(BQ) Part 1 book Analytical chemistry has contents: Analytical objectives, or What analytical chemists do; basic tools and operations of analytical chemistry; general concepts of chemical equilibrium; acid base titrations; gravimetric analysis and precipitation equilibria; potentiometric electrodes and potentiometry;...and other contents.
Christian7e ffirs.tex V1 - 08/16/2013 2:53 P.M Page i Christian7e ffirs.tex V1 - 08/16/2013 2:53 P.M Page i ANALYTICAL CHEMISTRY SEVENTH EDITION Gary D Christian University of Washington Purnendu K (Sandy) Dasgupta University of Texas at Arlington Kevin A Schug University of Texas at Arlington Christian7e ffirs.tex V1 - 08/16/2013 2:53 P.M Page ii To Nikola from Gary—for your interests in science You have a bright future,wherever your interests and talents take you Philip W West from Sandy—wherever you are Phil, sipping your martini with ppm vermouth, you know how it was: For he said, I will give you, A shelter from the storm Dad from Kevin—well its not hardcore P Chem., but it is still quite useful Thanks for your love, support, and guidance through the years VP & Publisher: Editorial Assistant: Senior Marketing Manager: Designer: Associate Production Manager: Petra Recter Ashley Gayle/Katherine Bull Kristine Ruff Kenji Ngieng Joyce Poh This book was set in 10.5 Times Roman by Laserwords Private Limited and printed and bound by Courier Kendallville The cover was printed by Courier Kendallville This book is printed on acid free paper Founded in 1807, John Wiley & Sons, Inc has been a valued source of knowledge and understanding for more than 200 years, helping people around the world meet their needs and fulfill their aspirations Our company is built on a foundation of principles that include responsibility to the communities we serve and where we live and work In 2008, we launched a Corporate Citizenship Initiative, a global effort to address the environmental, social, economic, and ethical challenges we face in our business Among the issues we are addressing are carbon impact, paper specifications and procurement, ethical conduct within our business and among our vendors, and community and charitable support For more information, please visit our website: www.wiley.com/go/citizenship Copyright © 2014, 2004 John Wiley & Sons, Inc All rights reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc 222 Rosewood Drive, Danvers, MA 01923, website www.copyright.com Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, (201)748-6011, fax (201)748-6008, website http://www.wiley.com/go/permissions Evaluation copies are provided to qualified academics and professionals for review purposes only, for use in their courses during the next academic year These copies are licensed and may not be sold or transferred to a third party Upon completion of the review period, please return the evaluation copy to Wiley Return instructions and a free of charge return mailing label are available at www.wiley.com/go/returnlabel If you have chosen to adopt this textbook for use in your course, please accept this book as your complimentary desk copy Outside of the United States, please contact your local sales representative Library of Congress Cataloging-in-Publication Data Christian, Gary D., author Analytical chemistry Seventh edition / Gary D Christian, University of Washington, Purnendu K (Sandy) Dasgupta, University of Texas at Arlington, Kevin A Schug, University of Texas at Arlington pages cm Includes index ISBN 978-0-470-88757-8 (hardback : alk paper) Chemistry, Analytic Quantitative Textbooks I Dasgupta, Purnendu, author II Schug, Kevin, author III Title QD101.2.C57 2014 543 dc23 2013019926 Printed in the United States of America 10 Christian7e ftoc.tex V1 - 08/20/2013 8:30 A.M Page iii Contents Chapter Analytical Objectives, or: What Analytical Chemists Do 1.1 What Is Analytical Science?, 1.2 Qualitative and Quantitative Analysis: What Does Each Tell Us?, 1.3 Getting Started: The Analytical Process, 1.4 Validation of a Method—You Have to Prove It Works!, 15 1.5 Analyze Versus Determine—They Are Different, 16 1.6 Some Useful Websites, 16 Chapter Basic Tools and Operations of Analytical Chemistry 20 2.1 The Laboratory Notebook—Your Critical Record, 20 2.2 Laboratory Materials and Reagents, 23 2.3 The Analytical Balance—The Indispensible Tool, 23 2.4 Volumetric Glassware—Also Indispensible, 30 2.5 Preparation of Standard Base Solutions, 42 2.6 Preparation of Standard Acid Solutions, 42 2.7 Other Apparatus—Handling and Treating Samples, 43 2.8 Igniting Precipitates—Gravimetric Analysis, 48 2.9 Obtaining the Sample—Is It Solid, Liquid, or Gas?, 49 2.10 Operations of Drying and Preparing a Solution of the Analyte, 51 2.11 Laboratory Safety, 57 Chapter Statistics and Data Handling in Analytical Chemistry 62 3.1 Accuracy and Precision: There Is a Difference, 62 3.2 Determinate Errors—They Are Systematic, 63 3.3 Indeterminate Errors—They Are Random, 64 3.4 Significant Figures: How Many Numbers Do You Need?, 65 3.5 Rounding Off, 71 3.6 Ways of Expressing Accuracy, 71 3.7 Standard Deviation—The Most Important Statistic, 72 3.8 Propagation of Errors—Not Just Additive, 75 3.9 Significant Figures and Propagation of Error, 81 3.10 Control Charts, 83 3.11 The Confidence Limit—How Sure Are You?, 84 3.12 Tests of Significance—Is There a Difference?, 86 3.13 Rejection of a Result: The Q Test, 95 3.14 Statistics for Small Data Sets, 98 3.15 Linear Least Squares—How to Plot the Right Straight Line, 99 3.16 Correlation Coefficient and Coefficient of Determination, 104 3.17 Detection Limits—There Is No Such Thing as Zero, 105 3.18 Statistics of Sampling—How Many Samples, How Large?, 107 3.19 Powering a Study: Power Analysis, 110 3.20 Use of Spreadsheets in Analytical Chemistry, 112 3.21 Using Spreadsheets for Plotting Calibration Curves, 117 iii Christian7e ftoc.tex V1 - 08/20/2013 8:30 A.M CONTENTS iv 3.22 Slope, Intercept, and Coefficient of Determination, 118 3.23 LINEST for Additional Statistics, 119 3.24 Statistics Software Packages, 120 Chapter Good Laboratory Practice: Quality Assurance and Method Validation 132 4.1 What Is Good Laboratory Practice?, 133 4.2 Validation of Analytical Methods, 134 4.3 Quality Assurance—Does the Method Still Work?, 143 4.4 Laboratory Accreditation, 144 4.5 Electronic Records and Electronic Signatures: 21 CFR, Part 11, 145 4.6 Some Official Organizations, 146 Chapter Stoichiometric Calculations: The Workhorse of the Analyst 149 5.1 Review of the Fundamentals, 149 5.2 How Do We Express Concentrations of Solutions?, 152 5.3 Expressions of Analytical Results—So Many Ways, 159 5.4 Volumetric Analysis: How Do We Make Stoichiometric Calculations?, 166 5.5 Volumetric Calculations—Let’s Use Molarity, 169 5.6 Titer—How to Make Rapid Routine Calculations, 179 5.7 Weight Relationships—You Need These for Gravimetric Calculations, 180 Chapter General Concepts of Chemical Equilibrium 6.1 Chemical Reactions: The Rate Concept, 188 6.2 Types of Equilibria, 190 6.3 Gibbs Free Energy and the Equilibrium Constant, 191 6.4 Le Chˆatelier’s Principle, 192 6.5 Temperature Effects on Equilibrium Constants, 192 6.6 Pressure Effects on Equilibria, 192 6.7 Concentration Effects on Equilibria, 193 6.8 Catalysts, 193 6.9 Completeness of Reactions, 193 6.10 Equilibrium Constants for Dissociating or Combining Species—Weak Electrolytes and Precipitates, 194 6.11 Calculations Using Equilibrium Constants—Composition at Equilibrium?, 195 6.12 The Common Ion Effect—Shifting the Equilibrium, 203 6.13 Systematic Approach to Equilibrium Calculations—How to Solve Any Equilibrium Problem, 204 6.14 Some Hints for Applying the Systematic Approach for Equilibrium Calculations, 208 6.15 Heterogeneous Equilibria—Solids Don’t Count, 211 6.16 Activity and Activity Coefficients— Concentration Is Not the Whole Story, 211 6.17 The