Modern Analytical Chemistry David Harvey DePauw University aw Boston Burr Ridge, IL Dubuque, IA Madison, WI New York San Francisco St Louis Bangkok Bogota Caracas Lisbon London Madrid Mexico City Milan New Delhi Seoul Singapore Sydney Taipei Toronto
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 CModern Analytical Chemistry hemistry David Harvey DePauw University 1400-Fm 9/9/99 7:37 AM Page i
Contents ntents Pr 2C.5 Conservation of electrons 2C.6 Using Conservation Principles in Chapter I Introduction 2D Basic Equipment and Instrumentation 25 2D. 1 Instrumentation for Measuring Mass 25 la What is Analytical Chemistry? 2 2D. 2 Equipment for Measuring Volume 26 1B The Analytical Perspective 5 2D.3 Equip Drying Ic Common Analytical Problems 8 2E Preparing Solutions 30 ID Key Terms 9 2E. I Preparing Stock Solutions 30 2E. 2 Preparing Solutions by Dilution 31 IF Problems 9 2F The Laboratory notebook 32 IG Suggested Readings 10 erms IH References 1 2I Problems 33 Chapter 2 2) Suggested Readings 34 Basic Tools of Analytical Chemistry ll 2K References 34 2A Numbers in Analytical Chemistry 12 Chapter 2A.1 Fundamental Units of measure 12 2A. 2 Significant Figures The Language of analytical Chemistry 35 2B Units for Expressing Concentration 15 3A Analysis, Determination, and Measurement 36 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 Rat 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 Contents Contents Preface xii Chapter 1 Introduction 1 1A What is Analytical Chemistry? 2 1B The Analytical Perspective 5 1C Common Analytical Problems 8 1D Key Terms 9 1E Summary 9 1F Problems 9 1G Suggested Readings 10 1H References 10 Chapter 2 Basic Tools of Analytical Chemistry 11 2A Numbers in Analytical Chemistry 12 2A.1 Fundamental Units of Measure 12 2A.2 Significant Figures 13 2B Units for Expressing Concentration 15 2B.1 Molarity and Formality 15 2B.2 Normality 16 2B.3 Molality 18 2B.4 Weight, Volume, and Weight-to-Volume Ratios 18 2B.5 Converting Between Concentration Units 18 2B.6 p-Functions 19 2C Stoichiometric Calculations 20 2C.1 Conservation of Mass 22 2C.2 Conservation of Charge 22 2C.3 Conservation of Protons 22 2C.4 Conservation of Electron Pairs 23 2C.5 Conservation of Electrons 23 2C.6 Using Conservation Principles in Stoichiometry Problems 23 2D Basic Equipment and Instrumentation 25 2D.1 Instrumentation for Measuring Mass 25 2D.2 Equipment for Measuring Volume 26 2D.3 Equipment for Drying Samples 29 2E Preparing Solutions 30 2E.1 Preparing Stock Solutions 30 2E.2 Preparing Solutions by Dilution 31 2F The Laboratory Notebook 32 2G Key Terms 32 2H Summary 33 2I Problems 33 2J Suggested Readings 34 2K References 34 Chapter 3 The Language of Analytical Chemistry 35 3A Analysis, Determination, and Measurement 36 3B Techniques, Methods, Procedures, and Protocols 36 3C Classifying Analytical Techniques 37 3D Selecting an Analytical Method 38 3D.1 Accuracy 38 3D.2 Precision 39 3D.3 Sensitivity 39 3D.4 Selectivity 40 3D.5 Robustness and Ruggedness 42 3D.6 Scale of Operation 42 3D.7 Equipment, Time, and Cost 44 3D.8 Making the Final Choice 44 1400-Fm 9/9/99 7:37 AM Page iii
