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Activity
coefficient and molality 166
coefficient in the concentration
scale 168
coefficient of a species in a real
solution 153
coefficient using convention I
157
coefficient using convention II
162
effect
of pressure and temperature on the — coefficient 155
of a
pure condensed phase 125
of a
species in a real solution 153
Adiabatic
chemical
equilibrium of an — isobaric system 121
chemical
equilibrium of an — isochoric system 122
closed — system
20, 53, 55
enclosure
2, 16
process
16
reversible
process 17
reversible
process of an ideal gas 29
Auxiliary
functions
39
state
variable 3
Azeotropy 158-162
Beau de Rochas cycle 34
Binary
mixture 139, 144
system 158
Boiling point
—
141, 144
elevation
of the — of a solvent in the presence of a solute 150
Bubble point 141
Carnot cycle
— 17, 30
reverse — 18
Change
isothermal reversible — of
a gas 11
of a state variable 5
of the Gibbs energy in a mixture of
chemical species 117
of the Gibbs energy with the extent
of reaction 117, 118
Characteristic variables 42-46
Châtelier
Le —'s principle 135
Chemical
conversion of — energy into work 113,
114
independent — reactions 128
reaction 103
Chemical equilibrium
effect of an inert gas on a — 137
effect of pressure on a — 136
effect of temperature on a — 136
effect of volume on a — 137
of an adiabatic isobaric system 121
of an adiabatic isochoric system 122
of an isobaric isothermal system 119
of an isothermal isochoric system 120
Chemical potential
definition 43
of a multiphase system at equilibrium
90
of a pure condensed phase 125
of a pure ideal gas 69
of a pure liquid 140
of a
pure real gas 76
of a
real gas in a mixture 83
of a
species in a real solution 153
of
an ideal gas in an ideal gas mixture 73
of
an ideal species 139
of
ions in solution 171
reference
state — 140, 157, 162, 166, 168
standard —
69, 157, 162, 166, 168
Chemical
reaction
energetics of —s 103
isothermal and isobaric — 104
system with several —s 131
Clapeyron equations 92
Clausius inequality 22
Clausius-Clapeyron equations 94
Closed
adiabatic system 20
system 1, 40-41
system with one chemical reaction, 103
Coefficient
activity
— and molality 166
activity
— and the concentration scale 168
fugacity —
of a pure real gas 77
fugacity —
of a real gas in a mixture 83
isobaric — of
thermal expansion 4
isothermal
compressibility — 4
Joule-Thomson —
82
of
performance 32
partition —
165
stoichiometric —s
103
thermal
expansion — 4
van
der Waals —s 79
Combustion
internal — engine 34
Components
number of — in a system 133
Composition
concentration scale, 167
molality scale, 165
mole fraction scale, 61, 72, 140, 153
of the vapor phase of a binary
solution 142, 144, 159, 161
Compressibility
factor 77, 81
isothermal — coefficient 4
Compression
isothermal — of an ideal gas 26
ratio 35
Concentration
and composition 167
scale 167
Condensation
— 78
curve 142, 144, 158, 161
Condensed phase
chemical potential of a pure— 125
Constant
Avogadro's — 13
critical —s 79
Henry's — 163
Raoult's — 141
standard equilibrium — 123
thermodynamic equilibrium — 123,
127
volume thermal expansion coefficient 4
Constant pressure
process at — 119, 121
Constant volume
process at — 40, 120, 122
Continuity of the fluid state 99
Convention
for aqueous systems 173
I for the standard state and activity
coefficient 157
II for the standard state and
activity coefficient 162
relation
between — I and II activity coefficients 164
relation
between — II and the molality scale 166
sign —
for energy exchanges 9
—s
for activity coefficients in solutions 153
Conversion
of chemical energy into work 113
Corresponding
states of real gases 80
Critical
constants
79
point
79
temperature
78
Curve
condensation — 142, 144, 158, 161
dew point — 142, 144
fusion — 98
inversion — 82
sublimation — 98
vaporization — 98, 141, 144, 161
