Physical and Chemical Equilibrium for Chemical Engineers

by De Nevers, Noel

• ISBN13: 9780470927106
• ISBN10: 0470927100
• Edition: 2nd
• Format: Hardcover
• Copyright: 2012-03-20
• Publisher: Wiley

Summary

Using the simplest mathematics, this resource accurately and rigorously covers physical and chemical equilibrium in depth. The second edition continues to cover topics found in the first edition, with numerous updates including: changes in naming and notation (this edition uses the more popular Gibbs Energy and Partial Molar Properties), changes in symbols (this edition only uses popular notation), as well as adding entirely new problems. Finally, the second edition includes an appendix about the Bridgman table and its use.

Author Biography

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.

Table of Contents

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 ¼ 298.15 K ¼ 25C, and P ¼ 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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