THERMODYNAMICS AND CHEMISTRY SECOND EDITION HOWARD DEVOE Thermodynamics and Chemistry Second Edition Version 5, May 2014 Howard DeVoe Associate Professor of Chemistry Emeritus University of Maryland, College Park, Maryland The first edition of this book was previously published by Pearson Education, Inc. It was copyright ©2001 by Prentice-Hall, Inc. The second edition, version 5 is copyright ©2014 by Howard DeVoe. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs License, whose full text is at http://creativecommons.org/licenses/by-nc-nd/3.0 You are free to read, store, copy and print the PDF file for personal use. You are not allowed to alter, transform, or build upon this work, or to sell it or use it for any commercial purpose whatsoever, without the written consent of the copyright holder. The book was typeset using the LATEX typesetting system and the memoir class. Most of the figures were produced with PSTricks, a related software program. The fonts are Adobe Times, MathTime, Helvetica, and Computer Modern Typewriter. I thank the Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland (http://www.chem.umd.edu) for hosting the Web site for this book. The most recent version can always be found online at http://www.chem.umd.edu/thermobook If you are a faculty member of a chemistry or related department of a college or uni- versity, you may send a request to [email protected] for a complete Solutions Manual in PDF format for your personal use. In order to protect the integrity of the solutions, requests will be subject to verification of your faculty status and your agreement not to reproduce or transmit the manual in any form. SHORT CONTENTS Biographical Sketches 15 Preface to the Second Edition 16 From the Preface to the First Edition 17 1 Introduction 19 2 Systems and Their Properties 27 3 The First Law 56 4 The Second Law 101 5 Thermodynamic Potentials 134 6 The Third Law and Cryogenics 149 7 Pure Substances in Single Phases 163 8 Phase Transitions and Equilibria of Pure Substances 192 9 Mixtures 222 10 Electrolyte Solutions 285 11 Reactions and Other Chemical Processes 302 12 Equilibrium Conditions in Multicomponent Systems 366 13 The Phase Rule and Phase Diagrams 418 14 Galvanic Cells 449 Appendix A Definitions of the SI Base Units 470 4 SHORT CONTENTS 5 Appendix B Physical Constants 471 Appendix C Symbols for Physical Quantities 472 Appendix D Miscellaneous Abbreviations and Symbols 476 Appendix E Calculus Review 479 Appendix F Mathematical Properties of State Functions 481 Appendix G Forces, Energy, and Work 486 Appendix H Standard Molar Thermodynamic Properties 504 Appendix I Answers to Selected Problems 507 Bibliography 511 Index 520 Thermodynamics and Chemistry, 2nd edition, version 5 © 2014 by Howard DeVoe. Latest version (free): www.chem.umd.edu/thermobook CONTENTS Biographical Sketches 15 Preface to the Second Edition 16 From the Preface to the First Edition 17 1 Introduction 19 1.1 Units . 19 1.1.1 Amount of substance and amount . 21 1.2 Quantity Calculus . 22 1.3 Dimensional Analysis . 24 Problem . 26 2 Systems and Their Properties 27 2.1 The System, Surroundings, and Boundary . 27 2.1.1 Extensive and intensive properties . 28 2.2 Phases and Physical States of Matter . 30 2.2.1 Physical states of matter . 30 2.2.2 Phase coexistence and phase transitions . 31 2.2.3 Fluids . 32 2.2.4 The equation of state of a fluid . 33 2.2.5 Virial equations of state for pure gases . 34 2.2.6 Solids . 36 2.3 Some Basic Properties and Their Measurement . 36 2.3.1 Mass . 36 2.3.2 Volume . 37 2.3.3 Density . 38 2.3.4 Pressure . 38 2.3.5 Temperature . 