Diverse Ion Effect: The Thermodynamic Equilibrium Constant and Activity Coefficients, 217 Chapter Acid–Base Equilibria 188 222 7.1 The Early History of Acid—Base Concepts, 222 7.2 Acid–Base Theories—Not All Are Created Equal, 223 7.3 Acid–Base Equilibria in Water, 225 7.4 The pH Scale, 227 7.5 pH at Elevated Temperatures: Blood pH, 231 7.6 Weak Acids and Bases—What Is the pH?, 232 7.7 Salts of Weak Acids and Bases—They Aren’t Neutral, 234 7.8 Buffers—Keeping the pH Constant (or Nearly So), 238 7.9 Polyprotic Acids and Their Salts, 245 7.10 Ladder Diagrams, 247 7.11 Fractions of Dissociating Species at a Given pH: α Values—How Much of Each Species?, 248 7.12 Salts of Polyprotic Acids—Acid, Base, or Both?, 255 Page iv Christian7e ftoc.tex V1 - 08/20/2013 8:30 A.M CONTENTS v 7.13 Physiological Buffers—They Keep You Alive, 261 7.14 Buffers for Biological and Clinical Measurements, 263 7.15 Diverse Ion Effect on Acids and Bases: c Ka and c Kb —Salts Change the pH, 266 7.16 log C—pH Diagrams, 266 7.17 Exact pH Calculators, 269 Chapter Acid–Base Titrations 9.5 Other Uses of Complexes, 336 9.6 Cumulative Formation Constants β and Concentrations of Specific Species in Stepwise Formed Complexes, 336 Chapter 10 Gravimetric Analysis and Precipitation Equilibria 281 8.1 Strong Acid versus Strong Base—The Easy Titrations, 282 8.2 The Charge Balance Method—An Excel Exercise for the Titration of a Strong Acid and a Strong Base, 285 8.3 Detection of the End Point: Indicators, 288 8.4 Standard Acid and Base Solutions, 290 8.5 Weak Acid versus Strong Base—A Bit Less Straightforward, 290 8.6 Weak Base versus Strong Acid, 295 8.7 Titration of Sodium Carbonate—A Diprotic Base, 296 8.8 Using a Spreadsheet to Perform the Sodium Carbonate—HCl Titration, 298 8.9 Titration of Polyprotic Acids, 300 8.10 Mixtures of Acids or Bases, 302 8.11 Equivalence Points from Derivatives of a Titration Curve, 304 8.12 Titration of Amino Acids—They Are Acids and Bases, 309 8.13 Kjeldahl Analysis: Protein Determination, 310 8.14 Titrations Without Measuring Volumes, 312 Chapter Complexometric Reactions and Titrations 322 9.1 Complexes and Formation Constants—How Stable Are Complexes?, 322 9.2 Chelates: EDTA—The Ultimate Titrating Agent for Metals, 325 9.3 Metal–EDTA Titration Curves, 331 9.4 Detection of the End Point: Indicators—They Are Also Chelating Agents, 334 342 10.1 How to Perform a Successful Gravimetric Analysis, 343 10.2 Gravimetric Calculations—How Much Analyte Is There?, 349 10.3 Examples of Gravimetric Analysis, 353 10.4 Organic Precipitates, 353 10.5 Precipitation Equilibria: The Solubility Product, 355 10.6 Diverse Ion Effect on Solubility: Ksp and Activity Coefficients, 361 Chapter 11 Precipitation Reactions and Titrations 366 11.1 Effect of Acidity on Solubility of Precipitates: Conditional Solubility Product, 366 11.2 Mass Balance Approach for Multiple Equilibria, 368 11.3 Effect of Complexation on Solubility: Conditional Solubility Product, 372 11.4 Precipitation Titrations, 374 Chapter 12 Electrochemical Cells and Electrode Potentials 12.1 What Are Redox Reactions?, 384 12.2 Electrochemical Cells—What Electroanalytical Chemists Use, 384 12.3 Nernst Equation—Effects of Concentrations on Potentials, 390 12.4 Formal Potential—Use It for Defined Nonstandard Solution Conditions, 394 12.5 Limitations of Electrode Potentials, 395 383 Page v Christian7e ftoc.tex V1 - 08/28/2013 2:26 P.M Page vi CONTENTS vi Chapter 13 Potentiometric Electrodes and Potentiometry 399 13.1 Metal Electrodes for Measuring the Metal Cation, 400 13.2 Metal–Metal Salt Electrodes for Measuring the Salt Anion, 401 13.3 Redox Electrodes—Inert Metals, 402 13.4 Voltaic Cells without Liquid Junction—For Maximum Accuracy, 404 13.5 Voltaic Cells with Liquid Junction—The Practical Kind, 405 13.6 Reference Electrodes: The Saturated Calomel Electrode, 407 13.7 Measurement of Potential, 409 13.8 Determination of Concentrations from Potential Measurements, 411 13.9 Residual Liquid-Junction Potential—It Should Be Minimized, 411 13.10 Accuracy of Direct Potentiometric Measurements—Voltage Error versus Activity Error, 412 13.11 Glass pH Electrode—Workhorse of Chemists, 413 13.12 Standard Buffers—Reference for pH Measurements, 418 13.13 Accuracy of pH Measurements, 420 13.14 Using the pH Meter—How Does It Work?, 421 13.15 pH Measurement of Blood—Temperature Is Important, 422 13.16 pH Measurements in Nonaqueous Solvents, 423 13.17 Ion-Selective Electrodes, 424 13.18 Chemical Analysis on Mars using Ion-Selective Electrodes, 432 Chapter 14 Redox and Potentiometric Titrations 14.1 First: Balance the Reduction–Oxidation Reaction, 437 14.2 Calculation of the Equilibrium Constant of a Reaction—Needed to Calculate Equivalence Point Potentials, 438 14.3 Calculating Redox Titration Curves, 441 14.4 Visual Detection of the End Point, 445 14.5 Titrations Involving Iodine: Iodimetry and Iodometry, 447 437 14.6 Titrations with Other Oxidizing Agents, 452 14.7 Titrations with Other Reducing Agents, 454 14.8 Preparing the Solution—Getting the Analyte in the Right Oxidation State before Titration, 454 14.9 Potentiometric Titrations (Indirect Potentiometry), 456 Chapter 15 Voltammetry and Electrochemical Sensors 466 15.1 Voltammetry, 467 15.2 Amperometric Electrodes—Measurement of Oxygen, 472 15.3 Electrochemical Sensors: Chemically Modified Electrodes, 472 15.4 Ultramicroelectrodes, 474 15.5 Microfabricated Electrochemical Sensors, 474 15.6 Micro and Ultramicroelectrode Arrays, 475 Chapter 16 Spectrochemical Methods 477 16.1 Interaction of Electromagnetic Radiation with Matter, 478 16.2 Electronic Spectra and Molecular Structure, 484 16.3 Infrared Absorption and Molecular Structure, 489 16.4 Near-Infrared Spectrometry for Nondestructive Testing, 491 16.5 Spectral Databases—Identifying Unknowns, 493 16.6 Solvents for Spectrometry, 493 16.7 Quantitative Calculations, 494 16.8 Spectrometric Instrumentation, 504 16.9 Types of Instruments, 519 16.10 Array Spectrometers—Getting the Entire Spectrum at Once, 522 16.11 Fourier Transform Infrared Spectrometers, 523 16.12 Near-IR Instruments, 525 16.13 Spectrometric Error in Measurements, 526 16.14 Deviation from Beer’s Law, 527 16.15 Fluorometry, 530 16.16 Chemiluminescence, 538 16.17 Fiber-Optic Sensors, 540 Christian7e ftoc.tex V1 - 08/20/2013 8:30 A.M CONTENTS Chapter 17 Atomic Spectrometric Methods vii 548 17.1 Principles: Distribution between Ground and Excited States—Most Atoms Are in the Ground State, 550 17.2 Flame Emission Spectrometry, 553 17.3 Atomic Absorption Spectrometry, 556 17.4 Sample Preparation—Sometimes Minimal, 567 17.5 Internal Standard and Standard Addition Calibration, 567 17.6 Atomic Emission Spectrometry: The Induction Coupled Plasma (ICP), 569 17.7 Atomic Fluorescence Spectrometry, 574 Chapter 18 Sample Preparation: Solvent and Solid-Phase Extraction 20.1 20.2 20.3 20.4 20.5 20.6 20.7 20.8 20.9 20.10 20.11 579 Distribution Coefficient, 579 Distribution Ratio, 580 Percent Extracted, 581 Solvent Extraction of Metals, 583 Accelerated and Microwave-Assisted Extraction, 585 18.6 Solid-Phase Extraction, 586 18.7 Microextraction, 590 18.8 Solid-Phase Nanoextraction (SPNE), 593 19.1 Countercurrent Extraction: The Predecessor to Modern Liquid Chromatography, 598 19.2 Principles of Chromatographic Separations, 603 19.3 Classification of Chromatographic Techniques, 604 19.4 Theory of Column Efficiency in Chromatography, 607 19.5 Chromatography Simulation Software, 616 21.1 21.2 21.3 21.4 21.5 21.6 21.7 21.8 21.9 21.10 21.11 596 649 High-Performance Liquid Chromatography, 651 Stationary Phases in HPLC, 654 Equipment for HPLC, 665 Ion Chromatography, 692 HPLC Method Development, 700 UHPLC and Fast LC, 701 Open Tubular Liquid Chromatography (OTLC), 702 Thin-Layer Chromatography, 702 Electrophoresis, 708 Capillary Electrophoresis, 711 Electrophoresis