Page 193 - Chemical equilibria Volume 4

A2.2.3. Partial molecular partition functions, pertaining to the
different motions Appendix 2 169
By applying the definition [A2.20], we can calculate the contributions of
each of the motions of the molecule to the molecular partition function.

A2.2.3.1. Translation
The molecule has three translational degrees of freedom. We can show
that if it is not subjected to any constraint other than the obligation to remain
within the volume V, the translational contribution is:

π
B ⎞
⎛ 2 mT 3/2
k
z = V [A2.24]
t ⎜ 2 ⎟
⎝ h ⎠
For the perfect gas, with no interaction (z I = 1) between the molecules,
the molecular partition function can be written as follows, in view of
relation [A2.24]:

π
B ⎞
⎛ 2 mT 3/2
k
z pf = V ⎜ ⎟ z int [A2.25]
⎝ h 2 ⎠
Thus, for the translational partition function of the perfect gas, we have:

π
⎛ 2 mT 3/2
k
B ⎞
z ( tpf ) = V ⎜ ⎟ [A2.26]
⎝ h 2 ⎠

A2.2.3.2. Rotation
A molecule may have two or three rotational degrees of freedom. We
distinguish three categories of molecules.

For homonuclear diatomic molecules (i.e. where the two atoms are
identical), the partition function for each degree of freedom is:
4π 2 k IT
z = B [A2.27]
r
h 2