SECOND EDITION HOWARD DEVOE

Transcription

1 THERMODYNAMICS AND CHEMISTRY SECOND EDITION HOWARD DEVOE

2 Thermodynamics and Chemistry Second Edition Version 7a, December 2015 Howard DeVoe Associate Professor of Chemistry Emeritus University of Maryland, College Park, Maryland

3 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 7a is copyright 2015 by Howard DeVoe. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs License, whose full text is at 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 ( for hosting the Web site for this book. The most recent version can always be found online at If you are a faculty member of a chemistry or related department of a college or university, you may send a request to hdevoe@umd.edu 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.

4 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 Thermodynamic Potentials The Third Law and Cryogenics Pure Substances in Single Phases Phase Transitions and Equilibria of Pure Substances Mixtures Electrolyte Solutions Reactions and Other Chemical Processes Equilibrium Conditions in Multicomponent Systems The Phase Rule and Phase Diagrams Galvanic Cells 449 Appendix A Definitions of the SI Base Units 470 4

5 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 7a 2015 by Howard DeVoe. Latest version:

6 CONTENTS Biographical Sketches 15 Preface to the Second Edition 16 From the Preface to the First Edition 17 1 Introduction Units Amount of substance and amount Quantity Calculus Dimensional Analysis Problem Systems and Their Properties The System, Surroundings, and Boundary Extensive and intensive properties Phases and Physical States of Matter Physical states of matter Phase coexistence and phase transitions Fluids The equation of state of a fluid Virial equations of state for pure gases Solids Some Basic Properties and Their Measurement Mass Volume Density Pressure Temperature The State of the System State functions and independent variables An example: state functions of a mixture More about independent variables

7 CONTENTS Equilibrium states Steady states Processes and Paths The Energy of the System Energy and reference frames Internal energy Problems The First Law Heat, Work, and the First Law The concept of thermodynamic work Work coefficients and work coordinates Heat and work as path functions Heat and heating Heat capacity Thermal energy Spontaneous, Reversible, and Irreversible Processes Reversible processes Irreversible processes Purely mechanical processes Heat Transfer Heating and cooling Spontaneous phase transitions Deformation Work Gas in a cylinder-and-piston device Expansion work of a gas Expansion work of an isotropic phase Generalities Applications of Expansion Work The internal energy of an ideal gas Reversible isothermal expansion of an ideal gas Reversible adiabatic expansion of an ideal gas Indicator diagrams Spontaneous adiabatic expansion or compression Free expansion of a gas into a vacuum Work in a Gravitational Field Shaft Work Stirring work The Joule paddle wheel Electrical Work Electrical work in a circuit Electrical heating Electrical work with a galvanic cell Irreversible Work and Internal Friction Reversible and Irreversible Processes: Generalities Problems Thermodynamics and Chemistry, 2nd edition, version 7a 2015 by Howard DeVoe. Latest version:

8 CONTENTS 8 4 The Second Law Types of Processes Statements of the Second Law Concepts Developed with Carnot Engines Carnot engines and Carnot cycles The equivalence of the Clausius and Kelvin Planck statements The efficiency of a Carnot engine Thermodynamic temperature Derivation of the Mathematical Statement of the Second Law The existence of the entropy function Using reversible processes to define the entropy Some properties of the entropy Irreversible Processes Irreversible adiabatic processes Irreversible processes in general Applications Reversible heating Reversible expansion of an ideal gas Spontaneous changes in an isolated system Internal heat flow in an isolated system Free expansion of a gas Adiabatic process with work Summary The Statistical Interpretation of Entropy Problems Thermodynamic Potentials Total Differential of a Dependent Variable Total Differential of the Internal Energy Enthalpy, Helmholtz Energy, and Gibbs Energy Closed Systems Open Systems Expressions for Heat Capacity Surface Work Criteria for Spontaneity Problems The Third Law and Cryogenics The Zero of Entropy Molar Entropies Third-law molar entropies Molar entropies from spectroscopic measurements Residual entropy Cryogenics Joule Thomson expansion Magnetization Thermodynamics and Chemistry, 2nd edition, version 7a 2015 by Howard DeVoe. Latest version:

