Physical chemistry 3th castellan

www.elsolucionario.org STANDARD ATOMIC MASSES 1979 (Scaled to the relative atomic mass , A ,.(I2C) = 12) Name Actinium Aluminium Americium Antimony Argon Arsenic Astatine Barium Berkelium Beryllium Bismuth Boron Bromine Cadmium Caesium Calcium Californium Carbon Cerium 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 Mercury Atomic Symbol number Ac 89 Al 13 Am 95 Sb 51 Ar 18 As 33 At 85 Ba 56 Bk 97 Be Bi 83 B Br 35 Cd 48 55 Cs Ca 20 Cf 98 C Ce 58 Cl 17 Cr 24 Co 27 Cu 29 Cm 96 Dy 66 Es 99 Er 68 Eu 63 Fm 100 F Fr 87 Gd 64 Ga 31 Ge 32 Au 79 Hf 72 He Ho 67 H I In 49 I 53 Ir 77 Fe 26 Kr 36 La 57 Lr 103 Pb 82 Li Lu 71 Mg 12 Mn 25 Md 101 Hg 80 Atomic mass 227.0278 26 98154 (243) 121.75* 39 948 74.9216 (210) 137 33 (247) 9.01218 208.9804 10.81 79 904 112.41 132 9054 40 08 (25 I) 12.011 140 12 35.453 51.996 58 9332 63 546* (247) 162 50* (252) 167.26* 151.96 (257) 18.998403 (223) 157.25 * 69.72 72 59* 196.9665 178.49* 4.00260 164.9304 1.0079 114.82 126.9045 192 22 * 55 847* 83 80 138.9055 * (260) 207 6.941 * 174 967 * 24.305 54.9380 (258) 200 59* Name 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 Samarium Scandium Selenium Silicon Silver Sodium Strontium Sulfur Tantalum Technetium Tellurium Terbium Thallium Thorium Thulium Tin Titanium Tungsten (U nnilhexium) (Unnilpentium) (U nnilquadium) Uranium Vanadium Xenon Ytterbium Yttrium Zinc Zirconium Atomic Symbol number Mo Nd Ne Np Ni Nb N No Os Pd P Pt Pu Po K Pr Pm Pa Ra Rn Re Rh Rb Ru Sm Sc Se Si Ag Na Sr S Ta Tc Te Tb TI Th Tm Sn Ti W (Unh) (Unp) (Unq) U V Xe Yb Y Zn Zr 42 60 10 93 28 41 102 76 46 15 78 94 84 19 59 61 91 88 86 75 45 37 44 62 21 34 14 47 II 38 16 73 43 52 65 81 90 69 50 22 74 106 105 104 92 23 54 70 39 30 40 Atomic mass 95.94 144.24* 20 179 237 0482 58.69 92.9064 14 0067 (259) 190.2 15 9994* 106.42 30.97376 195.08* (244) (209) 39.0983 140.9077 (145) 231 0359 226 0254 (222) 186.207 102 9055 85.4678 * 101.07* 150.36* 44.9559 78 96* 28.0855 * 107 868 22 98977 87 62 32 06 180.9479 (98) 127.60* 158.9254 204 383 232 0381 168.9342 118 69* 47 88 * 183.85* (263) (262) (261) 238.0289 50.9415 131.29* 173 04 * 88 9059 65.38 91.22 Source: Pure and Applied Chemistry , 51, 405 (1979 ) By permission Value s are considered reliable to ± I in the last digit or ± when followed by an asterisk(*) Values in parentheses are used for radioactive elements whose atomic weight s cannot be quoted precisel y without knowledge of the origin of the elements; the value given is the atomic mass number of the isotope of th at element of longest known half-life FUNDAMENTAL CONSTANTS (approximate values; best values are in Appendix IV) ! , Quantity Symbol Value Gas constant Zero of the Celsius scale Standard atmosphere Standard molar volume of ideal gas A vogadro constant Boltzmann constant Standard acceleration of gravity Elementary charge Faraday constant Speed of light in vacuum Planck constant R 8.314 J K- mol-I To 273.15 K 1.013 x 105 Pa 22.41 x 10- m3 mol-I Rest mass of electron Permittivity of vacuum Bohr radius Hartree energy Po Vo RTolpo = 6.022 x 1023 mol I 1.381 x 10- 23 J K- 9.807 m s -2 e F c Il Ii = = NAe h121T' In en 41T'eo 1/41T'eo ao = 41T'eoIi2/me2 Eh = el l41T'e oao 1.602 9.648 2.998 6.626 1.055 9.110 8.854 LIB 8.988 5.292 4.360 '>\ X x x X X '>\ X x x x: 10 19 C 104 C mol-I lOR m s I 10 34 J s 10- 34 J s 10- 31 kg 10- 12 C2 N- m 10- 10 C N- I m -2 109 N m C- 10 II m 10 I~ J "- CONVERSION FACTORS i I L = 10- m' (exactly) = dm I atm = 1.01325 Pa (exactly) I atm = 760 Torr (exactly) Torr = 1.000 mmHg cal = 4.184 J (exactly) erg = dyne cm = 10- J (exactly) eV = 96.48456 kJ/mol A = 10 10 m = 0.1 nm = 100 pm I inch = 2.54 cm (exactly) pound = 453.6 g I gallon = 3.785 L Btu = 1.055 kJ I hp = 746 W www.elsolucionario.org MATHEMATICAL DATA 1T = e = 2.7182818 3.14159265 In x = 2.302585 log x (all x) In I + x) =x - Y~x" + x )-1 - X (l - x )-1 + (I - X)-" + 2x + (l + X + + IA\"3 - Y4X + (x" x" - X3 + (x~ < X~ X3 + (x" < I) + 3x~ + 4x + (x" < 1) I) < 1) 51 PREFIXES Submultiple Prefix Symbol Multiple Prefix Symbol 10- [ deci d 10 deca da 10- centi c 10" hecto h 10- 10- milli m 10 kilo k mIcro 11 106 mega M nano 1} 109 giga G pico 10 12 tera T femto P f 10 peta P atto a 10 18 exa E 10- 10- [2 10 15 10 - IR 15 Physical Chemistry Third Edition Gilbert W Castellan University of Maryland "' Addison-Wesley Publishing Company Reading, Massachusetts Menlo Park, California • London • Amsterdam • Don Mills, Ontario • Sydney www.elsolucionario.org To Joan and our family Sponsoring Editor: Robert L Rogers Production Editor: Margaret Pinette Copy Editor: Jerrold A Moore Text Designer: Debbie Syrotchen Design Coordinator: Herb Caswell Illustrators: YAP International Communications, Ltd Cover Designer: Richard Hannus, Hannus Design Associates Cover Photograph: The Image Bank, U Schiller Art Coordinator: Joseph K Vetere Production Manager: Herbert Nolan The text of this book was composed in Monophoto Times Roman by Composition House Limited Reprinted with corrections, November 1983 Copyright © 983 , 97 , 964 by Addison-Wesley Publishing Company, 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, or otherwise, without the prior written permission of the publisher Printed in the United States of America Published simultaneously in Canada Library of Congress Catalog Card No 82-74043 ISBN 0-201-10386-9 BCDEFGHIJ -MA-89876543 www.elsolucionario.org m Foreword to the Student On most campuses the course in physical chemistry has a reputation for difficulty It is not, nor should it be, the easiest course available; but to keep the matter in perspective it must be said that the IQ of a genius is not necessary for understanding the subject The greatest stumbling block that can be erected in the path of learning physical chemistry is the notion that memorizing equations is a sensible way to proceed Memory should be reserved for the fundamentals and important definitions Equations are meant to be understood, not to be memorized In physics and chemistry an equation is not a jumbled mass of symbols, but is a statement of a relation between physical quantities As you study keep a pencil and scratch paper handy Play with the final equation from a derivation If it expresses pressure as a function of temperature, turn it around and express the temperature as a function of pressure Sketch the functions so that you can "see" the variation How does the sketch look if one of the parameters is changed? Read physical meaning into the various terms and the algebraic signs which appear in the equation If a simplifying assumption has been made in the derivation, go back and see what would happen if that assumption were omitted Apply the derivation to a different special case Invent problems of your own involving this equation and solve them Juggle the equation back and forth until you understand its meaning In the first parts of the book much space is devoted to the meaning of equations; I hope that I have not been too long-winded about it, but it is important to be able to interpret the mathematical statement in terms of its physical content By all means try to keep a good grasp on the fundamental principles that are being applied; memorize them and above all understand them Take the time to understand the methods that are used to attack a problem In Appendix I there is a brief recapitulation of some of the most important mathematical ideas and methods that are used If any of these things are unfamiliar to you, take the time to review them in a mathematics text Once the relations vi Foreword between variables have been established, the algebra and calculus are simply mechanical devices, but they should be respected as precision tools If problems baffle you, learn the technique of problem solving The principles contained in G Polya's book, How to Solve It, have helped many of my students.