Physical chemistry for the chemical sciences by raymond chang, jr thoman john pdf

PHYSICAL CHEMISTRY for the Chemical Sciences Raymond Chang WILLIAMS COLLEGE John W Thoman, Jr WILLIAMS COLLEGE University Science Books www.uscibooks.com University Science Books www.uscibooks.com Production Management: Jennifer Uhlich at Wilsted & Taylor Manuscript Editing: John Murdzek Design: Robert Ishi, with Yvonne Tsang at Wilsted & Taylor Composition & Illustrations: Laurel Muller Cover Design: Genette Itoko McGrew Printing & Binding: Marquis Book Printing, Inc This book is printed on acid-free paper Copyright © 2014 by University Science Books ISBN 978-1-891389-69-6 (hard cover) ISBN 978-1-78262-087-7 (soft cover), only for distribution outside of North America and Mexico by the Royal Society of Chemistry Reproduction or translation of any part of this work beyond that permitted by Section 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful Requests for permission or further information should be addressed to the Permissions Department, University Science Books Library of Congress Cataloging-in-Publication Data Chang, Raymond Physical chemistry for the chemical sciences / Raymond Chang, John W Thoman, Jr pages cm Includes index ISBN 978-1-891389-69-6 (alk paper) Chemistry, Physical and theoretical—Textbooks I Thoman, John W., Jr., 1960– QD453.3.C43 2014 541—dc23 2013038473 II Title Printed in Canada 10 About the cover art: Tunneling in the quantum harmonic oscillator The red horizontal line represents the zero-point energy _1–2 hνi and the shaded region is the classically forbidden region in which K0 , ^see Chapter 11h Preface Physical Chemistry for the Chemical Sciences is intended for use in a one-year introductory course in physical chemistry that is typically offered at the junior level (the third year in a college or university program) Students in the course will have taken general chemistry and introductory organic chemistry In writing this book, our aim is to present the standard topics at the appropriate level with emphasis on readability and clarity While mathematical treatment of many topics is necessary, we have provided a physical picture wherever possible for understanding the concepts Only the basic skills of differential and integral calculus are required for working with the equations The limited number of integral equations needed to solve the end-of-chapter problems may be readily accessed from handbooks of chemistry and physics or software such as Mathematica The 20 chapters of the text can be divided into three parts Chapters 1–9 cover thermodynamics and related subjects Quantum mechanics and molecular spectroscopy are treated in Chapters 10–14 The last part (Chapters 15–20) describes chemical kinetics, photochemistry, intermolecular forces, solids and liquids, and statistical thermodynamics We have chosen a traditional ordering of topics, starting with thermodynamics because of the accessibility of the concrete examples and the closeness to everyday experience For instructors who prefer the “atoms first” or molecular approach, the order can be readily switched between the first two parts without loss of continuity Within each chapter, we introduce topics, define terms, and provide relevant worked examples, pertinent applications, and experimental details Many chapters include end-of-chapter appendices, which cover more detailed derivations, background, or explanation than the body of the chapter Each chapter concludes with a summary of the most important equations introduced within the chapter, an extensive and accessible list of further readings, and many end-of-chapter problems Answers to the even-numbered numerical problems may be found in the back of the book The end-of-book appendices provide some review of relevant mathematical concepts, basic physics definitions relevant to chemistry, and thermodynamic data A glossary enables the student to quickly check definitions Inside of the front and back covers, we include tables of information that are generally useful throughout the book The second color (red) enables the student to more easily interpret plots and elaborate diagrams and adds a pleasing look to the book An accompanying