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.

• PREFACE xiNOTATIONS AND SYMBOLS xvCHAPTER 1. PURE LIQUIDS 11.1 Macroscopic modeling of liquids 11.2. Distribution of molecules in a liquid 21.2.1. Molecular structure of a nonassociated liquid 31.2.2. The radial distribution function 41.2.3 The curve representative of the radial distribution function 61.2.4. Calculation of the macroscopic thermodynamic values 81.3. Models extrapolated from gases or solids 91.3.1. Guggenheim’s smoothed potential model 101.3.2. Mie’s harmonic oscillator model 131.3.3. Determination of the free volume on the basis of the dilation and the compressibility 151.4. Lennard-Jones and Devonshire cellular model 161.5. Cellular and vacancies model 251.6. Eyring’s semi-microscopic formulation of the vacancy model 291.7. Comparison between the different microscopic models and experimental results 32CHAPTER 2. MACROSCOPIC MODELING OF LIQUID MOLECULAR SOLUTIONS 372.1. Macroscopic modeling of the Margules expansion 382.2. General representation of a solution with several components 392.3. Macroscopic modeling of the Wagner expansions 402.3.1. Definition of the Wagner interaction coefficients 402.3.2. Example of a ternary solution: experimental determination of Wagner’s interaction coefficients 412.4. Dilute ideal solutions 432.4.1. Thermodynamic definition of a dilute ideal solution 432.4.2. Activity coefficients of a component with a pure-substance reference 442.4.3. Excess Gibbs energy of an ideal dilute solution 442.4.4. Enthalpy of mixing for an ideal dilute solution 452.4.5. Excess entropy of a dilute ideal solution 462.4.6. Molar heat capacity of an ideal dilute solution at constant pressure 462.5. Associated solutions 462.5.1. Example of the study of an associated solution 472.5.2. Relations between the chemical potentials of the associated solution 492.5.3. Calculating the extent of the equilibrium in an associated solution 502.5.4. Calculating the activity coefficients in an associated solution 502.5.5. Definition of a regular solution 512.5.6. Strictly-regular solutions 522.5.7. Macroscopic modeling of strictly-regular binary solutions 532.5.8. Extension of the model of a strictly-regular solution to solutions with more than two components 562.6. Athermic solutions 572.6.1. Thermodynamic definition of an athermic solution 582.6.2. Variation of the activity coefficients with temperature in an athermic solution 582.6.3. Molar entropy and Gibbs energy of mixing for an athermic solution 582.6.4. Molar heat capacity of an athermic solution 59CHAPTER 3. MICROSCOPIC MODELING OF LIQUID MOLECULAR SOLUTIONS 613.1. Models of binary solutions with molecules of similar dimensions 623.1.1. The microscopic model of a perfect solution 683.1.2. Microscopic description of strictly-regular solutions 703.1.3. Microscopic modeling of an ideal dilute solution 723.2. The concept of local composition 743.2.1. The concept of local composition in a solution 743.2.2. Energy balance of the mixture 763.2.3. Warren and Cowley’s order parameter 783.2.4. Model of Fowler & Guggenheim’s quasi-chemical solution 803.3. The quasi-chemical method of modeling solutions 873.4. Difference of the molar volumes: the combination term 923.4.1. Combinatorial excess entropy 923.4.2. Flory’s athermic solution model 973.4.3. Staverman’s corrective factor 983.5. Combination of the different concepts: the UNIQUAC model 1013.6. The concept of contribution of groups: the UNIFAC model 1073.6.1. The concept of the contribution of groups 1083.6.2. The UNIFAC model 1083.6.3. The modified UNIFAC model (Dortmund) 1143.6.4. Use of the UNIFAC system in the UNIQUAC model 114CHAPTER 4. IONIC SOLUTIONS 1174.1. Reference state, unit of composition and activity coefficients of ionic solutions 1194.2. Debye and Hückel’s electrostatic model 1214.2.1. Presentation of the problem 1224.2.2. Notations 1234.2.3. Poisson’s equation 1244.2.4. Electrical potential due to the ionic atmosphere 1254.2.5. Debye and Hückel’s hypotheses 1274.2.6. Debye and Hückel’s solution for the potential due to the ionic atmosphere 1324.2.7. Charge and radius of the ionic atmosphere of an ion 1344.2.8. Excess Helmholtz energy and excess Gibbs energy due to charges 1364.2.9. Activity coefficients of the ions and mean activity coefficient of the solution 1384.2.10. Self-consistency of Debye and Hückel’s model 1414.2.11. Switching from concentrations to molalities 1444.2.12. Debye and Hückel’s law: validity and comparison with experimental data 1464.2.13. Debye and Hückel’s limit law 1474.2.14. Extensions of Debye and Hückel’s law 