Related Techniques, 724 Chapter 22 Mass Spectrometry 22.1 22.2 22.3 22.4 619 Performing GC Separations, 620 Gas Chromatography Columns, 623 Gas Chromatography Detectors, 630 Temperature Selection, 638 Quantitative Measurements, 639 Headspace Analysis, 641 Thermal Desorption, 641 Purging and Trapping, 642 Small and Fast, 643 Separation of Chiral Compounds, 644 Two-Dimensional GC, 645 Chapter 21 Liquid Chromatography and Electrophoresis 18.1 18.2 18.3 18.4 18.5 Chapter 19 Chromatography: Principles and Theory Chapter 20 Gas Chromatography 735 Principles of Mass Spectrometry, 735 Inlets and Ionization Sources, 740 Gas Chromatography–Mass Spectrometry, 741 Liquid Chromatography–Mass Spectrometry, 746 22.5 Laser Desorption/Ionization, 750 22.6 Secondary Ion Mass Spectrometry, 752 22.7 Inductively Coupled Plasma–Mass Spectrometry, 753 Page vii Christian7e ftoc.tex CONTENTS viii 22.8 Mass Analyzers and Detectors, 753 22.9 Hybrid Instruments and Tandem Mass Spectrometry, 764 Chapter 23 Kinetic Methods of Analysis Available on textbook website: www.wiley.com/college/christian Chapter G Century of the Gene—Genomics and Proteomics: DNA Sequencing and Protein Profiling G1 769 23.1 Kinetics—The Basics, 769 23.2 Catalysis, 771 23.3 Enzyme Catalysis, 772 Chapter 24 Automation in Measurements 24.1 24.2 24.3 24.4 24.5 24.6 784 Principles of Automation, 784 Automated Instruments: Process Control, 785 Automatic Instruments, 787 Flow Injection Analysis, 789 Sequential Injection Analysis, 791 Laboratory Information Management Systems, 792 G.7 G.8 G.9 G.10 G.11 G.12 Of What Are We Made?, G1 What Is DNA?, G3 Human Genome Project, G3 How Are Genes Sequenced?, G5 Replicating DNA: The Polymerase Chain Reaction, G6 Plasmids and Bacterial Artificial Chromosomes (BACs), G7 DNA Sequencing, G8 Whole Genome Shotgun Sequencing, G11 Single-Nucleotide Polymorphisms, G11 DNA Chips, G12 Draft Genome, G13 Genomes and Proteomics: The Rest of the Story, G13 APPENDIX A LITERATURE OF ANALYTICAL CHEMISTRY Chapter 25 Clinical Chemistry C1 25.1 Composition of Blood, C1 25.2 Collection and Preservation of Samples, C3 25.3 Clinical Analysis—Common Determinations, C4 25.4 Immunoassay, C6 EN1 Getting a Meaningful Sample, EN1 Air Sample Collection and Analysis, EN2 Water Sample Collection and Analysis, EN9 Soil and Sediment Sampling, EN11 Sample Preparation for Trace Organics, EN12 Contaminated Land Sites—What Needs to Be Analyzed?, EN12 26.7 EPA Methods and Performance-Based Analyses, EN13 794 APPENDIX B REVIEW OF MATHEMATICAL OPERATIONS: EXPONENTS, LOGARITHMS, AND THE QUADRATIC FORMULA 797 APPENDIX C TABLES OF CONSTANTS Available on textbook website: www.wiley.com/college/christian Chapter 26 Environmental Sampling and Analysis G.1 G.2 G.3 G.4 G.5 G.6 Available on textbook website: www.wiley.com/college/christian 26.1 26.2 26.3 26.4 26.5 26.6 V1 - 08/20/2013 8:30 A.M 801 Table C.1 Dissociation Constants for Acids, 801 Table C.2a Dissociation Constants for Basic Species, 802 Table C.2b Acid Dissociation Constants for Basic Species, 803 Table C.3 Solubility Product Constants, 803 Table C.4 Formation Constants for Some EDTA Metal Chelates, 805 Table C.5 Some Standard and Formal Reduction Electrode Potentials, 806 Available on textbook website: www.wiley.com/college/christian APPENDIX D SAFETY IN THE LABORATORY S1 Page viii Christian7e c12.tex 384 V2 - 08/12/2013 10:33 P.M Page 384 CHAPTER 12 ELECTROCHEMICAL CELLS AND ELECTRODE POTENTIALS Before beginning our discussions, it is helpful to describe some fundamental electrochemical terms, some of which will be discussed later on: Potential (volts) originates from separation of charge Ohm’s law: E = iR, where E potential in volts, i is current in amperes, and R is resistance in ohms P = Ei, where P is power in volt amperes The first law of thermodynamics says that there is a conservation of energy in a chemical reaction Work is done by the system or on the system to the extent of energy evolved or absorbed, work being equal to qE, where q is charge, in coulombs transferred across a potential difference E In the case of electrochemical cells, free energy change, G, is related to the electrical work done in the cell If Ecell is the electromotive force (emf) of the cell and n moles of electrons are involved in the reaction, the electrical work done will be G = −nFEcell , where F is the Faraday constant, 96,487 coulombs/equivalent If reactants and products are in their standard states, then G◦ = −nFE◦ , where E◦ is the standard cell potential While our emphasis in these chapters is on analytical applications of redox reactions and electrochemistry, such reactions are important in biochemistry, energy conversion, batteries, environmental chemistry, and other aspects of our lives, and your knowledge of basic redox chemistry and electrochemistry will be helpful in your understanding of these processes 12.1 What Are Redox Reactions? Note the similarity with the Brønsted-Lowry acid-base concept Whereas acid-base behavior is centered on proton transfer, redox behavior is centered on electron transfer Like conjugate acid-base pairs there are redox couples But redox couples may differ by more than just the gain or loss of electron(s) The oxidizing agent is reduced The reducing agent is oxidized A reduction–oxidation reaction—commonly called a redox reaction—is one that occurs between a reducing and an oxidizing agent: Ox1 + Red2 Red1 + Ox2 (12.1) Ox1 is reduced to Red1 , and Red2 is oxidized to Ox2 Ox1 is the oxidizing agent, and Red2 is the reducing agent The reducing or oxidizing tendency of a substance will depend on its reduction potential, described below An oxidizing substance will tend to take on an electron or electrons and be reduced to a lower oxidation state: Ma+ + ne− → M(a−n)+ − (12.2) for example, Fe + e → Fe Conversely, a reducing substance will tend to give up an electron or electrons and be oxidized: 3+ 2+ Ma+ → M(a+n)+ + ne− − (12.3) − for example, 2I → I2 + 2e If the oxidized form of a metal ion is complexed, it is more stable and will be more difficult to reduce; so its tendency to take on electrons will be decreased if the reduced form is not also complexed to make it more stable and easier to form We can better understand the oxidizing or reducing tendencies of substances by studying electrochemical cells and electrode potentials 12.2 Electrochemical Cells—What Electroanalytical Chemists Use There are two kinds of electrochemical cells, voltaic (galvanic) and electrolytic In voltaic cells, a chemical reaction spontaneously occurs to produce electrical energy The lead storage battery and the ordinary flashlight cell are common examples of Christian7e c12.tex 12.2 ELECTROCHEMICAL CELLS— —WHAT ELECTROANALYTICAL CHEMISTS USE voltaic cells In electrolytic cells, on the other hand, electrical energy is used to force a nonspontaneous chemical reaction to occur, that is, to go in the reverse direction it would in a voltaic cell An example is the electrolysis of water In both types of these cells, the electrode at which oxidation occurs is the anode, and that at which reduction occurs is the cathode Voltaic cells will be of importance in our discussions in the next two chapters, dealing with potentiometry Electrolytic cells are important in electrochemical methods such as voltammetry, in which electroactive substances like metal ions are reduced at an electrode to produce a measurable current by applying an appropriate potential to get the nonspontaneous reaction to occur (Chapter 15) The current that results from the forced electrolysis is proportional to the concentration of the electroactive substance VOLTAIC CELL AND SPONTANEOUS REACTIONS——WHAT IS THE CELL POTENTIAL? Consider the following redox reaction in a voltaic cell: Fe2+ + Ce4+ Fe3+ + Ce3+ 2+ (12.4) 4+ If we mix a solution containing Fe with one containing