Page 50 - Chemical equilibria Volume 4

26 Chemical Equilibria
If we apply de Donder’s inequality to the new state of rate ℜ , we obtain:
'
d A ℜ≥ 0 ' [2.1]
This relation gives us the general form of the system’s evolution after the
disturbance. In terms of chemical potentials, this inequality becomes:
∑ ν k dμ ℜ< [2.2]
'0
k
k
We shall examine a few particular cases.

2.1.2. Influence of a temperature disturbance

In terms of the variables pressure, temperature, and compositions, the
affinity is expressed by relation [1.39]. If we apply a disturbance to the
system at equilibrium by varying only the temperature – i.e. if the pressure
and extent of the reaction remain constant – the new value of the affinity
becomes:

d
d A = Δ ST [2.3]
r
However, at equilibrium, we have:

Δ Δ G = T Δ H − S = 0 [2.4]
r r r

Consequently, by extracting the entropy from that equation and
substituting it back into expression [2.3], we obtain:

Δ H
d A = r dT [2.5]
T

Suppose that we have an elevation in temperature (dT > 0). By virtue of
relations [2.1] and [2.5], we would have:
– if Δ H > 0 d A > 0 and therefore ℜ>
'0
r
'0
0
– if Δ H < , d A < 0 and therefore ℜ<
r
Hence, a temperature increase shifts the equilibrium in the endothermic
0
direction (Δ H > ) of the transformation.
r