Michel SOUSTELLE is a chemical engineer and Emeritus Professor at Ecole des Mines de Saint-Etienne in France. He taught chemical kinetics from postgraduate to Master degree level while also carrying out research in this topic.

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• Preface xiNotations and Symbols xvChapter 1. Phase Transformations of Pure Substances 11.1. Standard state: standard conditions of a transformation 11.2. Classification and general properties of phase transformations 21.2.1. First-order transformations and the Clapeyron relation  41.2.2. Second-order transformations 71.3. Liquid–vapor transformations and equilibrium states 161.3.1. Method of two equations of state, using the Clapeyron equation  161.3.2. Gibbs energy and fugacity method 181.3.3. Unique equation of state method  191.3.4. The region of the critical point and spinodal decomposition 211.3.5. Microscopic modeling  221.3.6. Liquid–vapor equilibrium in the presence of an inert gas 261.4. Solid–vapor transformations and equilibriums  281.4.1. Macroscopic treatment  281.4.2. Microscopic treatment  291.5. Transformations and solid–liquid equilibria 301.5.1. Macroscopic treatment 311.5.2. Microscopic treatment 311.6. Diagram for the pure substance and properties of the triple point 321.7. Allotropic and polymorphic varieties of a solid 351.7.1. Enantiotropy 361.7.2. Monotropy 391.7.3. Transition from enantiotropy to monotropy and vice versa  391.8. Mesomorphic states  40Chapter 2. Properties of Equilibria Between Binary Phases  432.1. Classification of equilibria between the phases of binary systems 432.2. General properties of two-phase binary systems 452.2.1. Equilibrium conditions for two-phase binary systems  452.2.2. Conditions of evolution of a two-phase binary system 462.3. Graphical representation of two-phase binary systems  472.3.1. Gibbs energy graphs 472.3.2. Phase diagram in the mono- and bi-phase zones 532.3.3. Isobaric cooling curves 632.4. Isobaric representation of three-phase binary systems 662.4.1. Gibbs energy curve 662.4.2. Isobaric phase diagram in tri-phase regions 682.4.3. Isobaric cooling curves with tri-phase zones 702.5. Isothermal phase diagrams 722.6. Composition/composition curves  732.7. Activity of the components and consequences of Raoult’s and Henry’s laws 73Chapter 3. Equilibria Between Binary Condensed Phases 753.1. Equilibria between phases of the same nature: liquid–liquid or solid–solid 763.1.1. Thermodynamics of demixing 763.1.2. Demixing in the case of low reciprocal solubilities 793.1.3. Demixing of strictly-regular solutions 813.2. Liquid–solid systems 843.2.1. Thermodynamics of the equilibria between a liquid phase and a solid phase 863.2.2. Isobaric phase diagrams of equilibria between a solid and a liquid  903.2.3. Solidus and liquidus in the vicinity of the pure substance 973.3. Equilibria between two solids with two polymorphic varieties of the solid  1003.4. Applications of solid–liquid equilibria 1023.4.1. Solubility of a solid in a liquid: Schröder–Le Châtelier law 1023.4.2. Determination of molar mass by cryometry  1043.5. Membrane equilibria – osmotic pressure 1063.5.1. Thermodynamics of osmotic pressure 1073.5.2. Osmotic pressure of infinitely-dilute solutions: the Van ‘t the Hoff law 1093.5.3. Application of osmotic pressure to the determination of the molar mass of polymers  1103.5.4. Osmotic pressure of strictly-regular solutions  1113.5.5. Osmotic pressure and the osmotic coefficient 112Chapter 4. Equilibria Between Binary Fluid Phases 1134.1. Thermodynamics of liquid–vapor equilibrium in a binary system 1134.2. Liquid–vapor equilibrium in perfect solutions far