Cycle
Beau de Rochas — 34
Carnot — 17, 30
dithermal — 17
Otto — 34
reverse Carnot — 18
Stirling — 36
Cyclic process 5, 16
Dalton's law 72
Debye-HŸckel theory 171
Degrees of freedom
number of — 91, 133
Delay
phase change —s 99
Dew point curve 142, 144
Diagram
isobaric — for a perfect binary
solution 143
isothermal — for a perfect
binary solution 141
phase — 98
Diathermal enclosure 2
Differential
exact — 6
Differential expression
for the enthalpy 43
for the free energy 44
for the free enthalpy 44
for the Gibbs energy 44
for the Gibbs function 44
for the Helmholtz energy 44
for the Helmholtz function 44
for the internal energy 42
of state functions (multiple phases)
89
—s for open systems, 45, 132
Dilute solutions 157, 166, 167
Dissociation equilibrium 172
Dithermal cycle 17
Effect
Joule–Thomson —
81
of an
inert gas on chemical
equilibria 137
of
pressure and temperature on
the activity coefficient 155
of
pressure and volume on entropy
at 0 K 101
of
pressure on chemical
equilibria 136
of
pressure on phase equilibrium
92
of
temperature on chemical
equilibria 136
of
temperature on the entropy of
reaction 112
of
temperature on the Gibbs
energy of reaction 112
of
temperature on the latent heat
97
of
temperature on vapor pressure
97
of volume
on chemical equilibria
137
Efficiency of an engine 31, 32
Electrical work 12
Electrode potential
and
standard entropy of reaction 175
definition
175
Electrolyte
chemical potential of ions in
solution 171
dissociation 170
Electroneutrality of a solution 170
Elevation
of the boiling temperature of a solvent in the presence of a solute 150
Enclosure
adiabatic —
2, 16
diathermal —
2
Endothermic reaction 109
Energetics of chemical reactions 103
Energy
free —
44
Gibbs
— 39
Helmholtz —
39, 44
internal —
15, 42
sign
convention for — exchanges 9
various
forms of — 13
Enthalpy
— 3, 39
explicit expression for the — 62
of an ideal gas mixture 71
of mixing 74, 84, 146
of phase change 94
of reaction 105
standard — of formation 107
Entropy
at 0 K 101
definition 19
effect of temperature on the —
of reaction 112
evaluating — 100
global — 27, 54
of an ideal gas 70
of mixing 74, 146, 155
of reaction 105
standard — 107
Equation
Clapeyron —s 92
Clausius-Clapeyron —s 94
Gibbs-Duhem — 62
Kirchhoff's — 110
van der Waals — of state 78
virial — 77
Equation of state
of an ideal gas 50
thermodynamic — 49
van der Waals — 78
Equilibria
simultaneous — 132
Equilibrium
chemical — displacement
laws 135
condition
24, 57
dissociation —
172
effect
of an inert gas on a chemical — 137
effect
of pressure and temperature on liquid vapor — 146
effect
of pressure on a chemical — 136
effect
of pressure on phase — 92
effect of temperature on a chemical —
136
effect of volume on a chemical — 137
gas and condensed phase — 94
liquid vapor — 141
of a chemical system 1, 117
of two phases 92
system in a state of — 1
thermal — 1, 2, 24
Equilibrium constant
— 123
effect of temperature on the — 134
in heterogeneous systems 126
in solutions 169
in the gas phase 124
in the liquid phase 169
standard — 123
thermodynamic — 123, 127
Euler's identity 59
Eutectic 149
Evaluation of entropies 100
Exact differential 6
Excess
entropy of mixing 155
entropy of mixing (gases) 86
Gibbs energy of mixing 154
Gibbs energy of mixing (gases) 85
variable of mixing (gases) 85
variables of mixing 154
Exothermic reaction 109
Expansion
isobaric
coefficient of thermal — 4
isothermal —
of an ideal gas 26
monothermal
— of an ideal gas 27
Expression
explicit — for
enthalpy 62
explicit —
for the Gibbs energy 62
explicit —
for the Helmholtz energy 62
explicit — for
the internal energy 62
of
the molar entropy of an ideal gas 70
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Extensive
properties of — variables, 60
variable 2, 39
Extent of
reaction
— 103
and expression of enthalpy 110
