lev38627_fm.qxd 4/9/08 12:32 PM Page i PHYSICAL CHEMISTRY lev38627_fm.qxd 4/9/08 12:32 PM Page ii lev38627_fm.qxd 4/9/08 12:32 PM Page iii PHYSICAL CHEMISTRY Sixth Edition Ira N Levine Chemistry Department Brooklyn College City University of New York Brooklyn, New York lev38627_fm.qxd 4/9/08 12:32 PM Page iv PHYSICAL CHEMISTRY, SIXTH EDITION Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY 10020 Copyright © 2009 by The McGraw-Hill Companies, Inc All rights reserved Previous editions © 2002, 1995, 1988, 1983, and 1978 No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning Some ancillaries, including electronic and print components, may not be available to customers outside the United States This book is printed on recycled, acid-free paper containing 10% postconsumer waste QPD/QPD ISBN 978–0–07–253862–5 MHID 0–07–253862–7 Publisher: Thomas Timp Senior Sponsoring Editor: Tamara L Hodge Director of Development: Kristine Tibbetts Senior Developmental Editor: Shirley R Oberbroeckling Marketing Manager: Todd L Turner Project Coordinator: Melissa M Leick Senior Production Supervisor: Sherry L Kane Senior Designer: David W Hash Cover Designer: Ron E Bissell, Creative Measures Design Inc Supplement Producer: Melissa M Leick Compositor: ICC Macmillan Inc Typeface: 10.5/12 Times Printer: Quebecor World Dubuque, IA Library of Congress Cataloging-in-Publication Data Levine, Ira N Physical chemistry / Ira N Levine 6th ed p cm Includes index ISBN 978–0–07–253862–5 - ISBN 0–07–253862–7 (hard copy : alk paper) Chemistry, Physical and theoretical I Title QD453.3.L48 2009 541 dc22 2008002821 www.mhhe.com lev38627_fm.qxd 4/9/08 12:32 PM Page v To the memory of my mother and my father lev38627_fm.qxd 4/9/08 12:32 PM Page vi Table of Contents Preface Chapter xiv THERMODYNAMICS 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 Chapter Chapter vi Physical Chemistry Thermodynamics Temperature The Mole Ideal Gases Differential Calculus Equations of State Integral Calculus Study Suggestions Summary 1 10 17 22 25 30 32 THE FIRST LAW OF THERMODYNAMICS 37 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 37 42 46 47 52 53 55 58 62 65 67 70 73 Classical Mechanics P-V Work Heat The First Law of Thermodynamics Enthalpy Heat Capacities The Joule and Joule–Thomson Experiments Perfect Gases and the First Law Calculation of First-Law Quantities State Functions and Line Integrals The Molecular Nature of Internal Energy Problem Solving Summary THE SECOND LAW OF THERMODYNAMICS 78 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 78 80 85 87 93 96 97 103 104 The Second Law of Thermodynamics Heat Engines Entropy Calculation of Entropy Changes Entropy, Reversibility, and Irreversibility The Thermodynamic Temperature Scale What Is Entropy? Entropy, Time, and Cosmology Summary lev38627_fm.qxd 4/9/08 12:32 PM Page vii vii Chapter MATERIAL EQUILIBRIUM 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 Chapter STANDARD THERMODYNAMIC FUNCTIONS OF REACTION 5.1 5.2 5.3 5.4 115 123 125 129 132 134 135 140 143 151 153 155 161 163 165 168 169 REACTION EQUILIBRIUM IN IDEAL GAS MIXTURES 174 6.1 6.2 6.3 6.4 6.5 6.6 6.7 Chapter 109 110 112 Standard States of Pure Substances Standard Enthalpy of Reaction Standard Enthalpy of Formation Determination of Standard Enthalpies of Formation and Reaction Temperature Dependence of Reaction Heats Use of a Spreadsheet to Obtain a Polynomial Fit Conventional Entropies and the Third Law Standard Gibbs Energy of Reaction Thermodynamics Tables Estimation of Thermodynamic Properties The Unattainability of Absolute Zero Summary 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 Chapter Material Equilibrium Entropy and Equilibrium The Gibbs and Helmholtz Energies Thermodynamic Relations for a System in Equilibrium Calculation of Changes in State Functions Chemical Potentials and Material Equilibrium Phase Equilibrium Reaction Equilibrium Entropy and Life Summary 109 Chemical Potentials in an Ideal Gas Mixture Ideal-Gas Reaction Equilibrium Temperature Dependence of the Equilibrium Constant Ideal-Gas Equilibrium Calculations Simultaneous Equilibria Shifts in Ideal-Gas Reaction Equilibria Summary ONE-COMPONENT PHASE EQUILIBRIUM AND SURFACES 7.1 7.2 7.3 7.4 The Phase Rule One-Component Phase Equilibrium The Clapeyron Equation Solid–Solid Phase Transitions 140 141 142 175 177 182 186 191 194 198 205 205 210 214 221 Table of Contents lev38627_fm.qxd 4/9/08 12:32 PM Page viii viii 7.5 7.6 7.7 7.8 7.9 7.10 Table of Contents Chapter REAL GASES 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 8.10 Chapter Compression Factors Real-Gas Equations of State Condensation Critical Data and Equations of State Calculation of Liquid–Vapor Equilibria The Critical State The Law of Corresponding States Differences Between Real-Gas and Ideal-Gas Thermodynamic Properties Taylor Series Summary SOLUTIONS 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 Chapter 10 Higher-Order Phase Transitions Surfaces and Nanoparticles The Interphase Region Curved Interfaces Colloids Summary Solution Composition Partial Molar Quantities Mixing Quantities Determination of Partial Molar Quantities Ideal Solutions Thermodynamic Properties of Ideal Solutions Ideally Dilute Solutions Thermodynamic Properties of Ideally Dilute Solutions Summary NONIDEAL SOLUTIONS 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 10.10 10.11 Activities and Activity Coefficients Excess Functions Determination of Activities and Activity Coefficients Activity Coefficients on the Molality and Molar Concentration Scales Solutions of Electrolytes Determination of Electrolyte Activity Coefficients The Debye–Hückel Theory of Electrolyte Solutions Ionic Association Standard-State Thermodynamic Properties of Solution Components Nonideal Gas Mixtures Summary 225 227 227 231 234 237 244 244 245 247 249 252 254 255 256 257 259 263 263 264 270 272 275 278 282 283 287 294 294 297 298 305 306 310 311 315 318 321 324 lev38627_fm.qxd 4/9/08 12:32 PM Page ix ix Chapter 11 REACTION EQUILIBRIUM IN NONIDEAL SYSTEMS 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 11.10 11.11 Chapter 12 MULTICOMPONENT PHASE EQUILIBRIUM 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 12.10 12.11 12.12 12.13 Chapter 13 The Equilibrium Constant Reaction Equilibrium in Nonelectrolyte Solutions Reaction Equilibrium in Electrolyte Solutions Reaction Equilibria