Thermodynamics: Fugacity for solution

The fugacity for ideal solution either in liquid phase or gaseous phase can be calculated from the equations

where fi(circumflex) is the fugacity of species i in solution. For gaseous phase it is calculated form fugacity coefficient (𝜙) and its value is 1 for and ideal gas solution (Residual Property) while in the liquid phase (ideal solution) we use activity coefficient (𝛶) and  its value is 1 for an ideal liquid solution (Lewis Randall rule). when the two phases are in equilibrium their fugacity value of the species will be same in either phase. for low pressure systems, the gas phase can be assumed to be ideal and 𝜙 = 1. but we can consider the non ideal liquid solution that will lead to modified Raoult' law which includes the activity coefficient.