from the critical conditions 1174.2.1. Partial pressures and total pressure of a perfect solution 1184.2.2. Isothermal diagram of a perfect solution 1194.2.3. Isobaric diagram of a perfect solution 1204.2.4. Phase composition curve  1214.3. Liquid–gas equilibria in ideal dilute solutions  1224.4. Diagrams of the liquid–vapor equilibria in real solutions 1254.4.1. Total miscibility in the liquid phase  1254.4.2. Partial miscibility in the liquid phase, heteroazeotropes 1284.5. Thermodynamics of liquid–vapor azeotropy 1294.5.1. Relation between the pressure of the azeotrope and the activity coefficients of the liquid phase at the azeotropic composition 1294.5.2. Relation between the activity coefficient and the temperature of the azeotrope 1304.6. Liquid–vapor equilibria and models of solutions 1324.6.1. Liquid–vapor equilibria in strictly-regular solutions  1324.6.2. Liquid–vapor equilibrium in associated solutions  1374.7. Liquid–vapor equilibria in the critical region 1404.8. Applications of liquid–vapor equilibria  1434.8.1. Solubility of a gas in a liquid  1434.8.2. Determination of molar masses by tonometry  1454.8.3. Determination of molar masses by ebulliometry  1464.8.4. Continuous rectification or fractional distillation  149Chapter 5. Equilibria Between Ternary Fluid Phases  1635.1. Representation of the composition of ternary systems 1635.1.1. Symmetrical representation of the Gibbs triangle 1635.1.2. Dissymmetrical representation of the right triangle 1685.2. Representation of phase equilibria 1695.2.1. Isothermal projections 1695.2.2. Conjugate points and conodes 1705.2.3. Isopleth sections 1715.3. Equilibria in liquid phases with miscibility gaps 1715.3.1. Representation of the miscibility gap 1715.3.2. Sharing in liquid–liquid systems 1735.3.3. Application of sharing between two liquids to solvent extraction  1775.4. Liquid–vapor systems 1825.4.1. Isothermal and isopleth sections (boiling and dew)  1825.4.2. Distillation trajectories  1845.4.3. Systems with two distillation fields  1865.4.4. Systems with three distillation fields 1875.5. Examples of applications of ternary diagrams between fluid phases 1875.5.1. Treatment of argentiferous lead 1875.5.2. Purity of oil products: aniline point 1885.5.3. Obtaining concentrated ethyl alcohol 189Chapter 6. Equilibria Between Condensed Ternary Fluid Phases 1916.1. Solidification of a ternary system with total miscibility in the liquid state and in the solid state 1926.2. Solidification of a ternary system with no miscibility and with a ternary eutectic 1926.2.1. Invariant transformations of a liquid–solid ternary system 1936.2.2. Representations of the ternary system with no miscibility in the solid state 1946.2.3. Lowering of the melting point of a binary system by the addition of a component  1996.2.4. Slope at the ternary eutectic 2026.3. Ternary systems with partial miscibilities in the solid state and ternary eutectic 2046.4. Solidification of ternary systems with definite compounds 2086.4.1. Ternary system with a binary definite compound binary with congruent melting  2086.4.2. Generalization to the case of a ternary compound and of multiple definite compounds 2116.4.3. Definite compound with incongruent melting: quasi-peritectic transformation 2136.5. A peritectic transformation in one binary system and total miscibility in the other two 2156.6. The ternary peritectic transformation 217Bibliography 219Index 221

Michel SOUSTELLE is a chemical engineer and Emeritus Professor at Ecole des Mines de Saint-Etienne in France. He taught chemical kinetics from postgraduate to Master degree level while also carrying out research in this topic.

