Chemical Thermodynamics

Mục Lục

1 Introduction ……………………………………………………… 1
Further Reading …………………………………………………… 2
2 Postulates of Thermodynamics …………………………………… 3
2.1 Thermodynamic Systems: Postulate 1 …………………………… 4
2.1.1 Constrained Systems and the Measurability
of Energy via Mechanical Work …………………………. 6
2.2 The Conditions of Equilibrium: Postulates 2, 3 and 4 ……………. 8
2.2.1 Properties of the Entropy Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.2 Properties of the Differential Fundamental Equation . . . . . . . . . 13
2.2.3 The Scale of Entropy and Temperature . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.4 Euler Relation, Gibbs–Duhem Equation
and Equations of State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.5 The Fundamental Equation of an Ideal Gas . . . . . . . . . . . . . . . . . . . 18
2.2.6 The Fundamental Equation of an Ideal
van der Waals Fluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3 Thermodynamic Equilibrium in Isolated and Isentropic Systems …. 29
3.1 Thermal Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2 Thermal and Mechanical Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3 Thermal and Chemical Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4 Thermodynamic Equilibrium in Systems with Other Constraints …. 43
4.1 Equilibrium in Constant Pressure Systems:
The Enthalpy Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.2 Equilibrium in Constant Temperature and Constant
Volume Systems: The Free Energy Function . . . . . . . . . . . . . . . . . . . . . . . . 46

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4.3 Equilibrium in Constant Temperature and Constant
Pressure Systems: The Gibbs Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.4 Summary of the Equilibrium Conditions: Properties
of the Energy-like Potential Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.4.1 Calculation of Heat and Work from Thermodynamic
Potential Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.4.2 Calculation of Entropy and Energy-like Functions
from Measurable Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.4.3 Calculation of Thermodynamic Quantities from the
Fundamental Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.5 Equations of State of Real Gases, Fluids and Solids . . . . . . . . . . . . . . . . . 58
4.5.1 Chemical Potential and Fugacity of a Real Gas . . . . . . . . . . . . . . . 64
Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5 Thermodynamic Processes and Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.1 Quasistatic, Reversible and Irreversible Processes . . . . . . . . . . . . . . . . . . . 69
5.2 Heat Engines: The Carnot Cycle and the Carnot Engine . . . . . . . . . . . . 72
5.3 Refrigerators and Heat Pumps: The Carnot Refrigerating
and Heat-Pump Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.4 Heat Engines and Refrigerators Used in Practice . . . . . . . . . . . . . . . . . . . . 77
5.4.1 Heat Engines Based on the Rankine Cycle . . . . . . . . . . . . . . . . . . . 77
5.4.2 Refrigerators and Heat Pumps Based
on the Rankine Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.4.3 Isenthalpic Processes: The Joule–Thompson Effect . . . . . . . . . . 80
Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6 Thermodynamics of Mixtures (Multicomponent Systems) . . . . . . . . . . . 87
6.1 Partial Molar Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.1.1 Chemical Potential as a Partial Molar Quantity . . . . . . . . . . . . . . . 89
6.1.2 Determination of Partial Molar Quantities
from Experimental Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
6.2 Thermodynamics of Ideal Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.2.1 Ideal Gas Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.2.2 Properties of Ideal Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.2.3 Alternative Reference States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.2.4 Activity and Standard State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.3 Thermodynamics of Real Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.3.1 Mixtures of Real Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.3.2 The Chemical Potential in Terms of Mole Fractions . . . . . . . . 106
6.3.3 The Chemical Potential in Terms of Solute Concentration … 108
6.3.4 Activity and Standard State: An Overview . . . . . . . . . . . . . . . . . . 109
6.3.5 Thermodynamic Properties of a Real Mixture . . . . . . . . . . . . . . . 115
6.4 Ideal Solutions and Ideal Dilute Solutions . . . . . . . . . . . . . . . . . . . . . . . . . 118
Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
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7 Phase Equilibria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
7.1 Stability of Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7.2 Phase Equilibria of Pure Substances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
7.2.1 Phase Diagrams of Pure Substances . . . . . . . . . . . . . . . . . . . . . . . . . . 135
7.2.2 Calculation of the Quantity of Coexisting phases:
the Lever Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
7.2.3 Calculation of Equilibrium Temperature and Pressure;
the Clausisus–Clapeyron Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
7.2.4 First-Order and Second-Order Phase Transitions . . . . . . . . . . . . 144
7.3 Liquid–Vapor Equilibrium of Ideal Binary Mixtures . . . . . . . . . . . . . . 147
7.4 Liquid–Vapor Equilibrium of Real Binary Mixtures . . . . . . . . . . . . . . 154
7.5 Solid–Liquid Equilibrium of Ideal Binary Mixtures . . . . . . . . . . . . . . . 158
7.6 Equilibrium of Partially Miscible Binary Mixtures . . . . . . . . . . . . . . . . 159
7.6.1 Liquid–Liquid Phase Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
7.6.2 Solid–Liquid Phase Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
7.6.3 Colligative Properties: Equilibrium of a Binary Mixture
Phase and a Pure Phase Containing One of the Mixture
Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
7.7 Phase Diagrams of Multicomponent Systems . . . . . . . . . . . . . . . . . . . . . . 185
7.8 Separation of Components Based on Different Phase Diagrams …. 190
Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
8 Equilibria of Chemical Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
8.1 Condition of a Chemical Equilibrium at Constant Temperature
and Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
8.1.1 Relation of the Equilibrium Constant and the
Stoichiometric Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
8.1.2 Affinity: The Driving Force of Chemical Reactions . . . . . . . . . 206
8.2 The Equilibrium Constant in Terms of Different Activities . . . . . . . 211
8.2.1 Heterogeneous Reaction Equilibria
of Immiscible Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
8.3 Calculation of the Equilibrium Constant from
Thermodynamic Data ………………………………………… 218
8.4 Temperature and Pressure Dependence of the Equilibrium
Constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
8.4.1 The Le Chaˆtelier–Braun Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
9 Extension of Thermodynamics for Additional Interactions
(Non-Simple Systems) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
9.1 Thermodynamics of Interfaces: Two-Dimensional
Equations of State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
9.1.1 Thermodynamic Properties of Curved Surfaces . . . . . . . . . . . . . 234