1484.3. Pitzer’s model 1504.4. UNIQUAC model extended to ionic solutions 155CHAPTER 5. DETERMINATION OF THE ACTIVITY OF A COMPONENT OF A SOLUTION 1595.1. Calculation of an activity coefficient when we know other coefficients 1605.1.1. Calculation of the activity of a component when we know that of the other components in the solution 1605.1.2. Determination of the activity of a component at one temperature if we know its activity at another temperature 1625.2. Determination of the activity on the basis of the measured vapor pressure 1645.2.1. Measurement by the direct method 1655.2.2. Method using the vaporization constant in reference II 1665.3. Measurement of the activity of the solvent of the basis of the colligative properties 1685.3.1. Use of measuring of the depression of the boiling point – ebullioscopy 1685.3.2. Use of measuring of the depression of the freezing point – cryoscopy 1705.3.3. Use of the measurement of osmotic pressure 1725.4. Measuring the activity on the basis of solubility measurements 1735.4.1. Measuring the solubilities in molecular solutions 1745.4.2. Measuring the solubilities in ionic solutions 1745.5. Measuring the activity by measuring the distribution of a solute between two immiscible solvents 1765.6. Activity in a conductive solution 1765.6.1. Measuring the activity in a strong electrolyte 1765.6.2. Determination of the mean activity of a weak electrolyte on the basis of the dissociation equilibrium 180APPENDICES 181APPENDIX 1 183APPENDIX 2 193APPENDIX 3 207BIBLIOGRAPHY 221INDEX 225

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.

• PREFACE xiNOTATIONS AND SYMBOLS xvCHAPTER 1. PURE LIQUIDS 11.1 Macroscopic modeling of liquids 11.2. Distribution of molecules in a liquid 21.2.1. Molecular structure of a nonassociated liquid 31.2.2. The radial distribution function 41.2.3 The curve representative of the radial distribution function 61.2.4. Calculation of the macroscopic thermodynamic values 81.3. Models extrapolated from gases or solids 91.3.1. Guggenheim’s smoothed potential model 101.3.2. Mie’s harmonic oscillator model 131.3.3. Determination of the free volume on the basis of the dilation and the compressibility 151.4. Lennard-Jones and Devonshire cellular model 161.5. Cellular and vacancies model 251.6. Eyring’s semi-microscopic formulation of the vacancy model 291.7. Comparison between the different microscopic models and experimental results 32CHAPTER 2. MACROSCOPIC MODELING OF LIQUID MOLECULAR SOLUTIONS 372.1. Macroscopic modeling of the Margules expansion 382.2. General representation of a solution with several components 392.3. Macroscopic modeling of the Wagner expansions 402.3.1. Definition of the Wagner interaction coefficients 402.3.2. Example of a ternary solution: experimental determination of Wagner’s interaction coefficients 412.4. Dilute ideal solutions 432.4.1. Thermodynamic definition of a dilute ideal solution 432.4.2. Activity coefficients of a component with a pure-substance reference 442.4.3. Excess Gibbs energy of an ideal dilute solution 442.4.4. Enthalpy of mixing for an ideal dilute solution 452.4.5. Excess entropy of a dilute ideal solution 462.4.6. Molar heat capacity of an ideal dilute solution at constant pressure 462.5. Associated solutions 462.5.1. Example of the study of an associated solution 472.5.2. Relations between the chemical potentials of the associated solution 492.5.3. Calculating the extent of the equilibrium in an associated solution 502.5.4. Calculating the activity coefficients in an associated solution 502.5.5. Definition of a regular solution 512.5.6. Strictly-regular solutions 522.5.7. Macroscopic modeling of strictly-regular binary solutions 532.5.8. Extension of the model of a strictly-regular solution to solutions with more than two components 562.6. Athermic solutions 572.6.1. Thermodynamic definition of an athermic solution 582.6.2. Variation of the activity coefficients with temperature in an athermic solution 582.6.3. Molar entropy and Gibbs energy of mixing for an athermic solution 582.6.4. Molar heat capacity of an athermic solution 59CHAPTER 3. MICROSCOPIC MODELING OF LIQUID MOLECULAR SOLUTIONS 613.1. Models of binary solutions with molecules of similar dimensions 623.1.1. The microscopic model of a perfect solution 683.1.2. Microscopic description of strictly-regular solutions 703.1.3. Microscopic modeling of an ideal dilute solution 723.2. The concept of local composition 743.2.1. The concept of local composition in a solution 743.2.2. Energy balance of the mixture 763.2.3. Warren and Cowley’s order parameter 783.2.4. Model of