* It is available as a paperback and is well worth studying Work as many problems as possible Numerical answers to all problems can be found in Appendix VII Make up your own problems as often as possible Watching your teacher perform will not make you into an actor; problem solving will To aid in this, get a good "scientific" calculator (the serious student will want a programmable one with continuous memory) and learn how to use it to the limit of its capability Reading the instructions will save you hundreds of hours! Finally, don't be put off by the reputation for difficulty Many students have enjoyed learning physical chemistry * G Polya, How to Solve It Anchor Book No 93 New York: Doubleday & Co , 957 1-4 Index complexion of a system, o f a n ensemble , 723 components , definition of, 272 compound, , 445 compound interest, 807 compressibility coefficient of, 72 table of values , 87 of a reactive system, 243 compressibility factor, 33ff" 7ff" compression, 09 Compton effect, 490 concentration cells, 392ff, conductance , 765 , 766 at high fields and frequencies , 786 in nonaqueous solvent s , 786 conductance measurements , applications of, 778ff, conductimetric titrations, 780 conductivity, 765 , 766 infinite dilution , determination of, 773 molar, 766, 772 of hydrogen ion, 783 of hydroxyl ion, 783 in ionic solutions , 769 in metals, 766 temperature dependence of, 784 conductivity cell, 770 conductors , energy bands in, conjugate coordinates and momenta, 489 conjugate solutions , 320 consecutive reactions , conservation of energy, law of, 93 , 446 conservation of mass and chemical equations , law of, consolute temperatures , 320, constants fundamental , A-22 mathematical, A-23 construction principle , 525 contact angle , continuity o f state , principle of, conventions for Gibbs energy , summary of, 374 coordination number, 552 , 683 , 688, 689 correlation diagram for diatomic molecules , 557 , 558 , 559 correspondence principle , 485 corresponding states , law of, 45 corrosion, 886ff by metal contact, 889 by oxygen, 888 of metals in acids, 886 corrosion inhibition, 889 Coulomb ' s law, 661 , 709 , A- l l coupled reactions , 246 covalent bond , 53 1ff" 538ff" 690 directional character of, 539ff, in elements of second and higher periods , 552 partial ionic character, 539 covalent crystals, 682 geometric requirements in , 690 critical constants, 45 critical solution temperature , 320 critical state , 43 crosslinking, cryohydrate , 327 crystal classes, 692 crystal habit, 694 crystal planes , designation of, 697 crystal structures for common metals, 686 crystal systems, 692 crystalline solids, 68 crystals covalent, 682 hydrogen bonded , 682 ionic , 682 metals, 682 packing in ionic , 686 symmetry of, 69 van der Waals , 682 x-ray examination of, 700 cubic close-packed structure , 683 , 684 cubic system, 692 Curie , M , 45 Curie , P , 45 current, 765 , 766 anodic , 875 cathodic , 875 current density, 766 at an electrode , 875ff, exchange, 876 rate of reaction and, 875 current-potential relation , 878ff, general consequences of, 884ff, cyanamide ion, 550 cyanate ion , 550 cyanide ion, 549 cycle definition of, l 03ff, reversible , 54 cyclic integrals, 1 cyclic rule , I 75jf cytosine , D lines , 596 , 597 Dalton, J , 445 Dalton' s law, , 27, 57 Daniell cell, 206 , 375 , 405 Davisson, 447 , 460 deBroglie , 447 , 459 deBroglie formula, 459 , 46 deBroglie wavelength for particle in a box , 483 Debye , P , 86 , 357 Debye equation, 664 Debye length , 364 Debye-Falkenhagen effect, 786 Debye-Hiickel limiting law, 363 , 365 , 863 Debye-Hiickel theory, 357jf , 784 Debye-Scherrer method, 703 Debye unit for dipole moment , 665 decay constant, 806 deDonder' s inequality , 854 degeneracy , 475 , 533 , 726 , 733 degree of dissociation , salt effect on, 366 degrees of freedom , 73 , 625 thermodynamic , 27 densitometer, 704 derivative , A- I detergents , 438 deuterium oxide , conductivity in, 782 dialysis , 437 diameter, molecular, 750 diamond structure , 690 diatomic molecules , 626 , 628 characteristic temperatures for, 732 charge distribution in, 626 heteronuclear, 626 homonuclear, 626 internal energy of, 500 selection rules for, 642 wave functions for, 642 dielectric , polarization in , 659jf dielectric constant, 66 Iff, , 673 www.elsolucionario.org Index Dieterici equation, 47 differentials - exact, 09 exact and inexact, 1 inexact, 09 diffraction angle , 460 diffraction pattern, 460 x-ray , 693 diffusion, 746, 755ff charge transport and, 786ff of an electrolyte , 789ff surface , 426 diffusion coefficient, 746 , 868 of electrolyte , 790, 79 of ions, 788 of macromolecule , 938 diffusion layer, 868 diffusion potential, 789, 792 dilution law, 774 dinitrogen tetroxide , dissociation of, 236 dipole moment, 626, 66 Debye unit for, 665 definition of, 626 per unit volume , 66 , 663 permanent, 663 table of, 665 direction of natural processes , 95 dispersion energy , 670 dispersion forces , 670 distillation columns, 303ff fractional, 302ff isothermal, 300ff of azeotropic mixtures , 305ff of immiscible liquids, 322 of partially miscible liquids, 322 distribution barometric, 22 Boltzmann, 88 classification interval, 57 energy , 69ff , 93ff Maxwell, 58ff , Maxwell-Boltzmann , 80, 90 of particles in a colloidal solution, 26 of solute between two solvents , 3 spatial, 57 uniform , 90 velocity, 57 verification of, distribution function , 57ff , 723ff gaussian, distribution law , Nernst , 3 DNA, Dobereiner' s triads , 447 donor molecule , 553 Dorn effect, 434 double layer, 432 Gouy , 432 Gouy-Chapman, 432 Helmholtz, 432 Stern , 433 double-salt formation , 340 doublet, 591 driving forces for natural changes , 208 droplets , vapor pressure of small, 4 dry cell, Dulong and Petit, 446 duNouy tensiometer, 409 D-line , 1 Edison storage cell , 402 EER, 70 Eigen, M , 828 eigenfunctions , 472 degenerate , 475 nondegenerate , 475 ortho-normal set, 477 eigenstates , 473 degenerate , 475 nondegenerate, 475 eigenvalues , 472 spectrum of, 474 einstein, definition of, Einstein, A , 447 , 455 , 456 Einstein coefficient of absorption, 649, 896 electric field, 766 , A- 1 in a