Ce , there is a certain tendency for the ions to transfer electrons Assume the Fe2+ and Ce4+ are in separate beakers connected by a salt bridge, as shown in Figure 12.1 (A salt bridge allows ion transfer into the solutions and prevents mixing of the solutions.) No reaction can occur since the solutions not make contact A salt bridge is not always needed—only when the reactants or products at the anode or cathode react with each other so that it is necessary to keep them from mixing freely Now put an inert platinum wire in each solution and connect the two wires The setup now constitutes a voltaic cell If a microammeter is connected in series, it indicates that a current is flowing The Fe2+ is being oxidized at the platinum wire (the anode): Fe2+ → Fe3+ + e− (12.5) The released electrons flow through the wire to the other beaker where the Ce4+ is reduced (at the cathode): Ce4+ + e− → Ce3+ (12.6) This process occurs because of the tendency of these ions to transfer electrons The net result is the reaction written in Equation 12.4, which would occur if Fe2+ and Ce4+ were added together in a single beaker (in that case, the electrical energy that could be harvested from the voltaic cell is simply liberated as heat) The platinum wires can be considered electrodes Each will adopt an electrical potential that is determined by the tendency of the ions to give off or take on electrons, and this is called the electrode potential A voltmeter placed between the electrodes will indicate the difference in the potentials between the two electrodes The larger the potential difference, the A e− e− Salt bridge Pt Fe2+ Fe3+ + e− Fe 2+ solution Ce4+ + e− Ce3+ Pt Ce 4+ solution Fig 12.1 Voltaic cell V2 - 08/12/2013 10:33 P.M Page 385 385 In a voltaic cell, a spontaneous chemical reaction produces electricity This occurs only when the cell circuit is closed, as when you turn on a flashlight The cell voltage (e.g., in a battery) is determined by the potential difference of the two half reactions When the reaction has gone to completion, the cell runs down, and the voltage is zero (the battery is “dead”) In an electrolytic cell, the reaction is forced the other way by applying an external voltage greater than and opposite to the spontaneous voltage A battery is a combination of cells in series A C-cell is a cell but if you break open a 9V battery you will find six individual cells The salt bridge typically contains a gel containing KCl KCl is the preferred ingredient since K+ and Cl− move at equal speeds As current flows, Cl− comes into the anode compartment and K+ comes into the cathode compartment to maintain charge balance Christian7e c12.tex 386 V2 - 08/12/2013 10:33 P.M Page 386 CHAPTER 12 ELECTROCHEMICAL CELLS AND ELECTRODE POTENTIALS greater the tendency for the reaction between Fe2+ and Ce4+ The driving force of the chemical reaction (the potential difference) can be used to perform work such as lighting a light bulb or running a motor, as is done with a battery HALF-REACTIONS——GIVING AND ACCEPTING ELECTRONS Equations 12.5 and 12.6 are half-reactions No half-reaction can occur by itself in much the same way as in the world of finance, there has to be a lender for a borrower to exist and without both, no transaction can occur There must be an electron donor (a reducing agent) and an electron acceptor (an oxidizing agent) In this case, Fe2+ is the reducing agent and Ce4+ is the oxidizing agent Each half-reaction will generate a definite potential that would be adopted by an inert electrode dipped in the solution HALF-REACTION POTENTIALS——THEY ARE MEASURED RELATIVE TO EACH OTHER If the potentials of all half-reactions could be measured, then we could determine which oxidizing and reducing agents will react Unfortunately, there is no way to measure individual electrode potentials But, as we just saw, the difference between two electrode potentials can be measured The electrode potential of the half-reaction1 2H+ + 2e− We arbitrarily define the potential of this half-reaction as zero (at standard conditions) All others are measured relative to this In the Gibbs–Stockholm convention, we always write the half-reaction as a reduction H2 (12.7) has arbitrarily been assigned a value of 0.000 V This is called the normal hydrogen electrode (NHE), or the standard hydrogen electrode (SHE) This consists of a platinized platinum electrode (one coated with fine “platinum black” by electroplating platinum on the electrode) contained in a glass tube, immersed in an acid solution in which aH+ = and where hydrogen gas (PH2 = atm) is bubbled at the electrode/ solution interface The platinum black catalyzes Reaction 12.7 The potential differences between this half-reaction and other half-reactions have been measured using voltaic cells and arranged in decreasing order Some of these are listed in Table 12.1 Potentials are dependent on concentrations, and all standard potentials refer to conditions of unit activity for all species (or atmosphere partial pressure in the case of gases, as for hydrogen in the NHE) The effects of concentrations on potentials are described below A more complete listing of potentials appears in Appendix C The potentials are for the half-reaction written as a reduction, and so they represent reduction potentials We will use the Gibbs–Stockholm electrode potential convention, adopted at the 17th Conference of the International Union of Pure and Applied Chemistry in Stockholm, 1953 In this convention, the half-reaction is written as a reduction, and the potential increases as the tendency for reduction (of the oxidized form to be reduced) increases Sn2+ is +0.15 V In other words, the The electrode potential for Sn4+ + 2e− potential of this half-reaction relative to the NHE in a cell like that in Figure 12.1 would be 0.15 V Since the above couple has a larger (more positive) reduction potential than the NHE, Sn4+ has a stronger tendency to be reduced than H+ has We can draw some general conclusions from the electrode potentials: The more positive the electrode potential, the greater the tendency of the oxidized form to be reduced In other words, the more positive the electrode potential, the stronger an oxidizing agent the oxidized form is and the weaker a reducing agent the reduced form is The reaction could have been written H+ + e− H2 The way it is written does not affect its potential Christian7e c12.tex 12.2 ELECTROCHEMICAL CELLS— —WHAT ELECTROANALYTICAL CHEMISTS USE V2 - 08/12/2013 10:33 P.M Page 387 387 Table 12.1 Some Standard Potentials E0 (V) Half-Reaction H2 O2 + 2H+ + 2e− 2H2 O MnO4 − + 4H+ + 3e− MnO2 + 2H2 O Ce4+ + e− Ce3+ Mn2+ + 4H2 O MnO4 − + 8H+ + 5e− + − 2− 2Cr3+ + 7H2 O Cr2 O7 + 14H + 6e 2+ + − MnO2 + 4H + 2e Mn + 2H2 O 2IO3 − + 12H+ + 10e− I2 + 6H2 O H2 O2 + 2e− 2OH− CuI Cu2 + I− + e− Fe3+ + e− Fe2+ O2 + 2H+ + 2e− H2 O2 I2 (aq) + 2e− 2I− H3 AsO4 + 2H+ + 2e− H3 AsO3 + H2 O I3 − + 2e− 3I− Sn2+ Sn4+ + 2e− 2S2 O3 2− S4 O6 2− + 2e− 2H+ + 2e− H2 Zn2+ + 2e− Zn 2H2 O + 2e− H2 + 2OH− 1.77 1.695 1.61 1.51 1.33 1.23 1.20 0.88 0.86 0.771 0.682 0.6197 0.559 0.5355 0.154 0.08 0.000 −0.763 −0.828 The more negative the electrode potential, the greater the tendency of the reduced form to be oxidized In other words, the more negative the reduction potential, the weaker an oxidizing agent is the oxidized form is and the stronger a reducing agent the reduced form is The reduction potential for Ce4+ + e− Ce3+ is very positive, so Ce4+ is a strong 3+ oxidizing agent, while Ce is a very weak reducing agent On the other hand, the potential for Zn2+ + 2e− Zn is very negative, and so Zn2+ is a very weak oxidizing agent, while metallic zinc is a very strong reducing agent WHAT SUBSTANCES REACT? The oxidized form of a species in a half-reaction is capable of oxidizing the reduced form of a species in a half-reaction whose reduction potential