Dependence of Excess Gibbs Energy on temperature and pressure

Dependence of G^E on temperature and pressure

The idea of the molar excess property has been introduced in section 6.5 with the following definition:

M^E = M – M^id(6.163)

Typically the property M can be an intensive property such as: V, U, H, S, G, A, etc. The relations between the molar excess properties of V, H and G is particular significant for description of non-ideal solution thermodynamics. One may start from the generic total derivative of the Gibbs free energy for a real solution and an ideal solution in the same way as eqns. 5.27 and 5.28:

One may write the same equation specifically for an ideal solution, whence:
Thus subtracting eqn. 6.165 from 6.164:
Thus we may write the following further generative relations:
And further: The sensitivity of the excess Gibbs free energy to changes in temperature and pressure may be estimated to show the effect of pressure and temperature on liquid phase properties. For example, for an equimolar mixture of benzene and cyclohexane at 298K and 1 bar are (source: J.M. Smith, H.C. Van Ness and M.M. Abbott, Introduction to Chemical Engineering Thermodynamics, 6th ed., McGraw-Hill, 2001): The above calculations suggest that to effect the same change in excess Gibbs free energy brought about a change of 1K, one needs to change the pressure to change by about 40bar. Hence the excess Gibbs free energy exhibits a relatively weak dependence on pressure.