Fowler & Guggenheim’s quasi-chemical solution 803.3. The quasi-chemical method of modeling solutions 873.4. Difference of the molar volumes: the combination term 923.4.1. Combinatorial excess entropy 923.4.2. Flory’s athermic solution model 973.4.3. Staverman’s corrective factor 983.5. Combination of the different concepts: the UNIQUAC model 1013.6. The concept of contribution of groups: the UNIFAC model 1073.6.1. The concept of the contribution of groups 1083.6.2. The UNIFAC model 1083.6.3. The modified UNIFAC model (Dortmund) 1143.6.4. Use of the UNIFAC system in the UNIQUAC model 114CHAPTER 4. IONIC SOLUTIONS 1174.1. Reference state, unit of composition and activity coefficients of ionic solutions 1194.2. Debye and Hückel’s electrostatic model 1214.2.1. Presentation of the problem 1224.2.2. Notations 1234.2.3. Poisson’s equation 1244.2.4. Electrical potential due to the ionic atmosphere 1254.2.5. Debye and Hückel’s hypotheses 1274.2.6. Debye and Hückel’s solution for the potential due to the ionic atmosphere 1324.2.7. Charge and radius of the ionic atmosphere of an ion 1344.2.8. Excess Helmholtz energy and excess Gibbs energy due to charges 1364.2.9. Activity coefficients of the ions and mean activity coefficient of the solution 1384.2.10. Self-consistency of Debye and Hückel’s model 1414.2.11. Switching from concentrations to molalities 1444.2.12. Debye and Hückel’s law: validity and comparison with experimental data 1464.2.13. Debye and Hückel’s limit law 1474.2.14. Extensions of Debye and Hückel’s law 1484.3. Pitzer’s model 1504.4. UNIQUAC model extended to ionic solutions 155CHAPTER 5. DETERMINATION OF THE ACTIVITY OF A COMPONENT OF A SOLUTION 1595.1. Calculation of an activity coefficient when we know other coefficients 1605.1.1. Calculation of the activity of a component when we know that of the other components in the solution 1605.1.2. Determination of the activity of a component at one temperature if we know its activity at another temperature 1625.2. Determination of the activity on the basis of the measured vapor pressure 1645.2.1. Measurement by the direct method 1655.2.2. Method using the vaporization constant in reference II 1665.3. Measurement of the activity of the solvent of the basis of the colligative properties 1685.3.1. Use of measuring of the depression of the boiling point – ebullioscopy 1685.3.2. Use of measuring of the depression of the freezing point – cryoscopy 1705.3.3. Use of the measurement of osmotic pressure 1725.4. Measuring the activity on the basis of solubility measurements 1735.4.1. Measuring the solubilities in molecular solutions 1745.4.2. Measuring the solubilities in ionic solutions 1745.5. Measuring the activity by measuring the distribution of a solute between two immiscible solvents 1765.6. Activity in a conductive solution 1765.6.1. Measuring the activity in a strong electrolyte 1765.6.2. Determination of the mean activity of a weak electrolyte on the basis of the dissociation equilibrium 180APPENDICES 181APPENDIX 1 183APPENDIX 2 193APPENDIX 3 207BIBLIOGRAPHY 221INDEX 225

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.

• PREFACE xiNOTATIONS AND SYMBOLS xvCHAPTER 1. PURE LIQUIDS 11.1 Macroscopic modeling of liquids 11.2. Distribution of molecules in a liquid 21.2.1. Molecular structure of a nonassociated liquid 31.2.2. The radial distribution function 41.2.3 The curve representative of the radial distribution function 61.2.4. Calculation of the macroscopic thermodynamic values 81.3. Models extrapolated from gases or solids 91.3.1. Guggenheim’s smoothed potential model 101.3.2. Mie’s harmonic oscillator model 131.3.3. Determination of the free volume on the basis of the dilation and the compressibility 151.4. Lennard-Jones and Devonshire cellular model 161.5. Cellular and vacancies model 251.6. Eyring’s semi-microscopic formulation of the vacancy model 291.7. Comparison between the different microscopic models and experimental results 32CHAPTER 2. MACROSCOPIC MODELING OF LIQUID MOLECULAR SOLUTIONS 372.1. Macroscopic modeling of the Margules expansion 382.2. General representation of a solution with several components 392.3. Macroscopic modeling of the Wagner expansions 402.3.1. Definition of the Wagner interaction coefficients 402.3.2. Example of a ternary solution: experimental determination of Wagner’s interaction coefficients 412.4. Dilute ideal solutions 432.4.1. Thermodynamic definition of a dilute ideal solution 432.4.2. Activity coefficients of a component with a pure-substance reference 442.4.3. Excess Gibbs energy of an ideal dilute solution 442.4.4. Enthalpy of