and work 113, 114
change of the Gibbs energy with the —
117, 118
Extraction
liquid-liquid — 165
Field
magnetic — 13
First law of thermodynamics 15
Fluid
continuity of the — state 99
Force
external — 9
van der Waals —s 75
work of an external — 9
Formation
standard enthalpy of — 107
standard Gibbs energy of — 107
standard variables of — 107
Free
energy 3, 39, 44
enthalpy 3, 39
Freezing point lowering by a solute
147
Fuel cell 114
Fugacity
and the law of mass action 123
coefficient of a pure real gas 77
definition 76
of a real gas in a mixture 83
Function
auxiliary state — 39
homogeneous —s 59
properties of homogeneous —s 59
state — 2, 89
Fusion 98
Gas
constant 8
effect of an inert — on vapor
pressure 95
equation of state of an ideal —
50
ideal — mixture 70
real —es 75
thermodynamics of —es 69
General process 5, 16
Generalization of Hess' law 108
Gibbs energy
— 3, 39, 55
and extent of reaction 117
at 0 K 102
effect of temperature on the — energy
112
excess — of mixing 154
excess — of mixing (gases) 85
explicit expression for the — 62
of a mixture of reactants 117
of formation of hydrogen ions 173
of mixing 74, 146, 154
of mixing in solutions 146
of mixing of real gases 85
of reaction 104, 105
Gibbs function 3, 39
Gibbs-Duhem equation 62
Gibbs-Helmholtz equations 46
Global entropy
— 27, 54
and spontaneity 27
Half-cell standard potential 175
Heat
—
15
engine
17, 31
pump
31, 34
source
1, 17, 53
system
in contact with one — source 17, 53, 55, 119, 120
system
in contact with several — sources 22
system
in contact with two — sources 17
transfer
24
Heat capacity
at
constant pressure 41
at
constant volume 40
molar —
29
of reaction 105
Helmholtz
energy
— 3, 39, 44, 53
at 0 K 102
explicit expression for the — 62
of reaction 105
Helmholtz function 3, 39, 44
Henry's
constant 163
law 163
Hess' law 108
Heterogeneous system
— 1
—s and the law of mass action 126
Homogeneous
functions 59
system 1
Hydrogen ion convention for aqueous
solutions 173
Ideal
gas mixture 70
mixture of gases 86
perfect and — solutions 139-152
species 140
Ideal gas
Chemical potential of a pure — 69
definition 50
law of mass action for —es 124
mixture of —es 70
partial pressure of an — 71
Identity
Euler's — 59
Implications
of the first law 16
of the second law 20
of the third law 101
Independent reactions
— 128
and the law of mass action 132
number of — 128
Inert
effect of an — gas on chemical
equilibria 137
Infinitesimal
process 16
Intensive
properties of — variables 60
variable 2, 39, 45, 61
Internal energy
— 15, 42
differential expression for the — 23
explicit expression for the — 62
expression for the — 23
of an ideal gas mixture 70
of mixing 85
of reaction 105
Inversion curve and temperature 82
Ionic strength 171
Ions
chemical potential of — in solutions
171
law of mass action for — 172
Irreversible
(real) process 7
process 19
Isenthalpic process 82
Isentropic process 20, 29
Isobaric
chemical equilibrium of an
adiabatic — system 121
coefficient of thermal expansion 4
diagram 161
diagram for a perfect binary solution
143
equilibrium of an — isothermal system
119
expansivity 4
process 40
Isochoric
chemical equilibrium of an
adiabatic — system 122
equilibrium of an
isothermal — system 120
Isochoric process 40, 120, 122
Isolated system 1
Isothermal
compressibility coefficient 4
compression of an ideal gas 26
diagram 141, 158
equilibrium of an isobaric —
system 119
equilibrium of an isochoric —
system 120
expansion of an ideal gas 26
representation of perfect solution
liquid vapor equilibrium
141
reversible process 17
Joule
energy unit 15
the — experiment 15
Joule-Thomson
coefficient 82
effect 81
Kirchhoff's equation 110
Latent heat
effect of temperature on the — 97
of phase change 94
Law
Dalton's — 72
displacement —s of equilibria 135
Henry's — 163
Hess' — 108
Raoult's — 141
Law of mass action
—
123
for