dielectric, 659 of light wave, 579 electric potential, 37 , 766, A- at surface of a sphere , 359 electrical conduction, 765ff electrical conductivity , 746 , 765 electrical double layer, 432 stability of lyophobic colloids, 437 electrical phenomena at interface s , 432 electrical transport, 765ff electrical work, 37 1ff electrochemical cell, 206 , 37 1ff as power source , 396 classification of, 396 diagrams for, 375ff fuel cell, 396 primary cell, 396 electrochemical potential, 373 , 787 electrochemical processes, technical, 395ff electrochemical terminology , 399 electrode calomel, 384 gas-ion, 383 irreversible , 876 kinds of, 383ff mercury-mercuric oxide , 384 mercury-mercurous sulfate , 384 metal ion-metal, 384 metal-insoluble salt-anion , 384 oxidation-reduction, 384 quinhydrone , 404 reversible , 876 silver-silver chloride , 384 electrode potentials, 380ff standard, table of, electrokinetic effects , 434 electrolysis , 874ff electrolyte activity of, 354ff chemical potential of, 355 diffusion of, 789ff electrolytic solutions electrical conduction in, 769ff equilibrium in, 365ff Gibbs energy of, 355 structure of, 358ff electromachining, 395 electromagnetic wave , 579 electromotive force , 377 electron discovery of, 446ff magnetic moment of, 523 shells , 525 subshells , 525 wavelength of, 447 electron cloud in hydrogen atom, i n hydrogen molecule , 536 in molecular orbitals, 556 in states with angular momentum, 521 1-5 1-6 I n d ex electron gas , heat capacity for, 729 electron groups , refraction of, 666 electron pair, 532ff wave function for, 533 electron probe , electron spectroscopy for chemical analysis , electron spin, 523 electronic band, 644 electronic configuration for water molecule , 646 of alkali metals , 527 of atoms , 526, 527 of eoinage metals, 527 of halogens , 527 of inert gase s , 527 of inner transition elements , 527 of transition elements, 527 table of, 526 term symbols from , 592ff electronic levels singlet, 89 triplet , 89 electronic spectra, 64 1ff of polyatomic molecules , 646 electronic structure , 583 acetylene , 549 acetylide ion, 549 azide ion , 550 carbon dioxide , 550 carbon monoxide , 549 cyanamide ion, 550 cyanate ion, 550 cyanide ion, 549 hexafluorophosphate ion, 553 macroscopic properties and , 709ff nitrogen , 549 nitronium ion, 550 nitrous oxide , 550 of solids, phosphorus pentafluoride , 553 sulfur hexafluoride , 553 electrons equivalent, 592 nonequivalent, 593 electroosmosi s , 434 electrophoresis , 434 electrophoretic effect , 784 electroplating, 395 electrostatics , fundamentals of, A- I I electro-osmotic counter pressure , 434 element, elementary reactions , 803 , equilibrium constants for, elements o f symmetry , emf, 377 emission spectra, 582, 585 of organic molecules , 899 emissive power, 453 Emmet, P , H" 428 emulsions, 439 endothermic reaction, 30 end-group analysis , 929 energy, 03 activation, 847ff average per molecule , 66 bond, 42 changes , 1 6ff conservation of, 93ff conservation of mechanical, 94 conversion between kinds of, 94ff dispersion, 670 electrical , 93 interaction , 670ff interaction, contributions to, 674ff, ionization, 670 kinds of, 93 kinetic , 93 , 95 magnetic , 93 mechanical, 93 nuclear, 93 of a system, 72 1ff, definition of, 14 of photon, 581 of transition, 682 of vaporization, 659 potential, 93 , 95 properties of, 1 relativistic , 93 rotational, 74 strain, 93 surface , 93 thermal, 93 , 95 translational, 74 vibrational, 74 energy band , i n conductors , i n insulators , i n ionic crystals , i n semiconductors , energy distribution, 93ff , 721ff energy efficiency rating (EER) , 170 energy levels, 583 for water molecule , 574 molecular, 554ff of diatomic molecules , 558 , 559 particle in a box, 484 rotational, 627 ensemble , 72 complexions of, 723 enthalpy, 20ff activation , 849 bond, conventional vlaues of, 133 of formation, standard , entropy , 53ff and probability , 89ff as function of T , 82 as function of T and P, 80ff as function of T and V , 78ff definition of, 164 of activation , 860 of mixing, 96 of mixing, 226ff, of the universe , 96 chemical reactions and, 245 of vaporization of associated liquids , 678 properties of, 1ff standard state for ideal gas , 84 standard values , table of, 87 statistical definition of, 192, 723 entropy changes at constant T , 72ff in chemical reactions , 188 in ideal gas , 82ff with changes in state variable s , 177ff entropy production , 853ff enzyme turnover number for, 838 enzyme catalysis , 836ff, EPR, 603 equation of state , 9, 14 for a gas mixture , thermodynamic, Off equilibrium and activity , 353ff www.elsolucionario.org I ndex and integration of Clapeyron equation , 268ff between condensed phases, 9ff conditions for, 203ff gas-solid, 336 heterogeneous , 240 homogeneous , 240 in electrochemical cells, i n ionic solutions , 365ff in non-ideal systems, 347ff in three-component systems, 337 liquid-gas , 264 liquid-liquid, 9ff in three-component system, 337 liquid-vapor, phase diagrams for, 297ff metastable , 268 phase (see phase equilibrium) solid-gas , 265 solid-liquid, 263 , 324ff vaporization, 242 equilibrium constant calorimetric measurements of, 239, 244 for elementary reactions , from half-cell potentials, 385ff in ionic solutions , 354 mole fraction, 234 partition function and , 738 pressure , 233ff temperature dependence of, 238ff equilibrium diagram (see phase diagram) equipartition of energy , Iff law of, 453 equivalent electrons , 592 equivalent weight, 769, 770 error function, 65ff , 497 table , 65 ESCA, escaping tendency , 223 contributions to, 373 of electrically charged particle , 372ff ESR, 603 ethane , decomposition of, 822ff ethylene cis-form, 548 molecular geometry, 547 trans-form, 548 Euler equation, 482 eutectic diagram, 324ff eutectic halt, 327 eutectic temperature , 325 exact differential, 65 , properties of, 74ff exaltation, 668 exchange current density, 880 definition of, 876 exchange degeneracy, 533 excited state , 77 exclusion principle , 524 exothermic reaction, 29 expansion theorem, 476 expansion work, 06 expectation values , 468 , 473 explosion limits , 826 explosions, 825 extensive properties , definition of, extensive variable s , , extent of reaction (see advancement of reaction) Eyring, H , 856 Eyring equation, 858 face-centered cubic structure , 683 , 684 factorial function, 62ff Faraday, 446 fcc , 683 , 684 1-7 Fick' s law, 746 , 788 Fick's second law, 758 first law of thermodynamics , 03 , 29ff , 53 , 446 first-order reactions , 804ff pseudo , 1 flash photolysis , 896ff Flory' s equation, 920 flow , 747 definition of, 746 fluorescence, 889, 89 1ff cross sections for quenching, 895 decay of, 896 quenching, 893ff flux (see flow) , 747 , A- foams, 439 forbidden transition, 649 force constants , 583 formaldehyde molecular geometry , 547 formation reaction, B lff fossil fuel, 64, 70 Fourier' s law , 746 fractional distillation, 302ff fractionating column, 303 Franck-Condon principle , 642 , 892 free energy (see Gibbs energy) , 205ff