Modern Analytical Chemistry 3E Developing the Procedure 45 4E. 4 Errors in Significance Testing 84 3E. I Compensating for Interferences 4 4F Statistical Methods for Normal distributions 85 BE2 Calibration and Standardization 47 paring X to 3E.3 Sampling 47 4F.2 Comparing s to o 87 3E.4 Validation 47 4F.3 Comparing Two Sample Variances 8 3F Protocols 48 4F.4 Comparing Two Sample Means 88 3G The Importance of Analytical Methodology 48 4F.5 Outline 3H Key Terms 50 4G Detection Limits 95 31 Summary 50 4H Key Terms 96 3 Problems 51 3K Suggested Readings 52 4] Suggested Experiments 9 3L Referene 4L Suggested Readings 102 Chapter 1 4M References 102 Evaluating Analytical Data 53 4A Characterizing Measurements and Results 54 Chapter 5 4A. 1 Measures of Central Tendency 54 Calibrations. Standardizations 4A. 2 Measures of Spread Ind blank Corrections 104 4B Characterizing Experimental Errors 57 5a Calibrating Signals 10. 5B Standardizing Methods 106 4B.2 Precision 62 5B. 1 Reagents Used as Standards 106 B3 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 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 C2 Unweighted Linear Regression with Errors 4C.6 Is Calculating Uncertainty Actually Useful? 68 4D The distribution of measurements and 5C.3 Weighted Linear Regression with Errors Results 70 4D.1 Populations and Samples 71 5C.4 Weighted Linear Regression with Errors 4D.2 Probability Distributions for Populations in Both x and y 127 4D.3 Confidence Intervals for Populations 75 C5 Curvilinear and multivariate 4D.4 Probability Distributions for Samples 77 4D.5 Confidence Intervals for Samples 80 5D Blank Corrections 128 4D.6 A Cautionary Statement 81 E Key Terms 130 4E Statistical Analysis of Data 82 ry130 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 ested Readings 133 I 5 References 134
iv Modern Analytical Chemistry 4E.4 Errors in Significance Testing 84 4F Statistical Methods for Normal Distributions 85 4F.1 Comparing – X to µ 85 4F.2 Comparing s2 to σ2 87 4F.3 Comparing Two Sample Variances 88 4F.4 Comparing Two Sample Means 88 4F.5 Outliers 93 4G Detection Limits 95 4H Key Terms 96 4I Summary 96 4J Suggested Experiments 97 4K Problems 98 4L Suggested Readings 102 4M References 102 Chapter 5 Calibrations, Standardizations, and Blank Corrections 104 5A Calibrating Signals 105 5B Standardizing Methods 106 5B.1 Reagents Used as Standards 106 5B.2 Single-Point versus Multiple-Point Standardizations 108 5B.3 External Standards 109 5B.4 Standard Additions 110 5B.5 Internal Standards 115 5C Linear Regression and Calibration Curves 117 5C.1 Linear Regression of Straight-Line Calibration Curves 118 5C.2 Unweighted Linear Regression with Errors in y 119 5C.3 Weighted Linear Regression with Errors in y 124 5C.4 Weighted Linear Regression with Errors in Both x and y 127 5C.5 Curvilinear and Multivariate Regression 127 5D Blank Corrections 128 5E Key Terms 130 5F Summary 130 5G Suggested Experiments 130 5H Problems 131 5I Suggested Readings 133 5J References 134 3E Developing the Procedure 45 3E.1 Compensating for Interferences 45 3E.2 Calibration and Standardization 47 3E.3 Sampling 47 3E.4 Validation 47 3F Protocols 48 3G The Importance of Analytical Methodology 48 3H Key Terms 50 3I Summary 50 3J Problems 51 3K Suggested Readings 52 3L References 52 Chapter 4 Evaluating Analytical Data 53 4A Characterizing Measurements and Results 54 4A.1 Measures of Central Tendency 54 4A.2 Measures of Spread 55 4B Characterizing Experimental Errors 57 4B.1 Accuracy 57 4B.2 Precision 62 4B.3 Error and Uncertainty 64 4C Propagation of Uncertainty 64 4C.1 A Few Symbols 65 4C.2 Uncertainty When Adding or Subtracting 65 4C.3 Uncertainty When Multiplying or Dividing 66 4C.4 Uncertainty for Mixed Operations 66 4C.5 Uncertainty for Other Mathematical Functions 67 4C.6 Is Calculating Uncertainty Actually Useful? 