Dedication ..................................................... xv
Preface ...................................................... xvii
CHAPTER 1 Definition, Development, and Applications of
Thermodynamics .................................................. 1
I Historical Development of Chemical Thermodynamics .......... 1
II Pioneering Applications in the Geosciences ................. 2
III Thermodynamics versus Kinetics ............................. 3
CHAPTER 2 Important Concepts and Mathematical Methods ........... 5
I Definitions ................................................ 5
II Pressure and Temperature ................................... 7
A. What is Temperature? .................................... 7
B. Temperature Measurement ................................. 8
C. Development of the International Temperature Scale ..... 13
D. What is Pressure? ...................................... 17
E. Pressure Measurement ................................... 19
III Boyle's Law ............................................... 21
IV Charles's or Gay-Lussac's Law ............................. 24
V Dalton's Law .............................................. 26
VI An Ideal Gas Thermometer .................................. 26
VII Ideal Gas Equation of State (The Ideal Gas Law) ........... 27
VIII The PVT Surface for an Ideal Gas .......................... 28
IX Complete Differentials and the PVT Surface of an Ideal
Gas ....................................................... 29
X Thermal Expansion Coefficient ............................. 33
XI Compressibility Coefficient ............................... 34
XII Some Further Notes about Differentials .................... 35
A. Perfect (or Exact) Differentials ....................... 36
B. Chain Rule ............................................. 37
C. Cyclic Rule ............................................ 38
Problems .................................................. 38
CHAPTER 3 The First Law of Thermodynamics ...................... 41
I Historical Overview of Ideas about Heat and Work .......... 41
A. The Caloric Theory of Heat and its Demise .............. 41
B. Robert Mayer's Work .................................... 44
C. Joule's Experiments on the Mechanical Equivalent of
Heat ................................................... 46
D. Helmholtz and the Conservation of Energy ............... 50
II The First Law of Thermodynamics ........................... 51
A. The Definition of Energy and Different Forms of
Energy ................................................. 51
B. Nuclear Reactions and the Conservation of Energy ....... 52
C. Mathematical Statement of the First Law ................ 53
A.
D. Use of the First Law to Analyze Joule's Paddle Wheel
Experiments ............................................ 53
E. Pressure-Volume Work and Indicator Diagrams ............ 54
F. A Graphical Illustration that Work and Heat are Path
Dependent .............................................. 56
G. The Definition of a Reversible Process ................. 59
H. Constant-Pressure Processes and Enthalpy, a New State
Function ............................................... 60
I. Heat Capacity and Specific Heat ........................ 61
J. Relationship between Cyand Cv and Cp ................... 65
K. The Meaning of the Difference between Cp and Сv ........ 66
L. Joule's Free Expansion Experiment ...................... 66
III Some Applications of the First Law to Ideal Gases ......... 67
A. Cp — Cv for Ideal Gases ................................ 67
B. Reversible Isothermal Expansion and Compression ........ 70
C. Reversible Constant-Volume (Isochoric) Processes ....... 71
D. Reversible Adiabatic Processes ......................... 71
E. The Amount of Work Done in Reversible and
Irreversible Processes ................................. 75
IV Adiabatic Processes and the Thermal Structure of
Planetary Atmospheres ..................................... 75
V Other Types of Work ....................................... 77
Problems .................................................. 78
CHAPTER 4 Thermal Properties of Pure Substances and Some
Applications ................................................... 81
I Some Basic Concepts about Heat Capacity and Enthalpy ...... 81
A. Mean and True Heat Capacity ............................ 81
B. Heat Capacity Contributions ............................ 82
Gases ..................................................... 82
Liquids ................................................... 83
Solids .................................................... 84
C. The Relationship between Heat Capacity and Enthalpy .... 84
D. Empirical Heat Capacity Equations ...................... 85
II An Overview of Calorimetry ................................ 87
A. Basic Definitions and Concepts ......................... 87
