Page 33 - Chemical equilibria Volume 4

If we define the value Q r, known as the reaction quotient of the
transformation r, by the relation: Physico-Chemical Transformations and Equilibria 9
r ∏
Q = a i i ν [1.28]
i
then the affinity takes the form:

T
A = A 0 − RlnQ r [1.29]

Using relation [1.25], the Gibbs energy associated with the reaction takes
the form:

0
Δ r Δ G = r G + RlnQ r [1.30]
T
The last two relations will be useful for the expression of the equilibrium
constants (see section 3.1).

1.3.5. Total differential of the affinity in variables Y l, X m, ξ

As the affinity is a function of state, its differential, expressed on the
basis of the chosen variables, will be of the form:

l ∑
d A = ∑ ∂A dY + ∂A d X + ∂A dξ [1.31]
m
l ∂ Y l m ∂ X m ∂ξ
Using relation [1.20], we find:

2
∂A =− ∂ Γ [1.32]
∂ξ ∂ξ 2

and by applying equation [1.23]:

∂A =− ν ∂μ i [1.33]
∑
∂ Z i i ∂ Z

with Z being one of the variables in the set (Y l,X m).