Index
A
Acentric factor:
and second virial coefficients, 165
and third virial coefficients, 168, 170
quantum gases, 112
effective value, 173
relation to critical compressibility factor, 165, 173
Activity:
equilibrium equation, 23
Flory-Huggins theory, 425, 427
ideal solution, 219
incipient instability, 273, 275
mean ionic, 514
residual, Prigogine-Flory-Patterson theory, 451
standard state, 787
Activity coefficient:
associated solutions, 355-360, 366
from data for other component, 232-236
Flory-Huggins theory, 426-429
at infinite dilution,
definition, 804
by differential ebulliometry, 804
by head-space analysis, 805
by gas-liquid chromatography, 428, 804
Margules equation, 226, 255, 587, 592, 645
and solubility limits, 794
van Laar equation, 807
Wilson equation, 807
lattice theory, random mixtures, 333
pressure and temperature dependence, 521
molality, 509
multicomponent systems, 280-294, 325, 614
normalization of, 222-225
NRTL, 262
Redlich-Kister expansion, 228, 238
regular-solution theory, 315, 606, 646
relation to average chain length, 361
relation to excess Gibbs energy, 219, 226
Scatchard-Hamer equation, 257
solvated solutions, 369-374
standard state, 214, 246, 508-511
temperature derivative, 220
UNIQUAC, 264
Wilson equation, 258
Additivity assumption, 132, 153, 154
corrections to, 154
Area fraction; see Surface fraction
Area test; see Thermodynamic consistency
Associated solutions:
Dolezalek model, 353
multiple association, 358
Flory-Scatchard model, 364
gas solubility in liquids, 618
SAFT, 368
in vapor phase, 174-179
Axilrod-Teller correction, 154
B
Barker method, 236
Benedict-Webb-Rubin equation, Lee-Kesler form, 113
Boiling-point method, 242-245
Boltzmann factor, 63
Boltzmann relation, 762
Branching, effect on:
boiling point, 77
cohesive-energy density, 323
enthalpy of mixing, 79
Buckingham potential, modified; see Exp-6 potential
C
Canonical ensemble, 754-762
statistical analogues of thermodynamic properties, 759
Canonical partition function, 105, 767-769
definition, 759
of lattice, 331
relation to equation of state, 106, 382, 761
van der Waals, generalized; see van der Waals partition function
Chain length, average, 361
Charge-transfer complexes, 88-93, 651
Chemical forces, comparison with physical forces, 78, 374, 619, 629
Chemical potential:
from canonical partition function, 382
excess, 787
as function of T and P, 34
as function of T and V, 45
in grand canonical ensemble, 767
of monomer, in associated or solvated solutions, 818
of pure ideal gas, 21
pressure derivative, 21
relation to activity, 21
relation to activity coefficient, 787
relation to fugacity, 21
residual, reduced, 451
and standard state, 20, 508-510
temperature derivative, 787
Chemical Theory:
associated solutions, 352-363
high-pressure phase equilibria, 730-737
second virial coefficient, 179-189
solvated solutions, 369-374
Closed system:
homogeneous, definition, 10
equilibrium equations, 11-14
heterogeneous, definition, 17
equilibrium equations, 17, 749-751
Cohesive-energy density:
combining rules, 315, 321, 324, 326
definition, 313
polar and nonpolar contributions, 323
relation to solubility parameter, 315
Collision diameter, 142
Combinatorial contribution, 263, 422, 450
Combinatorial relations, 757, 763, 771
Combining rules:
cohesive-energy density, 315, 321, 324, 326
critical constants, 160, 173, 724
Mollerup, 724
Plöcker, 725
equation-of-state parameters, 38, 49, 50, 311, 327, 699, 715
potential energy parameters, 110, 160, 397, 402, 473, 612, 779
volume, 650
Compressibility factor:
critical, characteristic, 173
Leenard-Jones potential, 109
relation to acentric factor, 173
definition, 35
generalized, 723
PHSC, 400
