CHEMICAL THERMODYNAMICS Basic Concepts and Methods Seventh Edition IRVING M. KLOTZ Late Morrison Professor Emeritus, Northwestern University ROBERT M. ROSENBERG MacMillen Professor Emeritus, Lawrence University, Adjunct Professor, Northwestern University Copyright # 2008 by John Wiley & Sons, Inc. All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada 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 Section 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, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. 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ISBN: 978-0-471-78015-1 Printed in the United States of America 10987654321 Dedicated to the Memory of Irving Myron Klotz January 22, 1916–April 27, 2005 Distinguished scientist, master teacher, dedicated mentor, and colleague CONTENTS PREFACE xix 1 INTRODUCTION 1 1.1 Origins of Chemical Thermodynamics / 1 1.2 Objectives of Chemical Thermodynamics / 4 1.3 Limitations of Classic Thermodynamics / 4 References / 6 2 MATHEMATICAL PREPARATION FOR THERMODYNAMICS 9 2.1 Variables of Thermodynamics / 10 Extensive and Intensive Quantities / 10 Units and Conversion Factors / 10 2.2 Analytic Methods / 10 Partial Differentiation / 10 Exact Differentials / 15 Homogeneous Functions / 18 Exercises / 21 References / 27 3 THE FIRST LAW OF THERMODYNAMICS 29 3.1 Definitions / 29 Temperature / 31 Work / 33 vii viii CONTENTS 3.2 The First Law of Thermodynamics / 37 Energy / 37 Heat / 38 General Form of the First Law / 38 Exercises / 40 References / 41 4 ENTHALPY, ENTHALPY OF REACTION, AND HEAT CAPACITY 43 4.1 Enthalpy / 44 Definition / 44 Relationship between QV and QP / 46 4.2 Enthalpy of Reactions / 47 Definitions and Conventions / 47 4.3 Enthalpy as a State Function / 52 Enthalpy of Formation from Enthalpy of Reaction / 52 Enthalpy of Formation from Enthalpy of Combustion / 53 Enthalpy of Transition from Enthalpy of Combustion / 53 Enthalpy of Conformational Transition of a Protein from Indirect Calorimetric Measurements / 54 Enthalpy of Solid-State Reaction from Measurements of Enthalpy of Solution / 56 4.4 Bond Enthalpies / 57 Definition of Bond Enthalpies / 57 Calculation of Bond Enthalpies / 58 Enthalpy of Reaction from Bond Enthalpies / 59 4.5 Heat Capacity / 60 Definition / 61 Some Relationships between CP and CV / 62 Heat Capacities of Gases / 64 Heat Capacities of Solids / 67 Heat Capacities of Liquids / 68 Other Sources of Heat Capacity Data / 68 4.6 Enthalpy of Reaction as a Function of Temperature / 68 Analytic Method / 69 Arithmetic Method / 71 Graphical or Numerical Methods / 72 Exercises / 72 References / 78 5 APPLICATIONS OF THE FIRST LAW TO GASES 81 5.1 Ideal Gases / 81 Definition / 81 CONTENTS ix Enthalpy as a Function of Temperature Only / 83 Relationship Between CP and Cv / 84 Calculation of the Thermodynamic Changes in Expansion Processes / 84 5.2 Real Gases / 94 Equations of State / 94 Joule–Thomson Effect / 98 Calculations of Thermodynamic Quantities in Reversible Expansions / 102 Exercises / 104 References / 108 6 THE SECOND LAW OF THERMODYNAMICS 111 6.1 The Need for a Second Law / 111 6.2 The Nature of the Second Law / 112 Natural Tendencies Toward Equilibrium / 112 Statement of the Second Law / 112 Mathematical Counterpart of the Verbal Statement / 113 6.3 The Carnot Cycle / 113 The Forward Cycle / 114 The Reverse Cycle / 116 Alternative Statement of the Second Law / 117 Carnot’s Theorem / 118 6.4 The Thermodynamic Temperature Scale / 120 6.5 The Definition of S, the Entropy of a System / 125 6.6 The Proof that S is a Thermodynamic Property / 126 Any Substance in a Carnot Cycle / 126 Any Substance in Any Reversible Cycle / 127 Entropy S Depends Only on the State of the System / 129 6.7 Entropy Changes in Reversible Processes / 130 General Statement / 130 Isothermal Reversible Changes / 130 Adiabatic