68 4D The Distribution of Measurements and Results 70 4D.1 Populations and Samples 71 4D.2 Probability Distributions for Populations 71 4D.3 Confidence Intervals for Populations 75 4D.4 Probability Distributions for Samples 77 4D.5 Confidence Intervals for Samples 80 4D.6 A Cautionary Statement 81 4E Statistical Analysis of Data 82 4E.1 Significance Testing 82 4E.2 Constructing a Significance Test 83 4E.3 One-Tailed and Two-Tailed Significance Tests 84 1400-Fm 9/9/99 7:37 AM Page iv
Contents ap 6 Chapter 7 Equilibrium Chemistry 135 obtaining and Preparing Samples fo nalySIs 79 6A Reversible reactions and Chemical quilibria 136 7A The Importance of Sampling 180 ling plan 1 Chemistry 136 7B. 1 Where to Sample the Target 6C Manipulating Equilibrium Constants 138 6D Equilibrium Constants for Chemica 7B.2 What Type of Sample to Collect 185 Reactions 139 B3 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 6D.3 Complexation Reactions 144 7C Implementing the Sampling Plan 193 D 4 Oxidation-Reduction Reactions 14 7C.1 Solutions 193 E Le Chatelier'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 nterferents 201 Equilibria 153 E General Theory of separation 6F. 3 Ladder Diagrams for Oxidation-Reduction 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 lon 6G.3 Systematic Approach to Solving Equilibrium of State 209 Problems 159 7F.5 Separations Based on a Partitioning Betwe 6G.4 pH of a Monoprotic Weak Acid 160 Phases 211 6G.5 pH of a Polyprotic Acid or Base 7G Liquid-Liquid Extractions 215 6G.6 Effect of Complexation on Solubilit 7G.1 Partition Coefficients and Distribution 6H Buffer Solutions 167 Ratio 6H. 1 Systematic Solution to Buffer G2 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 61 Activity Effects 171 7G.4 Liquid-Liquid Extractions Involving Metal 6] Two Final Thoughts About Equilibrium Chelators 221 Chemistry 175 7H Separation versus Preconcentration 223 6K Key Terms 17 71 Key Terms 224 6L Summary 175 6M Suggested Experiments 176 Suggested Experiments 225 6n Problems 176 Problems 226 60 Suggested Readings 178 7M Suggested Readings 230 6P References 178 7n References 231
Contents v Chapter 7 Obtaining and Preparing Samples for Analysis 179 7A The Importance of Sampling 180 7B Designing a Sampling Plan 182 7B.1 Where to Sample the Target Population 182 7B.2 What Type of Sample to Collect 185 7B.3 How Much Sample to Collect 187 7B.4 How Many Samples to Collect 191 7B.5 Minimizing the Overall Variance 192 7C Implementing the Sampling Plan 193 7C.1 Solutions 193 7C.2 Gases 195 7C.3 Solids 196 7D Separating the Analyte from Interferents 201 7E General Theory of Separation Efficiency 202 7F Classifying Separation Techniques 205 7F.1 Separations Based on Size 205 7F.2 Separations Based on Mass or Density 206 7F.3 Separations Based on Complexation Reactions (Masking) 207 7F.4 Separations Based on a Change of State 209 7F.5 Separations Based on a Partitioning Between Phases 211 7G Liquid–Liquid Extractions 215 7G.1 Partition Coefficients and Distribution Ratios 216 7G.2 Liquid–Liquid Extraction with No Secondary Reactions 216 7G.3 Liquid–Liquid Extractions Involving