Mass action, thermodynamic deduction

In the deduction of the Law of Mass Action it was assumed that the effective concentrations or active masses of the components could be expressed by the stoichiometric concentrations. According to thermodynamics, this is not strictly true. The rigorous equilibrium equation for, say, a binary electrolyte ... 

If the substance shared between two solvents can exist in different molecular states in them, the simple distribution law is no longer valid. The experiments of Berthelot and Jungfleiscli, and the thermodynamic deduction show, however, that the distribution law holds for each molecular state separately. Thus, if benzoic acid is shared between water and benzene, the partition coefficient is not constant for all concentrations, but diminishes with increasing concentration in the aqueous layer. This is a consequence of the existence of the acid in benzene chiefly as double molecules (C6H5COOH)2, and if the amount of unpolymerised acid is calculated by the law of mass action (see Chapter XIII.) it is found to be in a constant ratio to that in the aqueous layer, independently of the concentration (cf. Nernst, Theoretical Chemistry, 2nd Eng. trans., 486 Die Verteilnngssatz, W. Hertz, Ahrens h annulling, Stuttgart, 1909). 

ACTIVITY AND ACTIVITY COEFFICIENTS In our deduction of the law of mass action we used the concentrations of species as variables, and deduced that the value of the equilibrium constant is independent of the concentrations themselves. More thorough investigations however showed that this statement is only approximately true for dilute solutions (the approximation being the better, the more dilute are the solutions), and in more concentrated solutions it is not correct at all. Similar discrepancies arise when other thermodynamic quantities, notably electrode potentials or chemical free energies are dealt with. To overcome these difficulties, and still to retain the simple expressions derived for such quantities, G. N. Lewis introduced a new thermodynamic quantity, termed activity, which when applied instead of concentrations in these thermodynamic functions, provides an exact fit with experimental results. This quantity has the same dimensions as concentration. The activity, aA, of a species A is proportional to its actual concentration [A], and can be expressed as... 

Chemical equilibrium in homogeneous systems, from the thermodynamic standpoint—Gaseous systems—Deduction of the law of mass action—The van t Hoff isotherm—Principle of mobile equilibrium (Le Chateher and Braun)— Variation of the equilibrium constant with temperature—A special form of the equilibrium constant and its variation with pressure... 

Thermodynamic Deduction of the Mass Action Expression for Equilibrium in a Homogeneous Gaseous System We can do this by means of an isothermal reversible cycle The proposition we make use of is that the sum of all the work terms for 103... 

The proposed approach leads directly to practical results such as the prediction—based upon the chemical potential—of whether or not a reaction runs spontaneously. Moreover, the chemical potential is key in dealing with physicochemical problems. Based upon this central concept, it is possible to explore many other fields. The dependence of the chemical potential upon temperature, pressure, and concentration is the gateway to the deduction of the mass action law, the calculation of equilibrium constants, solubilities, and many other data, the construction of phase diagrams, and so on. It is simple to expand the concept to colligative phenomena, diffusion processes, surface effects, electrochemical processes, etc. Furthermore, the same tools allow us to solve problems even at the atomic and molecular level, which are usually treated by quantum statistical methods. This approach allows us to eliminate many thermodynamic quantities that are traditionally used such as enthalpy H, Gibbs energy G, activity a, etc. The usage of these quantities is not excluded but superfluous in most cases. An optimized calculus results in short calculations, which are intuitively predictable and can be easily verified. 

---