Table of Contents
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
2.12 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
8.4.4 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 ln g_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.1 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 ¼ 298.15 K ¼ 25_C and P ¼ 1.00 bar 313
A.9 Heat Capacities of Gases in the Ideal Gas State 317
Appendix B Equilibrium with other Restraints Other Approaches to Equilibrium 319
Appendix C The Mathematics of Fugacity Ideal Solutions
Activity and Activity Coefficients 323
C.1 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.1 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.1 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 f /P of Pure Species Based on Pressure-Explicit EOSs 339
F.3 Cubic Equations of State 340
F.4 fi /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