9.2 Thermodynamic Description of Systems Containing
Electrically Charged Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
9.2.1 Thermodynamic Consequences of the Electroneutrality
Principle: The Chemical Potential of Electrolytes
and the Mean Activity Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
9.2.2 Chemical Potential of Ions in an Electric Field:
The Electrochemical Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
9.2.3 Heterogeneous Electrochemical Equilibria:
The Galvanic Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
9.2.4 Electrodes and Electrode Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . 259
Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
10 Elements of Equilibrium Statistical Thermodynamics . . . . . . . . . . . . . . 265
10.1 The Microcanonical Ensemble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
10.1.1 Statistical Thermodynamics of the Einstein Solid
in Microcanonical Representation . . . . . . . . . . . . . . . . . . . . . . . . 269
10.1.2 Statistical Thermodynamics of a System
of Two-State Molecules in Microcanonical
Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
10.2 The Canonical Ensemble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
10.2.1 Calculation of the Canonical Partition Function
from Molecular Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
10.2.2 Statistical Thermodynamics of the Einstein
Solid and the System of Two-State Molecules
in Canonical Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
10.2.3 The Translational Partition Function. Statistical
Thermodynamics of a Monatomic Ideal Gas . . . . . . . . . . . . . 283
10.2.4 Calculation of the Rotational, Vibrational,
and Electronic Partition Functions . . . . . . . . . . . . . . . . . . . . . . . . 287
10.2.5 Statistical Characterization of the Canonical Energy . . . . . 291
10.2.6 The Equipartition Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
10.3 General Statistical Definition and Interpretation of Entropy . . . . . 297
10.4 Calculation of the Chemical Equilibrium Constant
from Canonical Partition Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306
11 Toward Equilibrium: Elements of Transport Phenomena . . . . . . . . . . 307
11.1 Transport Equations for Heat, Electricity, and Momentum . . . . . . 309
11.2 Equations for the Diffusive Material Transport . . . . . . . . . . . . . . . . . . . 311
11.2.1 Fick’s First Law: The Flux of Diffusion . . . . . . . . . . . . . . . . . . 312
11.2.2 Fick’s Second Law: The Rate of Change
of the Concentration Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
11.3 Principle Transport Processes and Coupled Processes . . . . . . . . . . . 316
Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
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Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
A1 Useful Relations of Multivariate Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . 319
A.1.1 Differentiation of Multivariate Functions . . . . . . . . . . . . . . . . . . 319
A.1.2 Differentiation of Composite Functions . . . . . . . . . . . . . . . . . . . . 322
A.1.3 Differentiation of Implicit Functions . . . . . . . . . . . . . . . . . . . . . . . 323
A.1.4 Integration of Multivariate Functions . . . . . . . . . . . . . . . . . . . . . . 324
A.1.5 The Euler Equation for Homogeneous
First-Order Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325

A2 Changing Extensive Variables to Intensive Ones:
Legendre Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326
A.2.1 Legendre Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
A.2.2 Legendre Transformation of the Entropy Function . . . . . . . . 329
A3 Classical Thermodynamics: The Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331
A.3.1 Zeroth Law and Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332
A.3.2 First Law and Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334
A.3.3 Second Law and Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336
A.3.4 Third Law and the Uniqueness of the Entropy Scale . . . . . . 341
Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343

 

 

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