Page 37 - Chemical equilibria Volume 4

Physico-Chemical Transformations and Equilibria 13
This inequality constitutes de Donder’s inequality, which is a general
formulation of the condition of transformation and does not depend on the
set of variables chosen.
We shall now discuss this inequality:
– if the affinity is positive, we need to have a positive or null rate to
respect the condition [1.50]. If the rate is positive, this means that the
transformation takes place from left to right in the chosen formula. If the rate
is zero, the transformation does not happen;
– if the affinity is negative, the inequality gives a negative or null rate,
and the transformation will take place spontaneously from right to left of the
chosen formula, or will not take place;

– if the affinity is null, then the rate is null because, if such were not the
case, the system would be the seat of a reversible transformation (null
entropy production) with a non-null rate, which is incompatible with the
definition of a reversible transformation.

Let us now examine the reciprocal of our discussion:
– if the rate is positive then inequality [1.50] necessarily leads to a
positive affinity. The affinity cannot be null because we would still have a
reversible transformation at non-null rate;

– if the rate is negative, then the affinity is also negative, with the reverse
reaction occurring;

– if the rate is null, then the system is at equilibrium. We can therefore
have either a null or a non-null affinity. In the first case (null affinity), we
say that the system is at thermodynamic equilibrium. In the second
case (non-null affinity), the system is said to be at false equilibrium. False
equilibrium is thus encountered for a transformation which does not take
place although its affinity is positive. For instance, we can cite the synthesis
of water under normal conditions of temperature and pressure. The
hydrogen-oxygen mixture does not react. Its rate is too slow for the reaction
to be perceptible. In such a case, we could use a catalyst to carry out such a
transformation, which would not alter the affinity but would modify the rate.
The choice of a catalyzer is useless and ineffectual if the affinity is null or
negative.