Enthalpy, Free Energy, and Equilibrium Constant

For the equilibrium between the axial and equatorial conformations of a monosubstituted cyclohexane, 

Inserting the appropriate values for R, T (298 K), and K gives the values of AG° listed in the table (page 107) for the various substituents discussed in Section 3.8. 

One of the fundamental equations of thermodynamics concerns systems at equilibrium and relates the equilibrium constant K to the difference in standard free energy (AG°) between the products and the reactants. 

Substituent X Percent axial Percent equatorial K kJ/mol kcal/mol 

Distribution of two products at equilibrium at 25 C as a function of the standard free energy difference (AG°) between them. 

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See the box entitled Enthalpy Free Energy and Equilibrium Constant accompanying this section for a discussion of these relationships... 

Enthalpy, Free Energy, and Equilibrium Constant CHAPTER 4... 

The importance of interactions amongst point defects, at even fairly low defect concentrations, was recognized several years ago. Although one has to take into account the actual defect structure and modifications of short-range order to be able to describe the properties of solids fully, it has been found useful to represent all the processes involved in the intrinsic defect equilibria in a crystal (with a low concentration of defects), as well as its equilibrium with its external environment, by a set of coupled quasichemical reactions. These equilibrium reactions are then handled by the law of mass action. The free energy and equilibrium constants for each process can be obtained if we know the enthalpies and entropies of the reactions from theory or... 

Tables of heat capacities, enthalpies, entropies, free energies, and equilibrium constants.)... 

Table 6.25 Enthalpy, Gibbs free energy and equilibrium constant of reaction (6.14)...

The partial molar entropy of a component may be measured from the temperature dependence of the activity at constant composition the partial molar enthalpy is then determined as a difference between the partial molar Gibbs free energy and the product of temperature and partial molar entropy. As a consequence, entropy and enthalpy data derived from equilibrium measurements generally have much larger errors than do the data for the free energy. Calorimetric techniques should be used whenever possible to measure the enthalpy of solution. Such techniques are relatively easy for liquid metallic solutions, but decidedly difficult for solid solutions. The most accurate data on solid metallic solutions have been obtained by the indirect method of measuring the heats of dissolution of both the alloy and the mechanical mixture of the components into a liquid metal solvent.05... 

Free energy changes and equilibrium constants calculated from the enthalpy and entropy values estimated by the group-contribution method generally are reliable only to the order of magnitude. For example, Andersen et al. [1] have found that their estimated enthalpies and entropies usually differ from experimental values [7]... 

Enthalpy and Gibbs free energy changes and equilibrium constants for the reaction CO(g)+2H2(g) = CH30H(g)... 

Note that Eqs. 3-49 and 3-50 are very general equations which also apply, for example, to describing temperature dependencies of reaction equilibrium constants, as will be discussed in Chapters 8 and 12 (of course, with the appropriate reaction free energy and enthalpy terms). 

We can now utilize some of the statistical mechanics relationships derived in Chapter 8 to find expressions for the free energy and the equilibrium constant in term of the molecular partition functions. From the definition of the free energy (Eq. 9.1) the expression for the enthalpy of an ideal gas (Eq. 8.121), and recalling that Ho = Eq (for an ideal gas), we obtain... 

Fig. 5.25 The reaction energy, the energy difference of products and reactants, determines the extent of a reaction, i.e. its equilibrium constant. The activation energy (the simple ab initio energy difference shown here is not exactly the conventional Arrhenius activation energy), the energy difference of transition state and reactants, partially determines the rate constant. Unfortunately, energy is ambiguous, since chemists use the terms potential energy, enthalpy (heat energy), and free energy see Section 5.5.2.1...

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