Preface ...................................................... xiii
About the Author ............................................... xv
Nomenclature ................................................. xvii
1 Introduction to Equilibrium .................................. 1
1.1 Why Study Equilibrium? .................................. 1
1.2 Stability and Equilibrium ............................... 4
1.3 Time Scales and the Approach to Equilibrium ............. 5
1.4 Looking Ahead, Gibbs Energy ............................. 5
1.5 Units, Conversion Factors, and Notation ................. 6
1.6 Reality and Equations ................................... 8
1.7 Phases and Phase Diagrams ............................... 8
1.8 The Plan of this Book .................................. 10
1.9 Summary ................................................ 10
References .................................................. 11
2 Basic Thermodynamics ........................................ 13
2.1 Conservation and Accounting ............................ 13
2.2 Conservation of Mass ................................... 14
2.3 Conservation of Energy; the First Law of
Thermodynamics ......................................... 15
2.4 The Second Law of Thermodynamics ....................... 17
2.4.1 Reversibility ................................... 17
2.4.2 Entropy ......................................... 18
2.5 Convenience Properties ................................. 19
2.6 Using the First and Second Laws ........................ 19
2.7 Datums and Reference States ............................ 21
2.8 Measurable and Immeasurable Properties ................. 22
2.9 Work and Heat .......................................... 22
2.10 The Property Equation .................................. 23
2.11 Equations of State (EOS) ............................... 24
2.11.1 EOSs Based on Theory ............................ 25
2.11.2 EOSs Based on Pure Data Fitting ................. 25
2.11.1 Corresponding States ............................ 26
2.13 Departure Functions .................................... 28
2.14 The Properties of Mixtures ............................. 28
2.15 The Combined First and Second Law Statement;
Reversible Work ........................................ 29
2.16 Summary ................................................ 31
References .................................................. 33
3 The Simplest Phase Equilibrium Examples and Some Simple
Estimating Rules ............................................ 35
3.1 Some General Statements About Equilibrium .............. 35
3.2 The Simplest Example of Phase Equilibrium .............. 37
3.2.1 A Digression, the Distinction between Vapor
and Gas ......................................... 37
3.2.2 Back to the Simplest Equilibrium ................ 37
3.3 The Next Level of Complexity in Phase Equilibrium ...... 37
3.4 Some Simple Estimating Rules: Raoult's and Henry's
"Laws" ................................................. 39
3.5 The General Two-Phase Equilibrium Calculation .......... 43
3.6 Some Simple Applications of Raoult's and Henry's Laws .. 43
3.7 The Uses and Limits of Raoult's and Henry's Laws ....... 46
3.8 Summary ................................................ 46
References .................................................. 48
4 Minimization of Gibbs Energy ................................ 49
4.1 The Fundamental Thermodynamic Criterion of Phase and
Chemical Equilibrium ................................... 49
4.2 The Criterion of Equilibrium Applied to Two
Nonreacting Equilibrium Phases ......................... 51
4.3 The Criterion of Equilibrium Applied to Chemical
Reactions .............................................. 53
4.4 Simple Gibbs Energy Diagrams ........................... 54
4.4.1 Comparison with Enthalpy and Entropy ............ 55
4.4.2 Gibbs Energy Diagrams for Pressure-Driven
Phase Changes ................................... 55
4.4.3 Gibbs Energy Diagrams for Chemical Reactions .... 57
4.5 Le Chatelier's Principle ............................... 58
4.6 Summary ................................................ 58
References .................................................. 60
5 Vapor Pressure, the Clapeyron Equation, and Single Pure
Chemical Species Phase Equilibrium .......................... 61
5.1 Measurement of Vapor Pressure .......................... 61
5.2 Reporting Vapor-Pressure Data .......................... 61
5.2.1 Normal Boiling Point (NBP) ...................... 61
