RE Thermodynamics, EN IG D E A visual, conceptual and contemporary approach to the fascinating L field of Physical Chemistry guides students through core concepts Statistical Thermodynamics, with visual narratives and connections to cutting-edge applications Th P H and research. e Y r S and Kinetics 4e m I C The fourth edition of Thermodynamics, Statistical Thermodynamics, o A & Kinetics includes many changes to the presentation and content d L y at both a global and chapter level. These updates have been made to n C a H enhance the student learning experience and update the discussion m E of research areas. M i c s IS Thomas Engel , T S R t MasteringTM Chemistry, with a new enhanced Pearson eText, has a Y Philip Reid t i been significantly expanded to include a wealth of new end-of-chapter s t i problems from the 4th edition, new self-guided, adaptive Dynamic c a Study Modules with wrong answer feedback and remediation, and l Th the new Pearson eText which is mobile friendly. e r m o d y n a m i c s , a n Please visit us at www.pearson.com for more information. d To order any of our products, contact our customer service K department at (800) 824-7799, or (201) 767-5021 outside of the U.S., or visit your campus bookstore. i n e t i www.pearson.com c s 4 e PHYSICAL CHEMISTRY Thermodynamics, Statistical Thermodynamics, and Kinetics FOURTH EDITION Thomas Engel University of Washington Philip Reid University of Washington A01_ENGE4583_04_SE_FM_i-xvi.indd 1 01/12/17 12:51 PM Director, Courseware Portfolio Management: Jeanne Zalesky Product Manager: Elizabeth Bell Courseware Director, Content Development: Jennifer Hart Courseware Analyst: Spencer Cotkin Managing Producer, Science: Kristen Flathman Content Producer, Science: Beth Sweeten Rich Media Content Producer: Nicole Constantino Production Management and Composition: Cenveo Publishing Services Design Manager: Mark Ong Interior/Cover Designer: Preston Thomas Illustrators: Imagineering, Inc. Manager, Rights & Permissions: Ben Ferrini Photo Research Project Manager: Cenveo Publishing Services Senior Procurement Specialist: Stacey Weinberger Credits and acknowledgments borrowed from other sources and reproduced, with permission, in this textbook appear on the appropriate page within the text or on page 643. Copyright © 2019, 2013, 2010 Pearson Education, Inc. All Rights Reserved. Printed in the United States of America. This publication is protected by copyright, and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise. For information regarding permissions, request forms and the appropriate contacts within the Pearson Education Global Rights & Permissions department, please visit www.pearsoned.com/permissions/. Unless otherwise indicated herein, any third-party trademarks that may appear in this work are the property of their respective owners and any references to third-party trademarks, logos or other trade dress are for demonstrative or descriptive purposes only. Such references are not intended to imply any sponsorship, endorsement, authorization, or promotion of Pearson’s products by the owners of such marks, or any relationship between the owner and Pearson Education, Inc. or its affiliates, authors, licensees or distributors. Library of Congress Cataloging-in-Publication Data Names: Engel, Thomas, 1942- author. | Reid, Philip (Philip J.), author. Title: Thermodynamics, statistical thermodynamics, and kinetics : physical chemistry / Thomas Engel (University of Washington), Philip Reid (University of Washington). Other titles: At head of title: Physical chemistry Description: Fourth edition. | New York : Pearson Education, Inc., [2019] | Includes bibliographical references and index. Identifiers: LCCN 2017044156 | ISBN 9780134804583 Subjects: LCSH: Statistical thermodynamics. | Thermodynamics. | Chemistry, Physical and theoretical. Classification: LCC QC311.5 .E65 2019 | DDC 541/.369--dc23 LC record available at https://lccn.loc.gov/2017044156 1 17 ISBN 10: 0-13-480458-9; ISBN 13: 978-0-13-480458-3 (Student edition) ISBN 10: 0-13-481461-4; ISBN 13: 978-0-13-481461-2 (Books A La Carte edition) A01_ENGE4583_04_SE_FM_i-xvi.indd 2 01/12/17 12:51 PM To Walter and Juliane, my first teachers, and to Gloria, Alex, Gabrielle, and Amelie. THOMAS ENGEL To my family. PHILIP REID A01_ENGE4583_04_SE_FM_i-xvi.indd 3 01/12/17 12:51 PM Brief Contents THERMODYNAMICS, STATISTICAL THERMODYNAMICS, AND KINETICS 1 Fundamental Concepts of Thermodynamics 5 12 Probability 321 2 Heat, Work, Internal Energy, Enthalpy, and the 13 The Boltzmann Distribution 349 First Law of Thermodynamics 29 14 Ensemble and Molecular Partition 3 The Importance of State Functions: Functions 373 Internal Energy and Enthalpy 65 15 Statistical Thermodynamics 407 4 Thermochemistry 87 16 Kinetic Theory of Gases 441 5 Entropy and the Second and Third Laws 17 Transport Phenomena 463 of Thermodynamics 107 18 Elementary Chemical Kinetics 493 6 Chemical Equilibrium 147 19 Complex Reaction Mechanisms 541 7 The Properties of Real Gases 189 20 Macromolecules 593 8 Phase Diagrams and the Relative Stability of Solids, Liquids, and Gases 207 APPENDIX A Data Tables 625 9 Ideal and Real Solutions 237 Credits 643 10 Electrolyte Solutions 273 Index 644 11 Electrochemical Cells, Batteries, and Fuel Cells 291 iv A01_ENGE4583_04_SE_FM_i-xvi.indd 4 01/12/17 12:51 PM Detailed Contents THERMODYNAMICS, STATISTICAL THERMODYNAMICS, AND KINETICS Preface x Math Essential 3 Partial Derivatives 3 The Importance of State Math Essential 1 Units, Significant Figures, and Functions: Internal Energy Solving End of Chapter Problems and Enthalpy 65 1 Fundamental Concepts 3.1 Mathematical Properties of State Functions 65 of Thermodynamics 5 3.2 Dependence of U on V and T 68 1.1 What Is Thermodynamics and Why Is It 3.3 Does the Internal Energy Depend More Strongly Useful? 5 on V or T? 70 1.2 The Macroscopic Variables Volume, Pressure, 3.4 Variation of Enthalpy with Temperature and Temperature 6 at Constant Pressure 74 1.3 Basic Definitions Needed to Describe 3.5 How are C and C Related? 76 Thermodynamic Systems 10 P V 3.6 Variation of Enthalpy with Pressure at Constant 1.4 Equations of State and the Ideal Gas Law 12 Temperature 77 1.5 A Brief Introduction to Real Gases 14 3.7 The Joule–Thomson Experiment 79 3.8 Liquefying Gases Using an Isenthalpic Math Essential 2 Differentiation and Integration Expansion 81 2 Heat, Work, Internal Energy, Enthalpy, and the First Law 4 Thermochemistry 87 of Thermodynamics 29 4.1 Energy Stored in Chemical Bonds Is Released or Absorbed in Chemical Reactions 87 2.1 Internal Energy and the First Law of Thermodynamics 29 4.2 Internal Energy and Enthalpy Changes Associated with Chemical Reactions 88 2.2 Heat 30 4.3 Hess’s Law Is Based on Enthalpy Being a State 2.3 Work 31 Function 91 2.4 Equilibrium, Change, and Reversibility 33 4.4 Temperature Dependence of Reaction 2.5 The Work of Reversible Compression or Enthalpies 93 Expansion of an Ideal Gas 34 4.5 Experimental Determination of ∆U and ∆H 2.6 The Work of Irreversible Compression or for Chemical Reactions 95 Expansion of an Ideal Gas 36 4.6 Differential Scanning Calorimetry 97 2.7 Other Examples of Work 37 2.8 State Functions and Path Functions 39 5 Entropy and the Second and 2.9 Comparing Work for Reversible and Irreversible Third Laws of Thermodynamics 107 Processes 41 2.10 Changing the System Energy from a Molecular- 5.1 What Determines the Direction of Spontaneous Level Perspective 45 Change in a Process? 