Physical chemistry 4th ed robert silbey

Physical chemistry 4th ed robert silbey Physical chemistry 4th ed robert silbey Physical chemistry 4th ed robert silbey Physical chemistry 4th ed robert silbey Physical chemistry 4th ed robert silbey Physical chemistry 4th ed robert silbey Physical chemistry 4th ed robert silbey Physical chemistry 4th ed robert silbey

Physical Chemistry Fourth Edition Robert J Silbey Class of 1942 Professor of Chemistry Massachusetts Institute of Technology Robert A Alberty Professor Emeritus of Chemistry Massachusetts Institute of Technology Moungi G Bawendi Professor of Chemistry Massachusetts Institute of Technology John Wiley & Sons, Inc ACQUISITIONS EDITOR Deborah Brennan SENIOR PRODUCTION EDITOR Patricia McFadden SENIOR MARKETING MANAGER Robert Smith SENIOR DESIGNER Kevin Murphy NEW MEDIA EDITOR Martin Batey This book was set in 10/12 Times Roman by Publication Services, Inc and printed and bound by Hamilton Printing The cover was printed by Lehigh Press, Inc This book is printed on acid-free paper.᭺ ϱ Copyright 2005 ᮊ John Wiley & Sons, Inc All rights reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center Inc 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600 Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, (201) 748-6011, fax (201) 748-6008 To order books or for customer service, call 1(800)-CALL-WILEY (225-5945) PREFACE The objective of this book is to make the concepts and methods of physical chemistry clear and interesting to students who have had a year of calculus and a year of physics The underlying theory of chemical phenomena is complicated, and so it is a challenge to make the most important concepts and methods understandable to undergraduate students However, these basic ideas are accessible to students, and they will find them useful whether they are chemistry majors, biologists, engineers, or earth scientists The basic theory of chemistry is presented from the viewpoint of academic physical chemists, but many applications of physical chemistry to practical problems are described One of the important objectives of a course in physical chemistry is to learn how to solve numerical problems The problems in physical chemistry help emphasize features in the underlying theory, and they illustrate practical applications There are two types of problems: problems that can be solved with a handheld calculator and COMPUTER PROBLEMS that require a personal computer with a mathematical application installed There are two sets of problems of the first type The answers to problems in the first set are given in the back of the textbook, and worked-out solutions to these problems are given in the Solutions Manual for Physical Chemistry The answers for the second set of problems are given in the Solutions Manual In the two sets of problems that can be solved using hand-held calculators, some problems are marked with an icon to indicate that they may be more conveniently solved on a personal computer with a mathematical program There are 170 COMPUTER PROBLEMS that require a personal computer with a mathematical application such as MathematicaTM , MathCadTM , MATLABTM , or MAPLETM installed The recent development of these mathematical applications makes it possible to undertake problems that were previously too difficult or too time consuming This is particularly true for two- and three-dimensional plots, integration and differentiation of complicated functions, and solving differential equations The Solutions Manual for Physical Chemistry provides MathematicaTM programs and printouts for the COMPUTER PROBLEMS The MathematicaTM solutions of the 170 COMPUTER PROBLEMS in digital form are available on the web at http://www.wiley.com/college/silbey They can be downloaded into a personal computer with MathematicaTM installed Students iv Preface can obtain Mathematica at a reduced price from Wolfram Research, 100 Trade Center Drive, Champaign, Illinois, 61820-7237 A password is required and will be available in the Solutions Manual, along with further information about how to access the Mathematica solutions in digital form Emphasis in the COMPUTER PROBLEMS has been put on problems that not require complicated programming, but make it possible for students to explore important topics more deeply Suggestions are made as to how to vary parameters and how to apply these programs to other substances and systems As an aid to showing how commands are used, there is an index in the Solutions Manual of the major commands used MathematicaTM plots are used in some 60 figures in the textbook The legends for these figures indicate the COMPUTER PROBLEM where the program is given These programs make it possible for students to explore changes in the ranges of variables in plots and to make calculations on other substances and systems One of the significant changes in the fourth edition is increased emphasis on the thermodynamics and kinetics of biochemical reactions, including the denaturation of proteins and nucleic acids In this edition there is more discussion of the uses of statistical mechanics, nuclear magnetic relaxation, nano science, and oscillating chemical reactions This edition has 32 new problems that can be solved with a hand-held calculator and 35 new problems that require a computer with a mathematical application There are 34 new figures and eight new tables Because the number of credits in physical chemistry courses, and therefore the need for more advanced material, varies at different universities and colleges, more topics have been included in this edition than can be covered in most courses The Appendix provides an alphabetical list of symbols for physical quantities and their units The use of nomenclature and units is uniform throughout the book SI (Syste`me International d’Unite´s) units are used because of their advantage as a coherent system of units That means that when SI units are used with all of the physical quantities in a calculation, the result comes out in SI units without having to introduce numerical factors The underlying unity of science is emphasized by the use of seven base units to represent all physical quantities HISTORY Outlines of Theoretical Chemistry, as it was then entitled, was written in 1913 by Frederick Getman, who carried it through 1927 in four editions The next four editions were written by Farrington Daniels In 1955, Robert Alberty joined Farrington Daniels At that time, the name of the book was changed to Physical Chemistry, and the numbering of the editions was started over The collaboration ended in 1972 when Farrington Daniels died It is remarkable that this textbook traces its origins back 91 years Over the years this book has profited tremendously from the advice of