Page 201 - Chemical equilibria Volume 4

In standard conditions, at temperature T, the Helmholtz energy of n moles
of component i becomes: Appendix 2 177
z
0
() =
()
fT f 0 (0) n T− R ln im [A2.55]
i
i
i
N a
For the reaction, we write:
()
Δ fT = ∑ a f 0 (0) = − RT ∑ a ln z im [A2.56]
0
()
ri i i i N
i i a
f i 0 (0) is the standard molar Helmholtz energy of the pure component i at
the temperature of 0 K, and z im is its molar partition function.
()
Using relations [A2.51] and [A2.54], the equilibrium constant is written as:

− Rln K = Δ f 0 () [A2.57]
T
T
r
x
Using relations [A2.47] and [A2.56], we find:
⎛ z ⎞ i a
()
− Rln K = Δ u ⎡ r ⎣ i 0 (0)⎤ ⎦ − R ln ⎜ ∏ ⎜ im ⎟ ⎟ [A2.58]
T
T
x
i ⎝ N a ⎠
For the equilibrium constant:
⎛ z ⎞ i a ⎛ Δ u 0 ⎞
x ∏
K = ⎜ ⎜ im ⎟ ⎟ exp − r ⎟ [A2.59]
()
⎜
i ⎝ N a ⎠ ⎝ RT ⎠
This relation, which is valid in the case of perfect or highly-dilute
solutions, exhibits the same form as relation [A2.52], obtained for a
homogeneous reaction between perfect gases.

Certain authors introduce the molecular partition function, defined by:

z
()
z * = im [A2.60]
()
im
N
a