free particle , quantum mechanics of, 480 free radicals, 82 Iff freezing point depression , 28 Iff and activities , 350 and mean ionic activity coefficient, 357 and practical activity , 353 of polymer solutions , 924 freezing point depression constant, 284 table of, 285 freezing point elevation , 333 free-radical mechanisms , 82 1ff frequency circular, 49 definition of, 579 frequency factor, , 858 Freundlich adsorption isotherm, 426 frictional coefficient, 746, 767 frictional force , 767 , 935 fuel cell, 396 , 399ff reactions , table of, 40 fugacity , , 224, 347 function , A- I complex, 467ff of several variables , A-3 operator corresponding to , 469 real, 467ff fundamental constants, A-22 fundamental equations of thermodynamics , 208ff fusion, heat of, 88 g, 652 gamma ray scattering, 489 gamma ray s , 450 gas constant, gas imperfection , 659 gases, 8ff heat capacity of, 75ff table , 76 ideal, 9ff· kinetic theory of, 1ff liquefaction of, 34 model of, pressure calculation, 52 real, 33ff structure of, gauss, 600 1-8 I ndex gaussian distribution , gaussian surface , 660 Gauss ' s law, A- Gay-Lussac , , 446 Geiger, 447 , 45 gel permeation chromatography, 928 gelatin, 436 gels , 435 geometric isomers , 548 geometric requirements in close-packed structure s , 682 in covalent crystals, 690 in ioni crystals, 686 geometry , molecular, 542 gerade , 652 Germer, 447 , 460 Gibbs , 447 Gibb s , J W , 272 Gibbs adsorption isotherm , 423 Gibbs energy , 205ff , 22 , 420 , 745 and cell potential, 377 as function of advancement, 23 electrical contribution to , 359 'emulsions and , 439 of a mixture , 223 of activation , 860 of cell reaction, 371 of electrolytic solution, 355 of electrons , 379 of formation, 235ff of ideal gas , o f liquids and solids, of mixing, 226ff of reaction, 230ff standard value, 232 of real gase s , of surface film, 407 partial molar, 224 properties of, standard , 235ff in lead-acid cell , 399 of adsorption, 43 standard state for, 13ff temperature dependence of, variation i n composition and , 221ff Gibbs energy of activation for electrode reactions , 878ft Gibbs free energy , 205 Gibbs function, 205 Gibbs-Duhem equation , 249 , 280 , 352 , 42 Gibbs-Helmholtz equation , , 283 Gibbs-Konovalov theorem , 305 glide plane , 695 Goudsmit, 523 Gouy, 432 Grahame , D C , 432 Graham' s law, 756 graph label s , A-20 gravitational distribution law (see barometric distribution) Grotthuss and Draper, law of, 890 ground state , 77 ground state energy, definition of, 532 group character table for, 564ff , A-28 classes of, 562 definition of, 562 irreducible representations of, 564ff multiplication table for, 563 orthogonality theorem , 569ff reducible representations of, 569ff representations of, 564 theory , 561 growth law , 807 guanine , gutta percha, gyro magnetic ratio (see magnetogyric ratio) , 599 habit, 694 half-cell, 375 half-cell potential, 380ff determination of standard value , 390 significance of, 387ff half-life , 804 half-reaction, 874 Hall coefficient, 768 Hall effect, 767ff Hall potential, 768 hamiltonian operator, 470 eigenfunctions of, 472 linearity , 475 symmetry operations and , 560 harmonic oscillator, 49 1ff classical mechanics of, 49 eigenfunctions for, 495 energy levels of, 494 partition function for, 728ff potential energy of, 629 quantum mechanics of, 493 selection rules for, 650 hcp , 683 , 684 heat definition of, 05 in operation of reversible cell , 383 mechanical equivalent of, 06 of combustion , 34ff of dilution , 136 of formation, of fusion, 88 of reaction , 29ff of solution, 36 of solution, differential , 250 of sublimation, 88 of vaporization, 88 heat capacity at constant pressure , constant volume , 75 Debye theory , 729 Debye-T-cubed law for, 186 difference (Cp c,,) , 22 Einstein theory , 73 of a reactive system, 243 of electron gas , 729 of gases, 75ff table of values , 40 of solids near K, 86 ratio (CpIC,.) , 23 table of, 76 vibrational, 77ff heat conduction, law of, 746, 750 heat engine, 54ff efficiency of, 57ff heat of combustion, 34ff heat of dilution , 136 heat of formation, 1ff determination of, 134 for gaseous atoms , table of values , 142 heat of mixing, 228 heat of reaction at constant volume, 37 dependence on temperature , 138 measurement of, 143 heat of solution, 136 differential, , 250 integral, 37 heat pump , 63 , 70 - www.elsolucionario.org Index heat reservoir, definition of, 54 Heisenberg, W , 447 , 460 , 49 Heisenberg uncertainty principle (see uncertainty principle) Heitler, 532 Helmholtz, 432, 446 Helmholtz double-layer, 432 Helmholtz energy, 205 properties of, 2 Helmholtz free energy , 205 Helmholtz function , 205 Helmholtz planes , 432 Henry' s law , 352 and solubility of gases , 1 Hermite equation, 494 Hermite polynomials, 494ff general expression for, 495 table of, 495 Hermitian operator, 474, 476 eigenvalues of, 474 Hertz, 447 , 452 Herzfeld, K F , 820 , 822 Hess' s law , 135 heterogeneous equilibrium, 240 heterogeneous reactions , 802 rate of, 867ff hevea, hexafluorophosphate ion, 553 hexagonal close-packed structure , 683 , 684 hexagonal system, 692 Hinschelwood , C N , 825 Hittorf method, 775 Hofeditz, W , 82 hole octahedral, 687 tetrahedral, 690 homogeneous equilibrium, 240 homogeneous reaction, 802 Hooke' s law , 628 Huckel, E , 357 Hund, 532 Hund ' s rule , 591 , 594 hybrid orbitals , 543 octohedral, 553 tetrahedral, 543 trigonal, 546 trigonal bipyramidal, 553 hybridization, 543 geometries of various , 553 hydrogen equilibrium, 737 normal, 736 ortho- and para-, 97 ortho-, 735ff para-, 735ff spectrum of, 584 hydrogen atom Bohr' s theory of, 447 electron cloud in, energy levels of, probability distribution in, quantum mechanics of, 1 radial equation solution of, selection rules for, 655 wave functions for, , 5 hydrogen bonding, 677ff and infrared spectra, 678 and x-ray diffraction , 678 hydrogen electrode overvoltage at, 882 polarization at, 876 standard, 374 hydrogen evolution reaction , 876 1-9 hydrogen fluoride , boiling point of, 676 hydrogen molecule covalent bond in, 53 Iff electron cloud in, 536 molecular orbitals in, 555 valence bond method, 534ff wave functions for, 533ff hydrogen-bromine reaction , 9ff hydrogen-iodine reaction , S 5ff hydrogen-oxygen cell, 400 ideal dilute solution, 295 , 307ff Chemical potentials in , 309ff standard states for, 309ff ideal gas , I 1ff chemical potential in a mixture of, 224ff chemical potential of (pure) , 224ff in Carnot cycle , properties of, ideal gas law, 1 deviation from , 33ff ideal gas mixture partial molar quantities in , 250 ideal law of solubility , 286 ideal mixture , definition of, 225ff ideal solid solution , 333 ideal solution as limiting law , 278 chemical equilibrium in, 3 chemical potential in , 280, 296 definition of, 225ff , 278 properties of, 255 imbibition, 436 incongruent melting point, 330 infrared absorption bands for water, 636 infrared photography , 906 infrared radiation , 583 infrared spectroscopy , applications of, 636 infrared spectrum and hydrogen