SAFT, 395
Configurational integral, 106, 769, 824
Configurational properties, 769, 823
Conformal-solution theory:
two-fluid, 344-350
Consolute temperature; see Critical solution temperature
Conversion factors, to SI units, 842
Coordination number, 330, 438, 727
effect on critical solution temperature, 341
Corresponding-states correlations:
fugacity of hypothetical liquid, 608
pseudocritical method, 190
quantum gases, 172
second virial coefficient, 159
third virial coefficient, 168
Corresponding-states theory:
classical, 104
molecular, 105
three-parameter, 112
Lee-Kesler form, 113
Coulomb relation, 60
Critical solution composition:
Margules equation, 276
polymer solutions, 431
van Laar equation, 277
Critical solution temperature, 271, 275-279
effect of third component, 695
lattice theory, 741
Margules equation, 276
pressure dependence, 686
pressure derivative, 693
van Laar equation, 277
D
de Broglie wavelength, 383, 442
reduced, 779
Debye-Hückel constant, 527, 830
Debye-Hückel limiting law, 524-530
Debye length, 525
Debye temperature, 77
Degeneracy, 332
Degrees of freedom, external, 384, 441
Density variables, 676
Dielectric constant, 61
Dimerization; see Association
Dipole-dipole interaction, potential energy, 63
Dipole-induced dipole interaction, potential energy, 66
Dipole-quadrupole interaction, potential energy, 65
Dipoles, induced, 66
definition, 61
units, 64
schematic representation, 64
Dispersion forces, 68-72
effect on cohesive-energy density, 649
London formula, 69
DISQUAC model, 368
Dissociation, gas solubility in liquids, 626
in vapor phase, 174
Distribution of solute:
liquid in liquids, chemical theory, 378-382
Nernst distribution law, 378
partition coefficient, 378
protein partitioning, 565
Donor number, 622
E
Effective critical constants, quantum gases, 172
Efectron-donor-acceptor complexes, 88, 651
Electrical potential, difference, 104, 569
Electrolyte, strong, 512
weak, 530
Electrolyte solutions, 507
excess properties, 522
McMillan-Mayer formalism, 556
Lewis-Randall formalism, 556
models:
Chen, 540
“chemical” hydration, 552-556
Debye-Hückel, 524
fundamental, 538
local composition, 540
semi-empirical, 539
salt solubility, 549
volatile electrolytes, phase equilibria, 557-565
Electrostatic forces, 60
Enhancement factor, 192
Ensemble, canonical, 756-762
grand canonical, 762-767
Enthalpy:
from canonical partition function, 761
configurational, conformal-solution theory, 345
of dimerization, 181
excess; see Excess enthalpy
as function of T and P, 34
of function of T and V, 44
from grand canonical partition function, 761
of hydrogen bonding, 88, 186, 366, 377
of mixing; see Excess enthalpy
of solution of gases in liquids, 596
Entropy:
Boltzmann relation, 762
from canonical partition function, 761
of dimerization, 181
excess, see Excess entropy
as function of T and P, 34
of function of T and V, 45
from grand canonical partition function, 761
of hydrogen bonding, 186
of mixing:
combinatorial, Flory-Huggins theory, 423
of ideal solution, 333
residual, Prigogine-Flory-Patterson theory, 450
partial molar, of solution of gases in liquids, 596
Equation of state:
from canonical partition function, 106, 382
from grand canonical partition function, 761
definition, 124
Prigogine-Flory-Patterson, 444
Sanchez-Lacombe, 462
Equilibrium constant:
of association, 354
multiple, 359
relation to second virial coefficient, 179, 186
temperature derivative, 337, 366
Equilibrium equation, general, 17, 23, 51
Equilibrium state, definition, 12
Equivalent translational degrees of freedom, 385, 442
ERAS model, 368
Ergodic hypothesis, 756
Excess enthalpy:
associated solutions, Flory-Scatchard model, 366
