Page 199 - Chemical equilibria Volume 4

relation and use Stirling’s first approximation [A2.1], relation [A2.43]
becomes: Appendix 2 175
() G
GT − i (0) = − N i k T ln z + k T (N i ln N − N i ) PV+ i [A2.44]
B
i
i
B
i
We shall use molar properties. In order to do so, we define a fraction of
molar partition z im given by:
()
z
z = i [A2.45]
()
im
n i
This definition is tantamount to replacing the volume V in the calculation
of the translational partition function with the molar volume v i(m).

In standard conditions, at temperature T, the Gibbs energy of n moles of
the component i, which is a supposedly-perfect gas (P iV = n iRT), becomes:

z
() =
()
0
gT g 0 (0) n T− R ln im [A2.46]
i
i
i
N a
For the reaction, we write:
()
Δ gT = ∑ a gT ∑ a g 0 i (0) RT− ∑ a i ln z im [A2.47]
( ) =
0
0
()
i
i
i
r
i
i i i N a
However, at the temperature of 0K, for a perfect gas, we have:
−
=
≅
+
g i 0 (0) u 0 i (0) PV TS = h i 0 (0) u i 0 (0) [A2.48]
Consequently, relation [A2.47] becomes:
()
() Δ u T=
0
Δ gT r 0 () RT− ∑ a i ln z im [A2.49]
i
r
i N a
()
0
The term Δ uT is the linear combination, weighted by the
r
stoichiometric numbers, of the residual energies of vibration of each of the