Acid–Base Equilibria 219 7G.4 Liquid–Liquid Extractions Involving Metal Chelators 221 7H Separation versus Preconcentration 223 7I Key Terms 224 7J Summary 224 7K Suggested Experiments 225 7L Problems 226 7M Suggested Readings 230 7N References 231 Chapter 6 Equilibrium Chemistry 135 6A Reversible Reactions and Chemical Equilibria 136 6B Thermodynamics and Equilibrium Chemistry 136 6C Manipulating Equilibrium Constants 138 6D Equilibrium Constants for Chemical Reactions 139 6D.1 Precipitation Reactions 139 6D.2 Acid–Base Reactions 140 6D.3 Complexation Reactions 144 6D.4 Oxidation–Reduction Reactions 145 6E Le Châtelier’s Principle 148 6F Ladder Diagrams 150 6F.1 Ladder Diagrams for Acid–Base Equilibria 150 6F.2 Ladder Diagrams for Complexation Equilibria 153 6F.3 Ladder Diagrams for Oxidation–Reduction Equilibria 155 6G Solving Equilibrium Problems 156 6G.1 A Simple Problem: Solubility of Pb(IO3)2 in Water 156 6G.2 A More Complex Problem: The Common Ion Effect 157 6G.3 Systematic Approach to Solving Equilibrium Problems 159 6G.4 pH of a Monoprotic Weak Acid 160 6G.5 pH of a Polyprotic Acid or Base 163 6G.6 Effect of Complexation on Solubility 165 6H Buffer Solutions 167 6H.1 Systematic Solution to Buffer Problems 168 6H.2 Representing Buffer Solutions with Ladder Diagrams 170 6I Activity Effects 171 6J Two Final Thoughts About Equilibrium Chemistry 175 6K Key Terms 175 6L Summary 175 6M Suggested Experiments 176 6N Problems 176 6O Suggested Readings 178 6P References 178 1400-Fm 9/9/99 7:38 AM Page v
Modern Analytical Chemistry Chapter 8 9B.7 Characterization Applications 309 9B.8 Evaluation of Acid-Base Titrimetry 31 Gravimetric Methods of analysis 232 9c Titrations Based on Complexation Reactions 314 8A Overview of Gravimetry 233 9C.1 Chemistry and Properties of EDTA 315 8A.1 Using Mass as a Signal 233 9C.2 Complexometric EDTA Titration Curves 317 8A.2 Types of Gravimetric Methods 234 9C.3 Selecting and Evaluating the End Point 322 8A.3 Conservation of mass 23 9C.4 Representative Method 324 8A.4 Why Gravimetry Is Important 235 9C.5 Quantitative Applications 327 8B Precipitation Gravimetry 235 9C.6 Evaluation of Complexation Titrimetry 331 8B. 1 Theory and Practice 235 9D Titrations Based on redox Reactions 331 8B.2 Quantitative Applications 247 9D.1 Redox Titration Curves 332 9D.2 Selecting and Evaluating the End Point 337 8B. 4 Evaluating Precipitation Gravimetry 254 Representative Method 340 8C Volatilization Gravimetry 255 9D. 4 Quantitative Applications 341 8C.1 Theory and Practice 255 9D.5 Evaluation of Redox Titrimetry 350 8C.2 Quantitative Applications 259 9E Precipitation Titrations 350 8C.3 Evaluating Volatilization Gravimetry 262 9E.1 Titration Curves 350 8D Particulate Gravimetry 262 9E.2 Selecting and Evaluating the End Point 354 8D.1 Theory and Practice 263 9E.3 Quantitative Applications 354 8D.2 Quantitative Applications 264 9E.4 Evaluation of Precipitation Titrimetry 357 8D.3 Evaluating Precipitation Gravimetry 265 9F Key Terms 357 8E Key terms Summary 357 8F Summary 266 9H Suggested Experiments 358 8G Suggested Experiments 26 9I Problems 360 8H Problems 267 9] Suggested Readings 366 9K References 367 8 References 272 Chapter Io Chapter 9 Spectroscopic Methods Titrimetric Methods of analysis 273 of analysis368 9A Overview of Titrimetry 274 10A.1 What Is Electromagnetic Radiation 369 9A. 1 Equivalence