physical chemists all over the world Many physical chemists who care how their subject is presented have written to us with their comments, and we hope that will continue We are especially indebted to colleagues at MIT who have reviewed various sections and given us the benefit of advice These include Sylvia T Ceyer, Robert W Field, Carl W Garland, Mario Molina, Keith Nelson, and Irwin Oppenheim Preface The following individuals made very useful suggestions as to how to improve this fourth edition: Kenneth G Brown (Old Dominion University), Thandi Buthelez (Western Kentucky University), Susan Collins (California State University Northridge), John Gold (East Straudsburg University), Keith J Stine (University of Missouri–St Louis), Ronald J Terry (Western Illinois University), and Worth E Vaughan (University of Wisconsin, Madison) We are also indebted to reviewers of earlier editions and to people who wrote us about the third edition The following individuals made very useful suggestions as to how to improve the MathematicaTM solutions to COMPUTER PROBLEMS: Ian Brooks (Wolfram Research), Carl W David (U Connecticut), Robert N Goldberg (NIST), Mark R Hoffmann (University of North Dakota), Andre Kuzniarek (Wolfram Research), W Martin McClain (Wayne State University), Kathryn Tomasson (University of North Dakota), and Worth E Vaughan (University of Wisconsin, Madison) We are indebted to our editor Deborah Brennan and to Catherine Donovan and Jennifer Yee at Wiley for their help in the production of the book and the solutions manual We are also indebted to Martin Batey for making available the web site, and to many others at Wiley who were involved in the production of this fourth edition Cambridge, Massachusetts January 2004 Robert J Silbey Robert A Alberty Moungi G Bawendi v CONTENTS PART ONE THERMODYNAMICS Zeroth Law of Thermodynamics and Equations of State First Law of Thermodynamics 31 Second and Third Laws of Thermodynamics 74 Fundamental Equations of Thermodynamics 102 Chemical Equilibrium Phase Equilibrium 132 177 Electrochemical Equilibrium 218 Thermodynamics of Biochemical Reactions 254 PART TWO QUANTUM CHEMISTRY Quantum Theory 295 10 Atomic Structure 348 11 Molecular Electronic Structure 12 Symmetry 396 437 13 Rotational and Vibrational Spectroscopy 14 Electronic Spectroscopy of Molecules 15 Magnetic Resonance Spectroscopy 16 Statistical Mechanics 568 458 502 537 Contents PART THREE KINETICS 17 Kinetic Theory of Gases 613 18 Experimental Kinetics and Gas Reactions 19 Chemical Dynamics and Photochemistry 20 Kinetics in the Liquid Phase 641 686 724 PART FOUR MACROSCOPIC AND MICROSCOPIC STRUCTURES 21 Macromolecules 763 22 Electric and Magnetic Properties of Molecules 23 Solid-State Chemistry 24 Surface Dynamics 786 803 840 APPENDIX A Physical Quantities and Units B Values of Physical Constants 863 867 C Tables of Physical Chemical Data D Mathematical Relations E Greek Alphabet 868 884 897 F Useful Information on the Web 898 G Symbols for Physical Quantities and Their SI Units H Answers to the First Set of Problems INDEX 933 912 899 vii This page intentionally left blank P A R T O N E Thermodynamics T hermodynamics deals with the interconversion of various kinds of energy and the changes in physical properties that are involved Thermodynamics is concerned with equilibrium states of matter and has nothing to with time Even so, it is one of the most powerful tools of physical chemistry; because of its importance, the first part of this book is devoted to it The first law of thermodynamics deals with the amount of work that can be done by a chemical or physical process and the amount of heat that is absorbed or evolved On the basis of the first law it is possible to build up tables of enthalpies of formation that may be used to calculate enthalpy changes for reactions that have not yet been studied With information on heat capacities of reactants and products also available, it is possible to calculate the heat of a reaction at a temperature where it has not previously been studied The second law of thermodynamics deals with the natural direction of processes and the question of whether a given chemical reaction can occur by itself The second law was formulated initially in terms of the efficiencies of heat engines, but it also leads to the definition of entropy, which is important in determining the direction of chemical change The second law provides the basis for the definition of the equilibrium constant for a chemical reaction It provides an answer to the question, “To what extent will this particular reaction go before equilibrium is reached?” It also provides the basis for reliable predictions of the effects of temperature, pressure, and concentration on chemical and physical equilibrium The third law provides the basis for calculating equilibrium constants from calorimetric measurements only This is an illustration of the way in which thermodynamics interrelates apparently unrelated measurements on systems at equilibrium After discussing the laws of thermodynamics and the various physical quantities involved, our first applications will be to the quantitative treatment of chemical equilibria These methods are then applied to equilibria between different phases This provides the basis for the quantitative treatment of distillation and for the interpretation of phase changes in mixtures of solids Then thermodynamics is applied to electrochemical cells and biochemical reactions 934 Index Boiling point, as a function of pressure, 182 Boltzmann constant, 89, 297 Boltzmann distribution, 461, 468, 542, 569 Bond angles, table, 883 Bond energy, 62 Bond lengths, table, 883 Bond order, 412 Bonding orbital, 399, 402, 412 Born-Oppenheimer approximation, 396 Bosons, 372, 601 Bound states, 350 Boyle temperature, 14 for a van der Waals gas, 20 Brackett series, 354 Bragg equation, 811 Bragg reflection, 812 Branched chain reactions, 674 Branching ratio, 655 Bravais lattices, 807 Brønsted equation, 741 Bubble point line, 187 Bubble point surface, 190 Buckmeisterfullerene, 446 Buffer, preparation, 260 C Cage, solvent, 734 Calorie, definition, 34, 865 Calorimeter, 33 adiabatic, 63 Calorimetry, 63 Canonical ensemble, 598 Canonical partition function, 570 for an ideal gas, 575 Capacitance, 787 Carnot cycle, 95 Catalysis: acid, 740 base, 740 enzyme, 745 general acid, 740 hydrogen ion, 740 Cathode, 222 Cells: with liquid junctions, 224 without liquid junction, 224 Celsius scale, Center of symmetry, 438, 441 Centrifugal distortion constant, 467 Centrosymmetric, 441 Chain reaction: branched, 674 determination of quantum yield, 712 unbranched, 674 Change in the binding of hydrogen ions, in a biochemical reaction, 275 Character of a representation, 452 Character tables, 452 