Page 68 - Chemical equilibria Volume 4

44 Chemical Equilibria
+
Thus, in total we have p +
R variables and N ϕ++
N ϕ +
R relations,

so the degree of indeterminacy, if we know the initial quantity of each
component, is:
v = p + N ϕ + R − (N ϕ + ) R = p [2.44]
+
+
D
This brings us to Duhem’s variance theorem:
THEOREM 2.2.– the equilibrium states of a closed system, wherein we know
the initial quantities of matter, are completely determined if we set p
variables.
2.3.3. Comparison between the Gibbs variance and the Duhem
variance

Consider a closed system. Gibbs’ theorem enables us to determine the
Gibbs variance v G pertaining solely to the intensive physico-chemical
variables (external and compositional). Duhem’s theorem gives a variance
v D = p pertaining to both the intensive and extensive values of a closed
system. Three cases may arise:
– if v G < v D the Gibbs variance gives the number of free intensive
physico-chemical variables, and the difference v D – v G, if the system is
closed, gives the number of free extensive variables;

– if v G = v D, there are only intensive variables (external and compositional)
that are free. The number thereof is determined by v G;

– if v G > v D, the conditions of the closed system are automatically
fulfilled simply by the application of Gibbs’ phase rule.

In the case of systems composed solely of condensed phases, except at
very high pressures, the pressure is no longer an equilibrium variable, which
means that the value of p decreases by 1.

2.4. Indifferent states

We shall now look at a particular class of states of a system: its
indifferent states.