| Preface |
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xiii | |
| About the Author |
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xv | |
| Nomenclature |
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xvii | |
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1 Introduction to Equilibrium |
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1 | (12) |
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1.1 Why Study Equilibrium? |
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1 | (3) |
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1.2 Stability and Equilibrium |
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4 | (1) |
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1.3 Time Scales and the Approach to Equilibrium |
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5 | (1) |
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1.4 Looking Ahead, Gibbs Energy |
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5 | (1) |
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1.5 Units, Conversion Factors, and Notation |
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6 | (2) |
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1.6 Reality and Equations |
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8 | (1) |
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1.7 Phases and Phase Diagrams |
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8 | (2) |
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1.8 The Plan of this Book |
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10 | (1) |
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10 | (3) |
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11 | (2) |
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13 | (22) |
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2.1 Conservation and Accounting |
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13 | (1) |
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14 | (1) |
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2.3 Conservation of Energy; the First Law of Thermodynamics |
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15 | (2) |
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2.4 The Second Law of Thermodynamics |
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17 | (2) |
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17 | (1) |
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18 | (1) |
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2.5 Convenience Properties |
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19 | (1) |
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2.6 Using the First and Second Laws |
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19 | (2) |
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2.7 Datums and Reference States |
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21 | (1) |
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2.8 Measurable and Immeasurable Properties |
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22 | (1) |
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22 | (1) |
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2.10 The Property Equation |
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23 | (1) |
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2.11 Equations of State (EOS) |
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24 | (2) |
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2.11.1 EOSs Based on Theory |
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25 | (1) |
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2.11.2 EOSs Based on Pure Data Fitting |
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25 | (1) |
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2.12 Corresponding States |
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26 | (2) |
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28 | (1) |
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2.14 The Properties of Mixtures |
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28 | (1) |
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2.15 The Combined First and Second Law Statement; Reversible Work |
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29 | (2) |
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31 | (4) |
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33 | (2) |
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3 The Simplest Phase Equilibrium Examples and Some Simple Estimating Rules |
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35 | (14) |
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3.1 Some General Statements About Equilibrium |
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35 | (2) |
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3.2 The Simplest Example of Phase Equilibrium |
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37 | (1) |
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3.2.1 A Digression, the Distinction between Vapor and Gas |
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37 | (1) |
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3.2.2 Back to the Simplest Equilibrium |
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37 | (1) |
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3.3 The Next Level of Complexity in Phase Equilibrium |
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37 | (2) |
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3.4 Some Simple Estimating Rules: Raoult's and Henry's "Laws" |
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39 | (4) |
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3.5 The General Two-Phase Equilibrium Calculation |
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43 | (1) |
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3.6 Some Simple Applications of Raoult's and Henry's Laws |
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43 | (3) |
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3.7 The Uses and Limits of Raoult's and Henry's Laws |
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46 | (1) |
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46 | (3) |
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48 | (1) |
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4 Minimization of Gibbs Energy |
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49 | (12) |
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4.1 The Fundamental Thermodynamic Criterion of Phase and Chemical Equilibrium |
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49 | (2) |
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4.2 The Criterion of Equilibrium Applied to Two Nonreacting Equilibrium Phases |
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51 | (2) |
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4.3 The Criterion of Equilibrium Applied to Chemical Reactions |
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53 | (1) |
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4.4 Simple Gibbs Energy Diagrams |
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54 | (4) |
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4.4.1 Comparison with Enthalpy and Entropy |
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55 | (1) |
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4.4.2 Gibbs Energy Diagrams for Pressure-Driven Phase Changes |
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55 | (2) |
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4.4.3 Gibbs Energy Diagrams for Chemical Reactions |
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57 | (1) |
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4.5 Le Chatelier's Principle |
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58 | (1) |
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58 | (3) |
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60 | (1) |
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5 Vapor Pressure, the Clapeyron Equation, and Single Pure Chemical Species Phase Equilibrium |
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61 | (12) |
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5.1 Measurement of Vapor Pressure |
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61 | (1) |
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5.2 Reporting Vapor-Pressure Data |
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61 | (1) |
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5.2.1 Normal Boiling Point (NBP) |
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61 | (1) |
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5.3 The Clapeyron Equation |
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62 | (1) |
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5.4 The Clausius-Clapeyron Equation |
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63 | (1) |
