Statistical Thermodynamics

9Law of Mass Action

In the physical chemistry course, the law of mass action was derived by equating the free energy of the reactants with the one for the products. For a reaction of A and B to produce C and D with stoichiometric coefficients, a, b, c, and d, respectively,

the law of mass action gives the relationship between the partial pressures of the four components, p_A, p_B, p_C, and p_D. The standard equilibrium constant is given as

where p° (typically, 1 bar or 1 atm) removes all the units.

In this chapter, we follow the method of Hückel to derive the law of mass action. The successful derivation is considered as one of the most triumphant accomplishments in the statistical thermodynamics applied to chemistry. In our derivation, we find what makes it possible for the reactants and products to follow the law of mass action, and what condition is required.

In Sections 9.3 and 9.4, we look at some simple reactions. In Section 9.3, we go back to the isomerization we looked at in Section 5.5 to uncover an implicit approximation employed in the method we learn in the first two sections. We prove the legitimacy of the method in Section 9.4 where we learn the method of the steepest ...