Page 52 - Chemical equilibria Volume 4

28 Chemical Equilibria
To proceed further, we need to know the variations of the chemical
potentials of the different components and the quantities of those
components. Two cases need to be considered. In the first case, component
A i is pure in its condensed phase. In the second case, component A i is either
a pure gas or it belongs to a polycomponent phase of the system.
If the component added is pure in a condensed phase, the chemical
potential of the other components, which are absent in the same phase will
∂
be: μ∂ k / n = 0. The chemical potential of the added component, which is
i
∂
only present in the phase will be: μ∂ / n = . The addition of component
0
i i
A i does not alter the state of equilibrium. This case is encountered, for
example, when we add any one of the solid components (carbonate or lime)
into the decomposition of calcium carbonate by reaction [1R.5].
If the component added is gaseous or belongs to one of the
polycomponent phases of the system, the application of relation [2.8] to
inequality [2.1] depends on the variations of the chemical potentials with the
quantity of the added component, i.e. definitively of the law of variation of
the activities of the components belonging to the same phase as that which
has been added. We know that there is no general law. The laws issuing
from the different models of solution can be applied, but the result will
depend on the model chosen.

To illustrate the displacement of equilibrium by adding a certain
amount of a component, consider a perfect solution, which will
immediately illustrate the diversity of the results obtained. We assign the
relative values to the component added with index i; for the other
components we use index k. When all the components are involved, we use
the index j (j = i + k).

In the case of a perfect solution, the expressions of the chemical potential
and of the molar fraction, for variations of the chemical potentials of the
existing components (k ≠ i), yield the relation:
∂ μ RT
k =− [2.9]
n ∂ i ∑ n j
j