Thermodynamics/Mass Transfer: Vapor-Liquid Composition

When the two phases are in equilibrium, their chemical potential or fugacity will be same. fi(L) = fi(V)

The simplest case is that the liquid phase is ideal solution (i.e. similar chemical nature molecules) and vapour phase is ideal gas (i.e. low pressure) which is the Raoult’s Law; i.e. 

fi(ideal solution) = fi(ideal gas)  

Xi.Pi(sat) = yi.P  

for the calculation of composition from this we have to know the saturation pressure of the molecule at a given temperature, which is generally found from Antoine equation but the condition is that the temperature should below its critical temperature. So for a given temperature/Pressure and composition in a phase we can find the composition in other phase.

For a system of air water we can not apply this law to find the composition of air in liquid because the critical temperature of air is less than room temperature and the vapour pressure or saturation pressure of air can not be find. The amount of water in vapour phase can be found by assuming no air is dissolved in water i.e. water is pure but the amount of air in the liquid phase can not be calculated from Raoult’s law. 

To get the composition of air in liquid we can use Henry's law. Henry's law can be applied for pressure low enough that the vapor phase may be assumed an ideal gas and a species present as a very dilute solute in the liquid phase. Henry's law yi.P = Hi.xi and the value of Henry's constant come from experiment. for the air water system the composition of air is calculated from Henry's Law and composition of water is calculated by Raoult's Law. 
For a real solution we can apply Henry Law in dilute region and Lewis Randall Rule at pure species composition for approximate values.