Page 203 - Chemical equilibria Volume 4

Appendix 2 179
NOTE.– in the case of solids, we do not need to make use of the molar
partition functions, because the partition functions of solids contain only
vibrational terms, which do not involve the volume of the chamber.
For the reaction, we write:
Δ f i 0 () = ∑ a f i 0 (0) = − RT ∑ a i ln z i [A2.67]
T
r
i
i i
f i 0 (0) is the standard molar Helmholtz energy of the pure component i at
the temperature of 0 K, and z is its partition function.

Using relations [A2.51] and [A2.651], the equilibrium constant is written:

− Rln K = Δ f 0 () [A2.68]
T
T
r
x
Using relations [A2.56] and [A2.66], we find
− Rln K = Δ u ⎡ r ⎣ i 0 (0)⎤ ⎦ − R ln ∏ () i a [A2.69]
T
z
T
i
x
i
For the equilibrium constant:
⎛
x ∏
i a
K = () exp − Δ u 0 ⎞ ⎟ [A2.70]
r
z
⎜
i
i ⎝ RT ⎠
Thus, the equilibrium constant in the solid phase can be calculated on the
basis of the molecular partition functions of vibration – i.e. the vibration
frequencies of the molecules. Those values also enable us to calculate the
residual energy of these molecules, and hence, in the case of perfect
solutions, to determine the exponential term in relation [A2.70].