B. Basic Types of Calorimeters ............................ 88
C. Ice Calorimeters ....................................... 88
D. Drop Calorimeters ...................................... 91
E. Low-Temperature Adiabatic Calorimeters ................. 95
F. High-Temperature Adiabatic Calorimeters ................ 97
G. Differential Scanning Calorimetry ...................... 99
H. Calorimeters for Gases ................................ 100
III Thermal Properties of Solids ............................. 102
A. Dulong-Petit and Neumann-Kopp Heat Capacity Rules ..... 102
B. Typical Shape of Heat Capacity Curves ................. 105
C. Einstein and Debye Models ............................. 106
D. Limitations of Debye's Model .......................... 111
E. Electronic Heat Capacity of Metals .................... 111
F. Magnetic Heat Capacity of Minerals .................... 113
Magnetic Properties of Solids ............................ 113
Magnetic Energy, Work, and Heat Capacity ................. 114
G. Lambda Transitions of Minerals ........................ 116
H. The Difference between Cp and Сv Solids ............... 117
I. Calculating Enthalpies for Solids with Phase
Changes ............................................... 119
Problems ................................................. 122
CHAPTER 5 Thermochemistry .................................... 127
I Some Basic Concepts ...................................... 127
A. The Distinction between the ΔH and ΔE of Reaction ..... 127
B. Exothermic and Endothermic Reactions .................. 129
C. Some Other Types of ΔH Values ......................... 132
D. Lavoisier-Laplace Law ................................. 133
E. Hess's Law ............................................ 134
F. Kirchhoff's Equation .................................. 135
G. Elemental Reference States ............................ 139
H. The Standard Enthalpy of Formation .................... 142
I. Enthalpies of Solution and Dilution ................... 147
J. Standard Enthalpies of Formation for Aqueous Ions ..... 149
II Calorimetric Measurement of Reaction Enthalpies .......... 151
A. Solution Calorimetry .................................. 151
Aqueous Acid Solution Calorimetry ........................ 151
Oxide Melt Calorimetry ................................... 157
B. Combustion Calorimetry ................................ 158
Combustion in Oxygen ..................................... 158
Combustion in Fluorine and Other Halogens ................ 160
III Some Applications of Thermochemistry ..................... 161
A. Calculations of Adiabatic Flame Temperatures .......... 161
B. Dissociation and Atomization Energies ................. 162
Dissociation Energy ...................................... 162
Atomization Energy ....................................... 163
C. Ionization Energy and Electron Affinity ............... 164
Ionization Energy ........................................ 165
Electron Affinity ........................................ 166
Problems ................................................. 167
CHAPTER 6 The Second Law of Thermodynamics and Entropy ....... 173
I A Review of Some Important Definitions ................... 175
II Historical Development of the Second Law ................. 175
III The Second Law of Thermodynamics ......................... 178
IV Carnot Cycle ............................................. 179
A. Steam Engines and Heat Engines ........................ 179
B. Carnot Heat Engine .................................... 180
C. Carnot Refrigerator ................................... 184
D. Unattainability of Absolute Zero ...................... 187
V Thermodynamic Temperature Scale .......................... 189
VI Entropy .................................................. 190
A. Definition of Entropy ................................. 190
B. Entropy Changes in Reversible and Irreversible
Processes ................................................ 191
VII Some Applications of the Second Law ...................... 192
A. The Combined First and Second Law ..................... 192
B. Entropy Change During Reversible Adiabatic
Processes ............................................. 192
C. Entropy Change During Reversible Isothermal
Processes ............................................. 193
D. Entropy Change During Reversible Isochoric
Processes ............................................. 194
E. Entropy Change During Reversible Isobaric Processes ... 194
F. Entropy Change During a Phase Transition .............. 195
G. Absolute Entropy Calculations for Solids, Liquids,
and Gases ............................................. 200
H. Entropy Changes for Chemical Reactions without Phase
Changes ............................................... 202
