Physical and Chemical Equilibrium for Chemical Engineers, Second Edition

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, gx 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 25C, 183 11.2.3 Partially Soluble Liquid Pairs at 25C, 183 11.2.4 Miscible Liquid Pairs at 25C, 183 11.2.5 Ternary LLE at 25C, 184 11.2.6 LLE at Temperatures Other Than 25C, 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 298.15 K 25C, and P 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