Page 69 - Chemical equilibria Volume 4

Properties of States of Physico-Chemical Equilibrium 45
2.4.1. Definition
A state is said to be indifferent if it is possible to subject the closed
system in that state to a virtual azeotropic displacement.

2.4.2. Condition of indifference of a state

As the initial state, take a system with N components, home to R
independent transformations, characterized by p external intensive variables
(P, T, etc.), the molar fractions of the different components A k in each phase
(α)
α ( x ) and by the quantity of matter in the different phases n .
(α)
k
Let us perform an azeotropic displacement (see section 1.9) of that state to
bring it to the final state characterized by the same variables assigned the
“prime” index. During the course of that transformation, as the system remains
closed, it obeys the closure condition [2.45], which enables us to write:

R
(α)
' x (α) ' n () α − x n ( ) α = ∑ νξ ρ [2.45]
k
k
ρ = 1 k ρ
As the transformation is azeotropic, the application of relation [1.90]
gives us:

x k (α) = ' x (α) [2.46]
k

Then, expression [2.45] becomes:

R
x k (α) ( 'n (α) − n (α) ) = ∑ νξ ρ [2.47]
ρ= 1 k ρ

By setting the following for the purposes of simplicity:

Δ n (α) = ' n (α) − n (α) [2.48]
r

we obtain a system of N equations in the form:

R
x k (α) Δ n (α) = ∑ νξ ρ [2.49]
r
ρ= 1 k ρ