athermal solutions, 253
effect on critical solution temperature, 693
electrolyte solutions, 524
in isobaric Gibbs-Duhem equation, 788
lattice model, quasichemical approximation, 339
Prigogine-Flory-Patterson theory, 450
regular solutions, 333
relation to excess Gibbs energy, 216, 328, 376
solvated solutions, 377
Excess entropy:
combinatorial, athermal solutions, 349
definition, 424
Flory-Huggins theory, 425
Lichtenthaler modification, 424
lattice model, quasichemical approximation, 339
regular solutions, 333
Excess functions, definition, 216
partial molar, definition, 217
relations between, 216
Excess Gibbs energy:
associated solutions, Flory-Scatchard model, 365
electrolyte solutions, 523
lattice model, quasichemical approximation, 339
Margules equation, 226, 240, 272, 695
multicomponent systems, 279-294
NRTL, 261
and phase stability, 272
pressure derivative, 217
Redlich-Kister expansion, 227, 278
regular-solution theory, 333
relation to activity coefficient, 219, 226
electrolyte solutions, 523
relation to excess Helmholtz energy, 326
temperature derivative, 217
van Laar equation, 251, 277, 311
Wilson equation, 258
Wohl’s expansion, relative to ideal-
dilute solution, 251
relative to ideal solution, 250
Excess Helmholtz energy:
athermal solutions, 349
lattice model, quasichemical,
approximation, 338
random mixtures, 333
relation to excess Gibbs energy, 326
relation to excess internal energy,
temperature derivative, 338, 348
UNIQUAC, 349
Excess internal energy:
conformal-solution theory, 348
definition, 328
lattice model, quasichemical, approximation, 338
random mixtures, 333
regular-solution theory, 315
Excess volume:
definition, 328
effect on critical solution temperature, 693
in isothermal Gibbs-Duhem equation, 789
Prigogine-Flory-Patterson theory, 451
regular solutions, 333
Exp-6 potential, 145
parameters, 146
schematic representation, 141, 150, 151
third virial coefficient from, 155
Extensive properties, 33
F
Field variables, 676
Flash calculation, 795
Flory-Huggins interaction parameter:
composition dependence, 431, 452
definition, 427
estimation, 430
and phase stability, 431
reduced residual chemical potential, 451
relation to solubility parameter, 430
temperature dependence, 455
Flory-Huggins theory:
athermal solutions, 421-423
Lichtenthaler modification, 424
gas solubility in mixed solvents, 617
Fourth virial coefficients, definition, 775
Free volume:
Flory equation, 443
fraction, 811
Percus-Yevick equation, 387
van der Waals equation, 384
Frisch-van der Waals equation, 327
Fugacity; see also Fugacity coefficient
of component in liquid solution, 196, 214
of condensed phase, 41, 195, 214
definition, 21
as function of T and P, 34
as function of T and V, 45
Henry’s law, 196, 378, 586, 589
of hypothetical liquid, 608, 636,
of ideal liquid solution, 214
Lewis fugacity rule, 24, 37, 124
pressure derivative, 215, 589, 702
standard state, 32, 214, 297, 636
of strongly dimerized component, 176
temperature derivative, 701
total differential, 699
van der Waals equation, 39, 50
Fugacity coefficient:
of condensed phase, 41
as function of T and P, 34, 123
as function of T and V, 45, 124, 713
Lewis fugacity rule, 125
Peng-Robinson equation, 720
pressure derivative, 711
van der Waals equation, 39, 50
Furter equation, 534
G
Gas-gas equilibrium, 696-699
Gels, polymer, 488
hydrogels, 491
model of Hino, 492
swelling, 489
ratio, 494
Geometric mean; see Combining rules
Gibbs energy:
from canonical partition function, 761
excess; see Excess Gibbs energy
as function of T and P, 34
as function of T and V, 45
from grand canonical partition function, 761
of mixing, Flory-Huggins, 423, 426
lattice theory, effect of nonrandomness, 342
