Generally, the activity coefficient express the deviation from the ideality and is deduced from excess partial molar energy quantities in thermodynamics.
Logically, the excess partial molar volume of liquids express certain deviation from the ideality due to some molecular interactions. Why in the literature we not found any relationship between the activity coefficient and the partial excess molar volume, at least is there any causal correlation ?
I've given the formal answer in the attached file, but in essence the excess partial molar volume is a measure for the change in the activity coefficient with changing pressure (note that this term is typically small and hence this dependency is often neglected)
the excess partial molar volume VPMR don't acount for the temperature dependence of the acituvity coefficient. gamma. This last dependence is more important then the pressure dependence of gamma, that you can acceed via VPME ( see too the answer of E. van Steen)
I can add to the above that for gases partial molar volumes are, mostly implicitly, always used for the calculation of activity. It is more common to work with concentration and partial pressures there, but it's the same.
Nasrine:
If you download my Ph.D Thesis from Research Gate, Appendix B. Page 135 you will find the relationship between Excess Volume and activity coefficient for a ionic solution, as deducted from Statistical Thermodynamics.
It is the same expression that Eric Van Steen already forwarded you.
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