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64 | (2) |
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5.6 The Antoine Equation and Other Data-Fitting Equations |
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66 | (1) |
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5.6.1 Choosing a Vapor-Pressure Equation |
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67 | (1) |
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5.7 Applying the Clapeyron Equation to Other Kinds of Equilibrium |
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67 | (1) |
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5.8 Extrapolating Vapor-Pressure Curves |
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68 | (1) |
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5.9 Vapor Pressure of Solids |
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69 | (1) |
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5.10 Vapor Pressures of Mixtures |
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69 | (1) |
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69 | (4) |
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72 | (1) |
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6 Partial Molar Properties |
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73 | (16) |
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6.1 Partial Molar Properties |
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73 | (1) |
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6.2 The Partial Molar Equation |
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74 | (1) |
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74 | (3) |
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77 | (1) |
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6.5 The Two Equations for Partial Molar Properties |
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78 | (1) |
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6.6 Using the Idea of Tangent Intercepts |
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79 | (1) |
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6.7 Partial Mass Properties |
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80 | (1) |
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6.8 Heats of Mixing and Partial Molar Enthalpies |
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80 | (2) |
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6.8.1 Differential Heat of Mixing |
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80 | (1) |
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6.8.2 Integral Heat of Mixing |
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81 | (1) |
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6.9 The Gibbs-Duhem Equation and the Counterintuitive Behavior of the Chemical Potential |
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82 | (2) |
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84 | (5) |
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87 | (2) |
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7 Fugacity, Ideal Solutions, Activity, Activity Coefficient |
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89 | (18) |
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89 | (1) |
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89 | (1) |
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7.3 The Use of the Fugacity |
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90 | (1) |
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7.4 Pure Substance Fugacities |
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90 | (5) |
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7.4.1 The Fugacity of Pure Gases |
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91 | (3) |
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7.4.2 The Fugacity of Pure Liquids and Solids |
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94 | (1) |
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7.5 Fugacities of Species in Mixtures |
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95 | (1) |
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7.6 Mixtures of Ideal Gases |
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95 | (1) |
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95 | (1) |
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7.8 Ideal Solutions Defined |
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96 | (2) |
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7.8.1 The Consequences of the Ideal Solution Definition |
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96 | (2) |
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7.9 Why Activity and Activity Coefficients? |
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98 | (1) |
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7.10 Activity and Activity Coefficients Defined |
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98 | (2) |
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7.11 Fugacity Coefficient for Pure Gases and Gas Mixtures |
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100 | (1) |
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7.12 Estimating Fugacities of Individual Species in Gas Mixtures |
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100 | (4) |
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7.12.1 Fugacities from Gas PvT Data |
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100 | (2) |
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7.12.2 Fugacities from an EOS for Gas Mixtures |
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102 | (1) |
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7.12.3 The Lewis and Randall (L-R) Fugacity Rule |
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102 | (1) |
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7.12.4 Other Mixing Rules |
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103 | (1) |
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7.13 Liquid Fugacities from Vapor-Liquid Equilibrium |
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104 | (1) |
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104 | (3) |
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105 | (2) |
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8 Vapor-Liquid Equilibrium (VLE) at Low Pressures |
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107 | (38) |
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107 | (3) |
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8.2 Presenting Experimental VLE Data |
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110 | (1) |
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8.3 The Mathematical Treatment of Low-Pressure VLE Data |
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110 | (2) |
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111 | (1) |
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8.4 The Four Most Common Types of Low-Pressure VLE |
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112 | (10) |
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8.4.1 Ideal Solution Behavior (Type I) |
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114 | (1) |
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8.4.2 Positive Deviations from Ideal Solution Behavior (Type II) |
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114 | (1) |
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8.4.3 Negative Deviations from Ideal Solution Behavior (Type III) |
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115 | (2) |
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117 | (1) |
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8.4.5 Two-Liquid Phase or Heteroazeotropes (Type IV) |
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118 | (2) |
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8.4.6 Zero Solubility and Steam Distillation |
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120 | (1) |
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8.4.7 Distillation of the Four Types of Behavior |
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121 | (1) |
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8.5 Gas-Liquid Equilibrium, Henry's Law Again |
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122 | (1) |
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8.6 The Effect of Modest Pressures on VLE |
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122 | (2) |
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123 | (1) |
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8.6.2 Gases, the L-R Rule |
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123 | (1) |
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8.7 Standard States Again |
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124 | (1) |