9 CONTENTS 9 Problem Pure Substances in Single Phases Volume Properties Internal Pressure Thermal Properties The relation between C V;m and C p;m The measurement of heat capacities Typical values Heating at Constant Volume or Pressure Partial Derivatives with Respect to T, p, and V Tables of partial derivatives The Joule Thomson coefficient Isothermal Pressure Changes Ideal gases Condensed phases Standard States of Pure Substances Chemical Potential and Fugacity Gases Liquids and solids Standard Molar Quantities of a Gas Problems Phase Transitions and Equilibria of Pure Substances Phase Equilibria Equilibrium conditions Equilibrium in a multiphase system Simple derivation of equilibrium conditions Tall column of gas in a gravitational field The pressure in a liquid droplet The number of independent variables The Gibbs phase rule for a pure substance Phase Diagrams of Pure Substances Features of phase diagrams Two-phase equilibrium The critical point The lever rule Volume properties Phase Transitions Molar transition quantities Calorimetric measurement of transition enthalpies Standard molar transition quantities Coexistence Curves Chemical potential surfaces The Clapeyron equation The Clausius Clapeyron equation Thermodynamics and Chemistry, 2nd edition, version 7a 2015 by Howard DeVoe. Latest version:

10 CONTENTS 10 Problems Mixtures Composition Variables Species and substances Mixtures in general Solutions Binary solutions The composition of a mixture Partial Molar Quantities Partial molar volume The total differential of the volume in an open system Evaluation of partial molar volumes in binary mixtures General relations Partial specific quantities The chemical potential of a species in a mixture Equilibrium conditions in a multiphase, multicomponent system Relations involving partial molar quantities Gas Mixtures Partial pressure The ideal gas mixture Partial molar quantities in an ideal gas mixture Real gas mixtures Liquid and Solid Mixtures of Nonelectrolytes Raoult s law Ideal mixtures Partial molar quantities in ideal mixtures Henry s law The ideal-dilute solution Solvent behavior in the ideal-dilute solution Partial molar quantities in an ideal-dilute solution Activity Coefficients in Mixtures of Nonelectrolytes Reference states and standard states Ideal mixtures Real mixtures Nonideal dilute solutions Evaluation of Activity Coefficients Activity coefficients from gas fugacities Activity coefficients from the Gibbs Duhem equation Activity coefficients from osmotic coefficients Fugacity measurements Activity of an Uncharged Species Standard states Activities and composition Pressure factors and pressure Mixtures in Gravitational and Centrifugal Fields Thermodynamics and Chemistry, 2nd edition, version 7a 2015 by Howard DeVoe. Latest version:

11 CONTENTS Gas mixture in a gravitational field Liquid solution in a centrifuge cell Problems Electrolyte Solutions Single-ion Quantities Solution of a Symmetrical Electrolyte Electrolytes in General Solution of a single electrolyte Multisolute solution Incomplete dissociation The Debye Hückel Theory Derivation of the Debye Hückel Equation Mean Ionic Activity Coefficients from Osmotic Coefficients Problems Reactions and Other Chemical Processes Mixing Processes Mixtures in general Ideal mixtures Excess quantities The entropy change to form an ideal gas mixture Molecular model of a liquid mixture Phase separation of a liquid mixture The Advancement and Molar Reaction Quantities An example: ammonia synthesis Molar reaction quantities in general Standard molar reaction quantities Molar Reaction Enthalpy Molar reaction enthalpy and heat Standard molar enthalpies of reaction and formation Molar reaction heat capacity Effect of temperature on reaction enthalpy Enthalpies of Solution and Dilution Molar enthalpy of solution Enthalpy of dilution Molar enthalpies of solute formation Evaluation of relative partial molar enthalpies Reaction Calorimetry The constant-pressure reaction calorimeter The bomb calorimeter Other calorimeters Adiabatic Flame Temperature Gibbs Energy and Reaction Equilibrium The molar reaction Gibbs energy Spontaneity and reaction equilibrium Thermodynamics and Chemistry, 2nd edition, version 7a 2015 by Howard DeVoe. Latest version:

12 CONTENTS General derivation Pure phases Reactions involving mixtures Reaction in an ideal gas mixture The Thermodynamic Equilibrium Constant Activities and the definition of K Reaction in a gas phase Reaction in solution Evaluation of K Effects of Temperature and Pressure on Equilibrium Position Problems Equilibrium Conditions in Multicomponent Systems Effects of Temperature Variation of i =T with temperature Variation of ı i =T with temperature Variation of ln K with temperature Solvent Chemical Potentials from Phase Equilibria Freezing-point measurements Osmotic-pressure measurements Binary Mixture in Equilibrium with a Pure Phase Colligative Properties of a Dilute Solution Freezing-point depression Boiling-point elevation Vapor-pressure lowering Osmotic pressure Solid Liquid Equilibria Freezing points of ideal binary liquid mixtures Solubility of a solid nonelectrolyte Ideal solubility of a solid Solid compound of mixture components Solubility of a solid electrolyte Liquid Liquid Equilibria Miscibility in binary liquid systems Solubility of one liquid in another Solute distribution between two partially-miscible solvents Membrane Equilibria Osmotic membrane equilibrium Equilibrium dialysis Donnan membrane equilibrium Liquid Gas Equilibria Effect of liquid pressure on gas fugacity Effect of liquid composition on gas fugacities The Duhem Margules equation Gas solubility Effect of temperature and pressure on Henry s law constants Thermodynamics and Chemistry, 2nd edition, version 7a 2015 by Howard DeVoe. Latest version:

13 CONTENTS Reaction Equilibria Evaluation of Standard Molar Quantities Problems The Phase Rule and Phase Diagrams The Gibbs Phase Rule for Multicomponent Systems Degrees of freedom Species approach to the phase rule Components approach to the phase rule Examples Phase Diagrams: Binary Systems Generalities Solid liquid systems Partially-miscible liquids Liquid gas systems with ideal liquid mixtures Liquid gas systems with nonideal liquid mixtures Solid gas systems Systems at high pressure Phase Diagrams: Ternary Systems Three liquids Two solids and a solvent Problems Galvanic Cells Cell Diagrams and Cell Reactions Elements of a galvanic cell Cell diagrams Electrode reactions and the cell reaction Advancement and charge Electric Potentials in the Cell Cell potential Measuring the equilibrium cell potential Interfacial potential differences Molar Reaction Quantities of the Cell Reaction Relation between r G cell and E cell, eq Relation between r G cell and r G Standard molar reaction quantities The Nernst Equation Evaluation of the Standard Cell Potential Standard Electrode Potentials Problems Appendix A Definitions of the SI Base Units 470 Appendix B Physical Constants 471 Thermodynamics and Chemistry, 2nd edition, version 7a 2015 by Howard DeVoe. Latest version:

14 CONTENTS 14 Appendix C Symbols for Physical Quantities 472 Appendix D Miscellaneous Abbreviations and Symbols 476 D.1 Physical States D.2 Subscripts for Chemical Processes D.3 Superscripts Appendix E Calculus Review 479 E.1 Derivatives E.2 Partial Derivatives E.3 Integrals E.4 Line Integrals Appendix F Mathematical Properties of State Functions 481 F.1 Differentials F.2 Total Differential F.3 Integration of a Total Differential F.4 Legendre Transforms Appendix G Forces, Energy, and Work 486 G.1 Forces between Particles G.2 The System and Surroundings G.3 System Energy Change G.4 Macroscopic Work G.5 The Work Done on the System and Surroundings G.6 The Local Frame and Internal Energy G.7 Nonrotating Local Frame G.8 Center-of-mass Local Frame G.9 Rotating Local Frame G.10 Earth-Fixed Reference Frame Appendix H Standard Molar Thermodynamic Properties 504 Appendix I Answers to Selected Problems 507 Bibliography 511 Index 520 Thermodynamics and Chemistry, 2nd edition, version 7a 2015 by Howard DeVoe. Latest version:

15 BIOGRAPHICAL SKETCHES Benjamin Thompson, Count of Rumford James Prescott Joule Sadi Carnot Rudolf Julius Emmanuel Clausius William Thomson, Lord Kelvin Max Karl Ernst Ludwig Planck Josiah Willard Gibbs Walther Hermann Nernst William Francis Giauque Benoit Paul Émile Clapeyron William Henry Gilbert Newton Lewis Peter Josephus Wilhelmus Debye Germain Henri Hess François-Marie Raoult Jacobus Henricus van t Hoff

16 PREFACE TO THE SECOND EDITION This second edition of Thermodynamics and Chemistry is a revised and enlarged version of the first edition published by Prentice Hall in The book is designed primarily as a textbook for a one-semester course for graduate or undergraduate students who have already been introduced to thermodynamics in a physical chemistry course. The PDF file of this book contains hyperlinks to pages, sections, equations, tables, figures, bibliography items, and problems. If you are viewing the PDF on a screen, the links are present, although they are not marked in any special way. If you click on a reference to a page number, equation number, and so on, it will take you to that location. Scattered through the text are sixteen one-page biographical sketches of some of the historical giants of thermodynamics. A list is given on the preceding page. The sketches are not intended to be comprehensive biographies, but rather to illustrate the human side of thermodynamics the struggles and controversies by which the concepts and experimental methodology of the subject were developed. The epigraphs on page 18 are intended to suggest the nature and importance of classical thermodynamics. You may wonder about the conversation between Alice and Humpty Dumpty. Its point, particularly important in the study of thermodynamics, is the need to pay attention to definitions the intended meanings of words. I welcome comments and suggestions for improving this book. My address appears below. Howard DeVoe hdevoe@umd.edu 16