Involving Pure Solids or Pure Liquids Reaction Equilibrium in Nonideal Gas Mixtures Computer Programs for Equilibrium Calculations Temperature and Pressure Dependences of the Equilibrium Constant Summary of Standard States Gibbs Energy Change for a Reaction Coupled Reactions Summary Colligative Properties Vapor-Pressure Lowering Freezing-Point Depression and Boiling-Point Elevation Osmotic Pressure Two-Component Phase Diagrams Two-Component Liquid–Vapor Equilibrium Two-Component Liquid–Liquid Equilibrium Two-Component Solid–Liquid Equilibrium Structure of Phase Diagrams Solubility Computer Calculation of Phase Diagrams Three-Component Systems Summary ELECTROCHEMICAL SYSTEMS 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 13.10 13.11 13.12 13.13 13.14 13.15 13.16 Electrostatics Electrochemical Systems Thermodynamics of Electrochemical Systems Galvanic Cells Types of Reversible Electrodes Thermodynamics of Galvanic Cells Standard Electrode Potentials Liquid-Junction Potentials Applications of EMF Measurements Batteries Ion-Selective Membrane Electrodes Membrane Equilibrium The Electrical Double Layer Dipole Moments and Polarization Bioelectrochemistry Summary 330 330 331 332 337 340 340 341 343 343 345 347 351 351 351 352 356 361 362 370 373 381 381 383 385 387 395 395 398 401 403 409 412 417 421 422 426 427 429 430 431 435 436 Table of Contents lev38627_index.qxd 4/10/08 5:04 PM Page 980 980 Molecular weight—Cont viscosity average, 487 weight average, 487 Molecular-weight determination: from freezing-point depression, 354–355 for gases, 15 from mass spectrometry, 356 from osmotic pressure, 359–360 for polymers, 356, 359–360, 486–487, 493 from sedimentation speed, 493 Molecularity, 531 Møller–Plesset perturbation theory, 709 Moment(s) of inertia, 622–623, 745, 758–759 Momentum: angular See Angular momentum linear, 445, 647 Monochromatic radiation, 742 Monte Carlo calculations, 950–951 MOPAC2007, 721 Motif, 922 Moving boundary method, 500 MP perturbation theory, 709 MP2, 709 Multiplication table of a group, 803 Multiplicity, spin, 657 N Nagle electronegativity scale, 676 Nanometer (nm), 736 Nanoparticles, 227 Nanoscopic systems, 2–3, 8, 102 Nanotubes, 427, 475, 915–916 Natural logarithm, 29–30 Nernst–Einstein equation, 491 Nernst equation, 414–417, 421, 429 Nernst–Simon statement of third law, 156–157 Nerve cells, 490 Nerve impulse, 436 Neutron diffraction, 937 Newton, Isaac, 37 Newton (unit), 38 Newtonian fluid, 481 Newton’s law of viscosity, 480, 482, 485, 494 Newton’s second law, 38, 103, 599, 601 NIST-JANAF tables, 164, 174 NMR spectroscopy, 779–793 of biological molecules, 791 carbon-13, 788, 789 chemical shifts in, 784–785 classical description of, 792–793 of dimethylformamide, 790 double resonance in, 789 dynamic, 792 of ethanol, 785, 787–788 experimental setup in, 783–784, 788–789 first-order analysis in, 786–788 Fourier-transform, 788–789 and imaging, 792 intensities in, 784, 790 and protein structure, 791 proton, 784–788 and rate constants, 790 selection rule in, 782 of solids, 791 spin–spin coupling in, 785–788 two-dimensional, 791 No-slip condition, 480 Node, 609, 620, 683, 685, 692 Nonactivated adsorption, 578 Nondissociative adsorption, 571 Nonideal gases: chemical potential of, 321 enthalpy of, 149–150, 257 entropy of, 158, 257 equation of state of, 23, 245–247, 250–251 internal energy of, 875 internal pressure of, 119, 120 mixtures of, 232–233, 321–322 reaction equilibrium for, 340 thermodynamic properties of, 149–150, 158, 256–257 Nonideal solution(s), 294–321 activities in, 294–297 activity coefficients in See Activity coefficients chemical potentials in, 294–297 liquid–vapor equilibrium for, 368–369 reaction equilibrium in, 330–339, 340–343 reaction rates in, 547–548, 907–908 standard states for components of, 295–297 vapor pressure of, 298–302, 368–369 Noninteracting particles in quantum mechanics, 618–619 Non-Newtonian fluid, 481 Nonpolar molecule, 432 Normal boiling point, 210 Normal distribution, 99, 455 Normal melting point, 211 Normal modes, 763–765, 768 symmetry species of, 810 Normalization, 602–603, 605, 607–608, 624, 650 Normalization constant, 603, 608 nth-order reaction, 523 Nuclear g factor(s), 781 table of See inside back cover Nuclear magnetic dipole moment, 781–782 Nuclear-magnetic-resonance spectroscopy See NMR spectroscopy Nuclear magneton, 782 Nuclear Overhauser effect (NOE), 790 Nuclear spin(s), 749–750, 781–783 energy levels of, 782 and entropy, 859 and rotational levels, 749–750, 760 table of See inside back cover Nuclear wave function, 679, 744–746 Nucleus, 638 Number average molecular weight, 360, 486–487 Numerical integration, 539–541 O Octanol/water partition coefficient, 372–373 Odd function, 684, 693 Ohm, 495 Ohm’s law, 495 Onsager conductivity equation, 507–509 Open system, 4, 47 Operator(s), 613–618 commutator of, 614 Coulomb, 664 electric dipole moment, 738 equality of, 613 exchange, 664 Hamiltonian, 615 See also Hamiltonian operator Hartree–Fock, 664, 692, 714 Hermitian, 627–630 Kohn–Sham, 712, 714 Laplacian, 615 linear, 616 momentum, 614 position, 614 product of, 613 square of, 613 sum of, 613 Oppenheimer, J R., 677 Optical activity, 794 lev38627_index.qxd 4/10/08 9:54 AM Page 981 981 Optical pyrometer, Optical rotatory dispersion, 795 Optimization, 724–725 Orbital(s), 651–652 antibonding, 684 atomic, 643–645, 651, 659, 663–665, 683 canonical, 696 crystal, 940–941 Hartree–Fock, 663–665, 687, 692–693 Kohn–Sham, 712, 713–714, 716 localized See Localized MOs molecular See Molecular orbital(s) pi, 684–685, 692, 693, 717 shape of, 643–644 sigma, 684–685, 692, 693, 717 Slater-type, 665, 708 virtual, 708 Orbital angular momentum, 647–649, 656 Orbital energy, 661–662, 664 Orbital exponent, 654, 665 ORCA, 721 Order–disorder transitions, 226 Order of a group, 801 Order of a matrix, 804 Order of a reaction, 517 determination of, 526–529 half-integral, 538 pseudo, 519 with respect to solvent, 519, 537 Ortho H2, 881 Orthogonal functions, 610, 628–629 Orthonormal set, 629 Oscillating reactions, 565–566 Osmosis, 360–361 Osmotic coefficient, practical, 311 Osmotic pressure, 356–361 definition of, 357, 358 of ideally dilute solution, 357 of nonideally dilute solutions, 358 Ostwald, Wilhelm, Ostwald viscometer, 483 Overall mole fraction, 362 Overall order, 517 Overlap integral, 682 Overtone bands, 753, 765 Oxidation, 407 Oxygen molecule, 