Characteristic rotational temperature, 583 Characteristic vibrational temperature, 580 Charge number, 220 Chemical dynamics, 686 Chemical equations, as matrix equations, 163 Chemical equilibrium, criteria, 139 Chemical potential, 103 as a function of pressure of an ideal gas, 120 four different definitions, 118 of a species at equilibrium, 134 of an ideal gas in a mixture, 122 of gases, liquids, and solids, 179 significance, 118 transformed, 268 when phases have different electric potentials, 222 Chemical reaction, equilibrium condition, 133 Chemical shift, 546, 548 proton, 549 Chemical thermodynamic properties, 870 Chemisorption, 842 Chiral molecules, 529 Cholesteric liquid crystals, 829 Chromophores, 517 Circular birefringence, 530 Circular dichroism, 530 Circularly polarized light, 529 Clapeyron equation, 181 Classical mechanical observables, 307 Clausius theorem, 77 Clausius-Clapeyron equation, 183 Close packing: cubic, 826 hexagonal, 826 Coexistence curve, 181 Colligative properties, 198 Collision complex, 666 Collision density, 628 Collision diameter, 626 Collision frequency, 627 Collision theory, of bimolecular reactions, 687 Collision with a surface, 624 Collisions, of hard-sphere molecules, 626 Colloid osmotic pressure, 767 Combustion of graphite, 59 Commutability, and precision of measurement, 321 Commutative, 308 Commutator, 309 Complementarity, 299 Complex conjugate, 302, 306, 894 Complex numbers, 894 Component, 156, 159 hydrogen, 268 Composition of atmosphere, as a function of height, 25 Compressibility factor, 11 for a van der Waals gas, 19 Compression of a gas, 40 irreversible, 42 Concentration gradient, 730 Conduction band, 833 Conformations, of n -butane, 770 Congruently melting compound, 204 Conjugate pairs, of work, 45 Conjugated molecule, 518 absorption spectrum, 519 Consecutive first-order reactions, 651 Conservation matrix, 164 Conservation: of components, 156 of energy, 35 Conservation, of orbital angular momentum, 388 Conservative system, 324 Continuous wave, 524 Contour surfaces, for one-electron atoms, 360 Convergence limit, 506, 509 Conversion factors, 865 Cooperative binding, 279 Cooperative denaturation, 281 Coordinates, spherical, 887 Correlation diagram, 412, 413 Correlation energy, 376 Correlation spectroscopy (COSY), 560 Correspondence principle, 314 Coulomb integral, 401 Coulomb’s law, 219 Coupling constant, 550 Coupling of biochemical reactions, 276 Covalent crystals, 825 Covalent radii of atoms, 819 Cramer’s rule, 890 Criteria for irreversibility and reversibility, 107 Critical constants: Index of gases, 14 in terms of van der Waals constants, 20 Critical exponents, 21 Critical opalescence, 17 Critical phenomena, 16 Critical point, 15, 17 Critical temperature, for superconductivity, 831 Cross product, 332 Crystal structure data, 818 Crystal structures, classification, 804 Crystallographic point groups, table, 806 Crystals: covalent, 825 hydrogen-bonded, 825 ionic, 824 molecular, 825 Cubic close packing, 826 Cubic expansion coefficient, 126 Cubic lattices, 814 characteristics, table, 827 Curie temperature, 800 Curie’s law, 797 Cyclic integral, 35 D Dalton’s law, 10 de Broglie wavelength, 298, 813, 848, of the electron, 298 Debye temperature, 603 Debye wavelength, 602 Debye-Huăckel constant, 230 Debye-Huăckel theory, 229 Defects, in a surface, 841 Degeneracy, 319, 355 Degree of polymerization, number average, 772 Degrees of freedom, 79, 155, 161 Denaturation: cooperative, 281 DNA, 282 of proteins, 280 Desorption, rate, 843 Detailed balance, 655 Determinants, 889 Dew point line, 187 Dew point surface, 190 Diamagnetism, 800 Diamonds, 183, 816 Diatomic molecule, 520 absorption, 520 fluorescence, 520 phosphorescence, 521 table of constants, 481 vibrational and rotational levels, 484 vibration-rotation spectra, 483 Differential operators, 304 Differentials, 886 exact, 31, 36 inexact, 36 Diffraction methods, 811 Diffusion coefficient, 633, 727 Diffusion: in a liquid, 726 in gases, 633 of a spherical molecule in a liquid, 727 Diffusion-controlled reaction, 734 Dilute real solutions, 194, 198 Dipole moment operator, 453, 462, 466 Dipole moment: allowed symmetry groups, 448 induced, 493 of a transition, 462 magnetic, 363 table, 791 Dipole-induced dipole interaction, 428 Direct spin-spin coupling, 550 Dispersion curve, 795 Dispersion force, 428 Dissociation constants: of magnesium complexes, 262 macroscopic, 280 microscopic, 280 Dissociation energy, 510 equilibrium, 479 of NaCl (g), 427 spectroscopic, 479 Dissociation, of weak acids, 255 Dissociative adsorption, 845 Dissociative chemisorption, 853 Distillation, 191 Distortion polarization, 789 DNA: denaturation, 282 structure, 282 Donnan effect, 767 Doppler broadening, 300, 622 E Early barrier, 695 Efficiency of a heat engine, 95 Effusion, 624 Eigenfunction, 305 for a particle in a box, 315 harmonic oscillator, 327 of hydrogenlike atoms, 356 Eigenvalue, 305 Einstein coefficient, 460 for spontaneous emission, 461 for stimulated absorption, 460 935 for stimulated emission, 461 Einstein temperature, 602 Einstein unit, in photochemistry, 704 Electric conductivity, 731 Electric dipole moment operator, 426 Electric dipole moment, 425 Electric dipole transitions, 388, 504 Electric dipole, transition moment, 476 Electric field strength, 219, 731 Electric mobility, 731 of ions on water, 732 Electric potential, 219 Electric susceptibility, 788 Electrical work, 45 Electrochemical cell, 222 Electrochemical equilibrium, 218 Electrochemical reaction, 225 Electrode reaction, 222 Electrolytes, activity, 227 Electrolytic cell, 222 Electromagnetic spectrum, table, 459 Electromotive force, 225 Electron affinity, 381 Electron configuration, 377 of homonuclear diatomic molecules, 411 Electron density: for atomic hydrogen, 362 for hydrogen molecule ion, 404 in a crystal, 822 in a one-dimensional crystal, 821 Electron emission from surfaces, 849 Electron g factor, 366, 539 Electron in a box, 311 Electron spin resonance (ESR), 562 Electron spin, 364, 539 Electron transfer reactions, 744 Electron, formal, 67 Electroneutrality condition, 220 Electronic absorption spectra, of diatomic molecules, 505 Electronic contributions to thermodynamic properties, 586 Electronic energy levels, 503 for the hydrogen atom, 351 Electronic spectroscopy, of molecules, 502, 517 Electronic states: of hydrogen molecules, 410 of polyatomic molecules, 416 Electrophoresis, 732 Electrostatic factor, 735 Elementary reactions, 659 Elongation work, 45 936 Index Enantiomers, 529 Encounter pairs and solvent cage, 733 End-centered unit cell, 808 Endothermic process, 56 End-to-end distance, 769 Energies of hydrogenlike atoms, in a magnetic field, 367 Energy density, 296 Energy gap, 833 Energy levels: electronic, 503 for a particle in a three-dimensional