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• Preface xiNotations and Symbols xvChapter 1. Phase Transformations of Pure Substances 11.1. Standard state: standard conditions of a transformation 11.2. Classification and general properties of phase transformations 21.2.1. First-order transformations and the Clapeyron relation  41.2.2. Second-order transformations 71.3. Liquid–vapor transformations and equilibrium states 161.3.1. Method of two equations of state, using the Clapeyron equation  161.3.2. Gibbs energy and fugacity method 181.3.3. Unique equation of state method  191.3.4. The region of the critical point and spinodal decomposition 211.3.5. Microscopic modeling  221.3.6. Liquid–vapor equilibrium in the presence of an inert gas 261.4. Solid–vapor transformations and equilibriums  281.4.1. Macroscopic treatment  281.4.2. Microscopic treatment  291.5. Transformations and solid–liquid equilibria 301.5.1. Macroscopic treatment 311.5.2. Microscopic treatment 311.6. Diagram for the pure substance and properties of the triple point 321.7. Allotropic and polymorphic varieties of a solid 351.7.1. Enantiotropy 361.7.2. Monotropy 391.7.3. Transition from enantiotropy to monotropy and vice versa  391.8. Mesomorphic states  40Chapter 2. Properties of Equilibria Between Binary Phases  432.1. Classification of equilibria between the phases of binary systems 432.2. General properties of two-phase binary systems 452.2.1. Equilibrium conditions for two-phase binary systems  452.2.2. Conditions of evolution of a two-phase binary system 462.3. Graphical representation of two-phase binary systems  472.3.1. Gibbs energy graphs 472.3.2. Phase diagram in the mono- and bi-phase zones 532.3.3. Isobaric cooling curves 632.4. Isobaric representation of three-phase binary systems 662.4.1. Gibbs energy curve 662.4.2. Isobaric phase diagram in tri-phase regions 682.4.3. Isobaric cooling curves with tri-phase zones 702.5. Isothermal phase diagrams 722.6. Composition/composition curves  732.7. Activity of the components and consequences of Raoult’s and Henry’s laws 73Chapter 3. Equilibria Between Binary Condensed Phases 753.1. Equilibria between phases of the same nature: liquid–liquid or solid–solid 763.1.1. Thermodynamics of demixing 763.1.2. Demixing in the case of low reciprocal solubilities 793.1.3. Demixing of strictly-regular solutions 813.2. Liquid–solid systems 843.2.1. Thermodynamics of the equilibria between a liquid phase and a solid phase 863.2.2. Isobaric phase diagrams of equilibria between a solid and a liquid  903.2.3. Solidus and liquidus in the vicinity of the pure substance 973.3. Equilibria between two solids with two polymorphic varieties of the solid  1003.4. Applications of solid–liquid equilibria 1023.4.1. Solubility of a solid in a liquid: Schröder–Le Châtelier law 1023.4.2. Determination of molar mass by cryometry  1043.5. Membrane equilibria – osmotic pressure 1063.5.1. Thermodynamics of osmotic pressure 1073.5.2. Osmotic pressure of infinitely-dilute solutions: the Van ‘t the Hoff law 1093.5.3. Application of osmotic pressure to the determination of the molar mass of polymers  1103.5.4. Osmotic pressure of strictly-regular solutions  1113.5.5. Osmotic pressure and the osmotic coefficient 112Chapter 4. Equilibria Between Binary Fluid Phases 1134.1. Thermodynamics of liquid–vapor equilibrium in a binary system 1134.2. Liquid–vapor equilibrium in perfect solutions far from the critical conditions 1174.2.1. Partial pressures and total pressure of a perfect solution 1184.2.2. Isothermal diagram of a perfect solution 1194.2.3. Isobaric diagram of a perfect solution 1204.2.4. Phase composition curve  1214.3. Liquid–gas equilibria in ideal dilute solutions  1224.4. Diagrams of the liquid–vapor equilibria in real solutions 1254.4.1. Total miscibility in the liquid phase  1254.4.2. Partial miscibility in the liquid phase, heteroazeotropes 1284.5. Thermodynamics of liquid–vapor azeotropy 1294.5.1. Relation between the pressure of the azeotrope and the activity coefficients of the liquid phase at the azeotropic composition 1294.5.2. Relation between the activity coefficient and the temperature of the azeotrope 1304.6. Liquid–vapor equilibria and models of solutions 1324.6.1. Liquid–vapor equilibria in strictly-regular solutions  1324.6.2. Liquid–vapor equilibrium in associated solutions  1374.7. Liquid–vapor equilibria in the critical region 1404.8. Applications of liquid–vapor equilibria  1434.8.1. Solubility of a gas in a liquid  1434.8.2. Determination of molar masses by tonometry  1454.8.3. Determination of molar masses by ebulliometry  1464.8.4. Continuous rectification