5.3 The Clapeyron Equation ................................. 62
5.4 The Clausius-Clapeyron Equation ........................ 63
5.5 The Accentric Factor ................................... 64
5.6 The Antoine Equation and Other Data-Fitting Equations .. 66
5.6.1 Choosing a Vapor-Pressure Equation .............. 67
5.7 Applying the Clapeyron Equation to Other Kinds of
Equilibrium ............................................ 67
5.8 Extrapolating Vapor-Pressure Curves .................... 68
5.9 Vapor Pressure of Solids ............................... 69
5.10 Vapor Pressures of Mixtures ............................ 69
5.11 Summary ................................................ 69
References .................................................. 72
6 Partial Molar Properties .................................... 73
6.1 Partial Molar Properties ............................... 73
6.2 The Partial Molar Equation ............................. 74
6.3 Tangent Slopes ......................................... 74
6.4 Tangent Intercepts ..................................... 77
6.5 The Two Equations for Partial Molar Properties ......... 78
6.6 Using the Idea of Tangent Intercepts ................... 79
6.7 Partial Mass Properties ................................ 80
6.8 Heats of Mixing and Partial Molar Enthalpies ........... 80
6.8.1 Differential Heat of Mixing ..................... 80
6.8.2 Integral Heat of Mixing ......................... 81
6.9 The Gibbs-Duhem Equation and the Counterintuitive
Behavior of the Chemical Potential ..................... 82
6.10 Summary ................................................ 84
References .................................................. 87
7 Fugacity, Ideal Solutions, Activity, Activity Coefficient ... 89
7.1 Why Fugacity? .......................................... 89
7.2 Fugacity Defined ....................................... 89
7.3 The Use of the Fugacity ................................ 90
7.4 Pure Substance Fugacities .............................. 90
7.4.1 The Fugacity of Pure Gases ...................... 91
7.4.2 The Fugacity of Pure Liquids and Solids ......... 94
7.5 Fugacities of Species in Mixtures ...................... 95
7.6 Mixtures of Ideal Gases ................................ 95
7.7 Why Ideal Solutions? ................................... 95
7.8 Ideal Solutions Defined ................................ 96
7.8.1 The Consequences of the Ideal Solution
Definition ...................................... 96
7.9 Why Activity and Activity Coefficients? ................ 98
7.10 Activity and Activity Coefficients Defined ............. 98
7.11 Fugacity Coefficient for Pure Gases and Gas Mixtures .. 100
7.12 Estimating Fugacities of Individual Species in Gas
Mixtures .............................................. 100
7.12.1 Fugacities from Gas PvT Data ................... 100
7.12.2 Fugacities from an EOS for Gas Mixtures ........ 102
7.12.3 The Lewis and Randall (L-R) Fugacity Rule ...... 102
7.12.4 Other Mixing Rules ............................. 103
7.13 Liquid Fugacities from Vapor-Liquid Equilibrium ....... 104
7.14 Summary ............................................... 104
References ................................................. 105
8 Vapor-Liquid Equilibrium (VLE) at Low Pressures ............ 107
8.1 Measurement of VLE .................................... 107
8.2 Presenting Experimental VLE Data ...................... 110
8.3 The Mathematical Treatment of Low-Pressure VLE Data ... 110
8.3.1 Raoult's Law Again ............................. 111
8.4 The Four Most Common Types of Low-Pressure VLE ........ 112
8.4.1 Ideal Solution Behavior (Type I) ............... 114
8.4.2 Positive Deviations from Ideal Solution
Behavior (Type II) ............................. 114
8.4.3 Negative Deviations from Ideal Solution
Behavior (Type III) ............................ 115
8.4.1 Azeotropes ..................................... 117
8.4.5 Two-Liquid Phase or Heteroazeotropes
(Type IV) ...................................... 118
8.4.6 Zero Solubility and Steam Distillation ......... 120
8.4.7 Distillation of the Four Types of Behavior ..... 121
8.5 Gas-Liquid Equilibrium, Henry's Law Again ............. 122
8.6 The Effect of Modest Pressures on VLE ................. 122
8.6.1 Liquids ........................................ 123
8.6.2 Gases, the L-R Rule ............................ 123
8.7 Standard States Again ................................. 124
8.8 Low-Pressure VLE Calculations ......................... 125