box, 318 in a magnetic field, 364, 555 of a hydrogen atom, 353 of a hydrogenlike atom, 350 of an electron in a magnetic field, 562 Energy: of a dipole in an electric field, 790 of a harmonic oscillator, 323 of hydrogen molecule ion, 400 of ionization, 354 of light, 459 zero-point, 311 Ensembles, 597 canonical, 598 microcanonical, 598 Enthalpy, 48 as a criterion for spontaneous change, 106 of adsorption, 843 transformed, 269 Enthalpy of fusion, 185 Enthalpy level diagram, 59 Enthalpy of formation, 60 of aqueous hydrogen ions, 67 Enthalpy of neutralization, 65 Enthalpy of reaction, 57, 61 Enthalpy of vaporization, 184 Entropy: as a state function, 75 Boltzmann postulate, 89 calorimetric determination of, 91 in terms of the number of microscopic states, 571 of freezing supercooled water, 86 of fusion, 185 of mixing ideal gases, 87 transformed, 269 Entropy and statistical probability, 88 Entropy and the dispersal of energy, 90 Entropy change: in a process, 80 in a reversible expansion of an ideal gas, 82 in a reversible process, 81 in a system and its surroundings, 83 in an isolated system, 79 in heating an ideal gas, 82 in irreversible processes, 85 Entropy of an ideal gas, as a function of temperature and pressure, 85 Entropy of expansion, in a isolated system, 80 Entropy of vaporization, 81 Enzyme catalysis, 745 Equation of continuity, 728 Equation of state, 8, 12, 104 ideal gas, Equilibria, involving potential differences, 220 Equilibrium composition: effect of inert gases, 150 effect of initial composition, 150 effect of pressure, 150 of a complicated system, 143 Equilibrium condition, for a chemical reaction, 133 Equilibrium constant: apparent, 265 as a function of temperature, 148, 149 calculated from the standard electrode potential, 241 calculation from tables, 143, 144 definition, 134 determination of, 138 for a cell reaction, 226 for a gaseous reaction, 136 for reactions in dilute aqueous solutions, 243 from equilibrium density, 141 from statistical mechanics, 591, 594 in terms of rate constants, 663 of enzyme-catalyzed reactions, 748 of gas reactions, in terms of concentrations, 152 thermodynamic, 137 Equilibrium dissociation energy, 479 Equilibrium, as a function of temperature, 145 between phases, 119, 177 thermal, vapor-liquid, 185 Equipartition, 596 Error function, 728 Ethylene, bonding, 420 Euler formula, 895 Euler’s criterion for exactness, 38 Euler’s theorem, 23, 105 Eutectic temperature, 203 Exact differential, 31, 36 Excited states, 354, 402 of hydrogen molecule ion, 407 Excited molecule, 669 lifetime, 707 Excluded volume, 771 Exothermic process, 56 Expansion of a gas, 41 irreversible, 42 Expansion, Joule-Thomson, 53 Expectation values, 309, 359 Experimental kinetics, 641 Explosion limits, 676 Exponential drop off, 25 Exponentials, 884 Extended Debye-Huăckel equation, 231 Extensive variables, Extent of reaction, 57 as a function of pressure, 140 as a function of temperature, 149 dimensionless form, 140 F Face-centered unit cell, 808 Face-centered cubic lattice, 814 Falloff region, 668 Faraday constant, 220 Femtosecond dynamics of a barrier reaction, 717 Femtosecond transition-state spectroscopy, 714 Fermi energy, 830 Fermi-Dirac distribution function, 830 Fermions, 372, 601 Ferromagnetism, 800 Fick’s first law, 727 Fick’s second law, 728 First law of thermodynamics, 30, 34 First order spectrum, 552 First-order phase transition, 180 First-order reactions, 645 consecutive, 651 reversible, 650 Flash photolysis, 644 Flow chart, for determining point groups, 447 Fluctuations, 17, 603, 781 Fluidity, 726 Fluoresence, 519 quantum yield, 708 spectrum, 522 Flux, 624, 841 Force constant, 323, 475 Index Force, 31 Formal electron, 67 Fourier transform, 564, 821, 895 infrared spectroscopy, 496 NMR spectrometer, 545, 546 Fourier’s theorem, 821 Fractional coordinates, 809, 820 Fractional distillation, 191 Fractional saturation, of hemoglobin and myoglobin, 278 Franck-Condon overlap integral, 508 Franck-Condon principle, 505 Free induction decay (FID), 545, 558 Free radical polymerization, 772 Freely jointed chain model, 768 Freely rotating chain model, 769 Freezing point lowering, 199 Freezing point, as a function of pressure, 182 Frequency domain, 545 Frequency, angular, 323 Frictional coefficient, 725, 778 Fuel cells, 245 Fugacity, 114, 136 coefficient, 116 of a van der Waals gas, 117 Fundamental equation, 102 for the enthalpy, 105 for the Gibbs energy, 107, 133 for the Helmholtz energy, 107 for the internal energy, 103 for the transformed Gibbs energy, 268, 270 with other kinds of work, 110 G Galvanic cell, 222 Gas constant, in various units, 10 recommended value, 10 Gaussian curve, 729 Gaussian functions, 419 Gay-Lussac’s law, General acid catalysis, 740 Gibbs energy, 106 additivity of contributions of species, 109 and non-PV work, 111 as a criterion for spontaneous change, 108 as a function of extent of reaction, 134 dependence on pressure, 112 dependence on temperature, 111 of a reaction system, 138 of an ideal solution, 188 transformed, 267 Gibbs equation for the entropy, 571 Gibbs paradox, 88 Gibbs, 103, 106 Gibbs-Duhem equation, 124 Gibbs-Helmholtz equation, 112, 148 Glass electrode, 244 Glide plane, 808 Gradient, 892 Gravitational acceleration, 23 Greek alphabet, 897 Grotrian diagram, 388 Ground electronic state, 587 Ground state, 353 Ground states, of homonuclear diatomic molecules, table, 414 Group, 443 multiplication table, 444 H Half life, 646 Hamiltonian function, 305 Hamiltonian operator, 304 for electronic motion, 397 for helium atom, 369 for nuclear motion, 464 for the hydrogen atom, 397 vibrational, 489 Hard-sphere potential, 599 Harmonic oscillator, 322 classical, 322 eigenfunctions, 327 quantum mechanical, 325 Hartree energy, 352 Hartree-Fock calculation, 375 Heat capacity, 50 as a function of temperature, 51 at constant pressure, 49 at constant volume, 47 of ideal gases, at high temperatures (table), 597 of solids, in statistical mechanics, 601 relations between, 51 Heat engines, 94 Heat of combustion, 65 Heat of solution, 65 Heat, 31 absorbed in expansion of a gas, 48 sign convention, 34 Heisenberg uncertainty principle, 299 Helium atom: Hamiltonian operator, 369 wave function, 370 Helmholtz energy, 106 937 in terms of the canonical partition function, 570 Henderson-Hasselbalch equation, 259 Henry’s law, 193 Hermann-Mauguin symbols, 806 Hermite polynomials, 326 Hermitian operator, 306 Heterogeneous catalysis, 853 reaction rate, 855 Heterogeneous reactions, 154 Heterogeneous system, Hexagonal close packing, 826 High polymers, 763 Highest occupied molecular orbital (HOMO), 421 Hole, 833 Homogeneous functions, 23 Homogeneous system, Homonuclear diatomic molecules: electron configurations, 411 ground states, 414 Huăckel molecular