Page 43 - Chemical equilibria Volume 4

Physico-Chemical Transformations and Equilibria 19
By stating the affinity on the basis of the chemical potentials of the N
components involved in the transformation, the condition becomes:
N
∑ ν k dμ = 0 [1.80]
k
k 1 =
Either of these last two expressions, [1.79] and [1.80], enables us to
define the set of equilibrium states of the transformation.

1.7. Closed systems accommodating multiple reactions

Consider a system in which, between the components, there are R
possible transformations. A component may not necessarily be involved in
multiple kinds of transformations (in a transformation in which it is not
th
involved, its stoichiometric coefficient will be zero). For the ρ
transformation, we can define an affinity according to relation [1.11], and by
applying relation [1.23], we find:

A ρ =− ∑ νμ k [1.81]
k ρ
k
th
If ν is the stoichiometric number of component A k in the ρ
k ρ
transformation, then by pursuing the same reasoning as in section 1.3.2, with
ξ representing the extent of the reaction ρ, we obtain:
ρ
∂Γ
A =− [1.82]
ρ
∂ξ ρ

The real transformation condition, therefore, will be:

dΓ =− ∑ A ρ dξ ρ ≤ 0 [1.83]
ρ

and consequently:

dξ
∑ A ρ ρ = ∑ A ρ ℜ ≥ 0 [1.84]
ρ
ρ dt ρ