107 2.11 Heat Capacity 47 5.2 The Second Law of Thermodynamics, Spontaneity, and the Sign of ∆S 109 2.12 Determining ∆U and Introducing the State 5.3 Calculating Changes in Entropy as T, P, or V Function Enthalpy 50 Change 110 2.13 Calculating q, w, ∆U, and ∆H for Processes 5.4 Understanding Changes in Entropy at the Involving Ideal Gases 51 Molecular Level 114 2.14 Reversible Adiabatic Expansion and Compression 5.5 The Clausius Inequality 116 of an Ideal Gas 55 v A01_ENGE4583_04_SE_FM_i-xvi.indd 5 01/12/17 12:51 PM vi CONTENTS 5.6 The Change of Entropy in the Surroundings and 8 Phase Diagrams and the Relative ∆Stot = ∆S + ∆Ssur 117 Stability of Solids, Liquids, 5.7 Absolute Entropies and the Third Law of and Gases 207 Thermodynamics 119 5.8 Standard States in Entropy Calculations 123 8.1 What Determines the Relative Stability of the Solid, Liquid, and Gas Phases? 207 5.9 Entropy Changes in Chemical Reactions 123 8.2 The Pressure–Temperature Phase Diagram 210 5.10 Heat Engines and the Carnot Cycle 125 8.3 The Phase Rule 217 5.11 How Does S Depend on V and T ? 130 8.4 Pressure–Volume and Pressure–Volume– 5.12 Dependence of S on T and P 131 Temperature Phase Diagrams 217 5.13 Energy Efficiency, Heat Pumps, Refrigerators, 8.5 Providing a Theoretical Basis for the P–T and Real Engines 132 Phase Diagram 219 8.6 Using the Clausius–Clapeyron Equation 6 Chemical Equilibrium 147 to Calculate Vapor Pressure as a Function 6.1 Gibbs Energy and Helmholtz Energy 147 of T 221 6.2 Differential Forms of U, H, A, and G 151 8.7 Dependence of Vapor Pressure of a Pure Substance on Applied Pressure 223 6.3 Dependence of Gibbs and Helmholtz Energies on P, V, and T 153 8.8 Surface Tension 224 6.4 Gibbs Energy of a Reaction Mixture 155 8.9 Chemistry in Supercritical Fluids 227 6.5 Calculating the Gibbs Energy of Mixing for Ideal 8.10 Liquid Crystal Displays 228 Gases 157 6.6 Calculating the Equilibrium Position for a Gas- 9 Ideal and Real Solutions 237 Phase Chemical Reaction 159 9.1 Defining the Ideal Solution 237 6.7 Introducing the Equilibrium Constant for a 9.2 The Chemical Potential of a Component in the Mixture of Ideal Gases 162 Gas and Solution Phases 239 6.8 Calculating the Equilibrium Partial Pressures 9.3 Applying the Ideal Solution Model to Binary in a Mixture of Ideal Gases 166 Solutions 240 6.9 Variation of K with Temperature 167 P 9.4 The Temperature–Composition Diagram 6.10 Equilibria Involving Ideal Gases and Solid and Fractional Distillation 244 or Liquid Phases 169 9.5 The Gibbs–Duhem Equation 246 6.11 Expressing the Equilibrium Constant in Terms 9.6 Colligative Properties 247 of Mole Fraction or Molarity 171 9.7 Freezing Point Depression and Boiling Point 6.12 Expressing U, H, and Heat Capacities Solely Elevation 248 in Terms of Measurable Quantities 172 9.8 Osmotic Pressure 250 6.13 A Case Study: The Synthesis of Ammonia 176 9.9 Deviations from Raoult’s Law in Real 6.14 Measuring ∆G for the Unfolding of Single RNA Solutions 252 Molecules 180 9.10 The Ideal Dilute Solution 254 7 The Properties of Real Gases 189 9.11 Activities are Defined with Respect to Standard States 256 7.1 Real Gases and Ideal Gases 189 9.12 Henry’s Law and the Solubility of Gases 7.2 Equations of State for Real Gases and Their in a Solvent 260 Range of Applicability 