is more negative than its own, and vice versa: The reduced form in a half-reaction is capable of reducing the oxidized form in a half-reaction with a more positive potential Ce4+ is a good oxidizing agent because of the high reduction potential (But Ce3+ is a poor reducing agent.) Zn is a good reducing agent because of the low reduction potential (But Zn2+ is a poor oxidizing agent.) Note again the similarity with conjugate acid-base pairs: The stronger the acid, the weaker is the conjugate base and vice-versa For example, consider the two half-reactions Fe3+ + e− Sn4+ + 2e− Fe2+ Sn2+ E0 = 0.771 V (12.8) E0 = 0.154 V (12.9) There are two combinations for possible reaction between an oxidizing and a reducing agent in these two half-reactions, which we arrive at by subtracting one from the other (multiplying the first half-reaction by so the electrons cancel): 2Fe3+ + Sn2+ 2Fe2+ + Sn4+ (12.10) Note again that the E0 value is a measure of the tendency of the reaction to occur Multiplying a half-reaction such as 12.8 by does not alter the tendency of the reaction to occur E0 remains the same Christian7e c12.tex V2 - 08/12/2013 10:33 P.M Page 388 CHAPTER 12 ELECTROCHEMICAL CELLS AND ELECTRODE POTENTIALS 388 and Sn4+ + 2Fe2+ Sn2+ + 2Fe3+ 3+ (12.11) 4+ [There is no possibility of reaction between Fe and Sn (both oxidizing agents) or between Fe2+ and Sn2+ (both reducing agents).] Perusal of the potentials tells us that Reaction 12.10 will take place; that is, the reduced form Sn2+ of Reaction 12.9 (with the more negative potential) will react with the oxidized form of Reaction 12.8 (with the more positive potential) Note that the number of electrons donated and accepted must be equal (see Chapter 14 on balancing redox reactions) Another way to combine two half-reactions is to take one of the half-reactions and write it as oxidation The E0 value will change sign If the number of electrons are different in the two half-reactions, one or both must be multiplied by appropriate multipliers first so that the number of electrons involved in half-reactions are the same Then when we add them up (the E0 values will also add algebraically), the reaction will proceed from left to right, if the summed E0 value is positive Thus, for example, we multiply Equation 12.8 by and reverse Equation 12.9 and then add them: 2Fe3+ + 2e− 2+ Sn 2Fe3+ + Sn2+ 2Fe2+ 4+ Sn − + 2e 2Fe2+ + Sn4+ E0 0.771 V (12.12) −0.154 V (12.13) E0 0.617 V (12.14) E The reaction in Equation 12.14 will proceed to the right because the net potential is positive The electrons will appear on both sides after the addition and are therefore canceled If we reversed Equation 12.8 (after multiplication with 2) and added to Equation 12.9, the net potential will be negative and the reaction will not proceed as written Example 12.1 For the following substances, list the oxidizing agents in decreasing order of oxidizing capability, and the reducing agents in decreasing order of reducing capability: MnO4 − , Ce3+ , Cr3+ , IO3 − , Fe3+ , I− , H+ , Zn2+ Solution Looking at Table 12.1, the following must be oxidizing agents (are in the oxidized forms) and are listed from the most positive E0 to the least positive: MnO4 − , IO3 − , Fe3+ , H+ , Zn2+ MnO4 − is a very good oxidizing agent, Zn2+ is very poor The remainder are in the reduced form, and their reducing power is in the order I− , Cr3+ , and Ce3+ I− is a reasonably good reducing agent; Ce3+ is poor The spontaneous cell reaction is the one that gives a positive cell voltage when subtracting one half-reaction from the other The net potential as represented in Equation 12.14 is called the cell voltage.2 To reiterate, if this calculated cell voltage is positive, the reaction goes as written If it is negative, the reaction will occur in the reverse direction This is the result of the convention that, for a spontaneous reaction, the free energy is negative The free energy at standard conditions is given by ◦ Coulomb (C) = 1Ampere-second (A · s), the quantity of electricity carried by a current of Ampere in second G = −nFE0 (12.15) where n is the number of moles of electrons involved in the balanced reaction and F is the Faraday constant (96, 487 C mol−1 ); and so a positive potential difference We refer to electrode potentials and cell voltages to distinguish between half-reactions and complete reactions Christian7e c12.tex 12.2 ELECTROCHEMICAL CELLS— —WHAT ELECTROANALYTICAL CHEMISTS USE V2 - 08/12/2013 10:33 P.M Page 389 389 provides the necessary negative free energy Hence, we can tell from the relative standard potentials for two reactions, and from their signs, which reaction combination will produce a negative free-energy change and thus be spontaneous For example, for the Ce4+ /Ce3+ half-reaction, E0 is +1.61 V (Table 12.1); and for the Fe3+ /Fe2+ half-reaction, E0 is +0.771 V G◦ for the former is more negative than for the latter, and subtraction of the iron half-reaction from the cerium one will provide the spontaneous reaction that would occur to give a negative free energy That is, Ce4+ would spontaneously oxidize Fe2+ WHICH IS THE ANODE? AND WHICH IS THE CATHODE? By convention, a cell is written with the anode on the left: anode/solution/cathode (12.16) The single lines represent a boundary between either an electrode phase and a solution phase or two solution phases In Figure 12.1, the cell would be written as Pt/Fe2+ (C1 ), Fe3+ (C2 )//Ce4+ (C3 ), Ce3+ (C4 )/Pt (12.17) where C1 , C2 , C3 , and C4 represent the concentrations of the different species The double line represents the salt bridge If a voltaic cell were constructed for the above iron and tin half-reactions with platinum electrodes, it would be written as Pt/Sn2+ (C1 ), Sn4+ (C2 )//Fe3+ (C3 ), Fe2+ (C4 )/Pt (12.18) Since oxidation occurs at the anode and reduction occurs at the cathode, the stronger reducing agent is placed on the left and the stronger oxidizing agent is placed on the right The potential of the voltaic cell is given by Ecell = Eright − Eleft = Ecathode − Eanode = E+ − E− (12.19) The anode is the electrode where oxidation occurs, i.e., the more negative or less positive half-reaction occurs in the anode compartment where E+ is the more positive electrode potential and E− is the more negative of the two electrodes When the cell is set up properly, the calculated voltage will always be positive, and the cell reaction is written correctly, that is, the correct cathode half-reaction is written as a reduction and the correct anode half-reaction is written as an oxidation In cell represented by Equation (12.18), we would have at standard conditions 0 = EFe Ecell 3+ ,Fe2+ − ESn4+ ,Sn2+ = 0.771 − 0.154 = 0.617 V To take some more examples of possible redox reactions, Fe3+ will not oxidize Mn2+ Quite the contrary, MnO4 − will oxidize Fe2+ I2 is a moderate oxidizing agent and will oxidize Sn2+ On the other hand, I− is a fairly good reducing agent and will reduce Fe3+ , Cr2 O7 2− , and so on To obtain a sharp end point in a redox titration, the reaction will need to be nearly quantitative, and there should be at least 0.2 to 0.3 V difference between the two electrode potentials Combining Equation 12.15 with 6.10 leads to an expression that relates difference in standard potentials to the equilibrium constant: ◦ G = −2.303RT log K = −nFE0 log K = nE0 2.303RT/F (12.20) At 298 K, 2.303RT/F is equal to 0.05915 V (see Section 12.3) For n = and E0 = 0.2 V, one calculates from Equation 12.20 that K ≈ 2400 In a redox titration (Chapter 14), the potential difference between the titrant and the analyte half-reaction should be 0.2–0.3 V for a sharp end point Christian7e c12.tex V2 - 08/12/2013 10:33 P.M Page 390 CHAPTER 12 ELECTROCHEMICAL CELLS AND ELECTRODE POTENTIALS 390 Example 12.2 From the potentials listed in Table 12.1, determine the reaction between the following