Index 1365
relative speed, 427–428
total rate of collisions, 429–430
pressure of, 424
self-diffusion in, 460–464, 461f
analysis of, 461, 461f
diffusion coefficient, 463
mean free path, 462–463
mean speed, 462
thermal conduction in, 464–465
transport processes in, 460–466, 482
viscosity of, 465–466
Hard-sphere potential, 422–423, 423f
Harmonic oscillator, 623–628, 623f, 626–628f
behavior of, 626, 626f
for diatomic molecule, 627–628, 628f
equation of motion, 624
Hooke’s law, 624
kinetic energy of, 626
potential energy of, 627, 627f
probability density of, 703–704, 703–704f
quantum, 674–679
for diatomic molecule, 678–679
energy eigenfunctions, 677–678, 678f
Hermite equation, 675–676, 1278–1280
total energy of, 627
vibrational states of, 1041, 1042t
Hartree, Douglas Rayner, 798
Hartree–Fock–Roothaan method, 798–799
for Beryllium hydride, 868–869, 868t
of delocalized bonding, 886–887
for lithium atom, 808
for lithium hydride, 852, 852t, 854–855
with more than three electron atoms,
808–809
for water, 894–895, 895t
Heat (q)
calculation of change in, 60–72
ideal gas for, 61–63
irreversible adiabatic processes, 71–72
Joule experiment, 63–67, 63f, 66f
reversible adiabatic processes,
67–71, 68f
caloric theory of, 51
energy transfer by, 39
enthalpy and, 83–84
latent, 51
principle of Le Châtelier and, 338
in statistical mechanics, 1117
transfer of
cyclic process, 114–119
to ideal gas, 62–63
during phase changes, 54
during temperature change, 51–53
Heat capacity (CV), 51
of bomb calorimeter, 96–97
at constant pressure, 51, 75–77
at constant volume, 51, 61
at critical point, 218
of dilute gas, statistical thermodynamics,
1086, 1093–1095
enthalpy change calculation with,
89–91, 90f
entropy and, 119
of first-order phase transitions, 217, 217f
of gases, 75–76
of helium, 217–218, 218f
of liquids, 76–77
molar, 52
of second-order phase transitions,
217, 218f
of solids, 76–77
specific, 52, 170–172
Heat conduction, 441–442, 482
driving force for, 445
Fourier’s law of heat conduction, 445–446
in hard-sphere gas, 464–465
heat flux for, 444
Heat death, of universe, 121
Heat engine.See alsoCarnot heat engine
efficiency of, 105, 109–110
Heat flux, 444
Heat of solution, enthalpy change
of mixing for, 278
Heat pump.SeeCarnot heat pump
Heisenburg uncertainty principle, 711–716
statistical and predictable case in, 713–714
time-energy relation, 715–716
uncertainty product, 712–713
Heisenburg, Werner Karl, 684
Helium atom, 764–766, 764f
excited states of, 803–805, 804f
orbitals of, 779–780, 779t
perturbation method application to,
799–802, 800f
phase diagram of, 207, 207f
phase transition of, 217–218, 218f
probability density for, 794–795
self-consistent field method for, 797–798
variation method application to, 791–793
zero-order approximation for, 765
angular momentum, 774–780
excited state, 772–773ground state of, 768–771, 794, 794f
probability density, 769–771
Helium, diatomic, 842–843
Helmholtz energy (A), 151, 153
differential of, 153
of dilute gas, statistical thermodynamics,
1087, 1098–1099
electrons and, 645
at equilibrium, 156
Maxwell relations, 162
of multicomponent systems, 183–184
work and, 156
Helmholtz free energy.SeeHelmholtz energy
Helmholtz function.SeeHelmholtz energy
von Helmholtz, Hermann Ludwig, 57, 153
Henderson–Hasselbalch equation, 332
Henry, William, 249
Henry’s law, 248–249, 299
dilute solutions
chemical potential, 250–251
composition measures, 252–255
nonelectrolyte solutes, 237
solute distribution in two solvents,
251–252
gas solubility in liquid, 255
Nernst’s distribution law and, 251
solutes and, 262–264
strong electrolytes and, 330, 330f
Henry’s law constant, 249
Henry’s law standard state, 250
Hermite, Charles, 675
Hermite equation, for quantum harmonic
oscillator, 675–676, 1278–1280
Hermite polynomials, 676
Hermitian conjugate, of matrix, 1251
Hermitian operators, 692–694
eigenfunctions of, 693–694, 709
properties of, 1247–1248
Hess, Germain Henri, 88
Hess’s law, 88
for standard-state, 88–89
at various temperatures, 89–91, 90f
HETCOR.SeeHeteronuclear correlation
Heterogenous catalysis, 566
Langmuir theory of adsorption, 566–568f,
566–570
rate of, 570–572
Heterogenous catalysts, 233–234
Heterogenous nucleation, 228
Heteronuclear correlation (HETCOR),
1028, 1032