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8.8 Low-Pressure VLE Calculations |
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125 | (7) |
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8.8.1 Bubble-Point Calculations |
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127 | (1) |
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8.8.1.1 Temperature-Specified Bubble Point |
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127 | (1) |
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8.8.1.2 Pressure-Specified Bubble Point |
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128 | (1) |
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8.8.2 Dew-Point Calculations |
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129 | (1) |
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8.8.2.1 Temperature-Specified Dew Point |
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129 | (1) |
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8.8.2.2 Pressure-Specified Dew Point |
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129 | (1) |
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8.8.3 Isothermal Flashes (T- and P-Specified Flashes) |
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130 | (1) |
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131 | (1) |
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8.9 Traditional K-Factor Methods |
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132 | (1) |
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8.10 More Uses for Raoult's Law |
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132 | (4) |
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8.10.1 Nonvolatile Solutes, Boiling-Point Elevation |
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132 | (3) |
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8.10.2 Freezing-Point Depression |
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135 | (1) |
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8.10.3 Colligative Properties of Solutions |
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136 | (1) |
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136 | (9) |
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143 | (2) |
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9 Correlating and Predicting Nonideal VLE |
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145 | (24) |
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9.1 The Most Common Observations of Liquid-Phase Activity Coefficients |
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145 | (2) |
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9.1.1 Why Nonideal Behavior? |
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145 | (1) |
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9.1.2 The Shapes of In, γ-x Curves |
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146 | (1) |
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9.2 Limits on Activity Coefficient Correlations, the Gibbs-Duhem Equation |
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147 | (1) |
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9.3 Excess Gibbs Energy and Activity Coefficient Equations |
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148 | (2) |
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9.4 Activity Coefficients at Infinite Dilution |
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150 | (1) |
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9.5 Effects of Pressure and Temperature on Liquid-Phase Activity Coefficients |
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151 | (2) |
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9.5.1 Effect of Pressure Changes on Liquid-Phase Activity Coefficients |
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151 | (1) |
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9.5.2 Effect of Temperature Changes on Liquid-Phase Activity Coefficients |
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152 | (1) |
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9.6 Ternary and Multispecies VLE |
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153 | (2) |
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9.6.1 Liquid-Phase Activity Coefficients for Ternary Mixtures |
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154 | (1) |
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9.7 Vapor-Phase Nonideality |
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155 | (3) |
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158 | (1) |
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158 | (2) |
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9.10 The Solubility of Gases in Liquids, Henry's Law Again |
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160 | (3) |
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163 | (6) |
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167 | (2) |
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10 Vapor-Liquid Equilibrium (VLE) at High Pressures |
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169 | (12) |
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10.1 Critical Phenomena of Pure Species |
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169 | (1) |
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10.2 Critical Phenomena of Mixtures |
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170 | (4) |
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10.3 Estimating High-Pressure VLE |
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174 | (4) |
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10.3.1 Empirical K-Value Correlations |
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175 | (1) |
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10.3.2 Estimation Methods for Each Phase Separately Not Based on Raoult's Law |
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175 | (1) |
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10.3.3 Estimation Methods Based on Cubic EOSs |
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176 | (2) |
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178 | (1) |
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178 | (3) |
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179 | (2) |
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11 Liquid-Liquid, Liquid-Solid, and Gas-Solid Equilibrium |
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181 | (36) |
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11.1 Liquid-Liquid Equilibrium (LLE) |
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181 | (1) |
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11.2 The Experimental Determination of LLE |
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181 | (6) |
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11.2.1 Reporting and Presenting LLE Data |
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182 | (1) |
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11.2.2 Practically Insoluble Liquid Pairs at 25°C |
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183 | (1) |
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11.2.3 Partially Soluble Liquid Pairs at 25°C |
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183 | (1) |
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11.2.4 Miscible Liquid Pairs at 25°C |
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183 | (1) |
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11.2.5 Ternary LLE at 25°C |
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184 | (2) |
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11.2.6 LLE at Temperatures Other Than 25°C |
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186 | (1) |
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11.3 The Elementary Theory of LLE |
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187 | (3) |
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11.4 The Effect of Pressure on LLE |
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190 | (1) |
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11.5 Effect of Temperature on LLE |
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191 | (3) |
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11.6 Distribution Coefficients |
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194 | (1) |
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11.7 Liquid-Solid Equilibrium (LSE) |
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195 | (5) |
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195 | (1) |
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11.7.2 The Experimental Determination of LSE |
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195 | (1) |
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11.7.3 Presenting LSE Data |
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195 | (2) |