orbitals: for 1,3-butadiene, 422 for benzene, 424 for ethylene, 420 theory, 419 Hybrid orbitals, 416, 430 Hybrid sp3 orbitals, 417 Hydrogen atom spectrum, 353 Hydrogen bond, 192, 430 Hydrogen component, 268 Hydrogen ion catalysis, 740 Hydrogen ions, standard enthalpy of formation, 67 Hydrogen molecule ion, 398 electron density, 404 energy, 400 Hydrogen-bonded crystals, 825 Hydrogenlike atom, total wave function, 356 Hydrogenlike radial wave function, 350 Hydrogenlike wave functions, real, 357 Hydrogen-oxygen fuel cell, 245 Hydroxyl ions, standard enthalpy of formation, 67 Hyperfine splitting constant, 563 I Ideal gas mixtures, 10 Ideal gas temperature scale, Ideal gas, single-molecule partition function, 574 Ideal solution, 186 Identity element, 438 Identity matrix, 164 938 Index Impact parameter, 631, 688 Improper axis, 442 Improper rotation axis, 438 Independent intensive properties, choices, 157 Indices, of a plane, 809 Indirect spin-spin coupling, 550 Induced dipole moment, 493 Inexact differential, 38 Infrared bond regions, 490 Infrared spectroscopy, Fourier transform, 496 Inhibition, 748 Initial reaction rate, 648 Integral heat of solution, 65 Integrals, 886 Integrated absorption coefficiemt, 515 Integrating factor, 39, 76 Intensity of light absorbed, 704 Intensive state of a system, 156 Intensive variables, Intermolecular energy transfer, rates, 706 Intermolecular forces, 427 Intermolecular potential energy, 429 Internal conversion, 520 Internal energy, 33 of combustion, 65 in terms of the canonical partition function, 570 with respect to a reference state, 33 Internal pressure, 48 Internal rotation, 489 Internuclear distance, 399 from rotational spectra, 468 Internuclear spin-spin coupling, 550 Interstitial site, 827 Intersystem crossing, 520 Intramolecular processes, rates, 706 Intrinsic viscosity, 776 relation to molar mass, 777 Inversion operation, 441 Ion product of water, at several temperatures, 879 Ion product, 255 Ion radii, 815 Ionic bonding, 425 Ionic crystals, 824 Ionic strength, 229 Ionization energy, 354, 378, 480 as a function of atomic number, 380 in electron volts, 380 of hydrogenlike atoms, 354 table, 883 Ionization potential, 480 Irreducible representations, 450 Irreversible compression of a gas, 42 Irreversible expansion of a gas, 42 Isobaric process, 48 Isolated system, Isolated system, spontaneous process, 78 Isolation method, 648 Isomer group, thermodynamic properties, 161, 163 Isomorphous replacement, 824 Isotherm, Isothermal compressibility, 17, 126 Isothermal expansion: of a van der Waals gas, 44 of an ideal gas, 113 J Joule, SI unit, 34 Joule-Thomson coefficient, 53 Joule-Thomson expansion, 53 K Kelvin equation, 208 Kelvin scale, Kinetic energy, rotational, 330 Kinetic theory of gases, 613 Kinetics, 611 in the liquid phase, 724 Klystron, 474 Kronecker delta, 303 L Langmuir adsorption isotherm, 843 assumptions, 846 for a mixture, 844 Laplacian operator, 317, 330 Laplacian, 301, 892 Larmor frequency, 538, 541, 542 Laser, 461, 523 chemical, 526 gas, 525 solid state, 524 Late barrier, 695 Lattice, 804 Laws of thermodynamics: first, 30 second, 74 third, 74, 92 zeroth law, LCAO molecular orbital, 398 Le Chaˆtelier’s principle, 146, 150 Legendre transform, 105, 267, 889 complete, 124 to introduce pH as an independent variable, 267 Lennard-Jones potential, 427, 429, 600, 631 Lever rule, 187 Lifetime, 463 of an excited molecule, 707 singlet, 708 total radiative, 463 Light amplification, 523 Light scattering, 781 Light: elliptically polarized, 532 plane polarized, 532 Line integral, 32 Linear operator, 304 Linear superposition, 309 Liquid crystals, 829 Liquids, structure, 828 Liquid-vapor equilibrium, 185 Logarithms, 884 London force, 428 Lone-pair electrons, 418 Lorentzian, 558 Low energy electron diffraction (LEED), 847 Lowest unoccupied molecular orbital (LUMO), 421 M Maclaurin series, 19, 885 Macromolecules, size and shape, 763 Macroscopic dissociation constants, 280 Magic-angle spinning, 561 Magnetic dipole moment, 363, 366 transitions, 542 vector, 795 Magnetic domains, 800 Magnetic field, 540, 795 rotating, 544 Magnetic flux density, 363, 540, 795 Magnetic properties, of nuclei, 538 Magnetic quantum number, 334 Magnetic resonance, spectroscopy, 537 Magnetic susceptibility, 364, 796 table, 797 units, 798 Magnetization, 542, 795 Magnetogyric ratio, 363, 538, 540 Mark-Houwink equation, 777 Mass average molar mass, 764, 773 Mass fractions, of polymers, 775 Mathematical applications, 895 MathematicaR , 895 Matrices, 163, 892 for a reaction system, 167 Matrix representations, 448 Index of a rotation, 451 Maxwell distribution of speeds, 617 Maxwell relations, 104, 109 applications, 125 Maxwell-Boltzmann distribution, 616 Mean free path, 630 Mean ionic activity coefficient, 228, 230 of hydrochloric acid, 232 of electrolytes, 233 Mean ionic molality, 228 Mean relative speed, 627 Mean speed, 620 Mean-square end-to-end distance, 769 Mechanisms, of chemical reactions, 659 Meissner effect, 831 Melting temperature, of DNA, 283 Membrane potential, 246 Metallic bonds, 825 Metastable states, 389 Michaelis constant, 747 Michaelis-Menten equation, 746 Microcanonical ensemble, 598 Microscopic dissociation constants, 280 Microscopic reversibility, 655 Microwave spectrometer, 473 Miller indices, 809 Mirror plane, 440 Mixing ideal gases, thermodynamic properties, 123 Mobility, of an ion, 730 Molar absorption coefficient, 512 Molar magnetic susceptibilities, 797, 799 Molar mass distributions, 772 Molar mass, from osmotic pressure, 765 from sedimentation and diffusion, 780 mass average, 764 number average, 764 of hemoglobin, 780 Molar polarization, 790 Mole fraction, 11 of a pseudoismer in a pseudoisomer group, 272 of polymers, 775 Mole, Molecular beam: experiments, 702 supersonic, 703 Molecular crystals, 825 Molecular electronic structure, 396 Molecular orbitals: bonding, 399 LCAO, 398 of hydrogen molecule, 407 theory, 398 Molecular properties, of gases (table), 590 Molecularity, 659 Moment of inertia, 329, 335, 469 Momentum, of a photon, 298 Monatomic ideal gas: thermodynamic properties, 52 translational energy, 52 Monod-Wyman-Changeux model, 752 Monolayer, 843 Morse potential, 482 Most probable speed, 620 Multilayer adsorption (BET), 847 Multiple unit cells, 804 Multiplicity, 552 Mutual exclusion rule, 495 N Nanocrystal, 835 Naperian molar absorption coefficient, 512 Natural logarithm, 43 Natural variables, 103, 108 Nematic liquid crystals, 829 Nernst equation, 226 Neutron diffraction, 813 Neutrons, thermal, 813 Newton, SI unit, 31 Newton’s law, 693 Newton-Raphson calculation, 143 Nonbonding molecular orbitals, 517 Nonideal gases, in statistical mechanics, 599 Nonideal mixture, vapor pressure, 192 Nonspontaneous processes, 75 Normal coordinates, 