I. Entropy Changes for Chemical Reactions with Phase
Changes ............................................... 205
J. Entropy Estimation Methods ............................ 206
VIII Gibbs and Helmholtz Free Energy .......................... 207
A. Helmholtz Free Energy ................................. 207
B. Gibbs Free Energy ..................................... 208
C. Gibbs Free Energy Changes for Chemical Reactions ...... 210
D. The Entropy of Aqueous Ions ........................... 211
IX Entropy and Probability .................................. 213
A. Some Basic Concepts about Probability ................. 213
B. Boltzmann-Planck Equation ............................. 215
C. Entropy of Mixing and Probability ..................... 216
D. The Entropy of Mixing of Gases ........................ 218
E. Configurational Entropy of Minerals ................... 219
F. Probability of Impossible Events ...................... 220
G. Maxwell's Demon ....................................... 221
Problems ................................................. 222
CHAPTER 7 Phase Equilibria of Pure Materials ................. 225
I Basic Concepts and Definitions ........................... 225
A. Phases ................................................ 225
Elements .............................................. 225
Chemical Compounds and Minerals ....................... 226
B. Polymorphs, Isomorphs, and Pseudomorphs ............... 228
C. Allotropes ............................................ 230
D. Enantiomorphs and Enantiomers ......................... 230
E. Enantiotropes and Monotropes .......................... 230
F. Phase Transitions and Phase Equilibria ................ 231
G. Metastable Phases ..................................... 233
H. Components ............................................ 236
I. Degrees of Freedom .................................... 237
II Phase Equilibria, the Clapeyron Equation, and the
Clausius-Clapeyron Equation .............................. 237
A. Phase Diagram for Water ............................... 237
B. Derivation of the Clapeyron Equation .................. 240
C. Water Ice Melting Curve and the Clapeyron Equation .... 243
D. Vaporization and Sublimation Curves of Water and
the Clapeyron Equation ................................ 246
E. Derivation of the Clausius-Clapeyron Equation ......... 248
F. Applications of the Clausius-Clapeyron Equation ....... 250
G. Polymorphic Phase Transitions ......................... 256
H. The Gibbs Phase Rule and Some of its Applications ..... 257
III Effect of Total Pressure on Vapor Pressure ............... 260
IV Types of Phase Transitions ............................... 264
A. First-Order Phase Transitions ......................... 264
B. Second-Order Phase Transitions ........................ 266
C. Lambda Transitions .................................... 267
V. Melting Curves and Polymorphic Phase Transitions
at High Pressures ..................................... 270
A. Effect of High Pressure on Melting Points ............. 270
B. Calculations of High-Pressure Phase Boundaries ........ 274
C. Retrieval of Thermodynamic Data from Phase
Equilibria ............................................ 279
Problems ... 281
CHAPTER 8 Equations of State ................................. 287
I The Maxwell Relations and Thermodynamic Formulas ......... 288
A. The Four Fundamental Equations ........................ 288
B. Extensive and Intensive Variables and Energy Function
(E, H, G, A) Derivatives .............................. 290
C. Maxwell Relations ..................................... 292
D. Bridgman's Thermodynamic Formulas ..................... 297
П. Real Gas Equations of State and Thermodynamics ........ 305
A. PVT Behavior of Ideal Gases............................ 305
B. Deviations from Ideality .............................. 306
C. Law of Corresponding States ........................... 309
D. Van der Waals Equation ................................ 317
E. Other Empirical Equations of State .................... 321
F. Virial Equation of State .............................. 325
III Thermodynamic Properties of Real Gases ................... 332
A. The Joule-Thomson Effect .............................. 332
B. Gibbs Free Energy, Pressure, and Fugacity ............. 338
C. Calculating the Fugacity of a Real Gas ................ 340
D. Calculating Fugacity from Reduced Variables ........... 344
IV Thermodynamic Properties of Gas Mixtures ................. 345
A. Lewis and Randall Fugacity Rule ....................... 346
B. Virial Equation for Gas Mixtures ...................... 348
C. Van der Waals Equation ................................ 350
D. Other Cubic Equations of State ........................ 352
V. Critical Phenomena of Real Gases ...................... 354