and phase stability, 271, 340, 687-690
pressure derivative, 688
partial molar; see Chemical potential scaled-particle theory, 612
Gibbs-Duhem equation, 18, 232, 520
thermodynamic consistency, 245-250
Gibbs-Helmholtz equation, 217, 328, 376
Grand canonical ensemble, 762-767
statistical analogues of thermodynamic properties, 765
Grand canonical partition function, 761, 766
Group-contribution methods:
activity coefficients from, 350, 808
equations of state, 810
H
Hard-core volume, 388, 443, 462, 811
Hard-sphere chain models, 389
PHSC, 400
SAFT, 390
pure components, 395
mixtures, 396
Hard-sphere potential, 139
schematic representation, 140
second virial coefficient from, 139
Heat capacities, definition, 15
Helmholtz energy:
from canonical partition function, 761
configurational, 107, 769, 823
excess; see Excess Helmholtz energy
as function of T and P, 34
as function of T and V, 45
from grand canonical partition function, 761
of mixing, definition, 332
reduced residual, 46
relation to pressure, 327
residual, 770
Henry’s constant:
effect of temperature, Benson-Krauser correlation, 600
Harvey correlation, 601
excess, 617
from an equation of state, 593, 609
excess, definition, 617
from Henry’s constant at other pressure, 222
in mixed solvents, 613-619
near solvent critical point, 602
pressure derivative, 589
scaled-particle theory, 610-613
Henry’s law, 378, 586, 626; see also Henry’s constant; Krichevsky-Ilinskaya equation; Krichevsky-Kasamovsky equation
pressure corrected form, 196, 589
Heterogeneous system, 17
Homogeneous system, 10-17
Homomorph, of polar molecule, 179
Hydrophobic, interaction, 94
effect, 95
Hydrogen bonding, 81-88; see also Association; Solvation
Hylotrope, 660
I
Ideal-dilute solution, 214, 221, 378, 587; see also Henry’s law
Ideal-gas potential, 139
schematic representation, 140
Ideal solution, 6, 24, 214, 219, 222
activity of, 219
activity coefficient of, 214, 219
chemical theory, 354, 359, 369, 375
deviations from, 216
entropy of mixing of, 333
excess functions for, 216
fugacity of, 214
partial molar enthalpy of, 215
partial molar volume of, 215
and phase stability, 272
Incipient instability, conditions for, 271, 340
Independent intensive variables, 3, 18, 750
Index of refraction, 68
Induced dipole-induced dipole interaction; see Dispersion forces
Induction forces, 66
Intensive properties, 3
Intensive thermodynamic potentials, 17, 749-751
Interchange energy, definition, 331
Kohler method, 334-336
relation to Flory-Huggins parameter, 428
relation to Prigogine-Flory-Patterson parameter, 449
Intermolecular forces; see also Potential energy; Potential energy functions
classification, 58
effect of molecular structure, 77
relation to potential energy, 59
relative magnitude, 71
Intermolecular potential energy; see Potential energy
Internal energy:
of dimerization, 183
from canonical partition function, 759-761
configurational, 769
excess; see Excess internal energy
as function of T and P, 34
as function of T and V, 44
from grand canonical partition function, 761, 765
of hydrogen bonding, 83
of mixing; see Excess internal energy
regular-solution theory, 314
multicomponent systems, 324
residual, 770
of solvation, 183
van der Waals equation, 310
van Laar theory, 309
of vaporization, of hypothetical liquid, 646
Internal equilibrium, 10, 17, 749
Ionic forces, 60
Ionic strength, definition, 524
lonization, effect on gas solubility in liquids, 626
lonization potential, in correlation of volume of mixing, 91
data, 70
definition, 69
Irreversible process, 12
Isolated system, 755
Isothermal compressibility, 445, 705
J
Joule-Thomson, coefficient, 29,
K
Kibara potential, 146