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197 | (2) |
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11.7.5 Gas Hydrates (Clathrates) |
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199 | (1) |
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11.8 The Elementary Thermodynamics of LSE |
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200 | (2) |
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11.9 Gas-Solid Equilibrium (GSE) at Low Pressures |
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202 | (1) |
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11.10 GSE at High Pressures |
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203 | (1) |
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11.11 Gas-Solid Adsorption, Vapor-Solid Adsorption |
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204 | (7) |
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11.11.1 Langmuir's Adsorption Theory |
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205 | (2) |
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11.11.2 Vapor-solid Adsorption, BET Theory |
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207 | (1) |
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11.11.3 Adsorption from Mixtures |
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208 | (1) |
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11.11.4 Heat of Adsorption |
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209 | (1) |
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210 | (1) |
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211 | (6) |
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215 | (2) |
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217 | (26) |
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12.1 Introduction to Chemical Reactions and Chemical Equilibrium |
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217 | (1) |
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12.2 Formal Description of Chemical Reactions |
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217 | (1) |
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12.3 Minimizing Gibbs Energy |
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218 | (1) |
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12.4 Reaction Rates, Energy Barriers, Catalysis, and Equilibrium |
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219 | (1) |
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12.5 The Basic Thermodynamics of Chemical Reactions and Its Convenient Formulations |
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220 | (3) |
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12.5.1 The Law of Mass Action and Equilibrium Constants |
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222 | (1) |
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12.6 Calculating Equilibrium Constants from Gibbs Energy Tables and then Using Equilibrium Constants to Calculate Equilibrium Concentrations |
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223 | (4) |
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12.6.1 Change of Reactant Concentration, Reaction Coordinate |
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224 | (3) |
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12.6.2 Reversible and Irreversible Reactions |
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227 | (1) |
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12.7 More on Standard States |
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227 | (2) |
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12.8 The Effect of Temperature on Chemical Reaction Equilibrium |
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229 | (5) |
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12.9 The Effect of Pressure on Chemical Reaction Equilibrium |
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234 | (4) |
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12.9.1 Ideal Solution of Ideal Gases |
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235 | (1) |
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12.9.2 Nonideal Solution, Nonideal Gases |
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236 | (1) |
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12.9.3 Liquids and Solids |
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237 | (1) |
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12.10 The Effect of Nonideal Solution Behavior |
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238 | (1) |
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12.10.1 Liquid-Phase Nonideality |
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238 | (1) |
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238 | (1) |
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239 | (4) |
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242 | (1) |
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13 Equilibrium in Complex Chemical Reactions |
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243 | (22) |
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13.1 Reactions Involving Ions |
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243 | (1) |
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244 | (5) |
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13.2.1 Sequential Reactions |
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244 | (1) |
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13.2.2 Simultaneous Reactions |
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245 | (1) |
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13.2.3 The Charge Balance Calculation Method and Buffers |
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246 | (3) |
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13.3 Reactions with More Than One Phase |
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249 | (3) |
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13.3.1 Solubility Product |
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249 | (1) |
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13.3.2 Gas-Liquid Reactions |
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249 | (3) |
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13.4 Electrochemical Reactions |
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252 | (3) |
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13.5 Chemical and Physical Equilibrium in Two Phases |
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255 | (2) |
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13.5.1 Dimerization (Association) |
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255 | (2) |
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257 | (8) |
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262 | (3) |
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14 Equilibrium with Gravity or Centrifugal Force, Osmotic Equilibrium Equilibrium with Surface Tension |
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265 | (14) |
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14.1 Equilibrium with Other Forms of Energy |
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265 | (1) |
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14.2 Equilibrium in the Presence of Gravity |
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266 | (3) |
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268 | (1) |
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14.3 Semipermeable Membranes |
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269 | (2) |
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270 | (1) |
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14.4 Small is Interesting! Equilibrium with Surface Tension |
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271 | (4) |
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14.4.1 Bubbles, Drops and Nucleation |
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271 | (4) |
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14.4.2 Capillary Condensation |
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275 | (1) |
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275 | (4) |
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278 | (1) |
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279 | (14) |
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15.1 How Many Phases Can Coexist in a Given Equilibrium Situation? |
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279 | (1) |
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15.2 What Does the Phase Rule Tell Us? What Does It Not Tell Us? |
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280 | (1) |
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280 | (1) |
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15.4 The Phase Rule is Simply Counting Variables |