or fractional distillation  149Chapter 5. Equilibria Between Ternary Fluid Phases  1635.1. Representation of the composition of ternary systems 1635.1.1. Symmetrical representation of the Gibbs triangle 1635.1.2. Dissymmetrical representation of the right triangle 1685.2. Representation of phase equilibria 1695.2.1. Isothermal projections 1695.2.2. Conjugate points and conodes 1705.2.3. Isopleth sections 1715.3. Equilibria in liquid phases with miscibility gaps 1715.3.1. Representation of the miscibility gap 1715.3.2. Sharing in liquid–liquid systems 1735.3.3. Application of sharing between two liquids to solvent extraction  1775.4. Liquid–vapor systems 1825.4.1. Isothermal and isopleth sections (boiling and dew)  1825.4.2. Distillation trajectories  1845.4.3. Systems with two distillation fields  1865.4.4. Systems with three distillation fields 1875.5. Examples of applications of ternary diagrams between fluid phases 1875.5.1. Treatment of argentiferous lead 1875.5.2. Purity of oil products: aniline point 1885.5.3. Obtaining concentrated ethyl alcohol 189Chapter 6. Equilibria Between Condensed Ternary Fluid Phases 1916.1. Solidification of a ternary system with total miscibility in the liquid state and in the solid state 1926.2. Solidification of a ternary system with no miscibility and with a ternary eutectic 1926.2.1. Invariant transformations of a liquid–solid ternary system 1936.2.2. Representations of the ternary system with no miscibility in the solid state 1946.2.3. Lowering of the melting point of a binary system by the addition of a component  1996.2.4. Slope at the ternary eutectic 2026.3. Ternary systems with partial miscibilities in the solid state and ternary eutectic 2046.4. Solidification of ternary systems with definite compounds 2086.4.1. Ternary system with a binary definite compound binary with congruent melting  2086.4.2. Generalization to the case of a ternary compound and of multiple definite compounds 2116.4.3. Definite compound with incongruent melting: quasi-peritectic transformation 2136.5. A peritectic transformation in one binary system and total miscibility in the other two 2156.6. The ternary peritectic transformation 217Bibliography 219Index 221

Michel SOUSTELLE is a chemical engineer and Emeritus Professor at Ecole des Mines de Saint-Etienne in France. He taught chemical kinetics from postgraduate to Master degree level while also carrying out research in this topic.

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• Preface xiNotations and Symbols xvChapter 1. Phase Transformations of Pure Substances 11.1. Standard state: standard conditions of a transformation 11.2. Classification and general properties of phase transformations 21.2.1. First-order transformations and the Clapeyron relation  41.2.2. Second-order transformations 71.3. Liquid–vapor transformations and equilibrium states 161.3.1. Method of two equations of state, using the Clapeyron equation  161.3.2. Gibbs energy and fugacity method 181.3.3. Unique equation of state method  191.3.4. The region of the critical point and spinodal decomposition 211.3.5. Microscopic modeling  221.3.6. Liquid–vapor equilibrium in the presence of an inert gas 261.4. Solid–vapor transformations and equilibriums  281.4.1. Macroscopic treatment  281.4.2. Microscopic treatment  291.5. Transformations and solid–liquid equilibria 301.5.1. Macroscopic treatment 311.5.2. Microscopic treatment 311.6. Diagram for the pure substance and properties of the triple point 321.7. Allotropic and polymorphic varieties of a solid 351.7.1. Enantiotropy 361.7.2. Monotropy 391.7.3. Transition from enantiotropy to monotropy and vice versa  391.8. Mesomorphic states  40Chapter 2. Properties of Equilibria Between Binary Phases  432.1. Classification of equilibria between the phases of binary systems 432.2. General properties of two-phase binary systems 452.2.1. Equilibrium conditions for two-phase binary systems  452.2.2. Conditions of evolution of a two-phase binary system 462.3. Graphical representation of two-phase binary systems  472.3.1. Gibbs energy graphs 472.3.2. Phase diagram in the mono- and bi-phase zones 532.3.3. Isobaric cooling curves 632.4. Isobaric representation of three-phase binary systems 662.4.1. Gibbs energy curve 662.4.2. Isobaric phase diagram in tri-phase regions 682.4.3. Isobaric cooling curves with tri-phase zones 702.5. Isothermal phase diagrams 722.6. Composition/composition curves  732.7. Activity of the components and consequences of Raoult’s and Henry’s laws 73Chapter 3. Equilibria Between Binary Condensed Phases 753.1. Equilibria between phases of the same nature: liquid–liquid or