488 Normal modes of vibration, 486, 488 Normalization factor, 303 Normalized wave function, 303 Nuclear g factor, 539 Nuclear magnetic moment, 539 Nuclear magnetic relaxation, 556 Nuclear magnetic resonance (NMR), 541, 537, 540 energy levels, 540 frequency, 541 two-dimensional, 560 Nuclear magnetism, 538 Nuclear magneton, 539 Nuclear spin, table, 538 Null space, 164, 894 Number average degree of polymerization, 772 Number average molar mass, 764 939 Number of degrees of freedom, 22, 157 Number of different phases, 22, 156 Number of independent chemical reactions, 156, 167 Number of independent properties, 158 Number of independent variables, 22, 157 Number of microscopic states, 571 Number of normal modes of vibration, 488 Number of variables, to describe a system, 22, 36 O Oblate top, 470 Octahedral complex, 518 One-electron atoms, contour surfaces, 360 Operator, 304 for the square of the angular momentum, 333 Hamiltonian, 304 Hermitian, 306 linear, 305 quantum mechanical, 306 Optical activity, 529 and symmetry, 448 Optical rotation, 529 Optical rotatory dispersion, 532 Orbital angular momentum, 355, 366, 797 of the hydrogenlike atom, 361 quantum numbers, 411 Orbital radius, 378 Orbital, 356 antibonding, 402 bonding, 402 Greek letter, 405 Order of reaction, 644 Order of a rotation, 439 Orientation polarization, 789 Orthogonal wavefunction, 303 Orthohydrogen, 584 Orthonormal wavefunction, 303 Oscillating chemical reactions, 752 Oscillator strength, 516 Oscillator, harmonic, 322 Osmotic pressure, 200 colloid, 767 of polymer solutions, 764 total, 767 virial equation, 201 Overall order, 644 Overlap integral, 399 940 Index Ozone layer: destruction by chlorine atoms, 714 in the stratosphere, 712 Ozone, decomposition of, 661 P Pair correlation function, 828 Pair interaction potential, 766 Pairs of molecular orbitals from pairs of atomic orbitals, 406 Parahydrogen, 584 Parallel reactions, 655 Paramagnetism, 563, 797 Parity, 388, 399 Partial molar entropy, 180 Partial molar Gibbs energy, 108 Partial molar properties, 23, 180 Partial molar volume, 23 Partial pressure, 11 Particle, in a one-dimensional box, 311 Particle, in a three-dimensional box, 317 Partition function: for an ideal gas, 573 single molecule, 572 Pascal unit of pressure, Pascal’s triangle, 552 Paschen series, 354 Path between two states, 36 Pauli exclusion principle, 371, 374 Pauli principle, 408 Peak speed, 703 Periodic table, 377 Permittivity: of vacuum, 219, 349, 787, 796 relative, 788 table, 788 Perovskite structure, 832 pH, 243 as an independent variable, 267 dependence on ionic strength, 257 Phase diagrams: for one-component systems, 178 for two-component systems, 202 Phase difference, 820 Phase equilibrium, 177 Phase problem, 822, 824 Phase rule, 155, 158 Phase transition: first order, 180 second order, 181 Phosphorescence, 519, 521 quantum yield, 709 spectrum, 522 Photochemical reactions, 710 Photochemistry, 686 principles, 704 Photodissociation coefficient, 713 Photoelectron spectroscopy (PES), 527, 849 Photoelectrons, 527 Photons, 296 Photosynthesis, 718 Physical adsorption, 842 Physical chemical data, list of tables, 868 Physical constants, values, 867 Physical quantities, 5, 863 pK, 255 of weak acids as a function of ionic strength, 258 table, 880 Planck’s blackbody distribution law, 462 Planck’s constant, 297 Point group symmetry, 438 Point group, of a molecule, identification, 443, 444, 445, 447 table, 806 Point of inflection, 17 Poiseuille equation, 725 Poisons, 854 Polarizability, 492 ellipsoid, 493 of a dielectric, 789 table, 791 Polarization, 787 distortion, 789 molar, 790 of a dielectric, 786 orientation, 789 Polarized light, circularly polarized, 529 Polyatomic molecules, electronic spectra, 517 Polymer chain, spatial configuration, 767 Polymer, molar mass, 202 Polymerization: free radical, 772 step-growth, 772 Polyprotic acids, statistical effects, 284 Population inversion, 462, 523 Population: of rotational states, 486 of vibrational levels, 478 Postulates of quantum mechanics, 336 Potential barrier, for adsorption, 843 Potential difference, 45 Potential energy: for a diatomic molecule, 475 for Cl2 , 477 for HCl, 482 for hydrogen molecules, 410 intermolecular, 429 surface, 690 of rotation around an axis, 771 Potentiometer, 223 Power series, 12 Precision of measurement, and commutability, 321 Precursor state, 853 Predissociation, 511 Pre-exponential factor, 657 for bimolecular reactions, 700 Pressure: in SI units, of an ideal gas, 623 partial, 11 Primary kinetic salt effect, 742 Primitive cubic lattice, 814 Primitive unit cell, 804 Principal axes, 440, 470, 471 Principal moments of inertia, 470 Principle of detailed balance, 656 Principles of photochemistry, 704 Probability density, 302, 310, 313, 326, 614 for a random walker, 768 for molecular speeds, 613 in terms of energy, 619 joint, 615 of various speeds, 618 Probability, 302 Processes: adiabatic, 32 endothermic, 56 exothermic, 56 in an isolated system, 78 irreversible, 79 nonspontaneous, 75 spontaneous, 75 types, 79 Products of inertia, 470 Prolate top, 470 Promoters, 854 Propagation reactions, 677 Proper rotation axis, 438 Proteins: denaturation, 280 structure, 280 physical constants, 780 Proton: charge, 220 chemical shift, 549 spins, 542 spin-spin coupling constants, 551 Pseudoisomer group, 272 Index Pulse length, 544 Pulse mode, 524 Pulse sequences, 560 P-V-T surface, 15 Pythagorean theorem, 627 Q Quantized energy levels, 311 Quantum confined structure, 833 Quantum dot, 835 absorption spectra, 836 Quantum mechanical harmonic oscillator, 325 Quantum mechanical operator, 306 Quantum mechanics, 296 postulates, 336 Quantum number: for angular momentum, 331, 334, 355 for spin, 365 magnetic, 334 vibrational, 325 Quantum theory, 295 Quantum well, 833 Quantum wire, 834 Quantum yield, 705 for fluorescence, 708 for phosphorescence, 709 of photochemical reactions, 710 Quasistatic, 32 Quenching process, 709 R Radial functions, 356 Radial probability densities, 376 for the hydrogen atom, 358 Radiant energy density, 297, 340, 460 Radiative lifetime, 464 Radius of curvature, 209 Radius of gyration, 771 Raman apparatus, 492 Raman spectra, 491 resonance, 496 of CO2 , 494 Raman transitions, selection rules, 503 Random walk, 768 Rank of a matrix, 165 Raoult’s law, 186 Rate constant: for a diffusion-controlled reaction, 735 in terms of molecular partition functions, 699 of enzyme-catalyzed reactions, as a function of pH, 750 of ionic reactions, 742 theoretical calculation, 692 Rate: of absorption, of photons, 460 of conversion, 642 of desorption, 843 of reaction, 642 of heterogeneous reaction, 854, 855 of intermolecular energy transfer, 706 of ionization of water, 739 Rate-determining step, 662 Reaction cross section, 688 Reaction enthalpy, 