parameters, 149
schematic representation, 141, 150, 151
second virial coefficient from, 147, 148
third virial coefficient from, 155
Kohler equation for excess properties, 284
Kohler method, 334-336
Krichevsky-Ilinskaya equation, 592
Krichevsky-Kasarnovsky equation, 589, 703
L
Lagrange method of undetermined multipliers, 758, 765
Lambert chemical theory, 179
Lattice model, 329-334
critical solution temperature with, 341
quasichemical approximation, 336-343
random mixtures, 332
Laws of thermodynamics, 10, 762
Lee-Kesler correlation, 113, 609, 725
Legendre transformations, 13, 285
Lennard-Jones potential, 73, 142
and gas solubility in liquids, 603, 612
parameters, 144
relation to critical constants, 109
temperature dependence, 143
schematic representation, 73, 140, 150
second virial coefficient from, 142, 147, 148, 152
third virial coefficient from, 155, 156
Lewis acid-base interactions, 353, 604, 620, 623
Lewis fagacity rule, 24, 37, 39, 124, 197
second virial coefficient with, 163
LFAS model, 368
Liquid-liquid equilibrium:
conditions for, 269-275, 340, 687
Flory-Huggins parameter, 431
Redlich-Kister expansion, 278
equilibrium equation, 690, 792
at high pressure, 687-696
from isothermal flash calculation, 795
Margules equation, 792
for multicomponent systems, 795-801
NRTL, 794
quasi-chemical theory, 340-343
UNIQUAC, 796
solubility limits, 793-796
Liquid-liquid-gas equilibrium, 678, 695
Liquids, hypothetical, properties of, 584, 608, 637, 659
Local-composition equations for excess Gibbs energy:
electrolyte solutions, 540
London forces; see Dispersion forces
M
Margules equation:
for multicomponent systems, 280, 613
n-suffix, 234
three-suffix, 237, 256, 282, 793
two-suffix, 226, 243, 272, 280, 592, 613, 645, 689, 695, 792
Maximum-term method, 758, 764, 771
Maxwell relations, 15
McMillan-Mayer theory, 97
Melting temperature, effect of pressure and composition, 700
Membranes, nonporous, 475
permeability, 480
separation factor, 480
separation process, 476
solution-diffusion model, 478, 487
vapor permeation, 476
Micelles, 94
reverse, 94
Microcanonical ensemble, 755, 762
Mie’s potential, 72
for condensed systems, 74
schematic representation, 73
Miscibility, conditions, see Critical solution temperature; Liquid-liquid equilibrium
Mixing rules:
equation of state parameters, 38, 49, 311, 327, 402, 464, 715
virial coefficients, 133, 134, 160, 164, 170
Wong-Sandier, 721
Molality,
definition, 509
mean ionic, 514
Mutual solubilities; see Liquid-liquid equilibrium
N
Nernst distribution law, 378
Nonrandom mixtures; see Lattice theory, quasichemical approximation; NRTL; UNIQUAC; Wilson equation
NRTL, 261
Chen model, 540
multicomponent systems, 290, 799,
liquid-liquid equilibrium, 261, 294, 794, 799
O
One-liquid theory; see Conformal-solution theory
Open system, definition, 14
homogeneous, fundamental relation, 16
Osmotic coefficient, 512, 517, 831
relation to excess Gibbs energy, 523
Debye-Hückel, 527
van’t Hoff equation, 99
Osmotic virial coefficients, 99, 132
p
Pairwise additivity; see Additivity assumption
Partial miscibility; see Critical solution temperature; Gas-gas equilibrium, Liquid-liquid equilibrium; Liquid-liquid-gas equilibrium
Partial molar excess properties; see Excess functions
Partial molar properties, 17, 34, 45, 217, 786
Partial pressure:
from Barker method, 236-242
from boiling-point method, 242-245
definition, 584
Partition coefficient, 570
definition, 378
infinite dilution, 602
Partition function:
canonical; see Canonical partition function
configurational; see Configurational partition function
generalized van der Waals, 383
mixtures, 386
grand canonical; see Grand canonical partition function
