaluation ...... 726 11E Key Terms ...... 727 11F Chapter Summary ...... 728 11G Problems ...... 729 11H Solutions to Practice Exercises ...... 742 Chromatographic and Electrophoretic Methods ....747 12A Overview of Analytical Separations ...... 748 12A.1 Two Limitations of Liquid–Liquid Extractions ...... 748 12A.2 A Better Way to Separate Mixtures ...... 748 12A.3 Chromatographic Separations ...... 751 12A.4 Electrophoretic Separations ...... 752 12B General Teory of Column Chromatography ...... 753 12B.1 Chromatographic Resolution ...... 755 12B.2 Solute Retention Factor ...... 756 12B.3 Selectivity ...... 759 12B.4 Column Efciency ...... 759 12B.5 Peak Capacity ...... 761 12B.6 Asymmetric Peaks ...... 761 12C Optimizing Chromatographic Separations...... 762 12C.1 Using the Retention factor to Optimize Resolution ...... 763 12C.2 Using Selectivity to Optimize Resolution ...... 765 12C.3 Using Column Efciency to Optimize Resolution ...... 766 12D Gas Chromatography ...... 770 12D.1 Mobile Phase ...... 771 12D.2 Chromatographic Columns ...... 771 12D.3 Sample Introduction ...... 774 12D.4 Temperature Control ...... 778 12D.5 Detectors for Gas Chromatography ...... 778 12D.6 Quantitative Applications ...... 781 12D.7 Qualitative Applications ...... 785 12D.8 Evaluation ...... 789 12E High-Performance Liquid Chromatography ...... 790 12E.1 HPLC Columns ...... 790 12E.2 Mobile Phases ...... 793 12E.3 HPLC Plumbing ...... 797 12E.4 Detectors for HPLC ...... 799 12E.5 Quantitative Applications...... 803 12E.6 Evaluation ...... 806 12F Other Forms of Liquid Chromatography ...... 806 12F.1 Liquid-Solid Adsorption Chromatography ...... 807 12F.2 Ion-Exchange Chromatography ...... 807 12F.3 Size-Exclusion Chromatography ...... 810 12F.4 Supercritical Fluid Chromatography ...... 812 12G Electrophoresis ...... 814 12G.1 Teory of Capillary Electrophoresis ...... 814 12G.2 Instrumentation ...... 819 12G.3 Capillary Electrophoresis Methods ...... 823 12G.4 Evaluation ...... 828 12H Key Terms ...... 828 12I Chapter Summary...... 829 12J Problems ...... 830 12K Solutions to Practice Exercises ...... 842 Kinetic Methods ...... 847 13A Kinetic Methods Versus Equilibrium Methods ...... 848 13B Chemical Kinetics ...... 849 13B.1 Teory and Practice ...... 849 13B.2 Classifying Chemical Kinetic Methods ...... 851 13B.3 Making Kinetic Measurements ...... 861 13B.4 Quantitative Applications ...... 863 13B.5 Characterization Applications ...... 866 13B.6 Evaluation of Chemical Kinetic Methods ...... 870 Accuracy ...... 870 13C Radiochemistry ...... 873 13C.1 Teory and Practice ...... 874 13C.2 Instrumentation ...... 875 13C.3 Quantitative Applications ...... 875 13C.4 Characterization Applications ...... 879 13C.5 Evaluation ...... 880 13D Flow Injection Analysis ...... 881 13D.1 Teory and Practice ...... 881 13D.2 Instrumentation ...... 884 13D.3 Quantitative Applications ...... 889 13D.4 Evaluation ...... 893 13E Key Terms ...... 894 13F Summary ...... 894 13G Problems ...... 895 13H Solutions to Practice Exercises ...... 903 Developing a Standard Method ...... 905 14A Optimizing the Experimental Procedure ...... 906 14A.1 Response Surfaces ...... 906 14A.2 Searching Algorithms for Response Surfaces ...... 907 14A.3 Mathematical Models of Response Surfaces ...... 914 14B Verifying the Method ...... 923 14B.1 Single Operator Characteristics ...... 923 14B.2 Blind Analysis of Standard Samples ...... 924 14B.3 Ruggedness Testing ...... 924 14B.4 Equivalency Testing ...... 927 14C Validating the Method as a Standard Method ...... 927 14C.1 Two-Sample Collaborative Testing ...... 928 14C.2 Collaborative Testing and Analysis of Variance ...... 932 14C.3 What is a Reasonable Result for a Collaborative Study? ...... 938 14D Using Excel and R for an Analysis of Variance ...... 939 14D.1 Excel ...... 939 14D.2 R ...... 940 14E Key Terms ...... 942 14F Summary ...... 942 14G Problems ...... 943 14H Solutions to Practice Exercises ...... 951 Quality Assurance ...... 953 15A Te Analytical Perspective—Revisited ...... 954 15B Quality Control ...... 955 15C Quality Assessment ...... 957 15C.1 Internal Methods of Quality Assessment ...... 957 15C.2 External Methods of Quality Assessment ...... 961 15D Evaluating Quality Assurance Data ...... 962 15D.1 Prescriptive Approach ...... 962 15D.2 Performance-Based Approach ...... 965 15E Key Terms ...... 972 15F Chapter Summary ...... 972 15G Problems ...... 973 15H Solutions to Practice Exercises ...... 976 Additional Resources ...... 979 Chapter 1 ...... 980 Chapter 2 ...... 982 Chapter 3 ...... 983 Chapter 4 ...... 984 Chapter 5 ...... 989 Chapter 6 ...... 993 Chapter 7 ...... 996 Chapter 8 ...... 1000 Chapter 9 ...... 1001 Chapter 10 ...... 1004 Chapter 11 ...... 1012 Chapter 12 ...... 1017 Chapter 13 ...... 1024 Chapter 14 ...... 1027 Chapter 15 ...... 1029 Active Learning Curricular Materials ...... 1030