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NOEL de NEVERS, PhD, followed five years of working for Chevron with thirty-seven years as a Professor in the Chemical Engineering Department of the University of Utah. His textbooks (and research papers) are in fluid mechanics, thermodynamics, and air pollution control engineering. He regularly consults as an expert on explosions, fires, and toxic exposures.
In addition to technical work, he has three "de Nevers's Laws" in a Murphy's Laws compilation and won the title "Poet Laureate of Jell-O Salad" in a Salt Lake City competition, with three limericks and a quatrain. He has climbed the Grand Teton, Mt. Rainier, Mt. Whitney, Kala Pattar, and Mt. Kilimanjaro, and is the official discoverer of Private Arch in Arches National Park.
Preface | p. xiii |
About the Author | p. xv |
Nomenclature | p. xvii |
Introduction to Equilibrium | p. 1 |
Why Study Equilibrium? | p. 1 |
Stability and Equilibrium | p. 4 |
Time Scales and the Approach to Equilibrium | p. 5 |
Looking Ahead, Gibbs Energy | p. 5 |
Units, Conversion Factors, and Notation | p. 6 |
Reality and Equations | p. 8 |
Phases and Phase Diagrams | p. 8 |
The Plan of this Book | p. 10 |
Summary | p. 10 |
References | p. 11 |
Basic Thermodynamics | p. 13 |
Conservation and Accounting | p. 13 |
Conservation of Mass | p. 14 |
Conservation of Energy; the First Law of Thermodynamics | p. 15 |
The Second Law of Thermodynamics | p. 17 |
Reversibility | p. 17 |
Entropy | p. 18 |
Convenience Properties | p. 19 |
Using the First and Second Laws | p. 19 |
Datums and Reference States | p. 21 |
Measurable and Immeasurable Properties | p. 22 |
Work and Heat | p. 22 |
The Property Equation | p. 23 |
Equations of State (EOS) | p. 24 |
EOSs Based on Theory | p. 25 |
EOSs Based on Pure Data Fitting | p. 25 |
Corresponding States | p. 26 |
Departure Functions | p. 28 |
The Properties of Mixtures | p. 28 |
The Combined First and Second Law Statement; Reversible Work | p. 29 |
Summary | p. 31 |
References | p. 33 |
The Simplest Phase Equilibrium Examples and Some Simple Estimating Rules | p. 35 |
Some General Statements About Equilibrium | p. 35 |
The Simplest Example of Phase Equilibrium | p. 37 |
A Digression, the Distinction between Vapor and Gas | p. 37 |
Back to the Simplest Equilibrium | p. 37 |
The Next Level of Complexity in Phase Equilibrium | p. 37 |
Some Simple Estimating Rules: RaoultâÇÖs and HenryâÇÖs âÇ£LawsâÇ | p. 39 |
The General Two-Phase Equilibrium Calculation | p. 43 |
Some Simple Applications of RaoultâÇÖs and HenryâÇÖs Laws | p. 43 |
The Uses and Limits of RaoultâÇÖs and HenryâÇÖs Laws | p. 46 |
Summary | p. 46 |
References | p. 48 |
Minimization of Gibbs Energy | p. 49 |
The Fundamental Thermodynamic Criterion of Phase and Chemical Equilibrium | p. 49 |
The Criterion of Equilibrium Applied to Two Nonreacting Equilibrium Phases | p. 51 |
The Criterion of Equilibrium Applied to Chemical Reactions | p. 53 |
Simple Gibbs Energy Diagrams | p. 54 |
Comparison with Enthalpy and Entropy | p. 55 |
Gibbs Energy Diagrams for Pressure-Driven Phase Changes | p. 55 |
Gibbs Energy Diagrams for Chemical Reactions | p. 57 |
Le ChatelierâÇÖs Principle | p. 58 |
Summary | p. 58 |
References | p. 60 |
Vapor Pressure, the Clapeyron Equation, and Single Pure Chemical Species Phase Equilibrium | p. 61 |
Measurement of Vapor Pressure | p. 61 |
Reporting Vapor-Pressure Data | p. 61 |
Normal Boiling Point (NBP) | p. 61 |
The Clapeyron Equation | p. 62 |
The ClausiusâÇôClapeyron Equation | p. 63 |
The Accentric Factor | p. 64 |
The Antoine Equation and Other Data-Fitting Equations | p. 66 |
Choosing a Vapor-Pressure Equation | p. 67 |
Applying the Clapeyron Equation to Other Kinds of Equilibrium | p. 67 |