Peng-Robinson equation, 718
fugacity coefficient, 720
parameters, characteristic binary constant, 720
solid solubility in compressed gases, 195
vapor-liquid equilibrium, 718-720
Permittivity:
absolute, 61
Perturbation theory, 821-827; see also Scaled-particle theory
Perturbed hard-chain theory, 387
gas solubility in polymers, 459
vapor-liquid equilibrium, 730
Perturbed hard-sphere-chain theory, 400, 471
Perturbed hard-sphere theory, 382, 387
Phase, definition, 10
Phase equilibrium, and classification of binary systems, 677-680
Phase stability; see also Critical solution temperature; Liquid-liquid equilibrium; Gas-gas equilibrium; Liquid-liquid-gas equilibrium
conditions for, 269-275, 340, 687
Physical forces, comparison with chemical forces, 78, 113, 363-369, 619, 629
Pitzer ion-interaction model, 543-552
multielectrolyte solutions, 829-839
Polar molecules; see also Stockmayer potential
cohesive-energy density, 323
potential energy between, 63
second virial coefficients, 166
third virial coefficients, 158
Polarizability, 66
volume, 66
Polymers:
average molecular weights, 420
glass-transition temperature, 419
polydispersity index, 420
properties, 418
Polymer solutions:
equation of state, PHSC, 471
Prigogine-Flory-Patterson, 444
SAFT, 471
Sanchez-Lacombe, 462
Flory-Huggins theory, 421
Bae correlation, 434
Hino model, 436
Lichtenthaler modification, 423
real, 427
Potential energy; see also Intermolecular forces; Potential energy functions; Potential energy parameters
between charged molecules, 60
between dipole and induced dipole, 67
between dipole and quadrupole, 65
between dipoles, 63
between nonpolar molecules:
repulsive, 72
between quadrupole and induced
quadrupole, 67
between quadrupoles, 65
of lattice, 331
relation to interchange energy, 331
relation to intermolecular forces, 59
Potential energy functions:
condensed system, 74
determination of best potential, 149
exp-6, 145
hard-sphere, 139
ideal gas, 139
Kihara, 146
Mie, 72
square-well, 143
Stockmayer, 150
Sutherland, 141
Potential energy parameters:
combining rules, 110, 160, 612, 779
estimation, 109
relation to critical constants, 109
Potential of mean force, 96, 132
Poynting correction, 41, 192, 608
Pressure; see also Partial pressure
configurational, 769
effective, 172
relation to potential energy parameters, 109
from partition function, 108, 382, 761
reduced, 105, 190, 388, 444, 462
with molecular parameters, 108
relation to Helmholtz energy, 327
residual, 770
scale, natural/chemical processes, 672
Prigogine-Flory-Patterson interaction parameter, 449
Prigogine-Flory-Patterson theory:
mixtures, 445-451
Protein partitioning, 565-572
Pseudocritical method, 190
Q
Quadrupole-induced quadrupole interaction, potential energy, 67
Quadrupole-quadrupole interaction, potential energy, 65
Quadrupoles, effect on cohesive-energy density, 650
moments, 65
definition, 64
schematic representation, 64
Quality, in vapor-liquid mixture, 684
Quantum gases:
effective critical constants, 172
virial coefficients, 779
Quantum state, 754
Quasichemical approximation; see Lattice theory
R
Radial distribution function, 825
Random mixtures; see Lattice theory
Raoult’s law, 24, 241, 308, 584
Redlich-Kister expansion, 227, 238, 240, 278
and classification of solutions, 228-231
contribution of each term, 229, 278
and phase stability, 278
Redlich-Kwong equation,
partial molar volumes, 711
combining rules, 715
mixing rules, 715
Soave’s modification, 714-717
Reference state; see Standard state
Regular-solution theory, 253, 313-326; see also Solubility parameter
gas solubility in liquids, 604
mixed solvents, 608
multicomponent systems, 325
Myers extension, 648