mixing for an ideal dilute solution 452.4.5. Excess entropy of a dilute ideal solution 462.4.6. Molar heat capacity of an ideal dilute solution at constant pressure 462.5. Associated solutions 462.5.1. Example of the study of an associated solution 472.5.2. Relations between the chemical potentials of the associated solution 492.5.3. Calculating the extent of the equilibrium in an associated solution 502.5.4. Calculating the activity coefficients in an associated solution 502.5.5. Definition of a regular solution 512.5.6. Strictly-regular solutions 522.5.7. Macroscopic modeling of strictly-regular binary solutions 532.5.8. Extension of the model of a strictly-regular solution to solutions with more than two components 562.6. Athermic solutions 572.6.1. Thermodynamic definition of an athermic solution 582.6.2. Variation of the activity coefficients with temperature in an athermic solution 582.6.3. Molar entropy and Gibbs energy of mixing for an athermic solution 582.6.4. Molar heat capacity of an athermic solution 59CHAPTER 3. MICROSCOPIC MODELING OF LIQUID MOLECULAR SOLUTIONS 613.1. Models of binary solutions with molecules of similar dimensions 623.1.1. The microscopic model of a perfect solution 683.1.2. Microscopic description of strictly-regular solutions 703.1.3. Microscopic modeling of an ideal dilute solution 723.2. The concept of local composition 743.2.1. The concept of local composition in a solution 743.2.2. Energy balance of the mixture 763.2.3. Warren and Cowley’s order parameter 783.2.4. Model of Fowler & Guggenheim’s quasi-chemical solution 803.3. The quasi-chemical method of modeling solutions 873.4. Difference of the molar volumes: the combination term 923.4.1. Combinatorial excess entropy 923.4.2. Flory’s athermic solution model 973.4.3. Staverman’s corrective factor 983.5. Combination of the different concepts: the UNIQUAC model 1013.6. The concept of contribution of groups: the UNIFAC model 1073.6.1. The concept of the contribution of groups 1083.6.2. The UNIFAC model 1083.6.3. The modified UNIFAC model (Dortmund) 1143.6.4. Use of the UNIFAC system in the UNIQUAC model 114CHAPTER 4. IONIC SOLUTIONS 1174.1. Reference state, unit of composition and activity coefficients of ionic solutions 1194.2. Debye and Hückel’s electrostatic model 1214.2.1. Presentation of the problem 1224.2.2. Notations 1234.2.3. Poisson’s equation 1244.2.4. Electrical potential due to the ionic atmosphere 1254.2.5. Debye and Hückel’s hypotheses 1274.2.6. Debye and Hückel’s solution for the potential due to the ionic atmosphere 1324.2.7. Charge and radius of the ionic atmosphere of an ion 1344.2.8. Excess Helmholtz energy and excess Gibbs energy due to charges 1364.2.9. Activity coefficients of the ions and mean activity coefficient of the solution 1384.2.10. Self-consistency of Debye and Hückel’s model 1414.2.11. Switching from concentrations to molalities 1444.2.12. Debye and Hückel’s law: validity and comparison with experimental data 1464.2.13. Debye and Hückel’s limit law 1474.2.14. Extensions of Debye and Hückel’s law 1484.3. Pitzer’s model 1504.4. UNIQUAC model extended to ionic solutions 155CHAPTER 5. DETERMINATION OF THE ACTIVITY OF A COMPONENT OF A SOLUTION 1595.1. Calculation of an activity coefficient when we know other coefficients 1605.1.1. Calculation of the activity of a component when we know that of the other components in the solution 1605.1.2. Determination of the activity of a component at one temperature if we know its activity at another temperature 1625.2. Determination of the activity on the basis of the measured vapor pressure 1645.2.1. Measurement by the direct method 1655.2.2. Method using the vaporization constant in reference II 1665.3. Measurement of the activity of the solvent of the basis of the colligative properties 1685.3.1. Use of measuring of the depression of the boiling point – ebullioscopy 1685.3.2. Use of measuring of the depression of the freezing point – cryoscopy 1705.3.3. Use of the measurement of osmotic pressure 1725.4. Measuring the activity on the basis of solubility measurements 1735.4.1. Measuring the solubilities in molecular solutions 1745.4.2. Measuring the solubilities in ionic solutions 1745.5. Measuring the activity by measuring the distribution of a solute between two immiscible solvents 1765.6. Activity in a conductive solution 1765.6.1. Measuring the activity in a strong electrolyte 1765.6.2. Determination of the mean activity of a weak electrolyte on the basis of the dissociation equilibrium 180APPENDICES 181APPENDIX 1 183APPENDIX 2 193APPENDIX 3 207BIBLIOGRAPHY 221INDEX 225