solid–solid 763.1.1. Thermodynamics of demixing 763.1.2. Demixing in the case of low reciprocal solubilities 793.1.3. Demixing of strictly-regular solutions 813.2. Liquid–solid systems 843.2.1. Thermodynamics of the equilibria between a liquid phase and a solid phase 863.2.2. Isobaric phase diagrams of equilibria between a solid and a liquid  903.2.3. Solidus and liquidus in the vicinity of the pure substance 973.3. Equilibria between two solids with two polymorphic varieties of the solid  1003.4. Applications of solid–liquid equilibria 1023.4.1. Solubility of a solid in a liquid: Schröder–Le Châtelier law 1023.4.2. Determination of molar mass by cryometry  1043.5. Membrane equilibria – osmotic pressure 1063.5.1. Thermodynamics of osmotic pressure 1073.5.2. Osmotic pressure of infinitely-dilute solutions: the Van ‘t the Hoff law 1093.5.3. Application of osmotic pressure to the determination of the molar mass of polymers  1103.5.4. Osmotic pressure of strictly-regular solutions  1113.5.5. Osmotic pressure and the osmotic coefficient 112Chapter 4. Equilibria Between Binary Fluid Phases 1134.1. Thermodynamics of liquid–vapor equilibrium in a binary system 1134.2. Liquid–vapor equilibrium in perfect solutions far from the critical conditions 1174.2.1. Partial pressures and total pressure of a perfect solution 1184.2.2. Isothermal diagram of a perfect solution 1194.2.3. Isobaric diagram of a perfect solution 1204.2.4. Phase composition curve  1214.3. Liquid–gas equilibria in ideal dilute solutions  1224.4. Diagrams of the liquid–vapor equilibria in real solutions 1254.4.1. Total miscibility in the liquid phase  1254.4.2. Partial miscibility in the liquid phase, heteroazeotropes 1284.5. Thermodynamics of liquid–vapor azeotropy 1294.5.1. Relation between the pressure of the azeotrope and the activity coefficients of the liquid phase at the azeotropic composition 1294.5.2. Relation between the activity coefficient and the temperature of the azeotrope 1304.6. Liquid–vapor equilibria and models of solutions 1324.6.1. Liquid–vapor equilibria in strictly-regular solutions  1324.6.2. Liquid–vapor equilibrium in associated solutions  1374.7. Liquid–vapor equilibria in the critical region 1404.8. Applications of liquid–vapor equilibria  1434.8.1. Solubility of a gas in a liquid  1434.8.2. Determination of molar masses by tonometry  1454.8.3. Determination of molar masses by ebulliometry  1464.8.4. Continuous rectification or fractional distillation  149Chapter 5. Equilibria Between Ternary Fluid Phases  1635.1. Representation of the composition of ternary systems 1635.1.1. Symmetrical representation of the Gibbs triangle 1635.1.2. Dissymmetrical representation of the right triangle 1685.2. Representation of phase equilibria 1695.2.1. Isothermal projections 1695.2.2. Conjugate points and conodes 1705.2.3. Isopleth sections 1715.3. Equilibria in liquid phases with miscibility gaps 1715.3.1. Representation of the miscibility gap 1715.3.2. Sharing in liquid–liquid systems 1735.3.3. Application of sharing between two liquids to solvent extraction  1775.4. Liquid–vapor systems 1825.4.1. Isothermal and isopleth sections (boiling and dew)  1825.4.2. Distillation trajectories  1845.4.3. Systems with two distillation fields  1865.4.4. Systems with three distillation fields 1875.5. Examples of applications of ternary diagrams between fluid phases 1875.5.1. Treatment of argentiferous lead 1875.5.2. Purity of oil products: aniline point 1885.5.3. Obtaining concentrated ethyl alcohol 189Chapter 6. Equilibria Between Condensed Ternary Fluid Phases 1916.1. Solidification of a ternary system with total miscibility in the liquid state and in the solid state 1926.2. Solidification of a ternary system with no miscibility and with a ternary eutectic 1926.2.1. Invariant transformations of a liquid–solid ternary system 1936.2.2. Representations of the ternary system with no miscibility in the solid state 1946.2.3. Lowering of the melting point of a binary system by the addition of a component  1996.2.4. Slope at the ternary eutectic 2026.3. Ternary systems with partial miscibilities in the solid state and ternary eutectic 2046.4. Solidification of ternary systems with definite compounds 2086.4.1. Ternary system with a binary definite compound binary with congruent melting  2086.4.2. Generalization to the case of a ternary compound and of multiple definite compounds 2116.4.3. Definite compound with incongruent melting: quasi-peritectic transformation 2136.5. A peritectic transformation in one binary system and total miscibility in the other two 2156.6. The ternary peritectic transformation 217Bibliography 219Index 221