solid solubility in liquids, 645-652
mixed solvents, 654
Relative volatility, definition, 206
Repulsive forces, between nonpolar molecules, 72
Residual contribution, 263, 422, 450
Retrograde, condensation, 685
vitrification, 469
Reversible process, definition, 11
S
SAFT model, 368
equation of state, pore components, 395
Salting-in effect, 534
Sanchez-Lacombe equation, 462
Scaled-particle theory, gas solubility in liquids, 610-613
Scatchard-Hamer equation, 256
Scatchard-Hildebrand theory; see Regular solution theory
Second virial coefficients:
chemical theory, 179-189
contributions from physical forces, 186
corresponding-states correlations,
McGlashan, 160-162
Pitzer-Tsonopoulos, 164-168
cross coefficient, 133, 140, 163, 182-187
quantum gases, 781-783
from hard-sphere potential, 139
from Kihara potential, 147, 148
from Lennard-Jones potential, 142, 147, 148, 152
quantum gases, 779
physical significance, 132
from potential energy, 132, 133, 159
from potential of mean force, 132
reduced, 147
from reduction of P-V-T data, 129
from square-well potential, 145
from Stockmayer potential, 152
from van der Waals equation, 27, 208
Segment fraction, 263, 291, 349, 422, 448, 811
Setchenov equation, 533
Shair correlation, 607
mixed solvents, 608
Solid solutions, 658-664
Solubility of gases in liquids, 703; see also Henry’s constant
Benedict-Webb-Rubin equation, Lee-Kesler form, 609
chemical effects, 619-629
contributions from physical and chemical forces, 618
dependence on solubility parameter, 603
effect of cohesive-energy density, 599
effect of pressure; see Krichevsky-Ilinskaya equation; Krichevsky-Kasarnovsky equation
effect of temperature, 596-603
equilibrium equation, 583, 702
Henry’s law, 586-588
ideal, 584
Lennard-Jones potential, 603, 612
maximum solubility, 702
in mixed solvents, 608, 613-619
Flory-Huggins theory, 617
regular-solution theory, 608
partial molar enthalpy, 597
partial molar entropy, 597
perturbed hard-chain theory, 609
pressure derivative, 703
regular-solution theory, 603
scaled-particle theory, 610
near solvent critical point, 602
temperature derivative, 596
Solubility limits; see Liquid-liquid equilibrium
Solubility of liquids in compressed gases, 191-200, 709
Solubility parameter; see also Regular-solution theory
in correlation of gas solubility in liquids, 603
as measure of nonideality, 317, 321
nonpolar, 323
polar, 323
relation to Flory-Huggins parameter, 430
solubility criterion, 430
temperature dependence, 316
volume fraction average, 325, 609
Solubility product, 548
Solubility of solids in compressed gases, 191-200, 708
enhancement factor, 192
equilibrium equation, 192, 707
ideal-gas equation, 197
Peng-Robinson equation, 195, 196
supercritical extraction, 706
virial equation, 197-199
Solubility of solids in liquids:
equilibrium equation, 636, 651
freezing diagrams, 642
mixed solvents, 653-658, 664-666
regular-solution theory, 645
Myers extension, 648
in two immiscible liquids; see Distribution of solute
Solvated solutions:
Dolezalek model, 369-374
gas solubility in liquids, 557-565, 619-629
in vapor phase, 174
Specific forces; see Chemical forces
Square-well potential, 143
schematic representation, 141, 150, 151
second virial coefficient from, 145, 155
third virial coefficient from, 155
Statistical thermodynamics, 753
Stockmayer potential, 150
parameters, 152
schematic representation, 140
second virial coefficient from, 152
Summation constant, 75
Supercritical extraction, 706
Surface fraction, 263, 291, 348, 449
Sutherland potential, 141
schematic representation, 140
T
Temperature:
Boyle, 29
critical, characteristic, 160, 173, 726
combining rules, 160, 173, 726
data, 844
effective, 172