A. Historical Background ................................. 354
B. Critical Behavior of Carbon Dioxide ................... 355
(C. Van der Waals Equation ............................ 361
D. Physical Properties at the Critical Point ............. 363
VI Equations of State for Solids and Liquids ................ 365
A. Some Basic Definitions ................................ 365
B. Equations of state for solids and liquids ............. 366
Problems ................................................. 367
CHAPTER 9 The Third Law of Thermodynamics ..................... 371
I Historical Development of the Nernst Heat Theorem ........ 371
II The Third Law and its Consequences ....................... 377
A. The Third Law of Thermodynamics ....................... 377
B. Entropy and Heat Capacity of Solids at Low
Temperatures .......................................... 377
C. Experimental Verification: Calorimetric Entropies of
Gases ................................................. 380
D. Experimental Verification: Calorimetric Entropies
of Polymorphic Solids ................................. 386
E. Clapeyron Slope of Melting Curves ..................... 387
F. Liquid Helium ......................................... 387
G. Thermal Expansion Coefficient ......................... 389
H. The Approach to Absolute Zero with Mechanical and
Magnetic Cooling ...................................... 391
III The Third Law and Entropy ................................ 392
A. Residual or Zero-Point Entropy of Glassy Materials .... 392
B. Entropy of Mixing in Solutions at Absolute Zero ....... 395
C. Configurational Entropy of Minerals ................... 397
D. Configurational Entropy of Imperfect Crystals ......... 399
E. Isotopic Entropy ...................................... 401
F. Magnetic Entropy ...................................... 401
Electron Configurations and Quantum Numbers ........... 403
Crystal Field and Mineral Site Symmetry ............... 406
G. Schottky Entropy ...................................... 407
H. Nuclear Spin Entropy .................................. 409
I Ortho-and Parahydrogen ................................... 410
IV Absolute Entropy Values and the Third Law ................ 413
A. Practical Entropy Values .............................. 413
B. Calculations with Practical Entropy Values ............ 414
C. Gibbs Free Energy Function ............................ 415
Problems ................................................. 417
CHAPTER 10 Chemical Equilibria ................................ 423
I Chemical Equilibria of Gases ............................. 423
A. Derivation of the Equilibrium Constant (Kp) ........... 424
B. Illustration that KP is a Constant .................... 429
C. Initial and Equilibrium Concentrations ................ 429
D. Temperature Dependence of Equilibrium Constants ....... 433
E. Integration of the van't Hoff Equation ................ 441
F. Pressure Effects on Equilibrium Constants ............. 446
G. Reversibility of Equilibria ........................... 447
H. Chemical Reaction Rates and Rate Constants ............ 450
I. The Equilibrium Constant and Reaction Rate
Constants ............................................. 453
J. Gas Mixing and Oxygen Fugacity Control ................ 456
K. Simultaneous Equilibria ............................... 458
L. Ammonia Synthesis ..................................... 459
M. Temperature and Pressure Dependence of Kp for
Ammonia Synthesis ..................................... 465
N. Nonideality and Ammonia Synthesis ..................... 468
II Gas-Condensed Phase Equilibria ........................... 470
A. Gas-Solid Reactions ................................... 470
B. Definition of Thermodynamic Activity .................. 473
C. Effect of Total Pressure on Thermodynamic Activity .... 474
D. Relationship between Activity and Gibbs Energy ........ 476
E. Oxygen Fugacity Buffers ............................... 477
Background Information ................................... 477
Application of the Gibbs Phase Rule to Oxygen Fugacity
Buffers .................................................. 478
Thermodynamic Activity and Buffer Reactions .............. 480
Pressure Dependence of Oxygen Fugacity Buffers ........... 481
F. Sulfur Fugacity Buffers ............................... 482
G. Mineral Buffer Reactions .............................. 486
Atmosphere-Surface Reactions on Venus .................... 486
Carbonate-Silicate Buffers for CO2 ....................... 486
Mineral Buffer Reactions for HCl on Venus ................ 488
Mineral Buffer Reactions for HP on Venus ................. 489
Metamorphic Reactions .................................... 490
III Gibbs Free Energy and Electrochemistry ................... 490
A. Electron Transfers During Chemical Reactions .......... 490