689, 750, 845 Ozone in stratosphere, 566–567 P P branch, 754–755 Pair-correlation function, 947–948 Paired electrons, 660 Para H2, 881 Parallel spins, 657 Paramagnetism, 663 Parameter, 28, 677–678 Partial derivative(s), 20–22 Partial miscibility: between gases, 371 between liquids, 370–373 Partial molar enthalpy(ies), 268, 273–274 in ideal solution, 291 in ideally dilute solution, 292 Partial molar entropy(ies), 268, 274 in ideal solution, 291 in ideally dilute solution, 292 Partial molar Gibbs energy, 268 See also Chemical potentials Partial molar internal energy, 268 Partial molar quantities, 264–270 in ideal solution, 281, 291 in ideally dilute solution, 281, 292 measurement of, 267, 272–274 in nonideal solution, 292 relations between, 269–270 Partial molar volume(s), 265–268 in ideal gas mixture, 266, 270 in ideal solution, 291 in ideally dilute solution, 292 infinite-dilution, 268 measurement of, 267–268, 272–273 of pure substance, 266 Partial orders, 517 Partial pressure, 16, 186–187, 321 Partial specific volume, 492 Particle in a box: one-dimensional case, 606–610 selection rule for, 738–739 three-dimensional case, 610–612 two-dimensional case, 612 Partition coefficient, 372–373 Partition function See Canonical partition function; Electronic partition function; Molecular partition function; Rotational partition function; Semiclassical partition function; Translational partition function; Vibrational partition function Pascal (unit), 11, 12 Path of a process, 44, 62 Pauli, Wolfgang, 653, 659 Pauli exclusion principle, 659 Pauli repulsion, 689, 864, 881 Pauling, Linus, 675 Pauling electronegativity, 676 Peng–Robinson equation, 251, 254, 260 Perfect gas, 58–62, 69, 122 See also Ideal gases Period, 619 Periodic table, 660–662 Peritectic phase transition, 378 Peritectic point, 379 Peritectic temperature, 377–378 Permeability of vacuum, 780 Permeable wall, Permittivity, 434 relative, 433–434 of vacuum, 395, 637, 735 Perturbation theory, 626–627 of liquids, 948 Møller–Plesset, 709 pH, 425–426, 428 Phase, 5–6, 205 Phase change: continuous, 225–227 discontinuous, 225 enthalpy change for, 63, 213 entropy change for, 87–88, 90, 157, 213–214 first-order, 225, 227 Gibbs energy change for, 113 higher-order, 225–227 lambda, 226–227 order–disorder, 226–227 in polymers, 914 second-order, 225–226 work in, 63 Phase diagram(s): of carbon, 225 for CO2, 212 computer calculation of, 383–385 liquid–liquid, 370–373 liquid–solid, 373–380 liquid–vapor, 362–370 one-component, 210–212 structure of, 381 for sulfur, 221–222 three-component, 385–387 two-component, 361–385 for water, 211–212, 222, 223 Phase equilibrium, 109, 129–131, 205, 214, 361, 402 in electrochemical systems, 402–403 multicomponent, 361–387 one-component, 210–227 solid–solid, 221–225 lev38627_index.qxd 4/10/08 9:54 AM Page 982 982 Phase equilibrium—Cont three-component, 385–387 two-component, 361–385 Phase rule, 205–210 See also Degrees of freedom Phase transition See Phase change Phase-transition loop, 377, 381 Phosphorescence, 797 Photochemical kinetics, 798–800 Photochemical reactions, 796–797, 799 Photochemistry, 796–800 Photoconductivity, 941 Photoelectric effect, 593–594 Photon, 593–594, 595, 597, 650, 737, 796 Photophysical processes, 797 Photosensitization, 798 Photostationary state, 800 Photosynthesis, 796, 798 Physical adsorption, 570–571, 574, 575 Physical chemistry, 1–2 Physical constants, table of See inside back cover Physical kinetics, 474 Physisorption, 570–571, 574 Pi bond, 699–700 Pi orbitals, 705, 747, 855 Pitzer equations, 315, 317–318 pK, 337 Planck, Max, 592–593 Planck’s constant, 592, 600 Plane defects, 947 Plane-polarized wave, 735 Plane of symmetry, 756, 802 Plasma, 561 PM3 method, 719 PM5 method, 719 PM6 method, 719 Point defects, 946–947 Point groups, 802–803 Poise, 481 Poiseuille’s law, 483 Poison, 568, 576, 578 Polar molecule, 432 Polarizability, electric, 432, 434, 773, 862–863 Polarization, 432–434 Polarized wave, 735, 795 Polyatomic molecules: MO theory of, 693–702 rotation of, 758–763 statistical mechanics of ideal gas of, 851–854 vibration of, 763–770 Polyelectrolyte, 306, 503 Polyethylene, 936 Polymer(s), 914 formation of, 554–556 molecular weights of See Polymer molecular-weight determination solid, 913, 914, 916, 936 solutions of See Polymer solutions Polymer molecular-weight determination: from mass spectrometry, 356 from osmotic pressure, 359–360 from sedimentation speed, 493 from solution viscosity, 486–487 Polymer solutions, 235 sedimentation in, 492–493 viscosity of, 481, 486–487 Polymerization kinetics, 554–556 Polymorphism, 221 Pople, John, 708, 721, 727 Population inversion, 741–742 Population of vibrational and rotational levels, 749, 755 Potential difference See Electric potential difference(s) Potential energy, 40–41, 600 electrostatic, 637 gravitational, 40–41 intermolecular, 861–866 Potential-energy surfaces for reactions, 880–887 calculation of rate constants from, 887–889 for F ϩ H2, 885 for H ϩ H2, 881–885 semiempirical calculation of, 886–887 for unimolecular reactions, 904–905 Potentiometer, 408–409 Potentiometric titrations, 426 Powder x-ray diffraction method, 936–937 Powell plot, 528–529 Power, 39 Power plants, 84–85 Practical osmotic coefficient, 311 Precession, 792 Pre-exponential factor, 541–544 collision-theory expression for, 878–879 TST expression for, 900, 909 Pressure, difference of across curved interface, 232 of earth’s atmosphere, 466 effect of surface tension on, 230 and equilibrium constant, 342 high, 223–224 in interphase region, 230 kinetic-theory derivation of, 443–446 negative, 251–252 osmotic, 357–359 partial, 16, 186–187, 321 standard-state, 140, 163 statistical-mechanical expression for, 826–827, 846, 853, 869 units of, 11–12 Pressure equilibrium constant, 179 Pressure-jump method, 558 Primary kinetic salt effect, 908 Primary quantum yield, 800 Primitive unit cell, 924, 928 Principal axes of inertia, 758–759 Principal diagonal, 804–805 Principal moments of inertia, 758–759, 761, 851 Principal quantum number, 640 Printed electrodes, 412 Prions, 795 Probability(ies) See also Probability density in canonical ensemble, 823–825, 828 of chemical reaction, 889–890 and entropy, 98–101 of independent events, 99, 449 in quantum mechanics, 601–603 Probability density, 448, 601, 602, 605 calculation of, 707 in DFT, 711–712, 714 in H atom, 645–646 in H ϩ2 , 683 in