bonding, 678 of acetone, 637 inhibitor, 799 , 802 , 833 anodic , 889 cathodic , 889 innertransition elements, electronic configuration of, 527 insulators , energy bands in, integrability , quadratic , 468 integral, A-2 cyclic , 1 integrals , for kinetic theory of gases , 64 intensive properties , definition (see variable intensive) , intensive variable s , , interaction , laws of, 673ff interaction energy , 670ff contributions to , 674ff interface , electrical phenomena at, 432 interfacial angles , constancy of, 699 interfacial tension liquid-liquid, solid-liquid, water-various liquids, intermolecular forces , , , 659ff , 668ff internal conversion , 893ff international system of units (SI) , 6, A- 17ff internuclear distances , 583 interstitial compound, 687 inversion operation, 652 , 692 ion conductivities , 778 ion product of water determination of, 778 table of values , 780 1- Index ionic atmosphere , 364 ionic crystals, 682 cohesive energy of, 53 , 709ff energy bands in, geometric requirements i n , 686 packing in, 686 ionic solutions (see electrolytic solutions) ionic structures in covalent bonding, 555 ionization energy, 528, 529, 670, 673 ions, migration of, 77 1ff irreversible thermodynamics , 853 irreversible changes in state , 1 isobars of ideal gas , isometrics o f ideal gas , isotherms of ideal gas , o f van der Waals equation, 42 isotonic solution , 291 isotope , isotopes , 450 IUPAC , 205 Jeans, J , 453 Joule , J , 446 Joule experiment, 106, 1 , 24 Joule-Thomson coefficient , 25 , Iff Joule-Thomson effect, 25 Joule-Thomson experiment, 1 , 24 Joule ' s law, 1 , 124, 1 junction potential, 375 , 392 , 792 Kekule , 447 Kelvin, 1 , 99, 446 Kelvin temperature scale , 60 kinetic energy , 93 , 95 average , 56 of a molecule , 55 of random motion, 56 kinetic theory of gases, 1ff integrals for, 64 kinetics (see chemical kinetics) Kohlrausch ' s law , 771 Kronecker delta, 476 K-state , 1 Laguerre polynomials, , Lamer, V , 864 laminar flow , 752 Lande g factor, 599 Langmuir, I , , 424, 425 , 756 Langmuir and Blodgett , method of, 425 Langmuir isotherm, 427 Langmuir tray , , 424 Larmor frequency, 60 , 604 laser, 638 lattice body-centered cubic , 683 , 685 Bravais , 695 , 696 CsCl, 686 face-centered cubic , 683 , 684 , 687 hexagonal close-packed, 683 , 684 NaCI , 687 simple cubic , 686 lattice constants for common metals, 686 Laue method, 701 Laue pattern, 701 Lavoisier, 445 LCAOS , 571 Ie systeme international d' unites (SI) , 6, A- 17ff lead storage cell , 398, 403 lead-antimony system , 325 least-squares , method of, A-5ff leBel, 446 LeChatelier principle, 239, 242ff LeChatelier shift, 737 Legendre equation, 505ff Legendre functions, table of, 506 Lennard-Jones potential, 673 lever rule , 299 Lewis , G N , 347 , 534 light, 579 light absorption, 585 light scattering, 929ff limestone decomposition, 240 limiting law, Debye-Huckel, 363 , 365 Lindemann mechanism, linear laws, 746ff linear operators , 470 Lineweaver-Burk equation, 837 , 870 liquefaction, 659 liquids , 85ff superheated, 43 x-ray diffraction in , 705 liquidus curve, 324, 332 London , F , 532, 670 London forces , 670 long-range order, 68 Lyman serie s , , 585 lyophilic colloids , 435 lyophobic colloids, 435 electrical double layer and stability of, 437 L-state , 1 macromolecules , 3ff macroscopic properties , electronic structure and, 709ff Madelung, E , Madelung constant, Madelung energy, magnetic field, 600 of light wave , 579 magnetic flux density , 600, 766 magnetic moment, 599 nuclear, 603 of electron, 523 orbital, 524 spin, 524 magnetic properties of atoms , 599ff magnetic quantum number, , , 590 magnetic resonance spectroscopy , 603ff magnetogyric ratio for electron , 599 magneton Bohr, 523 , 600 nuclear, 603 Marsden, 447 , 45 mathematical constants, A-23 mathematical interludes exact and inexact differentials, 174ff general ideas , A- Iff kinetic theory integrals , 62ff operator algebra, 469ff symmetry and group theory , 561 matrices , A-7ff symmetry operations as , A-9 maximum work function , 205 Maxwell, J C , 447 , 452 Maxwell distribution , 58ff as energy distribution, 69 average values and, 68ff experimental verification of, Maxwell relations , 209 Maxwell-Boltzmann distribution, 80, 90 mean free path, definition , 750 mean value theorem, A-2 mechanical equilibrium , condition for, 2 mechanical stability, 72 www.elsolucionario.org Index mechanism, I 3ff free-radical , 82 1ff Mendeleev , 447 mercuric oxide decomposition , 241 metals, 682 cohesive energy in , conduction in , 766 metastable states , 43 methane , molecular geometry, 544 Meyer, 447 micelles , 438 Michaelis-Menten law, 837, 870 microwave radiation, 583 microwave spectrum, 635 migration of ions , law of, 771 Miller indices , 698 Millikan, R A , 449 miscibility, partial in liquids , 9ff in solids, 334 mixed potential, 887 mixing entropy of, 196, 226ff Gibbs energy of, 226ff heat of, 228 volume of, 229 mixture composition variable , equation of state , gas , Gibbs energy for, 223 mobility, 766 , 767 generalized , 766 , 787 modes of motion, 625 molality definition of, mean ionic , 356 molar absorption coefficient , 586 molar conductivity , 789 at infinite dilution , 772 definition of, 772 degree of dissociation and , 773 molar ion conductivities , 778 molar mass, determination of, mass average , 928 number average , 926 of a gas , I I , o f polymers , 925ff methods of measuring, 929ff molar mass distribution , 925ff molar polarization, 663 molar refraction, 665 molarity , definition of, mole , , of reaction , 4, mole fraction, definition of, mole ratio , definition of, molecular diameter, 754 molecular energy level s , 554jf molecular geometry , 542 molecular orbital method , 532 molecular orbitals, 554ff construction of, 571 degeneracy of, 57 electron clouds in, 556 for ammonia, 570 for hydrogen molecule, 555 for water molecule , 571 symmetry adapted , 571 molecular partition functions , 725ff molecular spectroscopy , 625ff molecular weight (see molar mass) molecularity , molecule , , 446 geometry of, 635 moment of inertia, 503 monoclinic system, 692 monomer, MOs , Moseley' s law, motion modes of, 74, 625 rotational , 74 translational , 74 vibrational, 74 moving-boundary method, 777 Mulliken, R , 532 multiple bonds , 546 multiplicity , 590 M-state , Natta, G , natural changes driving forces for, 208 entropy and, 96 natural variable s , 209 negative plate , 399 neptunium , 827 Nemst, W , 86, 244, 868 Nemst equation , 377ff Nemst heat theorem, 186, 244 Nemst-Einstein equation , 789 Newland' s octaves , 447 Newtonian mechanics , 467 , 477 , 485 nitrate ion , geometry of, 548 nitrogen , 549 electronic structure , 549 nitronium ion, 550 nitrous oxide , 550 microwave spectrum of, 635 NMR, 58 , 603jf NMR spectrum of acetaldehyde , 607, 608 of ethanol, 606 nonaqueous solvents , conductance in , 786 nonequivalent electrons , 593 nonlinear molecules moments of inertia of, 635 spectra of, 635 nonpolar molecules , 664 normalization, 464, 476 nuclear