190 9.13 Chemical Equilibrium in Solutions 261 7.3 The Compression Factor 194 9.14 Solutions Formed from Partially Miscible 7.4 The Law of Corresponding States 197 Liquids 264 7.5 Fugacity and the Equilibrium Constant 9.15 Solid–Solution Equilibrium 266 for Real Gases 200 A01_ENGE4583_04_SE_FM_i-xvi.indd 6 01/12/17 12:51 PM CONTENTS vii 10 Electrolyte Solutions 273 Math Essential 4 Lagrange Multipliers 10.1 Enthalpy, Entropy, and Gibbs Energy of Ion 13 The Boltzmann Distribution 349 Formation in Solutions 273 13.1 Microstates and Configurations 349 10.2 Understanding the Thermodynamics of Ion 13.2 Derivation of the Boltzmann Distribution 355 Formation and Solvation 275 13.3 Dominance of the Boltzmann Distribution 360 10.3 Activities and Activity Coefficients for Electrolyte Solutions 278 13.4 Physical Meaning of the Boltzmann Distribution Law 362 10.4 Calculating g Using the Debye–Hückel { Theory 280 13.5 The Definition of b 363 10.5 Chemical Equilibrium in Electrolyte Solutions 284 14 Ensemble and Molecular Partition Functions 373 11 Electrochemical Cells, Batteries, 14.1 The Canonical Ensemble 373 and Fuel Cells 291 14.2 Relating Q to q for an Ideal Gas 375 11.1 The Effect of an Electrical Potential on the 14.3 Molecular Energy Levels 377 Chemical Potential of Charged Species 291 14.4 Translational Partition Function 378 11.2 Conventions and Standard States 14.5 Rotational Partition Function: in Electrochemistry 293 Diatomic Molecules 380 11.3 Measurement of the Reversible Cell 14.6 Rotational Partition Function: Potential 296 Polyatomic Molecules 388 11.4 Chemical Reactions in Electrochemical Cells 14.7 Vibrational Partition Function 390 and the Nernst Equation 296 14.8 The Equipartition Theorem 395 11.5 Combining Standard Electrode Potentials to Determine the Cell Potential 298 14.9 Electronic Partition Function 396 11.6 Obtaining Reaction Gibbs Energies and 14.10 Review 400 Reaction Entropies from Cell Potentials 300 11.7 Relationship Between the Cell EMF and the 15 Statistical Thermodynamics 407 Equilibrium Constant 300 11.8 Determination of E ~ and Activity Coefficients 15.1 Energy 407 Using an Electrochemical Cell 302 15.2 Energy and Molecular Energetic Degrees of Freedom 411 11.9 Cell Nomenclature and Types of Electrochemical Cells 303 15.3 Heat Capacity 416 11.10 The Electrochemical Series 304 15.4 Entropy 421 11.11 Thermodynamics of Batteries and Fuel Cells 305 15.5 Residual Entropy 426 11.12 Electrochemistry of Commonly Used 15.6 Other Thermodynamic Functions 427 Batteries 306 15.7 Chemical Equilibrium 431 11.13 Fuel Cells 310 11.14 Electrochemistry at the Atomic Scale 312 16 Kinetic Theory of Gases 441 11.15 Using Electrochemistry for Nanoscale 16.1 Kinetic Theory of Gas Motion and Machining 315 Pressure 441 16.2 Velocity Distribution in One 12 Probability 321 Dimension 442 12.1 Why Probability? 321 16.3 The Maxwell Distribution of Molecular 12.2 Basic Probability Theory 322 Speeds 446 12.3 Stirling’s Approximation 330 16.4 Comparative Values for Speed Distributions 449 12.4 Probability Distribution Functions 331 16.5 Gas Effusion 451 12.5 Probability Distributions Involving Discrete and Continuous Variables 333 16.6 Molecular Collisions 453 12.6 Characterizing Distribution Functions 336 16.7 The Mean Free Path 457 A01_ENGE4583_04_SE_FM_i-xvi.indd 7 01/12/17 12:51 PM viii CONTENTS 17 Transport Phenomena 463 19 Complex Reaction Mechanisms 541 17.1 What Is Transport? 