solids, 934–935, 936 Problem solving, 70–72 Process, 62 adiabatic, 61, 62, 64 cyclic, 49, 62, 66 irreversible, 44, 45–46, 87, 89–90, 93–95 isobaric, 50, 62, 63 isochoric, 52, 53, 62 isothermal, 23, 60, 62, 88 reversible, 43, 62, 87, 93 Product notation, 178 Products of inertia, 758 Propagation steps, 552, 554 Protein Data Bank, 935 Proteins, 914 antifreeze, 355 lev38627_index.qxd 4/10/08 9:54 AM Page 983 983 charge on, 515 denaturation of, 342–343 electronic absorption spectra of, 777 electrophoresis of, 503, 504 IR bands of, 769 MD simulation of folding of, 950 molecular-weight, determination of, 356, 493 NMR spectra of, 791 ORD and CD spectra of, 795 structures of, 791, 914, 935 T-jump kinetics of folding of, 558, 769–770 Pseudo order, 519 Pulse oximeter, 741 Pulsed-field electrophoresis, 504 Pure-rotation spectra See Rotational spectra Q Q branch, 765 Quadratic formula, 188 Quadratic integrability, 605 Quadruple bond, 705 Quantization of energy, 592–596, 605, 607, 608 Quantum, 593 Quantum chemistry, 1, 590 Quantum chemistry calculations, performing, 720–723 Quantum mechanics, 590–632 Quantum number, 609, 612, 640 for spin, 649–650, 656–657 Quantum yield, 799–800 Quasicrystal, 913, 925 R R branch, 754–755 Radial distribution function: in H atom, 646 in liquids, 947–948 Radiation: electromagnetic, 591, 734–737 of heat, 47, 476 Radiationless deactivation, 797 Radical(s) See Free radical Radioactive decay, 521, 582 Raman-active vibration, 768, 773 Raman effect, 772 Raman shift, 772 Raman spectroscopy, 771–774 Random coil, 498 Raoult’s law, 280–281, 285, 286, 298, 299, 362 deviations from, 285–286, 299, 301 Rate coefficients See Rate constant(s) Rate constant(s), 517 and activity coefficients, 548, 561, 907–908 apparent, 547–548 calculated from potential-energy surface, 887–889 calculated from trajectory calculations, 887–889 collision-theory expression for, 878 determination of, 530 diffusion-controlled, 562–564 and equilibrium constants, 531–532, 546–547 estimation of, 520 for ionic reactions, 908 and isotopic substitution, 901 and NMR spectra, 790 in nonideal systems, 547–548, 907–908 range of values of, 556 solvent effects on, 560 temperature dependence of, 541–546, 900 theories of, 877–910 TST expressions for, 897–898 unimolecular, 548–550 units of, 517 Rate of conversion, 516, 576–577 Rate-determining-step approximation, 532–534, 535, 536–537 Rate law, 516–517 for catalyzed reaction, 565 determination of, 526–530 for elementary reaction, 530–531 integration of, 520–526 in nonideal systems, 547–548, 908 and reaction mechanism, 518, 532–538 Rate-limiting-step approximation, 532–534, 535, 536–537 Rate of reaction, 516–518 See also Rate constant(s); Reaction(s) computer integration for, 539–541 in heterogeneous catalysis, 576–577 isotope effects on, 901 measurement of, 519–520, 556–560, 790 in photochemistry, 799–800 theories of, 877–911 Rayleigh scattering, 772 Reaction(s): autocatalytic, 565 bimolecular, 531 biochemical, 346 catalyzed See Catalysis; Catalyst chain, 551–556 chemically controlled, 564, 906–907 combustion, 554 competing, 525–526 complex, 518 composite, 518 consecutive, 524–525 coupled, 345–347 diffusion-controlled, 562–564, 570, 907, 909–911 elementary, 518, 531–532 equilibrium for a See Reaction equilibrium fast, 520, 556–560 first-order, 521 free radicals in, 520, 538, 543 half-life of, 521, 522, 523, 526–527 heterogeneous, 515, 575–578 homogeneous, 515 independent, 194 ionic, 561 mechanisms of See Reaction mechanism(s) molecular dynamics of, 887–892 nth-order, 523 nuclear, 521 order of See Order of a reaction oscillating, 565–566 photochemical, 798–800 polymerization, 554–556 rate of See Rate of reaction recombination, 543–544, 550–551, 563, 906 reversible, 524 second-order, 522–523 simple, 518 in solutions, 560–564, 906–911 slow, 556 third-order, 523 trimolecular, 531, 550–551, 906 unimolecular See Unimolecular reaction(s) Reaction coordinate, 895–896 Reaction dynamics, molecular, 887–892 Reaction equilibrium, 109, 132–134, 174–175, 402, 403 computer programs for, 340–341 in electrochemical systems, 402, 403 in electrolyte solutions, 332–337 at high T, 182, 185 in ideal gases, 174, 177–198 in ideally dilute solutions, 287 lev38627_index.qxd 4/10/08 9:54 AM Page 984 984 Reaction equilibrium—Cont involving pure solids or liquids, 337–339 at low T, 181–182, 185 in nonelectrolyte solutions, 331–332 in nonideal gas mixture, 340 in nonideal solutions, 330–339, 340–343 in nonideal systems, 330–347 qualitative discussion of, 181–182 shifts in, 194–198 Reaction intermediate, 518, 534, 538 Reaction kinetics, 515–581 See also Reaction(s); Rate constant(s) in photochemistry, 798–800 theories of, 877–911 Reaction mechanism(s), 518, 530, 532–539 compilations of, 539 of reverse reaction, 538–539 rules for, 536–538 Reaction order See Order of a reaction Reaction path, 883 Reaction quotient, 187, 195–197, 345, 414 Reaction rate See Rate of reaction Real gas See Nonideal gases Recombination reactions, 543–544, 550–551, 563, 906 Redlich–Kister equation, 326 Redlich–Kwong equation, 245, 246, 251, 252–253, 323 Reduced mass, 621, 622, 639 Reduced pressure, volume, and temperature, 255–256 Reducible representation, 806, 810–811 Reduction, 407 Reference form, 142, 163 Reference length, 724 Reference system in DFT, 711–712 Refractive index, 736 Relative atomic mass, Relative coordinates, 621 Relative molecular mass, See also Molecular weight Relative permittivity, 433–434 Relative viscosity, 486 Relativistic mass, 51–52 Relativity, theory of, 37, 51–52 effect on molecular properties, 679, 708 and spin, 649 Relaxation, 558, 789 Relaxation methods in kinetics, 558–560 Relaxation time, 559, 793 Representations, 805–807, 810–811 Residuals, 220 Resistance, 495 Resistance thermometer, Resistivity, 494 Resolution, 767 Resonance Raman spectroscopy, 774 Resonance structures, 703 Reverse osmosis, 360 Reversible electrodes, 409–411 Reversible process, 43, 62, 87, 93 Reynolds number, 511 Rideal–Eley mechanism, 576, 578 Rigid rotor, two-particle, 622–623, 649, 739–740 selection rule for, 739 Rigid wall, RM1 method, 719 RNA, 568 Room-temperature ionic liquids, 462, 920 Root-mean-square distance in diffusion, 489–490 Root-mean-square speed, 447–448 Rotation, 67 of diatomic molecules, 744–745, 748 of polyatomic molecules, 758–763 Rotational barriers, 705–706, 762 Rotational constants, 745, 752, 