8.8.1 Bubble-Point Calculations ...................... 127
8.8.1.1 Temperature-Specified Bubble Point .... 127
8.8.1.2 Pressure-Specified Bubble Point ....... 128
8.8.2 Dew-Point Calculations ......................... 129
8.8.2.1 Temperature-Specified Dew Point ....... 129
8.8.2.2 Pressure-Specified Dew Point .......... 129
8.8.3 Isothermal Flashes (T- and P-Specified
Flashes) ....................................... 130
8.8.4 Adiabatic Flashes .............................. 131
8.9 Traditional K-Factor Methods .......................... 132
8.10 More Uses for Raoult's Law ............................ 132
8.10.1 Nonvolatile Solutes, Boiling-Point Elevation ... 132
8.10.2 Freezing-Point Depression ...................... 135
8.10.3 Colligative Properties of Solutions ............ 136
8.11 Summary ............................................... 136
References ................................................. 143
9 Correlating and Predicting Nonideal VLE .................... 145
9.1 The Most Common Observations of Liquid-Phase
Activity Coefficients ...................................... 145
9.1.1 Why Nonideal Behavior? ......................... 145
9.1.2 The Shapes of In, γ-x Curves ................... 146
9.2 Limits on Activity Coefficient Correlations, the
Gibbs-Duhem Equation .................................. 147
9.3 Excess Gibbs Energy and Activity Coefficient
Equations ............................................. 148
9.4 Activity Coefficients at Infinite Dilution ............ 150
9.5 Effects of Pressure and Temperature on Liquid-Phase
Activity Coefficients ................................. 151
9.5.1 Effect of Pressure Changes on Liquid-Phase
Activity Coefficients .......................... 151
9.5.2 Effect of Temperature Changes on Liquid-Phase
Activity Coefficients .......................... 152
9.6 Ternary and Multispecies VLE .......................... 153
9.6.1 Liquid-Phase Activity Coefficients for
Ternary Mixtures ............................... 154
9.7 Vapor-Phase Nonideality ............................... 155
9.8 VLE from EOS .......................................... 158
9.9 Solubility Parameter .................................. 158
9.10 The Solubility of Gases in Liquids, Henry's Law
Again ................................................. 160
9.11 Summary ............................................... 163
References ................................................. 167
10 Vapor-Liquid Equilibrium (VLE) at High Pressures ........... 169
10.1 Critical Phenomena of Pure Species .................... 169
10.2 Critical Phenomena of Mixtures ........................ 170
10.3 Estimating High-Pressure VLE .......................... 174
10.3.1 Empirical K-Value Correlations ................. 175
10.3.2 Estimation Methods for Each Phase Separately,
Not Based on Raoult's Law ...................... 175
10.3.3 Estimation Methods Based on Cubic EOSs ......... 176
10.4 Computer Solutions .................................... 178
10.5 Summary ............................................... 178
References ................................................. 179
11 Liquid-Liquid, Liquid-Solid, and Gas-Solid Equilibrium ..... 181
11.1 Liquid-Liquid Equilibrium (LLE) ....................... 181
11.2 The Experimental Determination of LLE ................. 181
11.2.1 Reporting and Presenting LLE Data .............. 182
11.2.2 Practically Insoluble Liquid Pairs at 25°C ..... 183
11.2.3 Partially Soluble Liquid Pairs at 25°C ......... 183
11.2.4 Miscible Liquid Pairs at 25°C .................. 183
11.2.5 Ternary LLE at 25°C ............................ 184
11.2.6 LLE at Temperatures Other Than 25°C ............ 186
11.3 The Elementary Theory of LLE .......................... 187
11.4 The Effect of Pressure on LLE ......................... 190
11.5 Effect of Temperature on LLE .......................... 191
11.6 Distribution Coefficients ............................. 194
11.7 Liquid-Solid Equilibrium (LSE) ........................ 195
11.7.1 One-Species LSE ................................ 195
11.7.2 The Experimental Determination of LSE .......... 195
11.7.3 Presenting LSE Data ............................ 195
11.7.4 Eutectics ...................................... 197
11.7.5 Gas Hydrates (Clathrates) ...................... 199
11.8 The Elementary Thermodynamics of LSE .................. 200
11.9 Gas-Solid Equilibrium (GSE) at Low Pressures .......... 202
11.10 GSE at High Pressures ................................ 203
11.11 Gas-Solid Adsorption, Vapor-Solid Adsorption ......... 204
