Page 198 - Chemical equilibria Volume 4

174 Chemical Equilibria
To obtain the value of a function for a quantity n A (in moles) of the
component, for N A we use the product n A N a.
A2.5. Equilibrium constants and molecular partition functions

As the thermodynamic constants and, in particular, the Gibbs energies,
can be expressed on the basis of the partition functions, the same must be
true for the equilibrium constants.

We shall now express the equilibrium constant of a reaction by using the
partition functions of the reagents and the products.

Let us consider a chemical reaction between the reagents A r, giving rise
to the products A p, which can be written in the form:

p ∑
r ∑
0 = ∑ a p A + a r A = a i A
i
p r i
This formulation uses the algebraic stoichiometric numbers a i, which are
positive for a product of the reaction and negative for a reagent.

In view of relation [A2.42] and, taking account of the expression of the
pressure given by relation [A2.41], we can write the Gibbs energy of a
component i in the form:

GT − i (0) = − k T ln Z + PV [A2.43]
() G
i
i
B
iC
G i (0) is the Gibbs energy of the pure component i at the temperature of
0 K.
Here, we shall look at two types of equilibrium: homogeneous
equilibria in the gaseous phase and homogeneous equilibria in the liquid
phase.

A2.5.1. Homogeneous equilibria in the gaseous phase

Gas molecules are considered to be indiscernible molecules, so the
canonical partition function is given by relation [A2.36]. When we apply this