B. A Review of Some Electrical Concepts and Units ........ 491
C. Electrical Work and the First Law ..................... 493
D. Electrochemical Measurements of ΔƒG0 from the
Elements .............................................. 494
E. Entropy and Enthalpy of Reaction from emf
Measurements .......................................... 496
F. Effect of Concentration on Electromotive Force ........ 498
G. Oxygen Fugacity (Partial-Pressure) Sensors ............ 500
Problems ... 502
CHAPTER 11 Solutions .......................................... 509
I Basic Concepts ........................................... 509
A. Types of Solutions .................................... 509
B. Electrolyte and Nonelectrolyte Solutions .............. 509
C. Definitions and Conversion Formulae for Solution
Compositions .......................................... 510
II Partial Molal Properties ................................. 513
A. Definition and Illustration Using Partial Molal
Volume ................................................ 513
B. Partial Molal Gibbs Free Energy and Other Partial
Molal Properties ...................................... 516
C. Gibbs-Duhem Equation .................................. 518
D. Chemical Potential .................................... 518
E. Some Properties of the Chemical Potential ............. 521
III Thermodynamic Properties of Ideal and Dilute Solutions ... 522
A. Raoult's law .......................................... 522
B. Henry's law ........................................... 526
C. Thermodynamics of Gas Solubility in Aqueous
Solutions ............................................. 529
D. Effect of High Pressure on Gas Solubility in
Liquids ............................................... 531
E. Boiling-Point Elevation of Dilute Solutions ........... 532
F. Freezing-Point Depression of Dilute Solutions ......... 535
G. Gibbs Energy .......................................... 536
H. Entropy ............................................... 540
I. Enthalpy .............................................. 541
J. Heat Capacity ......................................... 542
K. Volume ................................................ 544
IV Thermodynamic Properties of Nonideal (Real) Solutions .... 544
A. Deviations from Raoult's Law .......................... 544
B. Excess Functions ...................................... 547
C. Gibbs Energy .......................................... 548
D. Entropy ............................................... 550
E. Enthalpy .............................................. 550
F. Volume ................................................ 551
G. An Example of a Real Solution ......................... 551
H. Regular Solutions and Margules Parameters ............. 554
I. Subregular or Asymmetric Solutions .................... 556
V Aqueous Solutions ........................................ 558
A. Ionic Strength ........................................ 558
B. Solubility and Solubility Product ..................... 559
C. Ionization Equilibrium of Water and pH ................ 566
D. Ionization Equilibria of Electrolytes ................. 567
E. Carbonic Acid-Calcium Carbonate System ................ 570
VI Activity Coefficients of Aqueous Electrolytes ............ 573
Problems ................................................. 580
CHAPTER 12 Phase Equilibria of Binary Systems ................. 585
I Binary Phase Diagrams .................................... 585
A. General Discussion .................................... 585
B. Interconversion of Molar and Weight Percentages ....... 586
C. Simple Eutectic Diagrams .............................. 588
D. Thermodynamics of Simple Eutectic Diagrams ............ 592
E. Monotectics ........................................... 595
F. Systems with Intermediate Compounds ................... 596
G. Thermodynamics of Systems with Intermediate
Compounds ............................................. 599
H. Binary Phase Diagrams of Water and Salts .............. 602
I. Mutual Liquid and Solid Solutions ..................... 605
Solid and Liquid Solutions with Continuous Liquidus
and Solidus Curves .................................... 607
Solid Solutions with Minimum Melting Points ........... 614
J. Partially Miscible Solids and Unmixing ................ 615
K. Unmixing and Margules Parameters ...................... 618
L. Nonstoichiometric Compounds ........................ 619
Problems ................................................. 620
Appendix 1 .................................................... 623
Appendix 2 .................................................... 635
References .................................................... 639
Index ......................................................... 661
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