fission , 826 nuclear magnetic moment, 603 nuclear magnetic resonance , 603ff nuclear magneton, 603 nuclear model of atom, 457 nuclear motions , 53 nuclear reactor, 826 nuclear spin, 603 quantum number, 735 wave function for, 735 nucleic acids , observables , expectation values of, 468 , 473 octahedral hole , 687 Ohm ' s law, 746, 765 oil-drop experiment , 449 Onsager equation, 784 operator differential, 469 for coordinates , 469 for momentum , 469 hamiltonian , 470ff Hermitian , 474 Laplacian, 47 1-1 1-1 I n d ex operator algebra, 469ff operators addition of, 469 commutation of, 470 multiplication of, 469 Oppenheimer, J R , opposing reactions , 5ff orbital antibonding, 557 bonding, 557 definition of, 532 hybrid, 543 order long-range , 68 short-range , 68 order of a reaction , determination of, orthogonality of wave functions , 476 theorem, 569f[ orthonormal set, 477 orthorhombic system , 692 ortho-hydrogen, 97 osmometer, 924 osmosis , 288ff osmotic coefficient, 353 osmotic pressure , 28 , 288 and activities , 350 measurement of, 29 of polymer solutions , 922ff Ostwald dilution law , 774 overlap , 536, 539f[ of p orbitals , 541 of s and p orbitals, 541 of s orbitals, 540 principle of maximum, 536 overlap integral, 539f[ definition, 537 overpotential, 876ff overtone bands , 636 overtone frequency, 632 overvoltage , 876ff activation , 878 hydrogen , 882ff measurement of, 877f[ oxygen, paramagnetism of, 557 ozone , decomposition of, 906 � P-branch, 629 Paneth, F , 82 paramagnetism of oxygen, 557 para-hydrogen, 97 partial molar quantities , 247 in ideal gas mixtures , 250 partial pressure , 224 concept, 20 Dalton' s law , 20, 57 proper quotient of, 232 partial pressure s , 232 equilibrium, 233 particle in a box, 48 1ff deBroglie wavelength for, 483 energy levels , 484 expectation values for position and momen­ tum, 486 wave functions, 48 particle in a three-dimensional box , 498f[ partition function, 722 chemical potential and , 726 equilibrium constant and, 738 electronic degrees of freedom, 73 1f[ for harmonic oscillator, 728f[ for monatomic solid, 729f[ for rigid rotor, 73 1ff for translational degrees of freedom , 727 general expressions for, 737 molecular, 725ff molecular and rate constant, 857 thermodynamic functions and, 724ff Paschen series , , 585 Pasteur, L , 446 path, definition of, 03ff pattern , units of, 69 Pauli exclusion principle , 524, 534, 735 Pauli principle , 588 Pauling, L , 536, 532 peptization , 437 periodic law , 447 periodic system, general trends in, 527 periodicity , 447 peritectic point, 330 peritectic reaction, 330 permittivity , 661 relative , 66 perpetual motion of first kind, 1 of the second kind, 55ff Perrin, Pfund series , phase condensed, 85ff definition of, stability of, 259 phase diagram brass , 335 carbon dioxide , 266 compound formation, 329 condensed phases , 321ff copper-nickel , 333 lead-antimony , 326 potassium-sodium, 3 pressure composition, 297ff pure substance s , 266f[ sulfur, 267 temperature composition , 301f[ water, 266 water-ammonium chloride-ammonium sulfate , 340 water-butanol, 323 water-copper sulfate , 336 water-ferric chloride, 330 water-nicotine , water-potassium carbonate-methyl alcohol, 343 water-sodium chloride , 328 water-sodium sulfate , 332 water-triethylamine , 321 phase equilibrium in simple systems , 259ff phase reaction , 330 phase rule , 259 , 27 1ff phosphorescence , 889, 89 1ff decay of, 896 phosphorus pentafluoride , 553 photochemical equivalence , law of, 890 photochemical reaction examples of, 903 hydrogen and bromine , 904 photochemistry , 889ff photoelectric effect, 447 , 455 , 456 Einstein' s interpretation of, 455 , 456 quantum hypothesis in, 447 photoelectric equation, 456 photoelectron spectrum of water, 620 photolysis of HI, 903 photon, 456, 460 photophysical processes, 89 1f[ photosensitization , 906 photosensitized reactions , 905ff photo stationary state , 907ff www.elsolucionario.org Index photosynthesis , 906ff pi bond, 547 Planck, M , , 244, 447 , 452 , 455 , 581 Planck' s constant, 455 plane of symmetry , 692 plutonium, 827 Poiseuille' s formula, 758ff Poiseuille' s law , 746 poisson equation, 360, A- Polanyi, M , 820 polarizability , 670 distortion , 663 orientation, 663 polarization , 874ff in a dielectric , 659 molar, 663 polyamide , polyatomic molecules electronic spectra of, 646 rotational and vibration-rotation spectra of, 632ff· selection rules for, 656 polyester, polyethylene , polyisoprenes cis- and trans - , polymer molecules , distribution i n gravity field , 26 polymer solutions , boiling point elevation of, 924 colligative properties of, 920ff freezing point depression of, 924 light scattering by, 929ff osmotic pressure of, 922ff thermodynamics of, 9ff turbidity of, 934ff vapor pressure of, 920 viscosity of, 9 , 940 polymers , 3ff addition, atactic , condensation, crystallinity in, 9 isotactic , linear, molar mass distributions of, 925ff molar masses of, 26, 925ff primary structure of, secondary structure of, syndiotactic , tertiary structure of, positive plate , 399 positive ray s , 446 , 450 potential electrode , 380 half-cell , 380 liquid junction, 392 mixed, 887 potential energy , 93 , 95 potentiometer, 389 powder method, 703 power plant, 64 , 70 Chalk Point, Md , 69 power sources, 396ff electrochemical cells as , 396 practical, 398 requirements for, 397 practical activity, 1ff pre-exponential factor, primary cell, 396 primitive translations , 69 principal quantum number, , probability, 722 and entropy , 89ff 1-13 probability amplitude , 464, 467 probability density, 464 , 468 probability distribution in hydrogen atom, i n s states , in states with angular momentum , 52 1ff probability factor, 850 problem working, 28 proces s , definition of, 03ff proper quotient of activities , 354 of activity coefficients, 354 of fugacity and activity, 380 of molalities , 354 of pressure s , 232 protein , a-helix structure , proton in magnetic field , 604 magnetic environment of, 605 Proust, 445 pseudo-first-order reactions , 1 quadratic integrability , 468 , 474 quantization , 74ff , 474 quantum hypothesis atom and, 447 blackbody radiation and, 447, 455 photoelectric effect and, 447 quantum mechanics , 447 , 460 Heisenberg's development of, 49 of free particle , 480ff of harmonic oscillator, 49 of hydrogen atom , 1ff of particle in a box, 48 1ff of particle in a three-dimensional box, 498ff of rigid rotor, 503ff of simple systems , 479 of time-dependent systems , 647 postulates of, 467f]" principles of, 467 quantum number azimuthal, , for total angular orbital angular momentum, 589 for total spin angular momentum, 590 for z-component of angular momentum, 590 for z-component of spin angular momentum , 590 J, 590 I, , L, 589 m, 512, magnetic , , , 590 MJ , 590 ML , 590 Ms , 590 in multielectron atoms , 589 n, , principal, , rotational, 629 S, 590 spin, 523 vibrational, 628 quantum of energy, 455 quantum theory , 459 quantum yield, definition of, 890 quartet, 591 quenching, 893ff cross section, 