Page 200 - Chemical equilibria Volume 4

176 Chemical Equilibria
substances. Therefore, if each component has k i vibrational degrees of
0
freedom with the fundamental frequency ν , we have:
i k
Nh
Δ u 0 (0) = a ∑∑ ν 0 ) [A2.50]
(a
i
r
2 i k i k
The equilibrium constant is defined by:
− Rln K = Δ g 0 () [A2.51]
T
T
r
P
In view of relation [A2.49], we obtain:
P ∏
()
K = ⎛ ⎜ z im ⎞ ⎟ i a exp− Δ u 0 (0) [A2.52]
r
i ⎝ N a ⎠ RT
Remember that this relation is valid for equilibria in the gaseous phase,
involving perfect gases.

A2.5.2. Homogeneous equilibria in the liquid phase

If the reaction occurs in the liquid phase, then all the components
involved in the reaction are components of a single liquid solution.

For such a solution, the variation in volume due to the reaction is
negligible, and therefore we have:

()
()
T
Δ G () = Δ FT + P Δ r Δ V ≅ r FT [A2.53]
r
r
We can express the Helmholtz energy by relation [A2.40]. The gas
molecules are considered as indiscernible molecules, so the canonical
partition function is given by relation [A2.36]. Using Stirling’s second
approximation [A2.1], we see relation [A2.53] become:

−
F i () F i (0) = − N i k T (ln z + ln N i ) [A2.54]
T
i
B
In this expression, we suppose we are dealing with a perfect solution, as
the equation does not take account of an enthalpy of mixing.