Extrapolating Vapor-Pressure Curves | p. 68 |
Vapor Pressure of Solids | p. 69 |
Vapor Pressures of Mixtures | p. 69 |
Summary | p. 69 |
References | p. 72 |
Partial Molar Properties | p. 73 |
Partial Molar Properties | p. 73 |
The Partial Molar Equation | p. 74 |
Tangent Slopes | p. 74 |
Tangent Intercepts | p. 77 |
The Two Equations for Partial Molar Properties | p. 78 |
Using the Idea of Tangent Intercepts | p. 79 |
Partial Mass Properties | p. 80 |
Heats of Mixing and Partial Molar Enthalpies | p. 80 |
Differential Heat of Mixing | p. 80 |
Integral Heat of Mixing | p. 81 |
The GibbsâÇôDuhem Equation and the Counterintuitive Behavior of the Chemical Potential | p. 82 |
Summary | p. 84 |
References | p. 87 |
Fugacity, Ideal Solutions, Activity, Activity Coefficient | p. 89 |
Why Fugacity? | p. 89 |
Fugacity Defined | p. 89 |
The Use of the Fugacity | p. 90 |
Pure Substance Fugacities | p. 90 |
The Fugacity of Pure Gases | p. 91 |
The Fugacity of Pure Liquids and Solids | p. 94 |
Fugacities of Species in Mixtures | p. 95 |
Mixtures of Ideal Gases | p. 95 |
Why Ideal Solutions? | p. 95 |
Ideal Solutions Defined | p. 96 |
The Consequences of the Ideal Solution Definition | p. 96 |
Why Activity and Activity Coefficients? | p. 98 |
Activity and Activity Coefficients Defined | p. 98 |
Fugacity Coefficient for Pure Gases and Gas Mixtures | p. 100 |
Estimating Fugacities of Individual Species in Gas Mixtures | p. 100 |
Fugacities from Gas PvT Data | p. 100 |
Fugacities from an EOS for Gas Mixtures | p. 102 |
The Lewis and Randall (L-R) Fugacity Rule | p. 102 |
Other Mixing Rules | p. 103 |
Liquid Fugacities from Vapor-Liquid Equilibrium | p. 104 |
Summary | p. 104 |
References | p. 105 |
VaporâÇôLiquid Equilibrium (VLE) at Low Pressures | p. 107 |
Measurement of VLE | p. 107 |
Presenting Experimental VLE Data | p. 110 |
The Mathematical Treatment of Low-Pressure VLE Data | p. 110 |
RaoultâÇÖs Law Again | p. 111 |
The Four Most Common Types of Low-Pressure VLE | p. 112 |
Ideal Solution Behavior (Type I) | p. 114 |
Positive Deviations from Ideal Solution Behavior (Type II) | p. 114 |
Negative Deviations from Ideal Solution Behavior (Type III) | p. 115 |
Azeotropes | p. 117 |
Two-Liquid Phase or Heteroazeotropes (Type IV) | p. 118 |
Zero Solubility and Steam Distillation | p. 120 |
Distillation of the Four Types of Behavior | p. 121 |
GasâÇôLiquid Equilibrium, HenryâÇÖs Law Again | p. 122 |
The Effect of Modest Pressures on VLE | p. 122 |
Liquids | p. 123 |
Gases, the L-R Rule | p. 123 |
Standard States Again | p. 124 |
Low-Pressure VLE Calculations | p. 125 |
Bubble-Point Calculations | p. 127 |
Temperature-Specified Bubble Point | p. 127 |
Pressure-Specified Bubble Point | p. 128 |
Dew-Point Calculations | p. 129 |
Temperature-Specified Dew Point | p. 129 |
Pressure-Specified Dew Point | p. 129 |
Isothermal Flashes (T- and P-Specified Flashes) | p. 130 |
Adiabatic Flashes | p. 131 |
Traditional K-Factor Methods | p. 132 |
More Uses for RaoultâÇÖs Law | p. 132 |
Nonvolatile Solutes, Boiling-Point Elevation | p. 132 |
Freezing-Point Depression | p. 135 |
Colligative Properties of Solutions | p. 136 |
Summary | p. 136 |
References | p. 143 |
Correlating and Predicting Nonideal VLE | p. 145 |
The Most Common Observations of Liquid-Phase Activity Coefficients | p. 145 |
Why Nonideal Behavior? | p. 145 |
The Shapes of ln, gx Curves | p. 146 |
Limits on Activity Coefficient Correlations, the GibbsâÇôDuhem Equation | p. 147 |
Excess Gibbs Energy and Activity Coefficient Equations | p. 148 |
Activity Coefficients at Infinite Dilution | p. 150 |
Effects of Pressure and Temperature on Liquid-Phase Activity Coefficients | p. 151 |