Points and End Points 274 9A.2 Volume as a Signal 274 10A.2 Measuring Photons as a Signal 372 9A.3 Titration Curves 275 OB Basic Components of Spectroscopic Instrumentation 374 9A.4 The buret 277 10B. 1 Sources of Energy 375 b 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 38 End point 287 10C Spectroscopy Based on Absorption 380 9B.3 Titrations in Nonaqueous Solvents 295 9B.4 Representative Method 296 10C.1 Absorbance of Electromagnetic Radiation 380 10C. 2 Transmittance and Absorbance 384 9B.5 Quantitative Applications 298 10C. 3 Absorbance and Concentration: Beers 9B.6 Qualitative Applications 308 Law 385
vi Modern Analytical Chemistry Chapter 8 Gravimetric Methods of Analysis 232 8A Overview of Gravimetry 233 8A.1 Using Mass as a Signal 233 8A.2 Types of Gravimetric Methods 234 8A.3 Conservation of Mass 234 8A.4 Why Gravimetry Is Important 235 8B Precipitation Gravimetry 235 8B.1 Theory and Practice 235 8B.2 Quantitative Applications 247 8B.3 Qualitative Applications 254 8B.4 Evaluating Precipitation Gravimetry 254 8C Volatilization Gravimetry 255 8C.1 Theory and Practice 255 8C.2 Quantitative Applications 259 8C.3 Evaluating Volatilization Gravimetry 262 8D Particulate Gravimetry 262 8D.1 Theory and Practice 263 8D.2 Quantitative Applications 264 8D.3 Evaluating Precipitation Gravimetry 265 8E Key Terms 265 8F Summary 266 8G Suggested Experiments 266 8H Problems 267 8I Suggested Readings 271 8J References 272 Chapter 9 Titrimetric Methods of Analysis 273 9A Overview of Titrimetry 274 9A.1 Equivalence Points and End Points 274 9A.2 Volume as a Signal 274 9A.3 Titration Curves 275 9A.4 The Buret 277 9B Titrations Based on Acid–Base Reactions 278 9B.1 Acid–Base Titration Curves 279 9B.2 Selecting and Evaluating the End Point 287 9B.3 Titrations in Nonaqueous Solvents 295 9B.4 Representative Method 296 9B.5 Quantitative Applications 298 9B.6 Qualitative Applications 308 9B.7 Characterization Applications 309 9B.8 Evaluation of Acid–Base Titrimetry 311 9C Titrations Based on Complexation Reactions 314 9C.1 Chemistry and Properties of EDTA 315 9C.2 Complexometric EDTA Titration Curves 317 9C.3 Selecting and Evaluating the End Point 322 9C.4 Representative Method 324 9C.5 Quantitative Applications 327 9C.6 Evaluation of Complexation Titrimetry 331 9D Titrations Based on Redox Reactions 331 9D.1 Redox Titration Curves 332 9D.2 Selecting and Evaluating the End Point 337 9D.3 Representative Method 340 9D.4 Quantitative Applications 341 9D.5 Evaluation of Redox Titrimetry 350 9E Precipitation Titrations 350 9E.1 Titration Curves 350 9E.2 Selecting and Evaluating the End Point 354 9E.3 Quantitative Applications 354 9E.4 Evaluation of Precipitation Titrimetry 357 9F Key Terms 357 9G Summary 357 9H Suggested Experiments 358 9I Problems 360 9J Suggested Readings 366 9K References 367 Chapter 10 Spectroscopic Methods of Analysis 368 10A Overview of Spectroscopy 369 10A.1 What Is Electromagnetic Radiation 369 10A.2 Measuring Photons as a Signal 372 10B Basic Components of Spectroscopic Instrumentation 374 10B.1 Sources of Energy 375 10B.2 Wavelength Selection 376 10B.3 Detectors 379 10B.4 Signal Processors 380 10C Spectroscopy Based on Absorption 380 10C.1 Absorbance of Electromagnetic Radiation 380 10C.2 Transmittance and Absorbance 384 10C.3 Absorbance and Concentration: Beer’s Law 385 1400-Fm 9/9/99 7:38 AM Page vi