Fugacity coefficient of an ideal solution

[nickelous]

Hi all. I have some confusion regarding the fugacity coefficient of a species in an ideal solution so hoping someone could clear it up for me. According to my textbook, for fugacity coefficient of a species i in a solution:

So if we were talking about an ideal liquid mixture of let's say species A and B, then the denominator y_i should be replaced by x_i as per stated by the textbook. So if i were to calculate the fugacity coefficient of species A, my question is what is the physical significance of x_AP? is it the vapour pressure of the vapour of species A above the liquid components? Why is it calculated in such a way (seems like the same way as how partial pressure of gas mixture is calculated). From what i know, the calculation of vapour pressure of a species in ideal mixture should be x_iPo where Po is the vapour pressures of i if it were to exist as pure liquid

 

[Chestermiller]

The fugacity of A in an ideal liquid solution is equal to the fugacity of pure liquid A at the same temperature and pressure as the solution times the mole fraction of A in the liquid. As a first approximation to the fugacity of the pure A in the liquid, you use its equilibirum vapor pressure at the solution temperature. This is what would usually go into Raolt's law. But then you need to correct the fugacity because the pressure P of the liquid is higher than the equilibrium vapor pressure of pure A. So you need to consider the change in free energy between the equilibrium vapor pressure and the total pressure. This is where the Poynting correction factor comes in.

Chet