Excess Properties
Unlike for real gases (pure or mixtures) the EOS based approach to calculation of thermodynamic properties of real liquid solutions have not proved very successful. However, as molar residual property is defined for real gases, for real liquid solutions one may formulate a different departure function called the molar excess property that quantify the deviation from ideal solution property. The mathematical formalism of excess properties is, therefore, analogous to that of the residual properties.

If M represents the molar (or unit-mass) value of any extensive thermodynamic property(e.g., V,U, H, S, G, etc.), then an excess propertyis defined as the difference between the actual property value of a solution and the value it would have as an ideal solution at the same temperature, pressure, and composition. Thus:

The excess property bear a relationship to the property change of mixing. One may take the example of excess Gibbs free energy to illustrate the point. Thus:
(6.79)
Or:  (6.80)
Thus:   (6.81)
Other relations include:
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Also: 
The non-ideality of real liquid solutions are depicted well by use of excess properties, especially through the behaviour of  The excess Gibbs energy is typically obtained from low pressure vapour-liquid equilibrium data, while  is obtained by measuring isothermal enthalpy change of mixing. Lastly  is derived using the following relation:

Fig. 6.5 shows the variation of each of the excess property as a function of liquid mole fraction for a number of binary solutions.
Fig. 6.5 Excess properties at 50°C for 6 binary liquid systems: (a) chloroform(1)/n-heptane(2); (b) acetone(1)/methanol(2);(c) acetone(1)/chloroform(2); (d) ethanol(1)/n-heptane(2); (e) ethanol(1)/chloroform(2); ( f) ethanol(1)/water(2). (Source: H.C Van Ness and M. M. Abbott, Perry’s Chemical Engineer’s Handbook (7th ed.), McGraw Hill, 1997.
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