Page 136 - Chemical equilibria Volume 4

112 Chemical Equilibria
From this relation, we deduce the enthalpy attached to a reaction r:
∂ Δ H = P Δ V [4.12]
r
∂ P r
By integrating this relation [4.12], we are able to calculate the value of an
enthalpy, associated with a reaction, at a pressure P, when we know its value
at another pressure and the relation between the volume and pressure (e.g.
the equation of state) for each of the components of the reaction.

Note, though, that:
– for reactions involving condensed substances, their contribution to the
term Δ rV is negligible within the usual pressure range; and
– as for gases, provided they are considered perfect, the term PΔ rV is
(Σν)RT at constant temperature.

4.2.4. Determination of the reaction enthalpies by calculation on
the basis of other thermodynamic data

There are three main methods used to calculate an enthalpy associated
with a reaction on the basis of other thermodynamic data. These methods
entail using:

– the variation of the Gibbs energy associated with the reaction with
temperature;

– the variation of the equilibrium constant of that reaction with
temperature; or

– indeed appropriately-chosen enthalpy values.

4.2.4.1. Calculation of an enthalpy on the basis of a value of Gibbs
energy

This method is based on Helmholtz’s law, which specifies the variations
of Gibbs energy with temperature:

⎛ G ⎞
d ⎜ ⎟
⎝ T ⎠ =− H [4.13]
dT T 2