Page 191 - Chemical equilibria Volume 4

Appendix 2 167
We can see that this limiting case keeps the formula of the Maxwell–
Boltzmann distribution. The value of α is therefore determined by the
relation:
N
exp( α ) ≅ A [A2.15]
−
A
z A
We can show that in this case. We also have the condition:
N << g i [A2.16]

This means that the number of particles is much less than the number of
possible states.

A2.2. Partition functions of a molecule object

A2.2.1. Definition

The partition function of molecule object of a collection is the sum z
defined by:

⎛ ε ⎞
⎜ ∑
( ε β
z = g i exp − i ⎟ = ∑ g i exp − i ) [A2.17]
B ⎠
i ⎝ k T i
The sum is extended to all the energy levels which that object can attain.

A2.2.2. Independence of energy values

The complete partition function for a system includes terms which refer
to the different forms of energy: nuclear, electronic, molecule vibration,
rotation, translation and the energy of interaction between the different
molecules.

For simplicity’s sake, we accept the hypothesis that those different forms
of energy, for a molecule, are independent.

In these conditions, we can write the total energy of a molecule as the
sum of the different contributions of the forms of energy: nuclear ε ,
n