Page 89 - Chemical equilibria Volume 4

Molecular Chemical Equilibria 65
0
Δ h pertains to the enthalpies of the pure substances, because the
r
reference state is that which chooses the pure substances.
Similarly, by deriving relation [3.14], we obtain the following, in the case
of gases:
(I) ∑ ν
∂ ln K () c = ∂ ln K − i i [3.30]
∂ T ∂ T T

Hence, considering relation [3.28]:

0
Δ h − RT ∑ ν
∂ ln K () c = r i i [3.31]
∂ T RT 2

For perfect gases, the enthalpy is independent of the pressure and the
internal energy does not depend on the volume:

Δ r 0 Δ h = r 0 Δ u + r ( Pv 0 0 ) [3.32]

For reactions involving perfect gases:

Δ r ( Pv 0 0 ) =− RT ∑ ν i [3.33]
i
By combining relations [3.32] and [3.33], we obtain:

0
Δ r 0 Δ h = r u + RT ∑ ν i [3.34]
i
and thus, by substituting back into relation [3.31], we obtain the following
for perfect gases:

∂ ln K () c = Δ u 0 [3.35]
r
∂ T RT 2

0
Δ u is the Helmholtz energy associated with the reaction r in the
r
standard state. This result constitutes the van’t Hoff isochore.