half-reactions, and calculate the corresponding cell voltage: Solution Fe3+ + e− Fe2+ E0 0.771 V I3 − + 2e− 3I− E0 0.5355 V Since the Fe3+ /Fe2+ potential is the more positive, Fe3+ is a better oxidizing agent than 0 = Ecathode − Eanode = EFe I3 − Hence, Fe3+ will oxidize I− and Ecell 3+ ,Fe2+ − EI3 − ,I− In the same fashion, the second half-reaction must be subtracted from the first (multiplied by 2) to give the overall cell reaction: 2Fe3+ + 3I− = 2Fe2+ + I3 − Ecell = 0.771 V − 0.536 V = +0.235 V Note again that multiplying a half-reaction by any number does not change its potential 12.3 Nernst Equation—Effects of Concentrations on Potentials Activities should be used in the Nernst equation We will use concentrations here because we are primarily concerned here with titrations Titrations end points involve large potential changes, and the errors are small by doing so The potentials listed in Table 12.1 were determined for the case when the concentrations of both the oxidized and reduced forms (and all other species) were at unit activity, and they are called the standard potentials, designated by E0 Volta originally set up empirical E0 tables under very controlled and defined conditions Nernst made them practical by establishing quantitative relationships between potential and concentrations This potential is dependent on the concentrations of the species and varies from the standard potential This potential dependence is described by the Nernst equation3 : aOx + ne− E = E0 − bRed [Red]b 2.3026RT log nF [Ox]a (12.21) (12.22) where a and b are the numbers of Ox and Red species in the half-reaction, E is the reduction potential at the specific concentrations, n is the number of electrons involved in the half-reaction (equivalents per mole), R is the gas constant (8.3143 V C K−1 mol−1 ), T is the absolute temperature in Kelvin, and F is the Faraday constant (96,487 C eq−1 ) At 25◦ C (298.16 K), the value of 2.3026RT/F is 0.05916 V, or 1.9842 × 10−4 (◦ C + 273.16 V) The concentration of pure substances such as precipitates and liquids (H2 O) is taken as unity Note that the log term of the reduction half-reaction is the ratio of the concentrations of the right-side product(s) over the left-side reactants(s) Example 12.3 A solution is 10−3 M in Cr2 O7 2− and 10−2 M in Cr3+ If the pH is 2.0, what is the potential of the half-reaction at 298K? More correctly, activities, rather than concentrations, should be used; but we will use concentrations for this discussion In the next chapter, involving potential measurements for direct calculation of concentrations, we will use activities Christian7e c12.tex 12.3 NERNST EQUATION— —EFFECTS OF CONCENTRATIONS ON POTENTIALS V2 - 08/12/2013 10:33 P.M Page 391 391 Solution Cr2 O7 2− + 14H+ + 6e− E = ECr O7 2− ,Cr3+ − 2Cr3+ + 7H2 O 0.05916 [Cr3+ ]2 log [Cr2 O7 2− ] [H+ ]14 = 1.33 − 0.05916 (10−2 )2 log (10−3 )(10−2 )14 = 1.33 − 0.05916 0.05916 log 1027 = 1.33 − 27 6 = 1.06 V This calculated potential is the potential an electrode would adopt, relative to the NHE, if it were placed in the solution, and it is a measure of the oxidizing or reducing power of that solution Theoretically, the potential would be infinite if there were no Cr3+ at all in solution In actual practice, the potential is always finite (but impossible to calculate from the simple Nernst equation) Either there will be a small amount of impurity of the oxidized or reduced form present or, more probably, the potential will be limited by another half-reaction, such as the oxidation or reduction of water, that prevents it from going to infinity EQUILIBRIUM POTENTIAL——AFTER THE REACTION HAS OCCURRED Imagine that I have a solution of Fe2+ containing a small amount of Fe3+ The potential of the solution can be readily calculated from Equations 12.8 and 12.22 Now a small amount of Ce4+ is added to the solution This results in a new equilibrium being reached, with some of the Fe2+ being oxidized to Fe3+ , with the concomitant production of a corresponding amount of Ce3+ Based on the new composition, a new potential can be calculated, either from the same two equations as before or from the Ce3+ -Ce4+ half reaction potential and Equation 12.22 The potential of an inert electrode in a solution containing the ions of two half-reactions at equilibrium (e.g., at different points in a titration) can be calculated relative to the NHE using the Nernst equation for either half-reaction This is because when the reaction comes to equilibrium after each aliquot of titrant addition, the potentials for the two halfreactions become identical; otherwise, the reaction would still be going on An electrode dipped in the solution will adopt the equilibrium potential The equilibrium potential is dictated by the equilibrium concentrations of either half-reaction and the Nernst equation Example 12.4 A 5.0 mL portion of 0.10 M Ce4+ solution is added to 5.0 mL of 0.30 M Fe2+ solution Calculate the potential at 298K of a platinum electrode dipping in the solution (relative to the NHE) Solution We start with 0.30 mmol mL−1 × 5.0 mL = 1.5 mmol Fe2+ and add 0.10 mmol mL−1 × 5.0 mL = 0.50 mmol Ce4+ So we form 0.50 mmol each of Fe3+ and Ce3+ and have 1.0 mmol Fe2+ remaining The reaction lies far to the right at equilibrium if there is at least 0.2 V difference between the standard electrode potentials of two To construct a titration curve, we are interested in the equilibrium electrode potential (i.e., when the cell potential is zero—after the titrant and analyte have reacted) The two electrodes have identical potentials then, as determined by the Nernst equation for each half-reaction Christian7e c12.tex 392 V2 - 08/12/2013 10:33 P.M Page 392 CHAPTER 12 ELECTROCHEMICAL CELLS AND ELECTRODE POTENTIALS half-reactions But a small amount of Ce4+ (= x) will exist at equilibrium, and an equal amount of Fe2+ will be formed: Fe2+ + Ce4+ 1.0 + x These are the equilibrium concentrations, following reaction x + Fe3+ 0.50 − x Ce3+ 0.50 − x where the numbers and x represent millimoles To calculate the concentration of each species, the amounts in millimoles will need to be divided by the total volume of 10 mL, but since this same divisor appears in both the numerator and denominator, it cancels out when calculating concentration ratios At equilibrium, the potential of the Fe3+ /Fe2+ half-reaction must be the same as that of the Ce4+ /Ce3+ half-reaction: 0.771 − 0.059 log (1.0 + x) (0.50 − x) = 1.61 − 0.059 log (0.50 − x) x 1.61 − 0.771 = 0.839 = 0.059 log (0.50 − x)2 x(0.10 + x) (0.50 − x)2 0.839 = 14.22 = log 0.059 x(0.10 + x) A solution to this quadratic equation that is also readily solved by Goal Seek will result in x = 1.51 × 10−15 M Putting this value of x in either half reaction will produce E = 0.753 V We could this, however, a lot simpler Consider that this reaction is analogous to “ionization” of the product in precipitation or acid–base reactions written as association reactions; a slight shift of the equilibrium here to the left would be the “ionization.” The quantity x is very small compared with 0.50 or 1.0 and can be neglected Either half-reaction can be used to calculate the potential Since the concentrations of both species in the Fe3+ /Fe2+ couple are known, we will use this: Fe3+ + e− Fe2+ 0.50 1.0 E = 0.771 − 0.05916 log E = 0.771 − 0.05916 log [Fe2+ ] [Fe3+ ] 1.0 mmol/10 mL = 0.771 − 0.05916 log 2.0 0.50 mmol/10 mL = 0.771 − 0.05916(0.30) = 0.753 V Note that this approach can only succeed where the standard potentials of the two half-reaction are sufficiently far apart such that the addition of Ce4+ will result in essentially quantitative conversion of a corresponding amount of Fe2+ to Fe3+ (assuming sufficient Fe2+ was present) CELL VOLTAGE— —BEFORE REACTION The voltage of a cell can be calculated by taking the difference in potentials of the