P H Y S I C A L C H E M I S T R Y Thermodynamics, Statistical Mechanics, & Kinetics This page intentionally left blank P H Y S I C A L C H E M I S T R Y Thermodynamics, Statistical Mechanics, & Kinetics A N D R E W C O O K S Y Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montréal Toronto Delhi Mexico City São Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo Editor in Chief: Adam Jaworski Executive Editor: Jeanne Zalesky Senior Marketing Manager: Jonathan Cottrell Project Editor: Jessica Moro Editorial Assistant: Lisa Tarabokjia Marketing Assistant: Nicola Houston Director of Development: Jennifer Hart Development Editor: Daniel Schiller Media Producer: Erin Fleming Managing Editor, Chemistry and Geosciences: Gina M. 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Manufactured in the United States of America. his 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 likewise. To obtain permission to use material from this work, please submit a written request to Pearson Education, Inc., Permissions Department, 1 Lake Street, Department 1G, Upper Saddle River, NJ 07458. Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks. Where those designations appear in this book, and the publisher was aware of a trademark claim, the designations have been printed in initial caps or all caps. Library of Congress Cataloging-in-Publication Data Cooksy, Andrew. Physical chemistry : thermodynamics, statistical mechanics, & kinetics / Andrew Cooksy. pages cm Includes index. ISBN-13: 978-0-321-81415-9 ISBN-10: 0-321-81415-0 1. Chemistry, Physical and theoretical--Textbooks. 2. hermodynamics--Textbooks. 3. Statistical mechanics--Textbooks. 4. Chemical kinetics--Textbooks. I. Title. QD453.3.C66 2013 541--dc23 2012037313 1 2 3 4 5 6 7 8 9 10—RRD—16 15 14 13 12 ISBN-10: 0-321-81415-0 www.pearsonhighered.com ISBN-13: 978-0-321-81415-9 DEDICATION To Mary, Wesley, and Owen Cragged, and steep, Truth stands, and he that will Reach her, about must, and about must go, And what the hill’s suddenness resists, winne so. —John Donne (1572-1631), Satire III PHYSICAL CHEMISTRY BRIEF CONTENTS Thermodynamics, Statistical Mechanics, & Kinetics A Introduction: Tools from Math and Physics 1 Classical Physical Chemistry Sets the Stage 2 Introduction to Statistical Mechanics: Building Up to the Bulk 3 Partitioning the Energy 4 Statistical Mechanics and Molecular Interactions 5 Mass Transport: Collisions and Diffusion 6 Energy Transport: Radiation and Matter 7 Introduction to Thermodynamics: Heat Capacity 8 The First Law: Expansion and Engines 9 The Second and Third Laws: Entropy 10 Phase Transitions and Phase Equilibrium 11 Solutions 12 The Thermodynamics of Chemical Reactions 13 Chemical Kinetics: Elementary Reactions 14 Chemical Kinetics: Multi-Step Reactions vi BRIEF TABLE OF CONTENTS FOR COOKSY’S QUANTUM ALSO AVAILABLE CHEMISTRY AND MOLECULAR INTERACTIONS Quantum Chemistry and Molecular Interactions A Introduction: Tools from Math and Physics PHYSICAL CHEMISTRY Quantum Chemistry 1 and Molecular Interactions Classical and Quantum Mechanics 2 The Schrödinger Equation 3 One-Electron Atoms 4 Many-Electron Atoms 5 Chemical Bonds and Nuclear Magnetic Resonance ANDREW COOKSY 6 Molecular Symmetry 7 Electronic States and Spectroscopy 8 Vibrational States and Spectroscopy 9 Rotational States and Spectroscopy 10 Intermolecular Forces 11 Nanoscale Chemical Structure 12 The Structure of Liquids 13 The Structure of Solids vii viii CONTENTS DETAILED CONTENTS P H Y S I C A L C H E M I S T R Y Thermodynamics, Statistical Mechanics, & Kinetics A Introduction: Tools from Math and Physics 3 a.1 Mathematics 3 a.2 Classical Physics 29 PROBLEMS 34 Part I EXTRAPOLATING FROM MOLECULAR TO MACROSCOPIC SYSTEMS 37 1 Classical Physical Chemistry Sets the Stage 38 1.1 he Classical Properties of Matter 39 1.2 hermodynamics 43 1.3 he Kinetic heory of Ideal Gases 47 BIOSKETCH Joseph Francisco 54 PROBLEMS 60 2 Introduction to Statistical Mechanics: Building Up to the Bulk 61 2.1 Properties of the Microscopic World 62 2.2 Bulk Properties 68 BIOSKETCH Juan J. de Pablo 71 2.3 Entropy 73 2.4 Temperature and the Partition Function 77 TOOLS OF THE TRADE Pressure Measurement 87 2.5 he Ideal Gas Law 89 PROBLEMS 93 viii CONTENTS ix 3 Partitioning the Energy 95 3.1 Separation of Degrees of Freedom 97 3.2 he Equipartition Principle 100 TOOLS OF THE TRADE Thermometers 106 3.3 Vibrational and Rotational Partition Functions 107 BIOSKETCH Lucy Ziurys 116 3.4 he Translational Partition Function 116 3.5 Temperature and the Maxwell-Boltzmann Distribution 124 PROBLEMS 131 4 Statistical Mechanics and Molecular Interactions 135 4.1 Molecular Interactions 136 4.2 Pressure of a Non-Ideal Gas 142 4.3 he Pair Correlation Function 155 4.4 Bose-Einstein and Fermi-Dirac Statistics 159 PROBLEMS 165 5 Mass Transport: Collisions and Diffusion 169 5.1 Collision Parameters 170 T OOLS OF THE TRADE Ion Cyclotron Resonance Mass Spectrometry (ICR-MS) 177 5.2 he Random Walk 179 5.3 Transport without External Forces 183 BIOSKETCH Facundo M. Fernandez 191 5.4 Transport with External Forces 192 PROBLEMS 196 6 Energy Transport: Radiation and Matter 201 6.1 Conduction, Convection, and Radiation 203 6.2 Blackbody Radiation 207 BIOSKETCH Stephen J. Klippenstein 208 6.3 Spectroscopic Intensities 212 6.4 Laser Dynamics 221 TOOLS OF THE TRADE Lasers 223 6.5 Spectroscopic Linewidths 224 PROBLEMS 229 ix