57, 136 calculated from K as a function of T, 145 Reaction entropy, 136 Reaction Gibbs energy, 133, 137 under specified conditions, 135 Reaction heat capacity, 62 Reaction order, 644 Reaction probability, 693, 695 Reaction quotient, 135 Reaction rate, 642 initial, 648 Reaction: activation-controlled, 734 bimolecular, 659 diffusion-controlled, 734 first order, 645 heterogeneous, 154 oscillating, 752 parallel, 655 second order, 646 trimolecular, 659 unimolecular, 659 zero order, 647 Reduced mass, 330, 349 Reduction potentials, 239 Reduction reaction, 222 Reference state, 60 Reflection operation, 440 Refractive index, 792 frequency dependence, 794 Relative humidity, 11 Relative permeability, 796 Relative permittivity, 219 as a function of frequency, 794 of HCl, 792 Relative velocity, 688 Relative viscosity, 776 Relaxation methods, 736 Relaxation time, 646 for a one-step reaction, 738 nuclear magnetic, 556 Renaturation of DNA, 283 Representations: in symmetry, 449 941 irreducible, 450 Resistivity, 731 Resonance integral, 401 Resonance Raman spectroscopy, 496 Resonance signal, 544 Resonate cavity, 524 Reversible adiabatic expansion, of an ideal monatomic gas, 55 Reversible first-order reactions, 650 Reversible process, 42 Rhodopsin, 719 Rigid rotor, 329 Root-mean-square speed, 620 Rotation operation, 439 Rotational constant, 466 Rotational contributions to the thermodynamic properties of an ideal gas, 583 Rotational energy, 330 linear molecule, 472 spherical top, 471 symmetric top, 472 Rotational levels of diatomic molecule, 466 Rotational spectroscopy, 458 of diatomic molecules, 465 of polyatomic molecules, 469 Rotational symmetry, 806 Rotational temperature, characteristic, 583 Rotatory dispersion, 530 RRKM theory, 670, 700 Russell-Saunders coupling, 384 Rydberg constant, 353 in electron volts, 354 S Sackur-Tetrode equation, 85, 578 Saddle point, 690, 698 Scalar product, 332, 891 Scalar sum, 381 Scanning tunneling microscopy (STM), 851 Scattering factor, 819 Scattering of X-rays from a unit cell, 819 Scattering of plane-polarized light, 782 Schoenflies groups, 443 Schoenflies symbols, table, 806 Schrodinger equation, 301 for hydrogen-like atoms, 349 for nuclear motion, 464 for the hydrogenlike atom, in atomic units, 391 time-dependent, 337 942 Index time-independent, 302 Screw axis, 808 Second law of thermodynamics, 74, 77 mathematical statement, 77 two parts, 78 Second order spectrum, 552 Second virial coefficient, 13 Second-order phase transition, 181 Second-order rate constant: for a reaction of two small radicals, 687 for a reaction of two spherical molecules, 689 Second-order reaction, 646 Sedimentation coefficient, 779 Selection rules, 387, 460, 463 for electronic spectroscopy, 504 for rotational spectra, 467 Semiconductor quantum well, 834 Semipermeable membranes, 200 Separability, of a Hamiltonian, 320 Series, 885 Shell, 376 Shielding constant, 547 Shock tube, 644 SI system of units, 863 Sigma bond framework, 420 Single-molecule partition function, 572 for an ideal gas, 574 Singlet lifetime, 708 Slater determinant, 372 Smectic liquid crystals, 829 Solid solutions, 205 Solid, one-dimensional, 432 Solid-state chemistry, 803 Solubility, in ideal solutions, 304 Solution, of simultaneous linear equations, 893 Solvents, “good” and “poor”, 765 Space group, 808 Space lattices, 807 Special point groups, 446 Specific rotation, 531 Specific viscosity, 776 Spectral radiant energy density, 460 Spectrometer, UV-visible, 512 Spectroscopic dissociation energy, 479 Spectroscopy: basic ideas, 459 photoelectron, 527 Raman, 491 rotational, 458 ultraviolet photoelectron (UPS), 527 vibrational, 458 X-ray photoelectron (XPS), 527 Spectrum: of hydrogen atoms, 353 vibrational, 475 Specular reflection, 623 Speed of light, 297 in a medium, 793 Speed, 614 mean, 620 most probable, 620 of sound, 621 root-mean-square, 620 Spherical coordinates, 331, 887 Spherical harmonics, 331 Spherical top, 470 Spin angular momentum, 365, 382 Spin multiplicity, 384 Spin quantum number, 365 of a solid, 798 of molecular oxygen, 799 Spin, electron, 362, 364 Spin-echo techniques, 559 Spin-lattice relaxation, 557 Spin-orbit coupling, 387 Spin-spin coupling: direct, 550 indirect, 550 of protons, 551 Spin-spin splitting, 552 Splitting of energy levels, 364 Spontaneous processes, 75 in an isolated system, 78 Standard deviation, 300, 311, 729 for a particle in a box, 315 Standard electrode potentials, 239 table, 240 Standard electromotive force of a cell, 226 Standard enthalpy of an ionic reaction: as a function of ionic strength, 238 as a function of temperature, 62 Standard enthalpy of formation, 60 as a function of ionic strength, 238 of an isomer group, 162 Standard enthalpy of reaction, 61 as a function of temperature, 61 calculation of, 146, 147 Standard Gibbs energy of an ionic reaction,, 238 Standard Gibbs energy of formation, 143 of an ion as a function of ionic strength, 238 of an isomer group, 162 Standard molar entropies of ions, 237 Standard reaction Gibbs energy, 135 Standard states, 58 Standard thermodynamic properties: of ions, 234 of reactions of ions, 235 of a species, 271 Standard transformed enthalpy, of a pseudoisomer group, 272 Standard transformed Gibbs energies: of formation at various pHs, 274 of hydrolysis, 277 of pseudoisomer group, 272 of species, as a function of ionic strength, 271 Standard transformed properties, calculation of, 271 Stark effect, 474 State functions, 76 State of a system, extensive, 156 intensive, 156 State of an ideal gas, reversible changes, 76 State variables, State: macroscopic, microscopic, Stationary state wavefunction, 303 Statistical effects, in polyprotic acids, 284 Statistical mechanics, 568 Statistical probability, and entropy, 88 Steady-state approximation, 652 Steady-state method, 660 Step-growth polymerization, 772 Stern-Volmer equation, 710 Sticking coefficient, 843 Stirling’s approximation, 573 Stoichiometric number matrix, 164 Stoichiometric number of the electron, 226 Stoichiometric number, 57, 642 Stokes lines, 491 Structural pattern, 804 Structure factor, 820 Structure, of liquids, 828 Subshell, 376 Superconductivity, 830 Supermolecule, 690 Superposition, 309, 340 linear, 309 state, 310 Supersonic molecular beam, 703 Surface area, determination of, 845 Surface coverage, 843 Surface dynamics, 840 Index Surface reactions, theory, 852 Surface reconstruction, 856 Surface tension, 44 effect on vapor pressure, 205 of some liquids, 206 Surface work, 45 Surface, of a solid, 857 Surroundings, in thermodynamics, Susceptibility, electric, 788 Svedberg unit, 779 Symbols, for physical quantities, 899 Symmetric top, 470, 472 Symmetric wave functions, 371 Symmetry element, 438 Symmetry number, 584 Symmetry of crystals, 805 Symmetry operations, 438 