mixing rule, 725
relation to potential energy parameters, 109
inversion, 29
reduced, 105, 190, 388, 444, 462
with molecular parameters, 108
statistical analogue, 760
Thermal expansion coefficient, 444
Thermal pressure coefficient, 445
Thermodynamic consistency, 245
area test, 247
differential (slope) test, 245
Van Ness method, 248
Thermodynamic probability, 762
Third virial coefficient:
corresponding-states correlations, 168
Besher-Lielmezs, 168
Orbey-Vera, 169
cross coefficient, data, 158
McGregor relation, 170
Orentlicher formula, 169
effect of additivity assumption, 153, 168
from exp-6 potential, 155
from Kihara potential, 155
from Lennard-Jones potential, 155
mixing rules, 134
physical significance, 132
polar gases, 158
from potential energy, 132, 134
quantum gases, correlations, 781
data, 781
reduced, 169
from reduction of P-V-T data, 129
from square-well potential, 155
Trouton’s constant, 84
True mole fraction; see Ideal solution, chemical theory
Two-liquid theory; see Conformal-solution theory
U
UNIFAC, activity coefficients, 351, 808
solid solubility in liquids, 651, 664
derivation, 346
multicomponent systems, 290, 795
liquid-liquid equilibrium, 266, 794
polymer-liquid equilibrium, 486
vapor-sorption in polymers, 486
Units, SI, 841
conversion factors, 842
V
van der Waals equation, 47, 384
approximate form, 37
fugacity coefficient, 39
corresponding-states theory, 104
fugacity coefficient, 48
gas-gas equilibrium, 697
parameters, combining rules, 50, 699
mixing rules, 38, 49, 311, 594
reduced form, 105
and van Laar theory, 310
van der Waals forces, 363
van der Waals-l theory; see Conformal solution theory
van der Waals partition function, generalized, 383
mixtures, 386
van Laar equation, 251, 277, 311
critical solution composition, 277
critical solution temperature, 277
liquid-liquid equilibrium, 794
multicomponent systems, 281, 288
relation to regular-solution equation, 316
van Laar solution theory, 309
van’t Hoff equation, 99
Vapor-liquid equilibrium:
equilibrium equation, 8, 24, 52, 297, 558, 712
at high pressure:
chemical theory, 730-737
corresponding-states correlations,
Lee-Kesler, 725
Mollerup, 724
Peng-Robinson equation, 718-723
perturbed hard-chain theory, 730
Soave-Redlich-Kwong equation, 714-717
number of unknowns and of independent equations, 52
regular-solution theory, 318
SAFT, 398
salt effect, 536
Vapor pressure, of hypothetical liquid, 584, 638, 646
Virial coefficients; see Second, Third, Fourth virial coefficients
Virial equation:
for dimerized vapor, 179
liquid solubility in compressed gases, 197
mixtures, 137
and perturbation theory, 822
pressure explicit (Leiden) form, 128, 775
comparison with volume explicit form, 128, 131, 776
fugacity coefficient, 137
range of applicability, 130
solid solubility in compressed gases, 194
volume explicit (Berlin) form, 128, 775
fugacity coefficient, 138
Volume:
combining rules, 650,
critical, combining rules, 160, 173, 724
correlation, α-olefins, 162
data, 844
effective, 172
mixing rule, 724
relation to potential energy parameters, 109
free; see Free volume
of hypothetical liquid, 606, 646
of mixing; see Excess volume
mixing rules, 618
partial molar, correlation, 705
of ideal solution, 215
at infinite dilution, definition, 594
near critical conditions, 704
Redlich-Kwong equation, Chueh modification, 711
relation to saturated molar volume, 704
pseudocritical, 725
molecular parameters, 108
Volume fraction, 314, 325, 372, 646
effective, 250
W
Wilson equation, 258
multicomponent systems, 287
liquid-liquid equilibrium, 261
Wohl’s expansion:
relative to ideal dilute solution, 251
relative to ideal solution, 250
multicomponent systems, 280