11.11.1 Langmuir's Adsorption Theory .................. 205
11.11.2 Vapor-solid Adsorption, BET Theory ............ 207
11.11.3 Adsorption from Mixtures ...................... 208
11.11.4 Heat of Adsorption ............................ 209
11.11.5 Hysteresis .................................... 210
11.12 Summary .............................................. 211
References ................................................. 215
12 Chemical Equilibrium ...................................... 217
12.1 Introduction to Chemical Reactions and Chemical
Equilibrium ........................................... 217
12.2 Formal Description of Chemical Reactions .............. 217
12.3 Minimizing Gibbs Energy ............................... 218
12.4 Reaction Rates, Energy Barriers, Catalysis, and
Equilibrium ........................................... 219
12.5 The Basic Thermodynamics of Chemical Reactions and
Its Convenient Formulations ........................... 220
12.5.1 The Law of Mass Action and Equilibrium
Constants ...................................... 222
12.6 Calculating Equilibrium Constants from Gibbs Energy
Tables and then Using Equilibrium Constants to
Calculate Equilibrium Concentrations .................. 223
12.6.1 Change of Reactant Concentration, Reaction
Coordinate ..................................... 224
12.6.2 Reversible and Irreversible Reactions .......... 227
12.7 More on Standard States ............................... 227
12.8 The Effect of Temperature on Chemical Reaction
Equilibrium ........................................... 229
12.9 The Effect of Pressure on Chemical Reaction
Equilibrium ........................................... 234
12.9.1 Ideal Solution of Ideal Gases .................. 235
12.9.2 Nonideal Solution, Nonideal Gases .............. 236
12.9.3 Liquids and Solids ............................. 237
12.10 The Effect of Nonideal Solution Behavior ............. 238
12.10.1 Liquid-Phase Nonideality ...................... 238
12.11 Other Forms of K ..................................... 238
12.12 Summary .............................................. 239
References ................................................. 242
13 Equilibrium in Complex Chemical Reactions .................. 243
13.1 Reactions Involving Ions .............................. 243
13.2 Multiple Reactions .................................... 244
13.2.1 Sequential Reactions ........................... 244
13.2.2 Simultaneous Reactions ......................... 245
13.2.3 The Charge Balance Calculation Method and
Buffers ........................................ 246
13.3 Reactions with More Than One Phase .................... 249
13.3.1 Solubility Product ............................. 249
13.3.2 Gas-Liquid Reactions ........................... 249
13.4 Electrochemical Reactions ............................. 252
13.5 Chemical and Physical Equilibrium in Two Phases ....... 255
13.5.1 Dimerization (Association) ..................... 255
13.6 Summary ............................................... 257
References ................................................. 262
14 Equilibrium with Gravity or Centrifugal Force, Osmotic
Equilibrium, Equilibrium with Surface Tension .............. 265
14.1 Equilibrium with Other Forms of Energy ................ 265
14.2 Equilibrium in the Presence of Gravity ................ 266
14.2.1 Centrifuges .................................... 268
14.3 Semipermeable Membranes ............................... 269
14.3.1 Osmotic Pressure .............................. 270
14.4 Small is Interesting! Equilibrium with Surface
Tension ............................................... 271
14.4.1 Bubbles, Drops and Nucleation .................. 271
14.4.2 Capillary Condensation ......................... 275
14.5 Summary ............................................... 275
References ................................................. 278
15 The Phase Rule ............................................. 279
15.1 How Many Phases Can Coexist in a Given Equilibrium
Situation? ............................................ 279
15.2 What Does the Phase Rule Tell Us? What Does It Not
Tell Us? .............................................. 280
15.3 What is a Phase? ...................................... 280
15.4 The Phase Rule is Simply Counting Variables ........... 281
15.5 More On Components .................................... 282
15.5.1 A Formal Way to Find the Number of
Independent Equations ......................... 285