two half-reactions, to give a positive potential, calculated using the Nernst equation, Ecell = E+ − E− as given in Equation 12.19 (12.23) Christian7e c12.tex 12.3 NERNST EQUATION— —EFFECTS OF CONCENTRATIONS ON POTENTIALS In Example 12.2 for 2Fe3+ + 3I− 393 2Fe2+ + I3 − at 298K, Ecell = EFe3+ ,Fe2+ − EI3 − ,I− = EFe 3+ ,Fe2+ Fe2+ 0.05916 − log [Fe3+ ]2 − EI03 − ,I− I− 0.05916 − log − [I3 ] [Fe2+ ]2 [I3 − ] 0.05916 log (12.24) [Fe3+ ]2 [I− ]3 Note that the log term for the cell potential of a spontaneous reaction is always the ratio of the product concentration(s) over the reactant concentration(s), that is, right side over left side (as for a reduction half-reaction) Notice it was necessary to multiply the Fe3+ /Fe2+ half-reaction by (as when subtracting the two half-reactions) in order to combine the two log terms (with n = 2), and the final equation is the same as we 0 would have written from the cell reaction Note also that EFe 3+ ,Fe2+ − EI3 − ,I− is the cell standard potential, Ecell The term on the right of the log sign is the equilibrium constant expression for the reaction: 0 = EFe 3+ ,Fe2+ − EI3 − ,I− − 2Fe3+ + 3I− 2Fe2+ + I3 − (12.25) The cell voltage represents the tendency of a reaction to occur when the reacting species are put together (just as it does in a battery; that is, it represents the potential for work) After the reaction has reached equilibrium, the cell voltage necessarily becomes zero and the reaction is complete (i.e., no more work can be derived from the cell) That is, the potentials of the two half-reactions are equal at equilibrium This is what happens when a battery runs down Example 12.5 One beaker contains a solution of 0.0200 M KMnO4 , 0.00500 M MnSO4 , and 0.500 M H2 SO4 ; and a second beaker contains 0.150 M FeSO4 and 0.00150 M Fe2 (SO4 )3 The two beakers are connected by a salt bridge, and platinum electrodes are placed in each The electrodes are connected via a wire with a voltmeter in between What would be the potential of each half-cell (a) before reaction and (b) after reaction? What would be the measured cell voltage (c) at the start of the reaction and (d) after the reaction reaches equilibrium? Assume H2 SO4 to be completely ionized and in equal volumes in each beaker Solution The cell reaction is 5Fe2+ + MnO4 − + 8H+ V2 - 08/12/2013 10:33 P.M Page 393 5Fe3+ + Mn2+ + 4H2 O and the cell is Pt/Fe2+ (0.150 M), Fe3+ (0.00300 M)//MnO4 − (0.0200 M), Mn2+ (0.00500 M), H+ (1.00 M)/Pt Christian7e c12.tex V2 - 08/12/2013 10:33 P.M Page 394 CHAPTER 12 ELECTROCHEMICAL CELLS AND ELECTRODE POTENTIALS 394 (a) [Fe2+ ] [Fe3+ ] 0.150 = 0.671 V = 0.771 − 0.05916 log 0.00300 EFe = EFe 3+ ,Fe2+ − 0.05916 log EMn = E0 MnO4 − Mn2+ − = 1.51 − [Mn2+ ] 0.05916 log [MnO4 − ] [H+ ]8 0.00500 0.05916 log = 1.52 V (0.0200)(1.00)8 (b) At equilibrium, EFe = EMn We can calculate E from either half-reaction First, calculate the equilibrium concentrations Five moles of Fe2+ will react with each mole of MnO4 − The Fe2+ is in excess It will be decreased by × 0.0200 = 0.100 M, so 0.050 M Fe2+ remains and 0.100 M Fe3+ is formed (total now is 0.100 + 0.003 = 0.103 M) Virtually all the MnO4 − is converted to Mn2+ (0.0200 M) to give a total of 0.0250 M A small unknown amount of MnO4 − remains at equilibrium, and we would need the equilibrium constant to calculate it; this can be obtained from Ecell = at equilibrium—as in Equation 12.24—and as carried out in Example 12.4, this is treated in more detail in Chapter 14 But we need not go to this trouble since [Fe2+ ] and [Fe3+ ] are known: 0.050 = 0.790 V 0.103 Note that the half-cell potentials at equilibrium are in between the values for the two half-cells before reaction (c) Ecell = EMn − EFe = 1.52 − 0.671 = 0.85 V (d) At equilibrium, EMn = EFe , and so Ecell is zero volts EMn = EFe = 0.771 − 0.05916 log Note that if one of the species had not been initially present in a half-reaction, we could not have calculated an initial potential for that half-reaction 12.4 Formal Potential—Use It for Defined Nonstandard Solution Conditions The formal potential is used when not all species are known In a sense, the formal potential provides the same convenience as available with the use of conditional complexation constants or solubility products The E0 values listed in Table 12.1 refer to standard conditions as denoted by the superscript 0; this means they presume all species are at an activity of M However, the potential of a half-reaction may depend on the conditions of the solution For Ce3+ is 1.61 V However, we can change this example, the E0 value for Ce4+ + e− potential by changing the acid used to acidify the solution (See Table C.5 in Appendix C.) This change in potential happens because the anions of the different acids differ in their ability to form complexes with one form of the cerium relative to the other, and the concentration ratio of the two forms of the free cerium ion is thereby affected If we know the form of the complex, we could write a new half-reaction involving the acid anion and determine an E0 value for this reaction, keeping the acid and all other species at unit activity However, the complexes are frequently of unknown composition So we define the formal potential and designate this as E0 This is the standard potential of a redox couple with the oxidized and reduced forms at M concentrations and with the solution conditions specified For example, the formal potential of the Ce4+ /Ce3+ couple in M HCl is 1.28 V The Nernst equation is written as usual, using the formal potential in place of the standard potential Table C.5 lists some formal potentials Christian7e c12.tex 12.5 LIMITATIONS OF ELECTRODE POTENTIALS V2 - 08/12/2013 10:33 P.M Page 395 395 DEPENDENCE OF POTENTIAL ON pH Hydrogen or hydroxyl ions are involved in many redox half-reactions We can change the potential of these redox couples by changing the pH of the solution Consider the As(V)/As(III) couple: H3 AsO4 + 2H+ + 2e− E = E0 − H3 AsO3 + H2 O [H3 AsO3 ] 0.05916 log [H3 AsO4 ] [H+ ]2 Many redox reactions involve protons, and their potentials are influenced greatly by pH (12.26) (12.27) This can be rearranged to4 E = E0 + 0.05916 log[H+ ] − or E = E0 − 0.05916 pH − 0.05916 [H AsO3 ] log [H3 AsO4 ] 0.05916 [H AsO3 ] log [H3 AsO4 ] (12.28) (12.29) The term E0 − 0.05916 pH, where E0 is the standard potential for the half-reaction, can be considered as equal to a formal potential E0 , which can be calculated from the pH of the solution.5 In 0.1 M HCl (pH 1), E0 = E0 − 0.05916 In neutral condition, it is E0 − 0.05916(7) = E0 − 0.41 In strongly acid solution, H3 AsO4 will oxidize I− to I2 But in neutral solution, the potential of the As(V)/As(III) couple (E0 = 0.146 V) is less than that for I2 /I− , and the reaction goes in the reverse; that is, I2 will oxidize H3 AsO3 DEPENDENCE OF POTENTIAL ON COMPLEXATION If an ion in a redox couple is complexed, the concentration of the free ion is reduced This causes the potential of the couple to change For example, E0 for the Fe3+ /Fe2+ couple is 0.771 V In HCl solution, the Fe3+ is complexed with the chloride ion This reduces the concentration of Fe3+ , and so the potential is decreased In M HCl, the formal potential is 0.70 V If we assume that the complex is FeCl4 − , then the half-reaction would be Fe2+ + 4Cl− (12.30) FeCl4 − + e− Complexing one ion reduces its effective concentration, which changes the potential and if we assume that [HCl] is constant at M, E = 0.70 − 0.05916 log [Fe2+ ] [FeCl4 − ] (12.31) In effect, we have stabilized the Fe3+ by complexing it, making it more difficult to reduce So the reduction potential is decreased If we complexed the Fe2+ , the reverse effect would be observed So the presence of complexing agents that have different affinities for one form of the couple over another will affect the potential 12.5 Limitations