17 FROM THE PREFACE TO THE FIRST EDITION Classical thermodynamics, the subject of this book, is concerned with macroscopic aspects of the interaction of matter with energy in its various forms. This book is designed as a text for a onesemester course for senior undergraduate or graduate students who have already been introduced to thermodynamics in an undergraduate physical chemistry course. Anyone who studies and uses thermodynamics knows that a deep understanding of this subject does not come easily. There are subtleties and interconnections that are difficult to grasp at first. The more times one goes through a thermodynamics course (as a student or a teacher), the more insight one gains. Thus, this text will reinforce and extend the knowledge gained from an earlier exposure to thermodynamics. To this end, there is fairly intense discussion of some basic topics, such as the nature of spontaneous and reversible processes, and inclusion of a number of advanced topics, such as the reduction of bomb calorimetry measurements to standard-state conditions. This book makes no claim to be an exhaustive treatment of thermodynamics. It concentrates on derivations of fundamental relations starting with the thermodynamic laws and on applications of these relations in various areas of interest to chemists. Although classical thermodynamics treats matter from a purely macroscopic viewpoint, the book discusses connections with molecular properties when appropriate. In deriving equations, I have strived for rigor, clarity, and a minimum of mathematical complexity. I have attempted to clearly state the conditions under which each theoretical relation is valid because only by understanding the assumptions and limitations of a derivation can one know when to use the relation and how to adapt it for special purposes. I have taken care to be consistent in the use of symbols for physical properties. The choice of symbols follows the current recommendations of the International Union of Pure and Applied Chemistry (IUPAC) with a few exceptions made to avoid ambiguity. I owe much to J. Arthur Campbell, Luke E. Steiner, and William Moffitt, gifted teachers who introduced me to the elegant logic and practical utility of thermodynamics. I am immensely grateful to my wife Stephanie for her continued encouragement and patience during the period this book went from concept to reality. I would also like to acknowledge the help of the following reviewers: James L. Copeland, Kansas State University; Lee Hansen, Brigham Young University; Reed Howald, Montana State University Bozeman; David W. Larsen, University of Missouri St. Louis; Mark Ondrias, University of New Mexico; Philip H. Rieger, Brown University; Leslie Schwartz, St. John Fisher College; Allan L. Smith, Drexel University; and Paul E. Smith, Kansas State University. 17

18 A theory is the more impressive the greater the simplicity of its premises is, the more different kinds of things it relates, and the more extended is its area of applicability. Therefore the deep impression which classical thermodynamics made upon me. It is the only physical theory of universal content concerning which I am convinced that, within the framework of the applicability of its basic concepts, it will never be overthrown. Albert Einstein Thermodynamics is a discipline that involves a formalization of a large number of intuitive concepts derived from common experience. J. G. Kirkwood and I. Oppenheim, Chemical Thermodynamics, 1961 The first law of thermodynamics is nothing more than the principle of the conservation of energy applied to phenomena involving the production or absorption of heat. Max Planck, Treatise on Thermodynamics, 1922 The law that entropy always increases the second law of thermodynamics holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell s equations then so much the worse for Maxwell s equations. If it is found to be contradicted by observation well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation. Sir Arthur Eddington, The Nature of the Physical World, 1928 Thermodynamics is a collection of useful relations between quantities, every one of which is independently measurable. What do such relations tell one about one s system, or in other words what do we learn from thermodynamics about the microscopic explanations of macroscopic changes? Nothing whatever. What then is the use of thermodynamics? Thermodynamics is useful precisely because some quantities are easier to measure than others, and that is all. M. L. McGlashan, J. Chem. Educ., 43, (1966) When I use a word, Humpty Dumpty said, in rather a scornful tone, it means just what I choose it to mean neither more nor less. The question is, said Alice, whether you can make words mean so many different things. The question is, said Humpty Dumpty, which is to be master that s all. Lewis Carroll, Through the Looking-Glass