759, 760, 761 Rotational energy, 67 classical, 759 of diatomic molecule, 744–745, 748 of linear molecule, 760 and nuclear spin, 750, 760 of polyatomic molecule, 758–760 Rotational partition function, 835, 842–843, 851–852 Rotational spectra: of diatomic molecules, 751–752 of polyatomic molecules, 760–763, 772 Rotor, two-particle rigid, 622–623, 739–740 RRKM theory, 906 Rumford, Count, 48 Runge–Kutta methods, 540–541 Rutherford, Ernest, 638, 670 Rydberg constant, 594, 595, 774 S Saddle point, 884 Salt bridge, 417, 422 Salt effect, 339 kinetic, 908 Sap, 252 Saturated liquid and vapor, 248 Scalar, 38 Scanning tunneling microscope, 938 Scattering of light, 772, 932 SCF wave function 692 See also Hartree–Fock wave function Schrödinger, Erwin, 600, 603 Schrödinger equation: electronic, 677 for nuclear motion, 679, 744–746 time-dependent, 599–601, 604, 615, 737 time-independent, 604–605, 615 Screening constant, 660 in NMR, 784 Second law of thermodynamics, 78–80, 95, 101, 102, 103 and life, 134–135 Second-order phase transition, 225–226 Second-order reaction, integration of rate law of, 522–523 Second virial coefficient, 245–246, 865, 869 Sedimentation, 236 of polymer molecules, 492–493 Sedimentation coefficient, 493 Selection rules, 738–739 for NMR transitions, 782 for particle in a box, 738–739 in Raman spectroscopy, 772–773 for rotational transitions, 739, 751, 760 for spin, 775, 801 for vibration–rotation transitions, 751, 764–765 Self-consistent-field wave function, 692 See also Hartree–Fock wave function Self-diffusion coefficient, 489 Self-interstitial, 946 Semiclassical partition function, 866–868 Semiconductor, 495, 941, 946–947 Semiconductor laser, 742 Semiempirical methods, 717–720, 886 Semipermeable membrane, 91, 356 Sensitivity, 770 Separation of variables, 612, 618 SERS, 774 Shake and Bake, 935 Shielding, 660 Shielding constant, NMR, 784–785 lev38627_index.qxd 4/10/08 9:54 AM Page 985 985 Shifts in reaction equilibrium, 194–198 Shock tube, 559 SI units, 9, 38, 395, 637, 780 Siemens, 495 Sigma bond, 699–701 Sigma orbitals, 684–685, 692, 693, 717 Silver–silver chloride electrode, 410–411 Similarity transformation, 806 Simple cubic lattice, 928 Simple eutectic system, 375 Simple reaction, 518 Simple solution, 326 Simple unit cell, 924, 929 Simultaneous equilibria, 191–194 Single-point calculation, 720 Single-valuedness, 605, 640 Singlet term, 775 Size effects on properties, 2–3, 227 Slater determinant, 658–659 Slater-type orbitals, 665, 708 Sleep, 32 Slope, 17–18 Slope method, 267 Slow reactions, 556 SMILES string, 723 Smog, 544 SN2 reaction, 886 Soave–Redlich–Kwong equation, 251, 254, 260 Sodium chloride: basis in solid, 922, 929 cohesive energy of, 918–920 dipole moment of, 680 dissociation energy of molecule of, 680 structure of solid, 929–930 Sol, 234 Solid(s), 913–947 a and k of, 25 amorphous, 913, 914 band theory of, 939–941 cohesive energies of, 916–921 covalent See Covalent solids crystalline, 913–914 Debye theory of, 943–946 defects in, 946–947 density of, 927 diffusion in, 377, 489, 490 heat capacity of, 158, 594, 943–946 hydrogen-bonded, 916, 918 interatomic distances in, 921–922, 935 ionic See Ionic solids metallic See Metals molecular See Molecular solids NMR of, 791 of polymers, 914, 916 solutions of, 375 statistical mechanics of, 941–946 structures of, 922–937 See also Structures of solids surfaces of, 937–939 thermodynamic properties of, 120–121 van der Waals, 916, 918 vapor pressure of, 211, 461–462 vibrations of, 941–946 Solid–liquid equilibrium, twocomponent, 373–380 compound formation in, 378–379 solid-phase immiscibility in, 373–374 solid-phase miscibility in, 375–376 solid-phase partial miscibility in, 376–378 Solid polymers, 913, 914, 916, 936 Solid–solid phase transitions, 221–225 Solid solutions, 375 Solubility: of gases in liquids, 286–287 of solids in liquids, 381–383 Solubility product, 338–339, 423–424 Solute, 263, 282 Solutions, 263–288 of electrolytes See Electrolyte solutions freezing point of, 352–356, 373–374, 381–383 Gibbs energy of, 269 ideal See Ideal solution(s) ideally dilute See Ideally dilute solution(s) measurement of partial molar quantities in, 267, 272–274 nonideal See Nonideal solution(s) reaction rates in, 560–564, 906–911 simple, 326, 384–385 solid, 375 volume of, 266–266 Solvation, 306, 560 Solvent, 263, 282 effect of on rate constants, 560 order with respect to, 519, 537 Solver in spreadsheet, 191, 193–194, 221, 252–254 Sound, speed of, 458 Source of emf, 404 Space lattice, 922–925 Spacing between molecular energy levels, 748–749 SPARTAN, 721 Specific conductance, 494 Specific enthalpy, 54 Specific heat (capacity), 46, 54 See also Heat capacity Specific internal energy, 124 Specific rotation, 785 Specific volume, 54 Spectroscopy, 737–794 Speed(s), 38, 443 average, 457–458 distribution of, 448–459 of light, 591, 637, 734–735, 736, 780 most probable, 456, 458 root-mean-square, 447–448 of sound, 458 Spherical coordinates, 639, 644 Spherical top, 759, 760 Spherically symmetric function, 642 Spin, 649–650, 652–653, 655, 656–657 half-integral, 652 integral, 652 nuclear, 749–750, 760, 781–784 selection rule for, 775 Spin coordinates, 650 Spin–lattice relaxation time, 793 Spin multiplicity, 657 Spin–orbit interaction, 657 Spin-orbital, 650, 659 Spin–spin coupling, 785–788 Spin–spin relaxation time, 793 Spin–statistics theorem, 652–653, 749–750 Spontaneous emission, 737 Spreadsheets: absolute references in, 155 and equilibrium calculations, 192–194 formulas in, 154 and least-squares fits, 219–221 and liquid–liquid phase diagrams, 384–385 and liquid–vapor equilibrium calculations, 252–254 polynomial fit and, 153–155, 171 relative reference in, 155 reliability of, 155 and simultaneous equilibria, 192–194 Solver in, 191, 193–194, 221, 253–254, 384–385 solving equations with, 191 lev38627_index.qxd 4/10/08 9:54 AM Page 986 986 Square matrix, 804 Stacking error, 947 Standard concentration equilibrium constant, 180, 332, 531–532 Standard deviation, 101 Standard electrode potentials, 417–420 table of, 419 Standard emf, 414, 416, 422–425 and equilibrium constants, 422–424 temperature dependence of, 424 Standard enthalpy change: and cell emf, 424 of combustion, 145 of formation, 142–144 of reaction, 141–149, 151 Standard entropy change, 161 of activation, 903–904, 909 and cell emf, 424–425 Standard equilibrium constant, 178, 331 See also