Page 62 - Chemical equilibria Volume 4

38 Chemical Equilibria
NOTE 2.1.– It is clear that the above criterion supposes that the number of
transformations (R) is less than or equal to the number of components N
(number of rows of the matrix less than or equal to the number of columns)
because, otherwise, it would no longer be possible to define a determinant of
non-null rank R.
Second problem: finding a base of the vector space for the balance
equations of a system.

This problem is important because the determination of a base will enable
us to calculate the dimension of the vector space, which is, specifically, the
number of transformations, which plays a part in Gibbs’ phase law, for
determining the number of independent components (see section 2.3). This
number can also be used (see Chapter 3) to calculate the associated values
and the equilibrium constant of the overall transformation.

There are a variety of practical methods to deal with our problem – each
of them adapted to the nature of the system under study. We shall discuss
three cases:

Systems composed of neutral molecules – for such a system, the most
practical and effective method is to first establish the list of all the chemical
species present in the system. Then, for each species, we write its
chemical reaction of synthesis on the basis of its simple monatomic
elements. By linear combination, we then eliminate the simple
monatomic substances that are not really present in the system, and finally
we eliminate the balance equations including simple substances that cannot
be eliminated.

Next, in systems with multiple phases, we need to add the
transformations of passage of the chemical species from one phase to
another, for each chemical species present in a couple of phases.

We shall illustrate this method by using an example where we find a base
for the vector space of the balance equations of a system containing methane
(gas), carbon dioxide (gas), carbon monoxide (gas) and graphite (solid
carbon).