Page 61 - Chemical equilibria Volume 4

Properties of States of Physico-Chemical Equilibrium 37
The affinity of the resulting transformation will be given by the same
linear combination of the affinities of the combined transformations.
A =− ∑∑ λν k () μ k [2.38]
ρ
ρ
ρ k
This expression enables us to calculate the affinity of the new, resulting
transformation – an affinity which is null if the system is at thermodynamic
equilibrium.

2.2.3. Base of the vector space of the balance equations –
Jouguet criteria

Because the set of balance equations at equilibrium constitutes a vector
space, it is sufficient, in order to obtain all of them, to find a base for that
vector space. The number of balance equations which constitute that base
will give us the dimension of the vector space – i.e. the number of
independent reactions in the system.

Two problems are posed in practice.

First problem: we have a list of R balance equations of a system at
equilibrium. Are they all independent?
In order to answer this question, let us construct the matrix (N × R) of the
algebraic stoichiometric coefficients ν of each component k in each
k ρ
reaction ρ.

ν ν ... ν
1 1 1 2 N 1
ν ν ... ν
2 1 2 2 N 2
... ... ... ...
ν ν ν
1 R 2 R N R
In order for all the balance equations to be independent, no rows of the
above matrix should be obtainable by a linear combination of other rows.
This means that this matrix must contain at least one determinant of a non-
null rank R. This condition is called the Jouguet criterion or criterion of
independence of the reactions.