Equilibrium constant Standard Gibbs energy change, 161–162, 330, 343–345 of activation, 903–904, 908, 909 and cell emf, 414, 422–423 for formation, 161–162 relation to equilibrium constant, 178, 181–182, 190, 331 Standard potential, 414, 416, 422–425 Standard pressure, 140, 163, 190, 210, 283, 284 Standard pressure equilibrium constant, 178 Standard state(s): Convention I, 295–296, 298–301 Convention II, 296–297, 301–302 for an electrolyte solute, 309 for ideal gas in mixture, 176 for ideal-solution component, 278 for ideally dilute solution components, 283–284 for molality scale, 305 for nonideal gas in mixture, 321 for nonideal-solution components, 295–297 pressure of, 140, 163, 190, 210, 278, 283, 284 for pure gas, 140 for pure solid or liquid, 140 summary of, 343, 344 Standard-state thermodynamic properties, table of, 959–960 Star superscript, 265, 278 Stardust, 237 Stark effect, 762 Stark–Einstein law, 796 State: change of, 62 in classical mechanics, 467, 599 intensive, 206 molecular, 821 in quantum mechanics, 599, 600–601, 603, 613, 821 stationary, 595, 605, 613, 617 steady, 5, 800 thermodynamic, 6, 821 versus energy level, 613, 755, 837 State function (in quantum mechanics), 599–605 State function(s) (in thermodynamics), dependences on T, P, V, 118–121 and line integrals, 65–66 Stationary state, quantum-mechanical, 595, 605, 613, 617 Stationary-state approximation, 534–536, 538 Statistical mechanics, 1, 820–870 of fluids, 866–870 of ideal gases, 834–836, 840–858 of liquids, 948–951 postulates of, 822, 823 of solids, 941–946 Statistical thermodynamics, 820 See also Statistical mechanics Statistical weight, 837 Steady state, 5, 475, 800 Steady-state approximation, 534–536, 538 Steam engine, 84 Steam point, 7, 14 Steric energy, 724–725 Steric factor, 879 Stern model, 444 Sticking coefficient, 578–579 Stimulated emission, 737, 738, 741–742 Stirling’s formula, 834 Stockmayer potential, 865 Stoichiometric coefficients, 132 Stoichiometric molality, 309 Stoichiometric numbers, 132, 518, 547 Stokes–Einstein equation, 491, 563 Stokes’ law, 484, 491, 502 Stokes lines, 772 Stokes shift, 778 Stopped-flow method, 557 Stratosphere, 479, 566–567 Stretching vibration, 764 Structures of molecules See Geometry of molecules Structures of solids, 922–937 for covalent solids, 930–931 determination of, 931–937 examples of, 928–931 general discussion of, 922–929 for ionic solids, 929–930 for metals, 928–929 for molecular solids, 931 Study suggestions, 30–32 Sublimation, 213 Subshell, 660 Substitutional impurity, 946 Substitutional solid solution, 375 Substrate, 568 Sulfur: phase diagram of, 221–222 viscosity of, 482 Sum, 25 replacement of by integral, 841 Superconductivity, 226 Supercooled liquid, 222, 355 Supercritical fluid, 249 Superheated liquid, 222 Supermolecule, 880 Supersaturated vapor, 222 Supersonic jet, 779 Surface chemistry, 227–237, 570–578, 937–939 Surface-enhanced Raman spectroscopy, 774 Surface melting, 222 Surface migration, 579 Surface reconstruction, 938 Surface relaxation, 922, 938 Surface structures of solids, 937–939 Surface tension, 229–233 of liquids, 229–230 measurement of, 232–233 temperature dependence of, 230 Surroundings, Svedberg (unit), 493 Symmetric function, 652, 750 Symmetric top, 759–760, 761 Symmetrical convention, 296 Symmetry elements, 756–757 Symmetry of molecules, 756–757, 801–803 Symmetry number, 842, 851–852, 899 Symmetry operations, 757, 801–802 Symmetry point groups, 801–803 Symmetry species, 809 lev38627_index.qxd 4/10/08 9:54 AM Page 987 987 Synchrotron, 937 System, closed, heterogeneous, homogeneous, isolated, 4, 95, 96 open, 4, 47 in statistical mechanics, 821 Systematic absences, 933–934 T T-jump method, 558 Tables of thermodynamic data, 163–165, 959–960 Taylor series, 257–258 Temperature, 6–8 absolute ideal-gas scale of, 12–14, 97, 446 Celsius, 14 ideal-gas scale of, 12–14, 97, 446 ITS-90, 13–14 low, attainment of, 168–169 measurement of, 7–8, 13 and molecular translational energy, 446–447 thermodynamic scale of, 96–97 Temperature-jump method, 558 Term(s) atomic, 656, 658, 663 molecular, 809, 810 Terminal speed of ions, 499, 501, 503 Terminals, 404, 405 Termination step, 552, 554, 555 Termolecular reactions See Trimolecular reactions Ternary system, 385 Tesla, 780 Tetramethylsilane, 785, 789 Thermal analysis, 380 Thermal conductivity, 475–479 kinetic theory of, 476–479 pressure dependence of, 479 temperature dependence of, 479 Thermal desorption, 579 Thermal equilibrium, 5, 6–7 Thermal expansivity, 24–25, 117 Thermal reaction, 796 Thermistor, Thermochemical calorie, 51, 163 Thermocouple, 8, 400 Thermodynamic control of products, 526 Thermodynamic data tables, 163–165, 959–960 Thermodynamic properties, 5–6 dependence of on T, P, V, 118–121 estimation of, 165–168 of ideal gas, 58–62, 64, 176, 846–849, 853–854 of ideal gas mixture, 176, 289 of ions in solution, 319–321 of nonequilibrium system, 475 of real gases, 149–150, 158, 256–257 of solution components, 318–321 tables of, 162–165, 959–960 Thermodynamic state, 6, 821 local, 475 Thermodynamic temperature scale, 96–97 Thermodynamics, 1, of electrochemical systems, 401–403 equilibrium, first law of, 47–51, 58 of galvanic cells, 412–417 irreversible, and living organisms, 134–135, 347 second law of, 78–80, 95, 101, 102, 103 third law of, 156–157, 168 zeroth law of, 7, Thermometer, 7–8, 13 Third law of thermodynamics, 156–157, 168, 858–860 Third-order reactions, 523 Thomson, George, 596, 638 Thomson, Joseph J., 596, 637–638 Thomson, William, 56, 79, 96 Three-body forces, 861 Three-center bond, 701–702 Three-component phase equilibrium, 385–387 Threshold energy, 877, 878, 889 Threshold frequency, 593 Tie line, 364–365, 369–370 Tilde, 752 Time, direction of, 103–104 TMS, 785, 789 Toms effect, 480 Torr, 11 Torsional vibration, 769 Total differential, 20 Totally symmetric representation, 807, 809 Trace of a matrix, 807 Tracer diffusion coefficient, 489 Trajectory calculations, 887–890 Transference numbers, 504–506, 507 Transition (dipole) moment, 738, 751 Transition elements, 662 Transition state, 884–886, 894, 904–905 Transition-state theory (TST), 892–904 assumptions of, 893, 895, 898 and collision theory, 899–900 for gas-phase reactions, 892–904 for H ϩ H2, 898–899 and isotope effects, 901 rate constant equation in, 897, 903, 907–908 for reactions in solution, 907–909 temperature dependence of rate