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281 | (1) |
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282 | (3) |
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15.5.1 A Formal Way to Find the Number of Independent Equations |
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285 | (1) |
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15.6 The Phase Rule for One- and Two-Component Systems |
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285 | (3) |
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15.7 Harder Phase Rule Problems |
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288 | (1) |
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288 | (5) |
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291 | (2) |
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16 Equilibrium in Biochemical Reactions |
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293 | (10) |
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16.1 An Example, the Production of Ethanol from Sugar |
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293 | (1) |
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16.2 Organic and Biochemical Reactions |
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293 | (1) |
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16.3 Two More Sweet Examples |
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294 | (1) |
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16.4 Thermochemical Data for Biochemical Reactions |
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295 | (1) |
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16.5 Thermodynamic Equilibrium in Large Scale Biochemistry |
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296 | (1) |
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16.6 Translating between Biochemical and Chemical Engineering Equilibrium Expressions |
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296 | (2) |
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16.6.1 Chemical and Biochemical Equations |
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297 | (1) |
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16.6.2 Equilibrium Constants |
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297 | (1) |
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298 | (1) |
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298 | (1) |
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16.7 Equilibrium in Biochemical Separations |
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298 | (1) |
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299 | (4) |
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300 | (3) |
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Appendix A Useful Tables and Charts |
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303 | (16) |
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A.1 Useful Property Data for Corresponding States Estimates |
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303 | (2) |
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A.2 Vapor-Pressure Equation Constants |
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305 | (1) |
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A.3 Henry's Law Constants |
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306 | (1) |
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A.4 Compressibility Factor Chart (z Chart) |
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307 | (1) |
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A.5 Fugacity Coefficient Charts |
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307 | (1) |
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308 | (4) |
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A.7 Van Laar Equation Constants |
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312 | (1) |
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A.8 Enthalpies and Gibbs Energies of Formation from the Elements in the Standard States, at T = 298.15 K = 25°C and P = 1.00 bar |
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313 | (4) |
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A.9 Heat Capacities of Gases in the Ideal Gas State |
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317 | (2) |
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Appendix B Equilibrium with other Restraints Other Approaches to Equilibrium |
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319 | (4) |
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Appendix C The Mathematics of Fugacity, Ideal Solutions Activity and Activity Coefficients |
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323 | (6) |
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C.1 The Fugacity of Pure Substances |
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323 | (1) |
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C.2 Fugacities of Components of Mixtures |
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324 | (2) |
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C.3 The Consequences of the Ideal Solution Definition |
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326 | (1) |
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C.4 The Mathematics of Activity Coefficients |
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326 | (3) |
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Appendix D Equations of State for Liquids and Solids Well Below their Critical Temperatures |
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329 | (6) |
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D.1 The Taylor Series EOS and Its Short Form |
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329 | (1) |
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D.2 Effect of Temperature on Density |
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330 | (1) |
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D.3 Effect of Pressure on Density |
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331 | (1) |
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332 | (3) |
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333 | (2) |
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Appendix E Gibbs Energy of Formation Values |
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335 | (4) |
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E.1 Values "From the Elements" |
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335 | (1) |
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E.2 Changes in Enthalpy, Entropy, and Gibbs Energy |
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335 | (1) |
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335 | (1) |
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336 | (1) |
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337 | (1) |
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E.4 Presenting these Data |
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337 | (2) |
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337 | (2) |
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Appendix F Calculation of Fugacities from Pressure-Explicit EOSs |
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339 | (8) |
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F.1 Pressure-Explicit and Volume-Explicit EOSs |
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339 | (1) |
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F.2 f/P of Pure Species Based on Pressure-Explicit EOSs |
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339 | (1) |
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F.3 Cubic Equations of State |
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340 | (2) |
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F.4 fi/Pyi for Individual Species in Mixtures, Based on Pressure-Explicit EOSs |
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342 | (1) |
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F.5 Mixing Rules for Cubic EOSs |
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343 | (1) |
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F.6 VLE Calculations with a Cubic EOS |
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344 | (1) |
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345 | (2) |
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346 | (1) |
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Appendix G Thermodynamic Property Derivatives and the Bridgman Table |
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347 | (4) |
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350 | (1) |
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Appendix H Answers to Selected Problems |
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351 | (2) |
| Index |
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353 | |