Reversible Changes / 131 Reversible Phase Transitions / 131 Isobaric Reversible Temperature Changes / 132 Isochoric Reversible Temperature Changes / 133 6.8 Entropy Changes in Irreversible Processes / 133 Irreversible Isothermal Expansion of an Ideal Gas / 133 Irreversible Adiabatic Expansion of an Ideal Gas / 135 Irreversible Flow of Heat from a Higher Temperature to a Lower Temperature / 136 x CONTENTS Irreversible Phase Transitions / 137 Irreversible Chemical Reactions / 138 General Statement / 139 6.9 General Equations for the Entropy of Gases / 142 Entropy of the Ideal Gas / 142 Entropy of a Real Gas / 143 6.10 Temperature–Entropy Diagram / 144 6.11 Entropy as an Index of Exhaustion / 146 Exercises / 150 References / 157 7 EQUILIBRIUM AND SPONTANEITY FOR SYSTEMS AT CONSTANT TEMPERATURE 159 7.1 Reversibility, Spontaneity, and Equilibrium / 159 Systems at Constant Temperature and Volume / 160 Systems at Constant Temperature and Pressure / 162 Heat of Reaction as an Approximate Criterion of Spontaneity / 164 7.2 Properties of the Gibbs, Helmholtz, and Planck Functions / 165 The Functions as Thermodynamic Properties / 165 Relationships among G, Y, and A / 165 Changes in the Functions for Isothermal Conditions / 165 Equations for Total Differentials / 166 Pressure and Temperature Derivatives of the Functions / 167 Equations Derived from the Reciprocity Relationship / 169 7.3 The Gibbs Function and Chemical Reactions / 170 Standard States / 170 7.4 Pressure and Temperature Dependence of DG / 172 7.5 Useful Work and the Gibbs and Helmholtz Functions / 175 Isothermal Changes / 175 Changes at Constant Temperature and Pressure / 177 Relationship between DHP and QP When Useful Work is Performed / 178 Application to Electrical Work / 179 Gibbs–Helmholtz Equation / 180 The Gibbs Function and Useful Work in Biologic Systems / 181 Exercises / 185 References / 191 CONTENTS xi 8 APPLICATION OF THE GIBBS FUNCTION AND THE PLANCK FUNCTION TO SOME PHASE CHANGES 193 8.1 Two Phases at Equilibrium as a Function of Pressure and Temperature / 193 Clapeyron Equation / 194 Clausius–Clapeyron Equation / 196 8.2 The Effect of an Inert Gas on Vapor Pressure / 198 Variable Total Pressure at Constant Temperature / 199 Variable Temperature at Constant Total Pressure / 200 8.3 Temperature Dependence of Enthalpy of Phase Transition / 200 8.4 Calculation of Change in the Gibbs Function for Spontaneous Phase Change / 202 Arithmetic Method / 202 Analytic Method / 203 Exercises / 205 References / 210 9 THERMODYNAMICS OF SYSTEMS OF VARIABLE COMPOSITION 211 9.1 State Functions for Systems of Variable Composition / 211 9.2 Criteria of Equilibrium and Spontaneity in Systems of Variable Composition / 213 9.3 Relationships Among Partial Molar Properties of a Single Component / 215 9.4 Relationships Between Partial Molar Quantities of Different Components / 216 Partial Molar Quantities for Pure Phase / 218 9.5 Escaping Tendency / 219 Chemical Potential and Escaping Tendency / 219 9.6 Chemical Equilibrium in Systems of Variable Composition / 221 Exercises / 223 Reference / 226 10 MIXTURES OF GASES AND EQUILIBRIUM IN GASEOUS MIXTURES 227 10.1 Mixtures of Ideal Gases / 227 The Entropy and Gibbs Function for Mixing Ideal Gases / 228 The Chemical Potential of a Component of an Ideal Gas Mixture / 230 xii CONTENTS Chemical Equilibrium in Ideal Gas Mixtures / 231 Dependence of K on Temperature / 232 Comparison of Temperature Dependence of DGm8 and ln K / 234 10.2 The Fugacity Function of a Pure Real Gas / 236 Change of Fugacity with Pressure / 237 Change of Fugacity with Temperature / 238 10.3 Calculation of the Fugacity of a Real Gas / 239 Graphical or Numerical Methods / 240 Analytical Methods / 244 10.4 Joule–Thomson Effect for a Van der Waals Gas / 247 Approximate Value of a for a Van der Waals Gas / 247 Fugacity