of Electrode Potentials Electrode potentials (E0 or E0 ) will predict whether a given reaction can occur, but they indicate nothing about the rate of the reaction If a reaction is reversible, it will occur fast enough for a titration But if the rate of the electron transfer step is slow, the The H+ term in the log term can be separated as (−0.05916/2) log (1/[H+ ]2 ) = (+ 0.05916/2) log [H+ ]2 The squared term can be brought to the front of the log term to give 0.05916 log [H+ ] Actually, this is an oversimplification of the effect of pH in this particular case because H AsO and H AsO 3 are also weak acids, and the effect of their ionization, that is, their Ka values, should be taken into account as well Electrode potentials predict whether a reaction can occur They say nothing about the kinetics or rate of the reaction Christian7e c12.tex 396 V2 - 08/12/2013 10:33 P.M Page 396 CHAPTER 12 ELECTROCHEMICAL CELLS AND ELECTRODE POTENTIALS reaction may be so slow that equilibrium will be reached only after a very long time We say that such a reaction is irreversible Some reactions in which one half-reaction is irreversible occur rapidly Several oxidizing and reducing agents containing oxygen are reduced or oxidized irreversibly but may be speeded up by addition of an appropriate catalyst The oxidation of arsenic(III) by cerium(IV) is slow, but it is catalyzed by a small amount of osmium tetroxide, OsO4 So, while electrode potentials are useful for predicting many reactions, they not assure that a given reaction will actually occur They are useful in that they will predict that a reaction will not occur if the potential differences are not sufficient Questions What is an oxidizing agent? A reducing agent? What is the Nernst equation? What is the standard potential? The formal potential? What is the function of a salt bridge in an electrochemical cell? What are the NHE and SHE? The standard potential for the half-reaction M4+ + 2e− = M2+ is +0.98 V Is M2+ a good or a poor reducing agent? What should be the minimum potential difference between two half-reactions so that a sharp end point will be obtained in a titration involving the two half-reactions? Why cannot standard or formal electrode potentials always be used to predict whether a given titration will work? Problems REDOX STRENGTHS Arrange the following substances in decreasing order of oxidizing strengths: H2 SeO3 , H3 AsO4 , Hg2+ , Cu2+ , Zn2+ , O3 , HClO, K+ , Co2+ 10 Arrange the following substances in decreasing order of reducing strengths: I− , V3+ , Sn2+ , Co2+ , Cl− , Ag, H2 S, Ni, HF 11 Which of the following pairs would be expected to give the largest end-point break in a titration of one component with the other in each pair? (a) Fe2+ − MnO4 − or Fe2+ − Cr2 O7 2− (b) Fe2+ − Ce4+ (H2 SO4 ) or Fe2+ − Ce4+ (HClO4 ) (c) H3 AsO3 − MnO4 − or Fe2+ − MnO4 − (d) Fe3+ − Ti2+ or Sn2+ − I3 − PROFESSOR’S FAVORITE PROBLEMS (The following two problems contributed by Professor Bin Wang, Marshall University) 12 Identify the oxidizing agent and the reducing agent on the left side of the following reactions: (a) 2VO2+ + Sn2+ + 4H+ 2V3+ + Sn4+ + 2H2 O (b) Fe2+ + Fe(CN)6 3− (c) Cu + 2Ag+ − (d) I2 + OH Fe3+ + Fe(CN)6 4− 2Ag + Cu2+ HOI + I− (e) 2Fe2+ + H2 O2 + 2H+ 2Fe3+ + 2H2 O 13 The titration of 1.0512 g of an unknown iron sample required 28.75 mL of 0.1023 N KMnO4 The iron was initially in the +2 oxidation state The solution was strongly acidic Write out the balanced reaction that takes place during this titration What is the percentage of iron in the unknown sample? Christian7e c12.tex PROBLEMS 397 VOLTAIC CELLS 14 Write the equivalent voltaic cells for the following reactions (assume all concentrations are M): (a) 6Fe2+ + Cr2 O7 2− + 14H+ 6Fe3+ + 2Cr3+ + 7H2 O (b) IO3 − + 5I− + 6H+ (c) Zn + Cu2+ V2 - 08/12/2013 10:33 P.M Page 397 3I2 + 3H2 O Zn2+ + Cu 2Cl− + SeO4 2− + 4H+ (d) Cl2 + H2 SeO3 + H2 O 15 For each of the following cells, write the cell reactions: (a) Pt/V2+ , V3+ //PtCl4 2− , PtCl6 2− , Cl− /Pt (b) Ag/AgCl(s)/Cl− //Fe3+ , Fe2+ /Pt (c) Cd/Cd2+ //ClO3 − , Cl− , H+ /Pt (d) Pt/I− , I2 //H2 O2 , H+ /Pt POTENTIAL CALCULATIONS 16 What is the electrode potential (vs NHE) in a solution containing 0.50 M KBrO3 and 0.20 M Br2 at pH 2.5? 17 What is the electrode potential (vs NHE) in the solution prepared by adding 90 mL of 5.0 M KI to 10 mL of 0.10 M H2 O2 buffered at pH 2.0? 18 A solution of a mixture of Pt4+ and Pt2+ is 3.0 M in HCl, which produces the chloro complexes of the Pt ions (see Problem 20) If the solution is 0.015 M in Pt4+ and 0.025 M in Pt2+ , what is the potential of the half-reaction? 19 Equal volumes of 0.100 M UO2 2+ and 0.100 M V2+ in 0.10 M H2 SO4 are mixed What would the potential of a platinum electrode (vs NHE) dipped in the solution be at equilibrium? Assume H2 SO4 is completely ionized CELL VOLTAGES 20 From the standard potentials of the following half-reactions, determine the reaction that will occur, and calculate the cell voltage from the reaction: PtCl6 2− + 2e− PtCl4 2− + 2Cl− E0 = 0.68 V V3+ + e− V2+ E0 = −0.255 V 21 Calculate the voltages of the following cells: (a) Pt/I− (0.100 M), I3 − (0.0100 M)//IO3 − (0.100 M), I2 (0.0100 M), H+ (0.100 M)/Pt (b) Ag/AgCl(s)/Cl− (0.100 M)//UO2 2+ (0.200 M), U4+ (0.050 M), H+ (1.00 M)/Pt (c) Pt/Tl+ (0.100 M), Tl3+ (0.0100 M)//MnO4 − (0.0100 M), Mn2+ (0.100 M), H+ (pH 2.00)/Pt 22 From the standard potentials, determine the reaction between the following half-reactions, and calculate the corresponding standard cell voltage: VO2 + + 2H+ + e− UO2 2+ + 4H+ + 2e− VO2+ + H2 O U4+ + 2H2 O PROFESSOR’S FAVORITE PROBLEM Contributed by Professor Bin Wang, Marshall University 23 Use the Nernst equation to calculate the voltage of the following cell: Ni (s)|NiSO4 (0.0020 M)||CuCl2 (0.0030 M) |Cu (s) Christian7e c12.tex 398 V2 - 08/12/2013 10:33 P.M Page 398 CHAPTER 12 ELECTROCHEMICAL CELLS AND ELECTRODE POTENTIALS PROFESSOR’S FAVORITE PROBLEM Contributed by Professor Yijun Tang, University of Wisconsin at Oshkosh 24 For a galvanic cell as shown below, assume that adding solid does not change the volume of the solution Cu(s) | 50.0 mL 0.0167 M Cu(NO3 )2 (aq) || 50.0 mL 0.100 M AgNO3 |Ag(s) (a) Calculate the potentials of the Cu electrode and the Ag electrode Is the Ag electrode anode or cathode? (b) If 0.271 g of KCl is added to the original AgNO3 solution, calculate the potential of the Ag electrode Is the Ag electrode anode or cathode? (c) If 0.812 g of KCl is added to the original AgNO3 solution, calculate the potential of the Ag electrode Is the Ag electrode anode or cathode? Recommended References NERNST EQUATION L Meites, “A ‘Derivation’ of the Nernst Equation for Elementary Quantitative Analysis,” J Chem Ed., 29 (1952) 142 ELECTRODE SIGN CONVENTIONS F C Anson, “Electrode Sign Convention,” J Chem Ed., 36 (1959) 394 T S Light and A J de Bethune, “Recent Developments Concerning the Signs of Electrode Conventions,” J Chem Ed., 34 (1957) 433 STANDARD POTENTIALS A J Bard, R Parsons, and J Jordan, eds., Standard Potentials in Aqueous Solution New York: Marcel Dekker, 1985 W M Latimer, The Oxidation States of the Elements and Their Potentials in Aqueous Solutions, 2nd ed New York: Prentice Hall, 1952 ... Paired Samples, 94 11 STDEV, 11 6 Paired t-test from Excel, 94 12 Intercept Slope and r-square, 11 9 Plotting in Excel, 10 2, 11 8 13 LINEST, 12 0 Christian7e fpref.tex V2 - 08 /13 /2 013 2 :12 P.M Page xiv... 19 .3 Classification of Chromatographic Techniques, 604 19 .4 Theory of Column Efficiency in Chromatography, 607 19 .5 Chromatography Simulation Software, 616 21. 1 21. 2 21. 3 21. 4 21. 5 21. 6 21. 7 21. 8... fpref.tex V2 - 08 /13 /2 013 2 :12 P.M Page xiii Error bars, 10 2 Solver, 87 Introduction to Excel, 11 3 Data Analysis Regression, 87, 12 0 Absolute Cell Reference, 11 5 F-test, 88 10 Average, 11 6 t-test for