463 19.1 Reaction Mechanisms and Rate Laws 541 17.2 Mass Transport: Diffusion 465 19.2 The Preequilibrium Approximation 543 17.3 Time Evolution of a Concentration Gradient 469 19.3 The Lindemann Mechanism 545 17.4 Statistical View of Diffusion 471 19.4 Catalysis 547 17.5 Thermal Conduction 473 19.5 Radical-Chain Reactions 558 17.6 Viscosity of Gases 476 19.6 Radical-Chain Polymerization 561 17.7 Measuring Viscosity 479 19.7 Explosions 562 17.8 Diffusion and Viscosity of Liquids 480 19.8 Feedback, Nonlinearity, and Oscillating 17.9 Ionic Conduction 482 Reactions 564 19.9 Photochemistry 567 18 Elementary Chemical Kinetics 493 19.10 Electron Transfer 579 18.1 Introduction to Kinetics 493 20 Macromolecules 593 18.2 Reaction Rates 494 18.3 Rate Laws 496 20.1 What Are Macromolecules? 593 18.4 Reaction Mechanisms 501 20.2 Macromolecular Structure 594 18.5 Integrated Rate Law Expressions 502 20.3 Random-Coil Model 596 18.6 Numerical Approaches 507 20.4 Biological Polymers 599 18.7 Sequential First-Order Reactions 508 20.5 Synthetic Polymers 607 18.8 Parallel Reactions 513 20.6 Characterizing Macromolecules 610 18.9 Temperature Dependence of Rate 20.7 Self-Assembly, Micelles, and Biological Constants 515 Membranes 617 18.10 Reversible Reactions and Equilibrium 517 APPENDIX A Data Tables 625 18.11 Perturbation-Relaxation Methods 521 Credits 643 18.12 The Autoionization of Water: A Temperature- Jump Example 523 Index 644 18.13 Potential Energy Surfaces 524 18.14 Activated Complex Theory 526 18.15 Diffusion-Controlled Reactions 530 A01_ENGE4583_04_SE_FM_i-xvi.indd 8 01/12/17 12:51 PM About the Authors THOMAS ENGEL taught chemistry at the University of Washington for more than 20 years, where he is currently professor emeritus of chemistry. Professor Engel received his bachelor’s and master’s degrees in chemistry from the Johns Hopkins University and his Ph.D. in chemistry from the University of Chicago. He then spent 11 years as a researcher in Germany and Switzerland, during which time he received the Dr. rer. nat. habil. degree from the Ludwig Maximilians University in Munich. In 1980, he left the IBM research laboratory in Zurich to become a faculty member at the University of Washington. Professor Engel has published more than 80 articles and book chapters in the area of surface chemistry. He has received the Surface Chemistry or Colloids Award from the American Chemical Society and a Senior Humboldt Research Award from the Alex- ander von Humboldt Foundation. Other than this textbook, his current primary science interests are in energy policy and energy conservation. He serves on the citizen’s advi- sory board of his local electrical utility, and his energy-efficient house could be heated in winter using only a hand-held hair dryer. He currently drives a hybrid vehicle and plans to transition to an electric vehicle soon to further reduce his carbon footprint. PHILIP REID has taught chemistry at the University of Washington since 1995. Professor Reid received his bachelor’s degree from the University of Puget Sound in 1986 and his Ph.D. from the University of California, Berkeley in 1992. He performed postdoctoral research at the University of Minnesota-Twin Cities before moving to Washington. Professor Reid’s research interests are in the areas of atmospheric chemistry, ul- trafast condensed-phase reaction dynamics, and organic electronics. He has published more than 140 articles in these fields. Professor Reid is the recipient of a CAREER Award from the National Science Foundation, is a Cottrell Scholar of the Research Cor- poration, and is a Sloan Fellow. He received the University of Washington Distinguished Teaching Award in 2005. ix A01_ENGE4583_04_SE_FM_i-xvi.indd 9 01/12/17 12:52 PM