Page 45 - Chemical equilibria Volume 4

the extremum is a maximum, then the equilibrium is unstable (see section
2.6.2). Physico-Chemical Transformations and Equilibria 21
At equilibrium, we therefore ought to have:
N
∑ μ k dn = 0 [1.88]
k
k 1 =
This relation is a generalization of relation [1.54], which takes that form
when we remember that, in a closed environment where only a single
transformation takes place, by definition we have the following formula for
the extent:

d n = ν dξ [1.89]
k k

1.9. Azeotropic transformations

A closed system undergoes an azeotropic transformation when, during the
course of the transformation, the masses of some of the phases increase at the
expense of others, without a change in the composition of the phases. This is
expressed, for all phases α and all compositions, by the property:

x k (α) = x 0(α) [1.90]
k

x 0(α) denotes the molar fraction of component A k in phase α at the initial
k
(α)
time of the transformation and x its molar fraction at any given moment
k
during the transformation.
By deriving equation [1.90] in relation to time, we find the following for
any component A k in any phase α:

d x (α)
k = 0 [1.91]
dt

In view of the definition of the molar fractions, this relation is written as:

N
d n (α) − x k ∑ dn (α) = 0 [1.92]
i
k
0(α)
dt i= 1 dt