Solutions Manual, written by Helen O Leung and Mark D Marshall, provides complete solutions to all of the problems in the text This supplement contains many useful ideas and insights into problem-solving techniques xv xvi Preface The lines drawn between traditional disciplines are continually being modified as new fields are being defined This book provides a foundation for further study at the more advanced level in physical chemistry, as well as interdisciplinary subjects that include biophysical chemistry, materials science, and environmental chemistry fields such as atmospheric chemistry and biogeochemistry We hope that you find our book useful when teaching or learning physical chemistry It is a pleasure to thank the following people who provided helpful comments and suggestions: Dieter Bingemann (Williams College), George Bodner (Purdue University), Taina Chao (SUNY Purchase), Nancy Counts Gerber (San Francisco State University), Donald Hirsh (The College of New Jersey), Raymond Kapral (University of Toronto), Sarah Larsen (University of Iowa), David Perry (University of Akron), Christopher Stromberg (Hood College), and Robert Topper (The Cooper Union) We also thank Bruce Armbruster and Kathy Armbruster of University Science Books for their support and general assistance We are fortunate to have Jennifer Uhlich of Wilsted & Taylor as our production manager Her high professional standard and attention to detail greatly helped the task of transforming the manuscript into an attractive final product We very much appreciate Laurel Muller for her artistic and technical skills in laying out the text and rendering many figures Robert Ishi and Yvonne Tsang are responsible for the elegant design of the book John Murdzek did a meticulous job of copyediting Our final thanks go to Jane Ellis, who supervised the project and took care of all the details, big and small Raymond Chang John W Thoman, Jr Contents Preface CHAPTER xv Introduction and Gas Laws 1.1 1.2 1.3 1.4 Nature of Physical Chemistry Some Basic Definitions An Operational Definition of Temperature Units • Force • Pressure • Energy • Atomic Mass, Molecular Mass, and the Chemical Mole 1.5 The Ideal Gas Law • The Kelvin Temperature Scale • The Gas Constant R 1.6 Dalton’s Law of Partial Pressures 11 1.7 Real Gases 13 • The van der Waals Equation 14 • The Redlich–Kwong Equation • The Virial Equation of State 16 1.8 Condensation of Gases and the Critical State 18 1.9 The Law of Corresponding States 22 Problems 27 CHAPTER Kinetic Theory of Gases 35 2.1 The Model 35 2.2 Pressure of a Gas 36 2.3 Kinetic Energy and Temperature 38 2.4 The Maxwell Distribution Laws 39 2.5 Molecular Collisions and the Mean Free Path 45 2.6 The Barometric Formula 48 2.7 Gas Viscosity 50 2.8 Graham’s Laws of Diffusion and Effusion 53 2.9 Equipartition of Energy 56 Appendix 2.1 Derivation of Equation 2.29 63 Problems 66 CHAPTER 3.1 3.2 3.3 The First Law of Thermodynamics 73 Work and Heat 73 • Work 73 • Heat 79 The First Law of Thermodynamics 80 Enthalpy 83 • A Comparison of ΔU and ΔH 84 15 vi Contents 3.4 3.5 A Closer Look at Heat Capacities 88 Gas Expansion 91 • Isothermal Expansion 92 • Adiabatic Expansion 92 3.6 The Joule–Thomson Effect 96 3.7 Thermochemistry 100 • Standard Enthalpy of Formation 100 • Dependence of Enthalpy of Reaction on Temperature 107 3.8 Bond Energies and Bond Enthalpies 110 • Bond Enthalpy and Bond Dissociation Enthalpy 111 Appendix 3.1 Exact and Inexact Differentials 116 Problems 120 CHAPTER The Second Law of Thermodynamics 129 4.1 4.2 Spontaneous Processes 129 Entropy 131 • Statistical Definition of Entropy 132 • Thermodynamic Definition of Entropy 134 4.3 The Carnot Heat Engine 135 • Thermodynamic Efficiency 138 • The Entropy Function 139 • Refrigerators, Air Conditioners, and Heat Pumps 139 4.4 The Second Law of Thermodynamics 142 4.5 Entropy Changes 144 • Entropy Change due to Mixing of Ideal Gases 144 • Entropy Change due to Phase Transitions 146 • Entropy Change due to Heating 148 4.6 The Third Law of Thermodynamics 152 • Third-Law or Absolute Entropies 152 • Entropy of Chemical Reactions 155 4.7 The Meaning of Entropy 157 • Isothermal Gas Expansion 160 • Isothermal Mixing of Gases 160 • Heating 