a heterogeneous system 126
for
ideal gases 124
for
ions 172
in a
liquid phase 168
in
solutions 168
Law of thermodynamics
first
— 15
second —
17
third —
101
zeroth
— 2
Le Châtelier's principle 135
Lennard-Jones interaction 75
Lever rule 143, 144, 159
Lewis-Randall rule 87
Lowering of the freezing point in the
presence of a solute
147
Magnetic field 13
Mass action
law of — 123
law of — for a heterogeneous
system 126
Maximum
amount of work 55, 56, 113
azeotrope 158
entropy 24
extent of reaction 117
Maxwell's relations 46-48
Measurement of partial molar volumes
67
Mechanical equilibrium 1, 89
Mixing
enthalpy of — 74, 84, 146
entropy of — 74, 146
excess entropy of — 155
excess variable of — (gases) 85
Gibbs energy of — 74, 146
Internal energy of — 85
irreversible — of two ideal
gases 75
properties of ideal solutions 145
variables of — 154
variables of — for ideal gases 74
variables of — for real gases 84
volume of — 145
volume of — of real gases 84
Mixture
binary 139, 144
chemical potential of an ideal gas
in an ideal
gas — 73
fugacity of a real gas in a — 83
ideal gas — 70
ideal — of gases 86
law of mass action for an ideal gas —
123
—s of ideal gases 70
—s of real gases 83
Molality
definition 165
scale 165
Molar
heat
capacity 29
partial — enthalpy
of an ideal gas 73
partial
— entropy in a solution 155
partial — entropy of an
ideal gas 73
partial — quantities 63, 67
partial — volume of an ideal gas 72
properties 65
quantities 65
Molarity 168
Mole fraction 61, 72, 140
Molecular interactions in real gases
75
Monobaric
and monothermal process 56
process 41
Monothermal
and monobaric process 56
process 17
Natural variables 42
Number
of chemical species in a system 91,
133
of components of a system 133
of independent reactions 128
of independent species in a system 133
of phases in a system 91
Open system 42, 90
Osmotic pressure 151
Otto cycle 34
Partial molar
enthalpy of an ideal gas 73
entropy in a solution 155
entropy of an ideal gas 73
quantities 63, 67
quantities of pure substances 65
volume of an ideal gas 72
Partial pressure of an ideal gas 71
Partition coefficient 165
Perfect
and
ideal solutions 139-152
solution
141
Phase
change
delays 99
chemical
potential of a condensed — 125
definition
89
diagram
98
law
of mass action in the liquid — 168
number
of —s in a system 91
rule
3, 91, 133
rule
and electrolytes 170
Physical meaning of
the
Gibbs function 55
the
Helmholtz function 53
Point
critical —
79
triple —
19, 99
Potential
half-cell
standard — 175
reduction —
175
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Pressure
effect
of — on chemical equilibria 136
effect
of — on the activity coefficient 155
intensive
variable 61
osmotic —
151
standard
state — 69, 105
Principle
Le Châtelier's — 135
Process
adiabatic —
16
at
constant external pressure 11, 41, 56
at
constant pressure 119, 121
at
constant volume 40, 120, 122
chemical —
103
cyclic
— 5, 16
irreversible —
7, 19
isenthalpic
— 82
isentropic —
20, 29
isobaric —
40
isochoric —
40, 120, 122
monobaric —
41
monothermal
and monobaric — 56
monothermal —
17
reverse —
and work 12
reversible
adiabatic — of an ideal gas 29
reversible
— 7, 19
spontaneous
— 75
Properties
of extensive variables 60
of homogeneous functions 59
of intensive variables 60
Pure
chemical potential of a — ideal
gas 69
chemical potential of a — real
gas 76
real gas 75
Rank of a matrix 129
Raoult's
constant 141
law 141
Reaction
endothermic — 109
exothermic — 109
extent of — 103
independent —s 128
Real
mixtures of — gases 83
solution 153
volume of mixing of — gases 84
Real gas
fugacity of a — in a mixture 83
partial molar volume of
a — 84
pure — 75
Reduced variables 79
Reduction potential 175
Reference state for entropy 101
Refrigerator 31, 33
Relation
between
activity coefficients in binary systems 160
between Cp and CV
51-52
Maxwell's
—s 46-48
