THERMODYNAMIC RELATIONSHIPS INVOLVING THE EQUILIBRIUM CONSTANT

Where G is the Gibbs Free Energy and R is the idea) gas constant. 

Thermodynamic Relationships Involving the Equilibrium Constant Appendix C 

Kp is a function of temperature only, and the temperature dependence of ATp is given by van t Floff s equation  

ATp neglecting ACp. Given the equilibrium constant at one temperature r,. ATp (ri) and the heat of reaction the partial pressure equilibrium constant at any temperature T is 

The equilibrium constant at temperature Tcan be calculated from the change in the Gibbs free energy using 

---

Appendix C THERMODYNAMIC RELATIONSHIPS INVOLVING THE EQUILIBRIUM CONSTANT 929... 

The equilibrium constants for vapor-liquid equilibria (VLB), aqueous dissociation equilibria and solid-liquid equilibria (SLE) can be obtained either by the thermodynamic relationship involving the AG , AH and ACp of the reaction or via the numerous articles in the literature providing functions, tables or graphs of the temperature dependent constants for various species. Prominent among these are the articles by Wilhelm, Battino and Wilcock (8) for VLE and Edwards, Newman and Prausnitz (PS) for liquid phase dissociation and/or hydrolysis. 

In this appendix, we will use statistical thermodynamics to relate the equilibrium constant of a chemical reaction to the microscopic properties of the molecules involved. Our strategy will be to define functions for the microscopic properties of molecules and then to connect these to the change in the free energy of a reaction. The relationship between this property and the equilibrium constant is well known. 

Definitions. Early in the history of chemical kinetics a catalyst was defined as a chemical species that changes the rate of a reaction without undergoing an irreversible change /fse//(Ostwald, 1902). Subsequent definitions of a catalyst included (1) a catalyst is a chemical species that may be chemically altered but is tan involved in a whole number stoichiometric relationship among reactants and prodacts and (2) a catalyst is a chemical species that appears in the rate law with a reaction order greater than its stoichiometric coefficient. In the latter case it was realized that either a product of the reaction (autocatalysis) or a reactant may also function as a catalyst. From a practical perspective, a catalyst is a chemical species that influences the rate of a chemical reaction regardless of the fate of the catalytic species. However, a catalyst has no influence on the thermodynamics of n reaction. In other words, the concentration of a catalyst is reflected in the rate law but is not reflected in the equilibrium constant. This latter definition was modified and approved by the International Union of Pure and Applied < hemistry (IUPAC, 1981) to read as follows ... 

This equation is identical to that which defines a concentration-based equilibrium constant, so it is tempting to say that such a result leads us immediately to the equilibrium constant of the reaction. If the reaction under consideration is truly an elementary step in the sense we shall discuss later, this is so. But many, even most, chemical transformations that we observe on a macroscopic scale and that observe overall stoichiometric relationships as given by (I) consist of a number of individual or elementary steps that for one reason or another are not directly observable. In such cases observation of the stationary condition expressed by equation (1-22) involves rate constants kf and k that are combinations of the constants associated with elementary steps. Further discussion of this and the relationship between rates and thermodynamic equilibria is given later in this chapter. 

From the EQCM data (see Fig. 14.4), it may be concluded that the thermodynamic analysis in Eqs. 14.7-14.9 is likely to be applicable on the voltammetric time scale due to the slow rate of the dissolution/reprecipitatiOTi process involving Red (solid) and Red(ionic liquid). As per Eqs. 14.5 and 14.6, the processes that contribute to the voltammetry are assumed to be (1) oxidation of Red(solid) to Ox (solid), which is accompanied by charge neutralization involving the insertion of [PFe] (2) dissolution of [Ox][PFg](solid) with the equilibrium relationship between the dissolved species (Ox (ionic liquid)) and [PFg] (ionic liquid), and [Ox] [PFe] (solid) at the particle/ionic liquid interface being governed by the equilibrium constant K, and (3) reduction of solution-phase Ox" to solution-phase Red. Thus, overall the processes to be modelled are as follows ... 

Thermodynamic equilibrium constant (K) the equilibrium constant in which the concentrations of gases are expressed in partial pressures in atmospheres, whereas the concentrations of solutes in liquid solutions are expressed in molarities. (19.6) Thermodynamics the study of the relationship between heat and other forms of energy involved in a chemical or physical process, (p. 225 and p. 764)... 

Equipment design procedures for separation operations require phase enthalpies and densities in addition to phase equilibrium ratios. Classical thermodynamics provides a means for obtaining all these quantities in a consistent manner from P-v-T relationships, which are usually referred to as equations of state. Although a large number of P-v-T equations have been proposed, relatively few are suitable for practical design calculations. Table 4.2 lists some of these. All the equations in Table 4.2 involve the universal gas constant R and, in all cases except two, other constants that are unique to a particular species. All equations of state can be applied to mixtures by means of mixing rules for combining pure species constants. 

Kinetic constants in Table 5 may be applied directly to calculate the thermodynamic equilibrium constant Keq and compare with the same constant obtained by independent methods. Testing for consistency with Haldane relationships is theoretically a good method, but in practice involves the combination of large numbers of constants, each of which may be in error to some degree the real use of Haldanes is to ensure that the experimental data are self-consistent. 

Where MH stands for methyl-hexane and DMP stands for dimethyl-pentane. The isoheptanes do not appear to be at thermodynamic equilibrium, nor are they fixed at some constant composition. Mango argued that it is difficult to explain the relationship between the isoheptanes by a mechanism involving the thermal decomposition of natural products or their respective kerogenous derivatives, and suggested a steady-state kinetics where certain product ratios are necessarily time-invariant. He proposed a catalytic process in which the four isoheptanes are formed pairwise through two cyclopropyl intermediates (Fig. 19). 

---