160 • Phase Transitions 161 • Chemical Reactions 161 4.8 Residual Entropy 161 Appendix 4.1 Statements of the Second Law of Thermodynamics 165 Problems 168 CHAPTER 5.1 5.2 5.3 5.4 5.5 5.6 Gibbs and Helmholtz Energies and Their Applications 175 Gibbs and Helmholtz Energies 175 The Meaning of Helmholtz and Gibbs Energies 178 • Helmholtz Energy 178 • Gibbs Energy 179 – Standard Molar Gibbs Energy of Formation (ΔfG°) 182 Dependence of Gibbs Energy on Temperature and Pressure 185 • Dependence of G on Temperature 185 • Dependence of G on Pressure 186 Gibbs Energy and Phase Equilibria 188 • The Clapeyron and the Clausius–Clapeyron Equations 190 • Phase Diagrams 192 • The Gibbs Phase Rule 196 Thermodynamics of Rubber Elasticity 196 Contents Appendix 5.1 Some Thermodynamic Relationships 200 Appendix 5.2 Derivation of the Gibbs Phase Rule 203 Problems 207 CHAPTER Nonelectrolyte Solutions 213 6.1 Concentration Units 213 • Percent by Weight 213 • Mole Fraction ^xh 214 • Molarity ^Mh 214 • Molality ^mh 214 6.2 Partial Molar Quantities 215 • Partial Molar Volume 215 • Partial Molar Gibbs Energy 216 6.3 Thermodynamics of Mixing 218 6.4 Binary Mixtures of Volatile Liquids 221 • Raoult’s Law 222 • Henry’s Law 225 6.5 Real Solutions 228 • The Solvent Component 228 • The Solute Component 229 6.6 Phase Equilibria of Two-Component Systems 231 • Distillation 231 • Solid–Liquid Equilibria 237 6.7 Colligative Properties 238 • Vapor-Pressure Lowering 239 • Boiling-Point Elevation 239 • Freezing-Point Depression 243 • Osmotic Pressure 245 Problems 255 CHAPTER Electrolyte Solutions 261 7.1 Electrical Conduction in Solution 261 • Some Basic Definitions 261 • Degree of Dissociation 266 • Ionic Mobility 268 • Applications of Conductance Measurements 269 7.2 A Molecular View of the Solution Process 271 7.3 Thermodynamics of Ions in Solution 274 • Enthalpy, Entropy, and Gibbs Energy of Formation of Ions in Solution 275 7.4 Ionic Activity 278 7.5 Debye–Hückel Theory of Electrolytes 282 • The Salting-In and Salting-Out Effects 286 7.6 Colligative Properties of Electrolyte Solutions 288 • The Donnan Effect 291 Appendix 7.1 Notes on Electrostatics 295 Appendix 7.2 The Donnan Effect Involving Proteins Bearing Multiple Charges 298 Problems 301 CHAPTER 8.1 8.2 Chemical Equilibrium 305 Chemical Equilibrium in Gaseous Systems 305 • Ideal Gases 305 • A Closer Look at Equation 8.7 310 • A Comparison of Δ rG° with Δ rG 311 • Real Gases 313 Reactions in Solution 315 vii viii Contents 8.3 Heterogeneous Equilibria 316 • Solubility Equilibria 318 8.4 Multiple Equilibria and Coupled Reactions 319 • Principle of Coupled Reactions 321 8.5 The Influence of Temperature, Pressure, and Catalysts on the Equilibrium Constant 322 • The Effect of Temperature 322 • The Effect of Pressure 325 • The Effect of a Catalyst 327 8.6 Binding of Ligands and Metal Ions to Macromolecules 328 • One Binding Site per Macromolecule 328 • n Equivalent Binding Sites per Macromolecule 329 • Equilibrium Dialysis 332 Appendix 8.1 The Relationship Between Fugacity and Pressure 335 Appendix 8.2 The Relationships Between K1 and K and the Intrinsic Dissociation Constant K 338 Problems 342 CHAPTER Electrochemistry 351 9.1 9.2 9.3 Electrochemical Cells 351 Single-Electrode Potential 353 Thermodynamics of Electrochemical Cells 356 • The Nernst Equation 360 • Temperature Dependence of EMF 362 9.4 Types of Electrodes 363 • Metal Electrodes 363 • Gas Electrodes 364 • Metal-Insoluble Salt Electrodes 364 • The Glass Electrode 364 • Ion-Selective Electrodes 365 9.5 Types of Electrochemical Cells 365 • Concentration Cells 365 • Fuel Cells 366 9.6 Applications of EMF Measurements 367 • Determination of Activity Coefficients 367 • Determination of pH 368 9.7 Membrane Potential 368 • The Goldman Equation 371 • The Action Potential 372 Problems 378 CHAPTER 10 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 Quantum Mechanics 383 Wave Properties of Light 383 Blackbody Radiation and Planck’s Quantum Theory 386 The Photoelectric Effect 388 Bohr’s Theory of the Hydrogen Emission Spectrum 390 de Broglie’s Postulate 397 The Heisenberg Uncertainty Principle 401 Postulates of Quantum Mechanics 403 The Schrödinger Wave Equation 409 Particle in a