constant in, 900 tests of, 901–902 thermodynamic formulation of, 902–904 and transport properties, 902 and unimolecular reactions, 904–906 variational, 902 Translation, 67 Translational energy, molecular, 67, 443, 446–447, 622, 744 distribution of, 459 in a fluid, 870 level spacings of, 748 Translational partition function, 835, 840–841, 851 Translational states, number of, 833 Transmembrane potential, 429, 435–436 Transmission coefficient, 897 Transmittance, 741 Transport numbers, 504–506, 507 Transport processes, 474–509 Transverse relaxation time, 793 Triangular coordinates, 385–386 Trimolecular reactions, 531, 550–551, 879–880, 906 Triple bond, 699, 701 Triple point, 13, 210–211, 212, 221 Triplet term, 775 Troposphere, 466 Trouton’s rule, 213 Trouton–Hildebrand–Everett rule, 213 Tunneling, 620, 888, 898, 901 Turbulent flow, 480, 481 Turnover number, 569 Two-component phase equilibrium, 361–385 Two-dimensional NMR, 791 Two-particle rigid rotor See Rigid rotor, two-particle lev38627_index.qxd 4/10/08 9:54 AM Page 988 988 Two-particle system in quantum mechanics, 621–622 Two-photon spectroscopy, 796 U Unattainability of absolute zero, 168 Uncertainty principle, 597–598, 603, 608 Ungerade (u), 684, 693 Unimolecular reaction(s), 531, 548–550 A factor of, 543 activation energy of, 543 falloff of rate constant of, 549–550 Lindemann mechanism of, 548–550 potential-energy surfaces for, 904–905 RRKM theory of, 906 and TST, 904–906 Unit cell, 923–925 body-centered, 924 coordinates of a point in, 925 end-centered, 924 face-centered, 924, 928 number of formula units in, 927 primitive, 924, 928 simple, 924, 928 Unit matrix, 805 Unpolarized light, 735 Unsymmetrical convention, 296 V Vacancy, 946 Vacuum decay, 223 Valence band, 742, 941 Valence-bond method, 702–703 van der Waals equation, 23, 122–123, 245, 246, 250, 255, 257 van der Waals force, 862 van der Waals molecules, 865–866 van der Waals radii, 921–922 van der Waals solid, 916 van der Waals well depth, 883 van’t Hoff, J H., van’t Hoff equation, 183–184 van’t Hoff’s law, 357 Vapor pressure, 210, 211, 216 effect of pressure on, 216 of electrolyte solution, 310 from equation of state, 252–254 of ideal solution, 279–281 of ideally dilute solution, 284–286 lowering of, 351–352 of nonideal solution, 298–302, 368–369 of a small drop, 232, 243 of a solid, 211, 216, 461–462 temperature dependence of, 216–217 Vaporization, heat of, 213, 216, 219 Variance, 206 Variation method, 624–626 Variational integral, 624 Variational transition-state theory, 902 Vector, 38 Velocity(ies), 38, 443 distribution of See Distribution function Velocity space, 449–450 Vibration, 67 of diatomic molecules, 745–749 of polyatomic molecules, 763–770 of solids, 941–946 Vibration–rotation coupling constant, 747–748 Vibration–rotation spectra: of diatomic molecules, 750–755 of polyatomic molecules, 763–770, 772–773 Vibrational energy, 67, 69 of diatomic molecules, 746–747, 748 of polyatomic molecules, 763–770, 773 of solids, 941–946 Vibrational frequencies: bond, 768–769 calculation of, 720, 854 of diatomic molecules, 746 fundamental, 753–754, 765 Vibrational partition function, 835, 843–844, 852 Vibrational relaxation, 778, 797 Vibrational spectra See Vibration– rotation spectra Vinyl cation, 710 Virial coefficients, 244–245, 323, 865, 869 Virial equation, 245–246, 257, 323, 869 Virtual orbitals, 708 Viscosity, 479–489 definition of, 480 and diffusion, 504 intrinsic, 486 kinetic theory of, 484–485 measurement of, 483–484 Newton’s law of, 480, 482, 485, 494 of polymer solutions, 481, 486–487 pressure dependence of, 485 relative, 486 of sulfur, 482 temperature dependence of, 481, 485 Viscosity-average molecular weight, 487 Viscosity ratio, 486 Viscous flow, 461 Volt, 397 Voltage, 495 Voltaic cell See Galvanic cell(s) Volume mean molar, 247 molar, 22 partial molar See Partial molar volume(s) partial specific, 492 of a solution, 266–267 units of, 12 Volume change: for forming an ideal solution, 276, 278 irreversible, 45–46 for mixing, 264–265, 267, 278 reversible, 42–43 Volume element in spherical coordinates, 644 Volumetric equation of state See Equation of state Vonnegut, Kurt, 223 VSEPR method, 673 W Wall, kinds of, Wall collisions, 460–461 Water: cohesive energy of ice, 920 dimer of, 710–711 expansion of, 7, 24 freezing-point depression constant of, 354 heat capacity of, 69 ionization of, 332–333, 342, 556, 559 isotherms of, 23, 247, 255 localized MOs of, 699 Monte Carlo simulation of liquid, 950–951 normal boiling point of, 14 normal modes of, 764 phase diagram of, 210–212, 223 supercritical, 249 symmetry operations of, 802 thermal conductivity of, 476 vibrational bands of, 765 Watt, 39 lev38627_index.qxd 4/10/08 9:54 AM Page 989 989 Wave function(s), 605 See also Harmonic oscillator; Hydrogen atom; etc of a degenerate level, 642–643 electronic, 677–678 nuclear, 679, 744–746 spin, 650, 652, 658 time-dependent, 599–605 time-independent, 604–605 units of, 608 well-behaved, 605 Wave mechanics, 600 Wave–particle duality, 594, 596–597 Wavelength, 591, 735 de Broglie, 596 Wavenumber, 736, 753 Weight, 38 Weight average molecular weight, 487 Weight percent, 264 Well-behaved function, 605 Wheatstone bridge, 496–497 Woodward–Hoffman rules, 718, 887 Work, 39–40, 42, 50–51 calculation of, 59–60, 63–64 irreversible, 45–46 non-P-V, 114–115 P-V, 42–46 surface, 229 Work–energy theorem, 39–40 Work function, 112–114, 594 X X-ray diffraction of solids, 931–937 X-ray emission, 775 Y YouTube, 950 Z Z-matrix, 721–722 Zero-point energy, 67, 608, 620, 705, 747, 764, 901 Zeroth law of thermodynamics, 7, Zinc sulfide structure, 931 lev38627_index.qxd 4/10/08 9:54 AM Page 990 Be 9.012 12 Mg 24.31 20 Ca 40.08 38 Sr 87.62 56 Ba 137.3 88 Ra (226) 11 Na 22.99 19 K 39.10 37 Rb 85.47 55 Cs 132.9 87 Fr (223) 89 Ac (227) 57 La 138.9 39 Y 88.91 104 Rf (267) 72 Hf 178.5 40 Zr 91.22 22 Ti 47.88 4B 106 Sg (271) 59 Pr 140.9 91 Pa 231.0 58 Ce 140.1 90 Th 232.0 74 W 183.8 42 Mo 95.96 24 Cr 52.00 6B 105 Db (268) 73 Ta 180.9 41 Nb 92.91 23 V 50.94 5B 92 U 238.0 60 Nd 144.2 107 Bh (272) 75 Re 186.2 43 Tc (98) 25 Mn 54.94 7B 93 Np (237) 61 Pm (145) 108 Hs (270) 76 Os 190.2 44 Ru 101.1 26 Fe 55.85 94 Pu (244) 62 Sm 150.4 109 Mt (276) 77 Ir 192.2 45 Rh 102.9 27 Co 58.93 8B 95 Am (243) 96 Cm (251) 64 Gd 157.3 97 Bk (247) 65 Tb 158.9 112 111 Rg (280) 110 Ds (281) 63 Eu 152.0 80 Hg 200.6 79 Au 197.0 48 Cd 112.4 30 Zn 