Page 44 - Chemical equilibria Volume 4

20 Chemical Equilibria
This inequality is a generalization of De Donder’s inequality (see
section 1.4). We can see that, for a transformation to be possible, it is no
longer necessary for inequality [1.50] to be satisfied, if that transformation
occurs in a system which contains multiple transformations, and such that
relation [1.84] will, itself, be satisfied. This phenomenon of a reaction which
is impossible on its own but is possible within a set of transformations, in the
same conditions, is known as chemical coupling.

At thermodynamic equilibrium, the sum appearing in relation [1.83] must
be zero, implying that all the individual terms A are zero regardless of the
ρ
transformation at hand. The condition of equilibrium of transformations in
the system, for any transformation ρ belonging to the set R, will therefore be:

A ρ = 0 [1.85]

NOTE 1.4.– We shall see (in section 2.2) that this condition is sufficient but
not necessary if not all the transformations are independent.

1.8. Direction of evolution and equilibrium conditions in an open
system

In an open system, the variations dn k in the amount of component A k are
no longer linked to one another by the transformation; these quantities can
also change because of exchanges of matter with the external environment.
In a chemical system, the variation of Gibbs energy is written in the form:

N
dG =− S dT V P + ∑ μ k dn k [1.86]
+
d
k 1 =
For equilibria at temperature and pressure that are both kept constant, the
Gibbs energy is a potential function and therefore in order for the system to
be able to evolve spontaneously, we need:

N
dG = ∑ μ k dn ≤ 0 [1.87]
k
k 1 =
At thermodynamic equilibrium, the potential function reaches an
extremum. If that extremum is a minimum, then the equilibrium is stable. If