Page 196 - Chemical equilibria Volume 4

172 Chemical Equilibria
N
Z =
z
[A2.33]
C
If the phase is made up of several different types of molecules – N A
molecules of A, N B molecules of B, etc. – then the canonical partition
function becomes:
Z = z N A .z N B .... [A2.34]
B
A
C
A2.3.3.2. Case of sets of indiscernible molecules
If the molecules are all identical and indiscernible, then we can show that
the following expression can be employed:
z N
Z = [A2.35]
C
N !
If the phase is made up of several different types of molecules – N A
molecules of A, N B molecules of B, etc., the canonical partition function
becomes:
z N A z N B z N A
Z = A . B ... = ∏ A [A2.36]
C
N A ! N B ! A N A !

In the case that the medium under study is a mixture of several phases
α, β, γ, etc., the canonical partition function of the set is the product of the
canonical partition functions of the different phases, in obeisance to:

Z = Z C ( ) α .Z C () β .Z C () γ .. [A2.37]
C

Each canonical partition function of each of the phases obeys one of
relations [A2.33], [A2.34], [A2.35] or [A2.36].

A2.4. Canonical partition functions and thermodynamic
functions

Let us look at the following expressions, used to express the
thermodynamic functions on the basis of the canonical partition function.