15.6 The Phase Rule for One- and Two-Component Systems ..... 285
15.7 Harder Phase Rule Problems ............................ 288
15.8 Summary ............................................... 288
References ................................................. 291
16 Equilibrium in Biochemical Reactions ....................... 293
16.1 An Example, the Production of Ethanol from Sugar ...... 293
16.2 Organic and Biochemical Reactions ..................... 293
16.3 Two More Sweet Examples ............................... 294
16.4 Thermochemical Data for Biochemical Reactions ......... 295
16.5 Thermodynamic Equilibrium in Large Scale
Biochemistry .......................................... 296
16.6 Translating between Biochemical and Chemical
Engineering Equilibrium Expressions ................... 296
16.6.1 Chemical and Biochemical Equations ............. 297
16.6.2 Equilibrium Constants .......................... 297
16.6.3 pH and Buffers ................................. 298
16.6.4 Ionic Strength ................................. 298
16.7 Equilibrium in Biochemical Separations ................ 298
16.8 Summary ............................................... 299
References ................................................. 300
Appendix A Useful Tables and Charts ........................... 303
A.l Useful Property Data for Corresponding States
Estimates ............................................. 303
A.2 Vapor-Pressure Equation Constants ..................... 305
A.3 Henry's Law Constants ................................. 306
A.4 Compressibility Factor Chart (z Chart) ................ 307
A.5 Fugacity Coefficient Charts ........................... 307
A.6 Azeotropes ............................................ 308
A.7 Van Laar Equation Constants ........................... 312
A.8 Enthalpies and Gibbs Energies of Formation from the
Elements in the Standard States, at T = 298.15 К =
25°C, and P = 1.00 bar ................................ 313
A.9 Heat Capacities of Gases in the Ideal Gas State ....... 317
Appendix В Equilibrium with other Restraints, Other
Approaches to Equilibrium .................................. 319
Appendix С The Mathematics of Fugacity, Ideal Solutions,
Activity and Activity Coefficients ............................ 323
C.l The Fugacity of Pure Substances ....................... 323
C.2 Fugacities of Components of Mixtures .................. 324
C.3 The Consequences of the Ideal Solution Definition ..... 326
C.4 The Mathematics of Activity Coefficients .............. 326
Appendix D Equations of State for Liquids and Solids Well
Below their Critical Temperatures .......................... 329
D.l The Taylor Series EOS and Its Short Form .............. 329
D.2 Effect of Temperature on Density ...................... 330
D.3 Effect of Pressure on Density ......................... 331
D.4 Summary ............................................... 332
References ................................................. 333
Appendix E Gibbs Energy of Formation Values ................... 335
E.l Values "From the Elements" ............................ 335
E.2 Changes in Enthalpy, Entropy, and Gibbs Energy ........ 335
E.2.1 Enthalpy Changes ............................... 335
E.2.2 Entropy Changes ................................ 336
E.3 Ions .................................................. 337
E.4 Presenting these Data ................................. 337
References ................................................. 337
Appendix F Calculation of Fugacities from Pressure-Explicit
EOSs ....................................................... 339
F.1 Pressure-Explicit and Volume-Explicit EOSs ............ 339
F.2 flP of Pure Species Based on Pressure-Explicit EOSs ... 339
F.3 Cubic Equations of State .............................. 340
F.4 ƒi/Pyi for Individual Species in Mixtures, Based on
Pressure-Explicit EOSs ................................ 342
F.5 Mixing Rules for Cubic EOSs ........................... 343
F.6 VLE Calculations with a Cubic EOS ..................... 344
F.7 Summary ............................................... 345
References ................................................. 346
Appendix G Thermodynamic Property Derivatives and the
Bridgman Table ................................................ 347
References ................................................. 350
Appendix H Answers to Selected Problems ...................... 351
Index ......................................................... 353
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