Chemical Equilibria

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 Physico-Chemical Transformations and Equilibria 11.1 Characteristic parameters of physico-chemical transformations 11.1.1 Balance equation of a transformation 11.1.2 Values associated with a transformation 21.1.3 Standard values associated with a transformation 31.1.4 Extent and rate of a transformation 31.2 Entropy production during the course of a transformation in a closed system 41.3 Affinity of a transformation 51.3.1 Definition 51.3.2 Affinity and characteristic functions 61.3.3 Affinity and chemical potentials 71.3.4 Affinity, reaction quotient and activities 81.3.5 Total differential of the affinity in variables Yl, Xm , ξ 91.3.6 Derivatives of the affinity in relation to the extent and the chemical potentials 111.4 De Donder’s inequality – direction of the transformations and equilibrium conditions 121.5 Heats of transformation 141.5.1 Heat of transformation at constant pressure and temperature 151.5.2 Heat of transformation at constant volume and temperature 161.5.3 Variations in the heat of transformation at constant pressure with changing temperature – Kirchhoff relation 171.6 Set of points representing the equilibrium states of a transformation 181.7 Closed systems accommodating multiple reactions 191.8 Direction of evolution and equilibrium conditions in an open system 201.9 Azeotropic transformations 21Chapter 2 Properties of States of Physico-Chemical Equilibrium 252.1 Laws of displacement of an equilibrium 252.1.1 General form of the displacement laws 252.1.2 Influence of a temperature disturbance 262.1.3 Influence of a pressure disturbance 272.1.4 Influence of the addition of a component 272.1.5 Influence of the addition of an inert component 322.2 Properties of all the equilibria in a system 332.2.1 Property of the set of balance equations of a system 342.2.2 Linear combinations of balance equations 362.2.3 Base of the vector space of the balance equations – Jouguet criteria 372.3 Phase laws 412.3.1 Reminder of Gibbs’ phase rule 412.3.2 Duhem’s phase rule in closed systems 422.3.3 Comparison between the Gibbs variance and the Duhem variance 442.4 Indifferent states 442.4.1 Definition 452.4.2 Condition of indifference of a state 452.4.3 Set of indifferent points of equilibrium 472.4.4 Gibbs–Konovalov theorem 472.5 Thermodynamically-equivalent systems 482.6 Stability of equilibria 482.6.1 De Donder’s general stability condition 492.6.2 Stability of a system with unilateral variations 492.6.3 Stability of a system with bilateral variations 512.6.4 Conditions of bilateral stability expressed in terms of chemical potentials 53Chapter 3 Molecular Chemical Equilibria 553.1 Law of mass action – equilibrium constants 553.1.1 Expression of the law of mass action 553.1.2 Different forms of the law of mass action 573.1.3 Use of solution models and application of the law of mass action 623.1.4 Systems composed of a set of equilibria 633.1.5 Unit of the equilibrium constants 643.1.6 Variations of the equilibrium constants with temperature 643.1.7 Influence of the choice of reference pressure on the equilibrium constant 663.1.8 Dissociative dissolution of a gas in a solid 673.2 Graphical representations of equilibria – pole diagrams 693.2.1 Principle of the pole diagram 693.2.2 Influence of a temperature change on a pole diagram 703.2.3 Pole diagrams of two reactions in the same family 723.3 Representation of the evolution of an equilibrium with the temperature 733.3.1 Diagram in van ’t Hoff coordinates 733.3.2 Ellingham diagrams 743.4 Binary diagrams for chemical equilibrium 883.5 Ternary diagrams of chemical equilibria 893.5.1 Mode of representation 903.5.2 Molar fractions at equilibrium and initial composition 933.5.3 Iso-Q curves in perfect solutions 953.5.4 Iso-composition curves in perfect solutions 983.6 Quaternary diagrams of chemical equilibria 100Chapter 4 Determination of the Values Associated with Reactions – Equilibrium Calculations 1054.1 Reminders of a few thermodynamic relations 1054.2 Enthalpies of reaction – thermochemistry 1104.2.1 Experimental determination of the reaction enthalpies by calorimetry 1114.2.2 Calculation of the standard enthalpy at another temperature 1114.2.3 Influence of the pressure on the reaction enthalpies 1114.2.4 Determination of the reaction enthalpies by calculation on the basis of other thermodynamic data 1124.2.5 Enthalpies of formation 1144.2.6 Enthalpies of combustion 1164.2.7 Dissociation energy, bond energy and enthalpies of formation 1194.3 Reaction entropies 1264.3.1 Planck’s hypothesis – calculation of the calorimetric entropies 1264.3.2 Spectroscopic determination of entropies – absolute entropies 1284.3.3 The third law 1284.4 Specific heat capacities 1314.4.1 Calorimetric measurements of the specific heat capacities 1314.4.2 Spectral measurements of the specific heat capacities 1344.5 Experimental determination of the equilibrium constants 1344.6 Calculation of the equilibrium constants on the basis of other thermodynamic data 1364.6.1 Calculation of the equilibrium constants – method 1 1374.6.2 Calculation of the equilibrium constants – method 2 1374.6.3 Calculation of the equilibrium constants – method 3 1374.6.4 Calculation of the equilibrium constants – method 4 1384.6.5 Calculation of the equilibrium constants – method 5 1384.7 Determination of the equilibrium constants on the basis of spectral data and statistical thermodynamics 1404.8 Thermodynamic tables and databanks 1404.9 Estimation of thermodynamic data 1424.9.1 Method of evaluating the energies of dissociation by spectroscopy 1434.9.2 Group contribution methods 1434.10 Thermodynamic calculations for complex systems 1464.10.1 Definition of the system 1474.10.2 Output mode – graphical representation 1474.10.3 Calculation method based on the equilibrium constants 1484.10.4 Method of minimization of the Gibbs energy function 149Appendices 151Appendix 1 153Appendix 2 163Bibliography 181Index 185