Page 202 - Chemical equilibria Volume 4

178 Chemical Equilibria
Equation [A2.59] then takes on the form:
⎛
x ∏
i a
K = ( i m ) exp − Δ u 0 ⎞ ⎟ [A2.61]
*
r
z
⎜
()
i ⎝ RT ⎠
For solutions exhibiting deviation from ideal behavior, we need to add to the
“zero internal energy” the internal energy of mixing, calculated by the relation:
Δ U mix = ∑ a i i u mix [A2.62]
r
i
and relation [A2.60] therefore takes the form:
i a
x ∏
*
K = ( i m ) exp − Δ ⎛ r 0 Δ u + r U mix ⎞ ⎟ [A2.63]
z
⎜
()
i ⎝ RT ⎠
A2.5.3. Homogeneous equilibria in the solid phase
If the reaction takes place in the solid phase, then all the components in
the reaction are components of the same solid solution.
For such a solution, as in the case of liquids, the variation in volume due
to the reaction is negligible, and therefore we have:

()
Δ G () = Δ FT + P Δ r Δ V ≅ r FT [A2.64]
()
T
r
r
We can express the Helmholtz energy by relation [A2.40]. The molecules
in the solid are considered to be discernible molecules, so the canonical
partition function is given by relation [A2.34]. Hence, relation [A2.70]
becomes:
−
T
F i () F i (0) = − N i k T ln z i [A2.65]
B
In that expression, we suppose the solution to be perfect, because we do
not take account of an enthalpy of mixing.

In standard conditions, at temperature T, the Helmholtz energy of n moles
of the component i becomes:

−
f i 0 () = f i 0 (0) n i R ln z i [A2.66]
T
T