895 Q-branch, 633 radial distribution function in liquid sodium, 706 radiation absorption and emission of, 458 1-14 Index and matter, 452 of various kinds, 583 radiation density , 649 radiative transition, 893ff radio frequencies , 58 radioactive decay , 805jf radioactivity, 450 discovery of, 447 radiofrequency radiation, 583 radius , atomic, 528 radius ratio rules , 689 Raman effect, 637 selection rules for, 640 Raman scattering, 638 random motion, kinetic energy of, 56 Raoult' s law, 307 , '2 79fL,,295fJ: and nonideal solilliOn s , 349�­ rate constant, 803 for very fast reactions , 832 rate determining step , rate laws, 802jf rate measurements , 799jf rate of reaction , , 75 , 799ff between ions, 862 collision theory of, 849 definition of, 800 dependence on temperature , , , 824, 847jf empirical laws, 799jf for an electrode reaction , 878ff in solution, 861 mechanism, 799jf of photochemical, 890ff salt effects on, 862 specific , 803 theory of, 856jf rational activities , 349ff rational intercepts, law of, 698 Rayleigh-Jeans treatment of blackbody radiation, 453 Rayleigh ratio , 933 Rayleigh scattering, 638 , 929 reaction equilibrium and activity, 353ff reaction Gibbs energy , 230 reaction order, 803 reactions in solution , 827 real gases , 33 Gibbs energy of, isotherms of, 40 real processe s , 1 reduced mas s , definition of, 502 refraction molar, 665 , 670 table of, 666 , 667 of bonds , 667 of electron groups , 666 refractive index , 666, 673 refrigerator, 62 , 69 relative humidity , 279 relative permittivity , 66 relativity theory , 447 , 523 relaxation methods , 828jf relaxation time , 665 , 828ff representations of a group , 564 resistance , 765 , 766 resistivity , 765 , 766 resonance , 535 resonance energy , 536, 538 resonance hybrid , 535 resonance structure s , 535 reversibility of electrochemical cell, 389 microscopic , 853 reversible changes in state , I I I reversible cycle , 154 reversible engine, 55 reversible path, 72 rhombohedral system, 692 Rice, F , 822 Rice-Herzfeld mechanism, 822 Rice-Ramsberger-Kassel theory , 852 rigid rotor, 503ff , 627 wave functions for, 506 Ritz, 457 Roentgen, 446 , 447 rotating crystal method, 703 rotation-inversion , 692 rotational constant, 627 rotational energy, 74ff rotational frequency , 627 rotational spectrum, 627jf rotations, 53 rotor, rigid, 506ff , 627 rubber, 5ff Rumford, 446 Rutherford, 447, 45 Rutherford model of the atom, 465 Rydberg, 457 Rydberg constant, 457 Rydberg formula, R-branch , 629 s states , probability distribution in, salt bridge , 375, 395 salt effect, 366 salting in, 367 scattering alpha ray , 447 , 45 gamma ray , 489 Schrodinger, E , 447 , 460, 49 Schrodinger equation , 447 , 46 1jf , 470ff , 480jf , 72 linear property of, 475 time dependent, 470 time independent, 472 SchrOdinger model of the atom, 464 Schulz-Hardy rule , 438 screw axis , 695 second law of thermodynamics , 53jf , 446 Clausius statement of, Kelvin-Planck statement of, 5 , second-order reactions , 808jf secondary cell , 396 sedimentation , 935ff sedimentation constant, 937 sedimentation equilibrium , 938 sedimentation potential , 434 selection rule s , 583 , 649 for diatomic molecules , 642 for harmonic oscillator, 650 for hydrogen atom, 655 for polyatomic molecules , 656 for rotation , 629 symmetry and , 65 self-energy of charged sphere , 359 semiconductors , 6jf energy bands in, separation o f variables , 499 series (mathematical) , A-23 series (spectroscopic) Balmer, , 585 Brackett, Lyman , , 585 Paschen, , 585 Pfund, series limit, sessile drops , www.elsolucionario.org I n d ex SHE, 374 shells , electron , 525 short-range order, 68 SI, 6, , A- 7jf sigma bond , 547 singlet, 591 Slater, J C , 532 Slater, N B , 852 soap s , 438 sodium chloride structure , 687 solar energy, 69 solid solutions , 332 solids , 85jf electronic structure of, structure of, 68 types of, 682 solidus curve , 332 sols , 435 solubility, 285 common-ion effect on, 339 ideal law of, 286 inert electrolyte effect on , 366ff of fine particles , 4 , o f gases and Henry' s law , 1 of salts, 339 solubility product, determination of, 780 solubility product constant, 387 solute , definition of, 277 solutions , 277jf , 295jf binary , 297ff ideal dilute , 307jf polymer, 8jf solid , 332 solvent , definition of, 277 spectra, 447 absorption, 584 atomic, , 523 , 587ff characteristic x-ray , electronic, 641jf emission, 585 infrared, 626 infrared for HCI, 630 magnetic field , effect on, 600 origins of, 582 , 583 rotational , 626 , 627 vibrational-rotational , 626 , 628 , 632 spectral regions , 579, 580 spectral terms, 591 spectroscopic terms, 589 spectroscopy absorption, 582 emission, 582 molecular, 625 ultraviolet photoelectron, x-ray , 609jf x-ray fluorescence , x-ray photoelectron , speed average , 69 most probable , 67 root-mean-square , 56 spin angular momentum, 524 spin quantum number, 523 spontaneity, conditions for, 203ff spreading coefficient , 420 stability constant , 387 stability of a system mechanical, 72 thermal, 72 standard half-cell potentials determination of, 390 equilibrium constants from , 385jf standard hydrogen electrode , 374 standard reaction Gibbs energy , 232 standard states for electrodes , 377 for Gibbs energy , 3jf summary of, 374 for hydrogen electrode , 379 for ideal gas , 84 for ideal dilute solution , 309jf for practical activity , Stark-Einstein law, 890 Stas , 447 state equation of, of a system , state of a system, variation with time , 648 state property, 1 state sum , 722 state variable , definition of, 04 statistical definition of entropy , 92 statistical thermodynamics , 89jf , 72 1jf Staudinger, steady-state approximation , 825 Stefan-Boltzmann constant, 453 Stefan-Boltzmann law, 453 steric factor, 850 Stern , 433 Stern double layer, 433 Stern-Volmer plot , 894 stimulated emission , 65 Stirling formula, 724 stoichiometry , Stokes line, 638 Stokes-Einstein equation , 788 , 938 Stoke ' s law , 78 1jf , 938 stove-refrigerator, 59 streaming potential , 434 structure CaP2(fluorite) , 689 CsCl, 686 , 688 determination by x-ray diffraction, 704 diamond , 690 NaCl, 687 , 688 of solids , 68 thermodynamic properties and, 72 1jf Ti02(rutile) , 689 ZnS(wurtzite) , 688 ZnS(zinc blende) , 688 sublimation, 261 heat of, 88 subshell s , electron , 525 substance, substrate , 834 sulfur, phase diagram for, 267 sulfur hexafluoride , 553 superposition, 533 , 543 principle of, 475 surface area, determination of, 43 surface energy , 407ff small particles and , 4 thermodynamic treatment, 1 surface exce s s , 42 surface film s , 424 surface potentials, 42(; surface reactions , mechanism of, 867ff surface tension, 90, 407jf adsorption and , 420 liquids, 408 magnitude of, 408 measurement of, 409 drop-weight method, maximum bubble-pressure method , tensiometer, 409 Wilhelmy slide method, 409 , surfaces bimolecular reactions on, 870jf 1- 1-1 Index decompositions on, 868ff role of in catalysis , 872 surroundings , definition of, 103 Svedberg equation, 939 symmetric top , 635 symmetry center of, 561 improper axis of, 561 in the atomic pattern, 694 n-fold axis of, 561 of crystals, 691 of wave functions , 556, 560 plane of, 561 selection rules and, 65 symmetry elements , 561 , 692 symmetry number, 733 symmetry operations , 560ff as matrice s , A-9 hamiltonian operator and, 560jf symmetry specie s , 57 system closed, definition of, 03 definition of, 03 isolated , 03 of variable composition, 221jf open, definition of, 03 properties of, 03 state of, 03 table headings , A-20 Tafel equation, 880ff Tafel slope , 883 Taylor, H S , 873 Taylor' s theorem, A-3 Teller, E , 428 temperature absolute zero of, 56 as parameter of distribution , 68 concept of, 96 flame , gas scale , 1 scale , 1 , 98jf thermodynamic scale , I I temperature scale , 1 , 98ff absolute , 99 current definition of, 99 ideal gas , 1 , 98 , 60 kelvin, 99, 60 thermodynamic , 99 , 60 temperature-jump , 828 tensiometer, 409 term symbols, 59 , 641 from electron configuration, 592ff termolecular reaction, , 850 terms, 589, 591 tesla, 600 tetragonal system, 692 tetrahedral hole s , 690 tetrahedral hybrids, 543 tetramethyl silane, 607 theoretical plate , 305 thermal analysis , 327 thermal conductivity , 748ff thermal contact, 96 thermal equilibrium, 96 condition for, 204 law of, 96 thermal expansion coefficient of, table o f values of, 87 thermal motion, 56, 664 thermal stability , 72 thermochemistry , 103ff thermodynamic equation of state , 0ff thermodynamic functions dependence on composition, 246 partition functions and, 724ff thermodynamic properties , A-24ff thermodynamic temperature scale, 60 thermodynamics chemical reaction, 29ff definitions for, 03 first law of, 93 , 03ff , 29ff , 153 , 446 fundamental equations of, 208ff heat, definition of, 05 irreversible , 853ff of polymer solutions , 9ff second law of, 94jf , 53ff , 446 Clausius statement of, Kelvin statement, 155 Kelvin-Planck statement of, statistical , 72 1jf structure and, 72 1ff term s , 03ff third law of, 1jf , 85ff , 96jf , 244 work definition of, 04 maximum and· minimum values of, 1 Zeroth law of, 96 thermometric equation, 97jf thermometry, 97ff third law of thermodynamics, 1ff , 85jf , 96jf , 244 Thomson, J J , 446 , 447 , 448 thymine, tie line , 299 time-dependent systems , quantum mechanics of 647 TMS , 607 transference numbers , 393 , 775ff Hittorf method, 775 moving-boundary method, 777 transients in a photochemical system, 896ff transition, vertical, 642 transition elements , electronic configuration of, 527 transition moment, 649 integrals, 649, 656 translational energy, 74jf transmittance , 586 transport diffusive , 746 electrical, 765ff general equation for, 747ff of electrical charge , 746 of energy , 746 of mas s , 746 of momentum, 746 transport numbers , 393 transport properties , 745ff in a gas , 757 nonsteady state , 757 triangular diagrams , 337ff triclinic system, 692 trigonal hybrids , 546 trigonal system, 692 triple point, 261 triplet, 591 Trouton' s rule , 72jf , 659 tunnel effect, 497 turbidity, 934jf turnover number, 838 two-body problem, 500ff wave equation for, 500, 502 T-cubed law for heat capacity 86 u, 652 Uhlenbeck, 523 www.elsolucionario.org Index ultracentrifugation, 929 ultracentrifuge, 935ff ultraviolet catastrophe , 453 ultraviolet photoelectron spectroscopy, ultraviolet radiation, 583 uncertainty , definition of, 487ff uncertainty principle , 477 , 489ff ungerade, 652 unimolecular reactions , , theory of, 852 universe , entropy of, 96 uranium fission, 827 fluorescence of salts of, 450 valence bond method, 532 for hydrogen molecule , 534 valence shell electron pair repulsion, 546 van der Waals bonds, 690 van der Waals constants , 67 1ff table of, 36 van der Waals crystal s , 682 van der Waals equation, 47 , 34ff isotherms of, 42 van der Waals forces , 85, 427, 437 , 659 , van der Waals solid, van't Hoff, 446 van't Hoff equation , 289 vapor pressure, 40, 88 activities and, 350 effect of pressure on, 270 lowering, 279, o f binary solution, 297ff of polymer solutions, 920ff of salt hydrates , 336 of small droplets , 414 vaporization, heat of, 88 vaporization equilibrium, 242 variable dependent, , A- I , A-3 independent, , A- I , A-3 of state, definition of, 04 variables composition, natural , 209 reduced, 45 separation of, 499 variation theorem, 532 vectors , A-7 velocity components , velocity distribution , 57 velocity space, velocity vector, component of, 54 vertical transition, 642 vibration-rotation band, 626, 628ff for Hel molecule , 630 P-branch, 629 Q-branch , 633 R-branch , 629 vibrational energy, 74ff vibrations , 53 , 628 virial equation, 47 viscosimeter, 760 viscosity , 90, 746 coefficient of, 752, 766, 781 film, 426 intrinsic , 940 of polymer solutions , 9 , 940 specific , 940 visible radiation , 583 Yolta, A , 395 voltage efficiency , 398 volume of mixing, 229 von Laue, M , 700 von Weimarn ' s law, YSEPR, 546 vulcanization, Walden' s rule , 782 water boiling point of, 676 infrared absorption bands , 636 microwave spectrum of, 635 molecular geometry, 543 phase diagram, 266 photoelectron spectrum of, 620 water molecule electronic configuration for, 646 energy levels for, 574 symmetry properties of, 562 wave functions for, 57 lff wave equation, classical, 460ff wave function, 463ff determinantal, 588 , 593 for electron pair, 533 for hydrogen atom, for hydrogen molecule , 533ff for particle in a box , 48 interpretation of, 463 normalized, 464, 468 nuclear spin, 735 one-electron, 588 symmetry of, , 556 , 560 symmetry under interchange , 735 wave mechanics , 460 wave nature of matter, 447 wave number, 627 definition of, wavelength definition of, o f a particle , 459ff of electrons , 447 Werner, A , 447 wet residues , method of, 342 Wheatstone bridge , 770 Wien effect, 786 Wien' s displacement law , 453 Wilhelmy, 799 Wohler, 446 work electrical, 206 expansion, 06 maximum and minimum, 10 thermodynamic , definition of, 04 work function, 205 x-ray diffraction and hydrogen bonding, 678 in liquids, 705 pattern, symmetry of, 693 x-ray diffractometer, 702 x-ray examination of crystals, 700 x-ray fluorescence spectroscopy , 14ff x-ray frequencies , x-ray microanalysis , x-ray photoelectron spectroscopy, x-ray spectroscopy, 609ff x-ray s , 446 , 583 absorption of, 622 discovery of, 447 Zeeman effect, 600, 622 anomalous , 602 normal, 601 Zeroth law (see thermodynamics), 96 zeta potential, 435 , 438 Ziegler, K , 1· ... enjoyed learning physical chemistry * G Polya, How to Solve It Anchor Book No 93 New York: Doubleday & Co , 957 www.elsolucionario.org Preface An introductory course in physical chemistry must... tera T femto P f 10 peta P atto a 10 18 exa E 10- 10- [2 10 15 10 - IR 15 Physical Chemistry Third Edition Gilbert W Castellan University of Maryland "' Addison-Wesley Publishing Company Reading,... of all the physical quantities are expressed in the correct SI unit, the quantity desired will be obtained in the correct SI unit The net result is that the calculations of physical chemistry