—s between
partial molar quantities 64
Reverse process and the sign of work
12
Reversible
adiabatic
process of an ideal gas 29
isothermal
expansion or compression of an ideal gas 26
process
7, 19
Rule
lever — 143, 144, 159
Lewis-Randall — 87
phase — 3, 91, 133
phase — and electrolytes 170
Schwarz theorem 7, 46, 52
Second law of thermodynamics
Spontaneous processes and
the — 57
— 17-37
Application to chemical equilibrium
119
Kelvin formulation of the — 17
Selection of the standard state
pressure 69
Sign convention for energy exchanges 9
Simultaneous
independent — reactions 128
reactions 131
Solute
— 147, 162
effect of a — on the boiling
temperature 150
freezing point lowering by a —
147
Solution
ideal — 140
isothermal diagram 141
non ideal — 153
perfect and ideal — 139-152
perfect — 141
real — 153
Solvent
— 147, 162
elevation of the boiling temperature
of a — by a
solute 150
lowering of the freezing point
of a — by a solute
147
Spontaneous
evolution of a system 57
process 20, 75
transfer of species between phases 90
Standard
chemical potential 69
chemical potential in liquids 157
chemical potential using
convention I 157
chemical potential using
convention II 163
entropy 107
equilibrium constant 123
Gibbs energy of formation 107
heat capacity at constant pressure 107
molar heat capacity at constant
pressure 107
variables of reaction 105
Standard state
— 106
of a real gas 76
on the molality scale 166
pressure 69, 105
temperature 105
State
corresponding —s of real gases 80
equation of — 8
function 2, 3, 15, 89
standard — 106
standard — and convention I for
the activity
coefficient 157
standard — and convention II for
the activity
coefficient 162
variable of — 3
Stirling cycle 36
Stoichiometric coefficients 103
Sublimation 98
System
at equilibrium 1
binary — 158
closed adiabatic — 20
closed — 1, 40-41
heterogeneous — 1, 126
heterogeneous — and the law of
mass action 126
homogeneous — 1
in contact with one thermal reservoir
17, 21, 53-56
in contact with several thermal
reservoirs 22
in contact with two heat sources 17
irreversible process in a — 20
isolated — 1
open — 1, 42-46, 90
without chemical reaction 89
Temperature
critical — 78
effect of — on chemical equilibria 136
effect of — on the activity
coefficient 155
effect of — on the equilibrium
constant 134
inversion — 82
standard state — 105
thermodynamic — 18
Thermal
coefficients
4
equilibrium
1, 2
equilibrium
and entropy 24
expansion
coefficient 4
machines
31
Thermal reservoir
definition
of a — 1
entropy
change of a — 21, 26, 54, 75
system
in contact with one — 17, 21, 53
system
in contact with several —s 22
Thermodynamic equilibrium constant
123, 127
Thermodynamic temperature 18
Third Law of thermodynamics 101
Transfer
heat —
24
spontaneous —
of species 90
Triple point 19, 99
Van der Waals
coefficients
79
equation
of state 78
Vapor pressure
—
95, 140
effect
of an inert gas on — 95
effect
of temperature on — 97
of
an ideal solution 141
Vaporization curve 98, 141, 144, 161
Variable
auxiliary state — 3, 39
auxiliary — 39
excess — of mixing 154
extensive — 2, 39
intensive — 2, 39
natural —s 42
of mixing 154
of mixing for real gases 84
of reaction 104, 105
of state 3
reduced —s 79
standard —s of formation 107
standard —s of reaction 105
Variance of a system 91, 133
Variation of heat capacities with
volume and pressure 52
Virial coefficients and equation 77
Volume
effect of — on chemical equilibria 137
of mixing 145
of reaction 105
partial molar — of a real gas 84
partial molar — of an ideal gas
72
work due to — change 10
Work
any form of — 113
due to volume change 10
electrical — 12
mechanical — 9
other than volume — 114
sign convention for — 9
various expressions for — 13
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Modified December 17 2006
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