applied to wavefunctions, 453 multiplication, 450 Symmetry plane, 438, 440 Symmetry, 437 System: closed, isolated, open, T Taylor series, 475 Temperature scale: ideal gas, Kelvin, Temperature, theta, 766 Temperature-jump apparatus, 738 Tensor, 493 Term symbol, of a molecule, 411 Term values, 465 Termination reactions, 677 Tesla, 795 Test for exactness, 37 Theoretical plates, 192 Thermal conduction, in gases, 633 Thermal equilibrium, Thermal neutrons, 813 Thermal wavelength, 576 Thermochemistry, 56 Thermodynamic equilibrium constant, 137 Thermodynamic potentials, 105 Thermodynamic properties: acid dissociation, 256 at several temperatures, table, 874 from statistical mechanics, 588 of a monatomic ideal gas, 52 of species in biochemical reactions, 266 table, 870 Thermodynamic standard states, 58 Thermodynamic temperature, Thermodynamic variables, Thermodynamics of isomer groups, 161 Theta temperature, 766 Third law of thermodynamics, 74, 92 and the calculation of equilibrium constants, 94 apparent deviations, 93 Third virial coefficient, 13 Tie line, 16, 187 Time domain, 545 Time-dependent Schrodinger equation, 337 Titration curve, of a weak acid, 259 Total angular momentum, 333 of an atom, 383 Total osmotic pressure, 767 Total spin angular momentum, 538 Trajectory of a molecular collision, 694 Transformed chemical potential, 268 in a phase with an electric potential, 221 Transformed enthalpy, 269 Transformed entropy, 269 Transformed Gibbs energy, 267 as a criterion for equilibrium, 267 fundamental equation, 268, 270 in a phase with an electric potential, 221 Transistor, 833 Transition dipole moment, 462 Transition moment, 464, 508 Transition state theory, 697 Transition state, 691 Transition-state spectroscopy, femtosecond, 714 Translational contributions to the properties of an ideal gas, 576 Translational partition function, 576 for a hydrogen atom, 576 Transmittance, 511 Transport coefficients, in gases, 635 Transport phenomena in gases, 632 Transpose of a matrix, 166 Trial wave function, 368 Trimolecular reaction, 659, 670 rate constants, 672 Triple point, 15 of water, Triplet state, 374, 521, 563 Tunneling, 326, 338 Turbidity, 781 Turnover number, 747 943 Two-dimensional NMR, 560 U Ultracentrifuge, 779 Ultraviolet photoelectron spectroscopy (UPS), 527, 850 Unbranched chain reactions, 674 Uncertainty principle, 299 Unimolecular reaction, 659, 667 Unit cell, 804 body centered, face centered, end centered, 808 of NaCl, 815 primitive, 804 multiple, 804 United atom, 412 Units: atomic, 390 derived, 864 non-SI, 865 of physical quantities, 863 supplementary, 864 V Valence band, 833 Valence bond method, 416 Valence electrons, 385 van der Waals constants, 18 in terms of critical constants, 20 van der Waals equation, 17 van der Waals forces, 428 Van’t Hoff equation, 145 Vapor pressure, 16, 182 effect of radius of curvature, 209 effect on surface tension, 205 from effusion, 625 of a nonideal mixture, 192 of ice and water, 184 Variables: extensive, intensive, state, thermodynamic, Variance, 311 Variational method, 368, 409 Vector force, 31 Vector product, 891 Vectors, 891 Velocity distribution, 615 Velocity gradient, 635 Velocity vector, 614 Vibrational and rotational levels, of diatomic molecules, 484 Vibrational contributions to the properties of an ideal gas, 580 944 Index Vibrational coordinates, 464 Vibrational degrees of freedom, 465 Vibrational quantum number, 325 Vibrational spectra, 458 of diatomic molecules, 475 of HCl, 477 of polyatomic molecules, 486 characteristic, 580 Vibrational term value, 476 Vibration-rotation coupling constant, 485 Vibration-rotation spectra, of diatomic molecules, 483 Virial coefficients: from Lennard-Jones potential, 600 relations between, 13 Virial equation, 11 for a van der Waals gas, 19 Virial expansion, 765 Viscosity, 634 of a liquid, 725 of DNA solution, 778 of water, 726 intrinsic, 776 relative, 776 specific, 776 Viscous flow, in gases, 633 Vision, 718 Volume, of a unit cell, 809 W Water, lone-pair electrons, 418 Watson-Crick base pairs, 283 Wave function, 301 symmetric, 372 Wave number, 353, 459 Wave packet, 299, 340, 715 in a parabolic barrier, 342 Wavefunction: antisymmetric, 372 for a particle in a three-dimensional box, 318 normalized, 303 orthogonal, 303 orthonormal, 303 Wavelength, of a particle, 299 Weak acids: dissociation, 255 practical calculations, 257 Web addresses, 898 Wien displacement law, 340 Work, 31 conjugate pairs, 45 electric, 45 from a reversible isothermal expansion, 43 hydrostatic, 45 of adiabatic expansion, 54 of elongation, 45 of compression, 39 of expansion, 39, 44 SI unit, 31 sign convention, 33 various kinds, 44 X X-ray photoelectron spectroscopy (XPS), 527, 850 Z Zeeman effect, 364 Zero matrix, 164 Zero point energy, 311, 325, 580 Zero-order reaction, 647 Zeroth law of thermodynamics, 3, PHYSICAL CONSTANTSa (ROUNDED TO FOUR SIGNIFICANT FIGURES) Quantity Symbol Value Speed of light in vacuum Permeability of vacuum c ␮0 Permittivity of vacuum ⑀0 Planck constant h /2␲ Elementary charge Bohr magneton Nuclear magneton Rydberg constant Bohr radius Hartree energy Electron mass Proton mass Neutron mass Deuteron mass Avogadro constant Atomic mass constant Faraday constant Gas constant h ប e ␮B ␮N Rϱ a0 Eh me mp mn md NA mu F R Boltzmann constant Acceleration due to gravity k g 2.998 ϫ 108 m sϪ1 (exact) 4␲ ϫ 10Ϫ7 N AϪ2 (exact) Ϸ 12.57 ϫ 10Ϫ7 N AϪ2 1/␮0 c (exact) Ϸ 8.854 ϫ 10Ϫ12 C2 NϪ1 mϪ2 6.626 ϫ 10Ϫ34 J s 1.055 ϫ 10Ϫ34 J s 1.602 ϫ 10Ϫ19 C 9.274 ϫ 10Ϫ24 J TϪ1 5.051 ϫ 10Ϫ27 J TϪ1 1.097 ϫ 107 mϪ1 5.292 ϫ 10Ϫ11 m 4.360 ϫ 10Ϫ18 J 9.109 ϫ 10Ϫ31 kg 1.673 ϫ 10Ϫ27 kg 1.675 ϫ 10Ϫ27 kg 3.344 ϫ 10Ϫ27 kg 6.022 ϫ 1023 molϪ1 1.661 ϫ 10Ϫ27 kg 9.649 ϫ 104 C molϪ1 8.315 J KϪ1 molϪ1 8.315 ϫ 10Ϫ2 L bar KϪ1 molϪ1 1.987 cal KϪ1 molϪ1 8.206 ϫ 10Ϫ2 L atm KϪ1 molϪ1 1.381 ϫ 10Ϫ23 J KϪ1 9.806 65 m sϪ2 a The best values and their uncertainties are given in Appendix B SOME NUMERICAL CONSTANTS AND CONVERSION FACTORS ␲ ‫ ס‬3.141 592 65 e ‫ ס‬2.718 281 828 ln x ‫ ס‬log x / log e ‫ ס‬2.302 585 09 log x 101 325 N mϪ2 atmϪ1 105 N mϪ2 barϪ1 1.013 25 bar atmϪ1 2.54 cm inchϪ1 453.6 g lbϪ1 4.184 J calϪ1 (exactly) 1.602 ϫ 10Ϫ19 J eVϪ1 10Ϫ3 m3 LϪ1 133.32 Pa torrϪ1 .. .Physical Chemistry Fourth Edition Robert J Silbey Class of 1942 Professor of Chemistry Massachusetts Institute of Technology Robert A Alberty Professor Emeritus of Chemistry Massachusetts... number of credits in physical chemistry courses, and therefore the need for more advanced material, varies at different universities and colleges, more topics have been included in this edition than... in four editions The next four editions were written by Farrington Daniels In 1955, Robert Alberty joined Farrington Daniels At that time, the name of the book was changed to Physical Chemistry,