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 ...................................