Effect of Pressure Changes on Liquid-Phase Activity Coefficients | p. 151 |
Effect of Temperature Changes on Liquid-Phase Activity Coefficients | p. 152 |
Ternary and Multispecies VLE | p. 153 |
Liquid-Phase Activity Coefficients for Ternary Mixtures | p. 154 |
Vapor-Phase Nonideality | p. 155 |
VLE from EOS | p. 158 |
Solubility Parameter | p. 158 |
The Solubility of Gases in Liquids, HenryâÇÖs Law Again | p. 160 |
Summary | p. 163 |
References | p. 167 |
VaporâÇôLiquid Equilibrium (VLE) at High Pressures | p. 169 |
Critical Phenomena of Pure Species | p. 169 |
Critical Phenomena of Mixtures | p. 170 |
Estimating High-Pressure VLE | p. 174 |
Empirical K-Value Correlations | p. 175 |
Estimation Methods for Each Phase Separately, Not Based on RaoultâÇÖs Law | p. 175 |
Estimation Methods Based on Cubic EOSs | p. 176 |
Computer Solutions | p. 178 |
Summary | p. 178 |
References | p. 179 |
LiquidâÇôLiquid, LiquidâÇôSolid, and GasâÇôSolid Equilibrium | p. 181 |
LiquidâÇôLiquid Equilibrium (LLE) | p. 181 |
The Experimental Determination of LLE | p. 181 |
Reporting and Presenting LLE Data | p. 182 |
Practically Insoluble Liquid Pairs at 25C | p. 183 |
Partially Soluble Liquid Pairs at 25C | p. 183 |
Miscible Liquid Pairs at 25C | p. 183 |
Ternary LLE at 25C | p. 184 |
LLE at Temperatures Other Than 25C | p. 186 |
The Elementary Theory of LLE | p. 187 |
The Effect of Pressure on LLE | p. 190 |
Effect of Temperature on LLE | p. 191 |
Distribution Coefficients | p. 194 |
LiquidâÇôSolid Equilibrium (LSE) | p. 195 |
One-Species LSE | p. 195 |
The Experimental Determination of LSE | p. 195 |
Presenting LSE Data | p. 195 |
Eutectics | p. 197 |
Gas Hydrates (Clathrates) | p. 199 |
The Elementary Thermodynamics of LSE | p. 200 |
GasâÇôSolid Equilibrium (GSE) at Low Pressures | p. 202 |
GSE at High Pressures | p. 203 |
GasâÇôSolid Adsorption, VaporâÇôSolid Adsorption | p. 204 |
LangmuirâÇÖs Adsorption Theory | p. 205 |
Vapor-solid Adsorption, BET Theory | p. 207 |
Adsorption from Mixtures | p. 208 |
Heat of Adsorption | p. 209 |
Hysteresis | p. 210 |
Summary | p. 211 |
References | p. 215 |
Chemical Equilibrium | p. 217 |
Introduction to Chemical Reactions and Chemical Equilibrium | p. 217 |
Formal Description of Chemical Reactions | p. 217 |
Minimizing Gibbs Energy | p. 218 |
Reaction Rates, Energy Barriers, Catalysis, and Equilibrium | p. 219 |
The Basic Thermodynamics of Chemical Reactions and Its Convenient Formulations | p. 220 |
The Law of Mass Action and Equilibrium Constants | p. 222 |
Calculating Equilibrium Constants from Gibbs Energy Tables and then Using Equilibrium Constants to Calculate Equilibrium Concentrations | p. 223 |
Change of Reactant Concentration, Reaction Coordinate | p. 224 |
Reversible and Irreversible Reactions | p. 227 |
More on Standard States | p. 227 |
The Effect of Temperature on Chemical Reaction Equilibrium | p. 229 |
The Effect of Pressure on Chemical Reaction Equilibrium | p. 234 |
Ideal Solution of Ideal Gases | p. 235 |
Nonideal Solution, Nonideal Gases | p. 236 |
Liquids and Solids | p. 237 |
The Effect of Nonideal Solution Behavior | p. 238 |
Liquid-Phase Nonideality | p. 238 |
Other Forms of K | p. 238 |
Summary | p. 239 |
References | p. 242 |
Equilibrium in Complex Chemical Reactions | p. 243 |
Reactions Involving Ions | p. 243 |
Multiple Reactions | p. 244 |
Sequential Reactions | p. 244 |
Simultaneous Reactions | p. 245 |
The Charge Balance Calculation Method and Buffers | p. 246 |
Reactions with More Than One Phase | p. 249 |
Solubility Product | p. 249 |
Gas-Liquid Reactions | p. 249 |
Electrochemical Reactions | p. 252 |
Chemical and Physical Equilibrium in Two Phases | p. 255 |
Dimerization (Association) | p. 255 |