40 2.4 The State of the System . 45 2.4.1 State functions and independent variables . 45 2.4.2 An example: state functions of a mixture . 46 2.4.3 More about independent variables . 47 6 CONTENTS 7 2.4.4 Equilibrium states . 48 2.4.5 Steady states . 50 2.5 Processes and Paths . 50 2.6 The Energy of the System . 52 2.6.1 Energy and reference frames . 53 2.6.2 Internal energy . 53 Problems . 55 3 The First Law 56 3.1 Heat, Work, and the First Law . 56 3.1.1 The concept of thermodynamic work . 57 3.1.2 Work coefficients and work coordinates . 59 3.1.3 Heat and work as path functions . 60 3.1.4 Heat and heating . 61 3.1.5 Heat capacity . 62 3.1.6 Thermal energy . 62 3.2 Spontaneous, Reversible, and Irreversible Processes . 62 3.2.1 Reversible processes . 62 3.2.2 Irreversible processes . 66 3.2.3 Purely mechanical processes . 66 3.3 Heat Transfer . 67 3.3.1 Heating and cooling . 67 3.3.2 Spontaneous phase transitions . 68 3.4 Deformation Work . 69 3.4.1 Gas in a cylinder-and-piston device . 69 3.4.2 Expansion work of a gas . 71 3.4.3 Expansion work of an isotropic phase . 73 3.4.4 Generalities . 74 3.5 Applications of Expansion Work . 74 3.5.1 The internal energy of an ideal gas . 74 3.5.2 Reversible isothermal expansion of an ideal gas . 75 3.5.3 Reversible adiabatic expansion of an ideal gas . 75 3.5.4 Indicator diagrams . 77 3.5.5 Spontaneous adiabatic expansion or compression . 78 3.5.6 Free expansion of a gas into a vacuum . 79 3.6 Work in a Gravitational Field . 79 3.7 Shaft Work . 81 3.7.1 Stirring work . 83 3.7.2 The Joule paddle wheel . 84 3.8 Electrical Work . 86 3.8.1 Electrical work in a circuit . 86 3.8.2 Electrical heating . 88 3.8.3 Electrical work with a galvanic cell . 89 3.9 Irreversible Work and Internal Friction . 91 3.10 Reversible and Irreversible Processes: Generalities . 94 Problems . 96 Thermodynamics and Chemistry, 2nd edition, version 5 © 2014 by Howard DeVoe. Latest version (free): www.chem.umd.edu/thermobook CONTENTS 8 4 The Second Law 101 4.1 Types of Processes . 101 4.2 Statements of the Second Law . 102 4.3 Concepts Developed with Carnot Engines . 105 4.3.1 Carnot engines and Carnot cycles . 105 4.3.2 The equivalence of the Clausius and Kelvin–Planck statements . 108 4.3.3 The efficiency of a Carnot engine . 110 4.3.4 Thermodynamic temperature . 113 4.4 Derivation of the Mathematical Statement of the Second Law . 115 4.4.1 The existence of the entropy function . 115 4.4.2 Using reversible processes to define the entropy . 119 4.4.3 Some properties of the entropy . 122 4.5 Irreversible Processes . 123 4.5.1 Irreversible adiabatic processes . 123 4.5.2 Irreversible processes in general . 124 4.6 Applications . 125 4.6.1 Reversible heating . 126 4.6.2 Reversible expansion of an ideal gas . 126 4.6.3 Spontaneous changes in an isolated system . 127 4.6.4 Internal heat flow in an isolated system . 127 4.6.5 Free expansion of a gas . 128 4.6.6 Adiabatic process with work . 128 4.7 Summary . 129 4.8 The Statistical Interpretation of Entropy . 129 Problems . 132 5 Thermodynamic Potentials 134 5.1 Total Differential of a Dependent Variable . 134 5.2 Total Differential of the Internal Energy . 135 5.3 Enthalpy, Helmholtz Energy, and Gibbs Energy . 137 5.4 Closed Systems . 139 5.5 Open Systems . 141 5.6 Expressions for Heat Capacity . 142 5.7 Surface Work . 143 5.8 Criteria for Spontaneity . 144 Problems . 147 6 The Third Law and Cryogenics 149 6.1 The Zero of Entropy . 149 6.2 Molar Entropies . 151 6.2.1 Third-law molar entropies . 151 6.2.2 Molar entropies from spectroscopic measurements . 154 6.2.3 Residual entropy . ..