Page 183 - Chemical equilibria Volume 4

A1.2.7. Influence of temperature on the reference chemical
potentials Appendix 1 159
We shall base our discussion on chemical systems.

The expression [A1.7] of the chemical potential of a component in the
solution can be written as:

μ i = μ i 0 + Rlnγ + Rln x [A1.19]
T T i i
However, in view of Helmholtz’s second relation, we have:

⎛ i ⎞ μ
∂ ⎜ ⎟
⎝ T ⎠ =− H i [A1.20]
∂ T T 2

Similarly, we are able to apply this relation to the reference state of the
solution, as follows:

⎛ 0 ⎞ μ
∂ ⎜ i ⎟
⎝ T ⎠ =− H i 0 [A1.21]
∂ T T 2

0
H is the partial molar enthalpy of the component in the reference state,
i
at temperature T.
This expression can be integrated if we know the variations of the
enthalpy with the temperature. Usually, we consider, for finite temperature
ranges, that the enthalpy is constant.

A1.2.8. Influence of pressure on the reference chemical
potentials

If we choose an intensive variable Y, which is the conjugate of the
extensive variable X, we know that the variation of the generalized chemical
potential of a component with that variable Y is of the form:

∂μ i =− X [A1.22]
∂ Y i