Summary | p. 257 |
References | p. 262 |
Equilibrium with Gravity or Centrifugal Force, Osmotic Equilibrium, Equilibrium with Surface Tension | p. 265 |
Equilibrium with Other Forms of Energy | p. 265 |
Equilibrium in the Presence of Gravity | p. 266 |
Centrifuges | p. 268 |
Semipermeable Membranes | p. 269 |
Osmotic Pressure | p. 270 |
Small is Interesting! Equilibrium with Surface Tension | p. 271 |
Bubbles, Drops and Nucleation | p. 271 |
Capillary Condensation | p. 275 |
Summary | p. 275 |
References | p. 278 |
The Phase Rule | p. 279 |
How Many Phases Can Coexist in a Given Equilibrium Situation? | p. 279 |
What Does the Phase Rule Tell Us? What Does It Not Tell Us? | p. 280 |
What is a Phase? | p. 280 |
The Phase Rule is Simply Counting Variables | p. 281 |
More On Components | p. 282 |
A Formal Way to Find the Number of Independent Equations | p. 285 |
The Phase Rule for One- and Two-Component Systems | p. 285 |
Harder Phase Rule Problems | p. 288 |
Summary | p. 288 |
References | p. 291 |
Equilibrium in Biochemical Reactions | p. 293 |
An Example, the Production of Ethanol from Sugar | p. 293 |
Organic and Biochemical Reactions | p. 293 |
Two More Sweet Examples | p. 294 |
Thermochemical Data for Biochemical Reactions | p. 295 |
Thermodynamic Equilibrium in Large Scale Biochemistry | p. 296 |
Translating between Biochemical and Chemical Engineering Equilibrium Expressions | p. 296 |
Chemical and Biochemical Equations | p. 297 |
Equilibrium Constants | p. 297 |
pH and Buffers | p. 298 |
Ionic Strength | p. 298 |
Equilibrium in Biochemical Separations | p. 298 |
Summary | p. 299 |
References | p. 300 |
Useful Tables and Charts | p. 303 |
Useful Property Data for Corresponding States Estimates | p. 303 |
Vapor-Pressure Equation Constants | p. 305 |
HenryâÇÖs Law Constants | p. 306 |
Compressibility Factor Chart (z Chart) | p. 307 |
Fugacity Coefficient Charts | p. 307 |
Azeotropes | p. 308 |
Van Laar Equation Constants | p. 312 |
Enthalpies and Gibbs Energies of Formation from the Elements in the Standard States, at T Â¼ 298.15 K Â¼ 25C, and P Â¼ 1.00 bar | p. 313 |
Heat Capacities of Gases in the Ideal Gas State | p. 317 |
Equilibrium with other Restraints, Other Approaches to Equilibrium | p. 319 |
The Mathematics of Fugacity, Ideal Solutions, Activity and Activity Coefficients | p. 323 |
The Fugacity of Pure Substances | p. 323 |
Fugacities of Components of Mixtures | p. 324 |
The Consequences of the Ideal Solution Definition | p. 326 |
The Mathematics of Activity Coefficients | p. 326 |
Equations of State for Liquids and Solids Well Below their Critical Temperatures | p. 329 |
The Taylor Series EOS and Its Short Form | p. 329 |
Effect of Temperature on Density | p. 330 |
Effect of Pressure on Density | p. 331 |
Summary | p. 332 |
References | p. 333 |
Gibbs Energy of Formation Values | p. 335 |
Values âÇ£From the ElementsâÇ | p. 335 |
Changes in Enthalpy, Entropy, and Gibbs Energy | p. 335 |
Enthalpy Changes | p. 335 |
Entropy Changes | p. 336 |
Ions | p. 337 |
Presenting these Data | p. 337 |
References | p. 337 |
Calculation of Fugacities from Pressure-Explicit EOSs | p. 339 |
Pressure-Explicit and Volume-Explicit EOSs | p. 339 |
f /P of Pure Species Based on Pressure-Explicit EOSs | p. 339 |
Cubic Equations of State | p. 340 |
fi /Pyi for Individual Species in Mixtures, Based on Pressure-Explicit EOSs | p. 342 |
Mixing Rules for Cubic EOSs | p. 343 |
VLE Calculations with a Cubic EOS | p. 344 |
Summary | p. 345 |
References | p. 346 |
Thermodynamic Property Derivatives and the Bridgman Table | p. 347 |
References | p. 350 |
Answers to Selected Problems | p. 351 |
Index | p. 353 |
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