One-Dimensional Box 412 • Electronic Spectra of Polyenes 418 10.10 Particle in a Two-Dimensional Box 420 Contents 10.11 Particle on a Ring 425 10.12 Quantum Mechanical Tunneling 428 • Scanning Tunneling Microscopy 431 Appendix 10.1 The Bracket Notation in Quantum Mechanics Problems 437 CHAPTER 11 433 Applications of Quantum Mechanics to Spectroscopy 447 11.1 Vocabulary of Spectroscopy 447 • Absorption and Emission 447 • Units 448 • Regions of the Spectrum 448 • Linewidth 449 • Resolution 452 • Intensity 453 • Selection Rules 455 • Signal-to-Noise Ratio 456 • The Beer–Lambert Law 457 11.2 Microwave Spectroscopy 458 • The Rigid Rotor Model 458 • Rigid Rotor Energy Levels 463 • Microwave Spectra 464 11.3 Infrared Spectroscopy 469 • The Harmonic Oscillator 469 • Quantum Mechanical Solution to the Harmonic Oscillator 471 • Tunneling and the Harmonic Oscillator Wave Functions 474 • IR Spectra 475 • Simultaneous Vibrational and Rotational Transitions 479 11.4 Symmetry and Group Theory 482 • Symmetry Elements 482 • Molecular Symmetry and Dipole Moment 483 • Point Groups 484 • Character Tables 484 11.5 Raman Spectroscopy 486 • Rotational Raman Spectra 489 Appendix 11.1 Fourier-Transform Infrared Spectroscopy 491 Problems 496 CHAPTER 12 Electronic Structure of Atoms 503 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 The Hydrogen Atom 503 The Radial Distribution Function 505 Hydrogen Atomic Orbitals 510 Hydrogen Atom Energy Levels 514 Spin Angular Momentum 515 The Helium Atom 517 Pauli Exclusion Principle 519 Aufbau Principle 523 • Hund’s Rules 524 • Periodic Variations in Atomic Properties 12.9 Variational Principle 530 12.10 Hartree–Fock Self-Consistent-Field Method 536 12.11 Perturbation Theory 540 Appendix 12.1 Proof of the Variational Principle 546 Problems 551 528 ix x Contents CHAPTER 13 Molecular Electronic Structure and the Chemical Bond 557 13.1 13.2 13.3 13.4 13.5 The Hydrogen Molecular Cation 557 The Hydrogen Molecule 561 Valence Bond Approach 563 Molecular Orbital Approach 567 Homonuclear and Heteronuclear Diatomic Molecules 570 • Homonuclear Diatomic Molecules 570 • Heteronuclear Diatomic Molecules 573 • Electronegativity, Polarity, and Dipole Moments 576 13.6 Polyatomic Molecules 578 • Molecular Geometry 578 • Hybridization of Atomic Orbitals 579 13.7 Resonance and Electron Delocalization 585 13.8 Hückel Molecular Orbital Theory 589 • Ethylene ^C2H4h 590 • Butadiene ^C4H6h 595 • Cyclobutadiene ^C4H4h 598 13.9 Computational Chemistry Methods 600 • Molecular Mechanics ^Force Fieldh Methods 601 • Empirical and Semi-Empirical Methods 601 • Ab Initio Methods 602 Problems 605 CHAPTER 14 14.1 Electronic Spectroscopy and Magnetic Resonance Spectroscopy 611 Molecular Electronic Spectroscopy 611 • Organic Molecules 613 • Charge-Transfer Interactions 616 • Application of the Beer–Lambert Law 617 14.2 Fluorescence and Phosphorescence 619 • Fluorescence 619 • Phosphorescence 621 14.3 Lasers 622 • Properties of Laser Light 626 14.4 Applications of Laser Spectroscopy 629 • Laser-Induced Fluorescence 629 • Ultrafast Spectroscopy 630 • Single-Molecule Spectroscopy 632 14.5 Photoelectron Spectroscopy 633 14.6 Nuclear Magnetic Resonance Spectroscopy 637 • The Boltzmann Distribution 640 • Chemical Shifts 641 • Spin–Spin Coupling 642 • NMR and Rate Processes 644 • NMR of Nuclei Other Than 1H 646 • Solid-State NMR 648 • Fourier-Transform NMR 649 • Magnetic Resonance Imaging ^MRIh 651 14.7 Electron Spin Resonance Spectroscopy 652 Appendix 14.1 The Franck–Condon Principle 657 Appendix 14.2 A Comparison of FT-IR and FT-NMR 659 Problems 665 ... Cataloging-in-Publication Data Chang, Raymond Physical chemistry for the chemical sciences / Raymond Chang, John W Thoman, Jr pages cm Includes index ISBN 978-1-891389-69-6 (alk paper) Chemistry, Physical and theoretical—Textbooks... represents the zero-point energy _1–2 hνi and the shaded region is the classically forbidden region in which K0 , ^see Chapter 11h Preface Physical Chemistry for the Chemical Sciences is intended for. .. on the walls of the container depends on both the frequency of molecular collisions with the walls and the momentum imparted by the molecules to the walls Both contributions are diminished by the