65.38 12 2B 78 Pt 195.1 47 Ag 107.9 29 Cu 63.55 28 Ni 58.69 46 Pd 106.4 11 1B 10 98 Cf (251) 66 Dy 162.5 113 81 Tl 204.4 49 In 114.8 31 Ga 69.72 99 Es (252) 67 Ho 164.9 114 82 Pb 207.2 50 Sn 118.7 32 Ge 72.64 14 Si 28.09 13 Al 26.98 100 Fm (257) 68 Er 167.3 115 83 Bi 209.0 51 Sb 121.8 33 As 74.92 15 P 30.97 N 14.01 101 Md (258) 69 Tm 168.9 116 84 Po (209) 52 Te 127.6 34 Se 78.96 16 S 32.07 O 16.00 16 6A 102 No (259) 70 Yb 173.0 (117) 85 At (210) 53 I 126.9 35 Br 79.90 17 Cl 35.45 F 19.00 17 7A 103 Lr (262) 71 Lu 175.0 118 86 Rn (222) 54 Xe 131.3 36 Kr 83.80 18 Ar 39.95 10 Ne 20.18 12:17 PM 21 Sc 44.96 3B C 12.01 B 10.81 15 5A 2/20/08 Li 6.941 14 4A 13 3A He 4.003 H 1.008 2A 18 8A 1A lev38627_es.qxd Page lev38627_es.qxd 2/20/08 12:17 PM Page Atomic Numbers and Atomic Weights a Actinium Aluminum Americium Antimony Argon Arsenic Astatine Barium Berkelium Beryllium Bismuth Boron Bromine Cadmium Calcium Californium Carbon Cerium Cesium Chlorine Chromium Cobalt Copper Curium Dysprosium Einsteinium Erbium Europium Fermium Fluorine Francium Gadolinium Gallium Germanium Gold Hafnium Helium Holmium Hydrogen Indium Iodine Iridium Iron Krypton Lanthanum Lawrencium Lead Lithium Lutetium Magnesium Manganese Mendelevium aFrom Ac Al Am Sb Ar As At Ba Bk Be Bi B Br Cd Ca Cf C Ce Cs Cl Cr Co Cu Cm Dy Es Er Eu Fm F Fr Gd Ga Ge Au Hf He Ho H In I Ir Fe Kr La Lr Pb Li Lu Mg Mn Md 89 13 95 51 18 33 85 56 97 83 35 48 20 98 58 55 17 24 27 29 96 66 99 68 63 100 87 64 31 32 79 72 67 49 53 77 26 36 57 103 82 71 12 25 101 (227) 26.981538 (243) 121.760 39.948 74.92160 (210) 137.327 (247) 9.012182 208.98040 10.811 79.904 112.41 40.078 (251) 12.011 140.116 132.90545 35.453 51.9961 58.93320 63.546 (247) 162.50 (252) 167.26 151.964 (257) 18.998403 (223) 157.25 69.723 72.64 196.96657 178.49 4.002602 164.93032 1.00794 114.818 126.90447 192.22 55.845 83.798 138.9055 (262) 207.2 6.941 174.967 24.3050 54.93805 (258) Mercury Molybdenum Neodymium Neon Neptunium Nickel Niobium Nitrogen Nobelium Osmium Oxygen Palladium Phosphorus Platinum Plutonium Polonium Potassium Praseodymium Promethium Protactinium Radium Radon Rhenium Rhodium Rubidium Ruthenium Rutherfordium Samarium Scandium Selenium Silicon Silver Sodium Strontium Sulfur Tantalum Technetium Tellurium Terbium Thallium Thorium Thulium Tin Titanium Tungsten Uranium Vanadium Xenon Ytterbium Yttrium Zinc Zirconium Hg Mo Nd Ne Np Ni Nb N No Os O Pd P Pt Pu Po K Pr Pm Pa Ra Rn Re Rh Rb Ru Rf Sm Sc Se Si Ag Na Sr S Ta Tc Te Tb Tl Th Tm Sn Ti W U V Xe Yb Y Zn Zr 80 42 60 10 93 28 41 102 76 46 15 78 94 84 19 59 61 91 88 86 75 45 37 44 104 62 21 34 14 47 11 38 16 73 43 52 65 81 90 69 50 22 74 92 23 54 70 39 30 40 200.59 95.96 144.24 20.1797 (237) 58.6934 92.90638 14.00674 (259) 190.23 15.9994 106.42 30.97376 195.08 (244) (209) 39.0983 140.90765 (145) 231.03588 (226) (222) 186.207 102.90550 85.4678 101.07 (267) 150.36 44.95591 78.96 28.0855 107.8682 22.989769 87.62 32.065 180.9479 (98) 127.60 158.92535 204.3833 232.0381 168.93421 118.710 47.867 183.84 238.0289 50.9415 131.29 173.05 88.90585 65.38 91.224 “Atomic Weights of the Elements 2007” (www.chem.qmul.ac.uk/iupac/AtWt/) A value in parentheses is the mass number of the longest-lived isotope lev38627_es.qxd 2/20/08 12:17 PM Page Fundamental Constantsa Constant Symbol Gas constant R 8.3145 J molϪ1 KϪ1 8.3145 m3 Pa molϪ1 KϪ1 Avogadro constant Faraday constant Speed of light in vacuum Planck constant Boltzmann constant Proton charge Electron rest mass Proton rest mass Electric constant NA F 6.022142 ϫ 1023 molϪ1 96485.34 C molϪ1 c h k e me mp e0 4pe0 1/4pe0 m0 2.99792458 ϫ 108 m sϪ1 6.626069 ϫ 10Ϫ34 J s 1.38065 ϫ 10Ϫ23 J KϪ1 1.6021765 ϫ 10Ϫ19 C 9.109382 ϫ 10Ϫ31 kg 1.672622 ϫ 10Ϫ27 kg 8.85418782 ϫ 10Ϫ12 C NϪ1 mϪ2 1.112650056 ϫ 10Ϫ10 C NϪ1 mϪ2 8.98755179 ϫ 109 N m2 CϪ2 4p ϫ 10Ϫ7 N CϪ2 s2 G 6.674 ϫ 10Ϫ11 m3 sϪ2 kgϪ1 Magnetic constant Gravitational constant SI value Non-SI value 8.3145 ϫ 107 erg molϪ1 KϪ1 83.145 cm3 bar molϪ1 KϪ1 82.0575 cm3 atm molϪ1 KϪ1 1.9872 cal molϪ1 KϪ1 aAdapted from P J Mohr, B N Taylor, and D B Newell (2007), “CODATA Recommended Values of the Fundamental Physical Constants: 2006” (physics.nist.gov/constants and arxiv.org/abs/0801.0028) Defined Constants Standard gravitational acceleration gn ϵ 9.80665 m/s2 Zero of the Celsius scale ϵ 273.15 K Greek Alphabet Alpha Beta Gamma Delta Epsilon Zeta Eta Theta 〈 〉 ⌫ ⌬ ⌭ ⌮ ⌯ ⌰ a b g d e z h u Iota Kappa Lambda Mu Nu Xi Omicron Pi ⌱ ⌲ ⌳ ⌴ ⌵ ⌶ ⌷ ⌸ i k l m n j o p Rho Sigma Tau Upsilon Phi Chi Psi Omega ⌹ ⌺ ⌻ ⌼ ⌽ ⌾ ⌿ ⍀ r s t y f x c v lev38627_es.qxd 2/20/08 12:17 PM Page Conversion Factorsa eV ϭ 1.6021765 ϫ 10Ϫ19 J Å ϵ10Ϫ10 m ϭ 10Ϫ8 cm L ϵ 1000 cm3 ϭ1 dm3 D ־3.335641 ϫ 10Ϫ30 C m P ϭ 0.1 N s mϪ2 G ־10Ϫ4 T atm ϵ 101325 Pa 1 torr ϵ 760 atm ϭ133.322 Pa bar ϵ 105 Pa ϭ 0.986923 atm ϭ 750.062 torr dyn ϭ 10Ϫ5 N 1erg ϭ 10Ϫ7 J calth ϵ 4.184 J a The symbol ־means “corresponds to.” SI Prefixes 10Ϫ1 10Ϫ2 10Ϫ3 10Ϫ6 10Ϫ9 10Ϫ12 10Ϫ15 10Ϫ18 10Ϫ21 deci centi milli micro nano pico femto atto zepto d c m n p f a z 10 102 103 106 109 1012 1015 1018 1021 deca hecto kilo mega giga tera peta exa zetta da h k M G T P E Z Properties of Some Isotopesa Isotope 1H 2H 11B 12C 13C 14N 15N 16O 19F 23Na 31P 32S 35Cl 37Cl 39K 79Br 81Br 127I aAbundances Abundance,% Atomic mass I gN 99.988 0.012 80.1 98.9 1.1 99.64 0.36 99.76 100 100 100 95.0 75.8 24.2 93.26 50.7 49.3 100 1.0078250 2.014102 11.009305 12.000 13.003355 14.003074 15.00011 15.994915 18.998403 22.98977 30.97376 31.972071 34.968853 36.965903 38.96371 78.91834 80.91629 126.90447 1/2 3/2 1/2 1/2 1/2 3/2 1/2 3/2 3/2 3/2 3/2 3/2 5/2 5.58569 0.85744 1.7924 — 1.40482 0.40376 Ϫ0.56638 — 5.25774 1.47844 2.2632 — 0.547916 0.456082 0.261005 1.40427 1.51371 1.1253 are for the earth’s crust Atomic masses are the relative masses of the neutral atoms on the 12C scale ... Mechanics The Canonical Ensemble Canonical Partition Function for a System of Noninteracting Particles Canonical Partition Function of a Pure Ideal Gas The Boltzmann Distribution Law for Noninteracting... putting everything that depends on V on one side and everything that depends on P on the other side k is an intensive quantity that depends on T and P, and T is constant, so k belongs on the... changes by an infinitesimal amount dx while y remains constant What is the infinitesimal change dz in z brought about by the infinitesimal change in x? If z were a function of x only, then [Eq