**Question **# The excess Gibbs free energy of a binary liquid mixture at T and P is given by: \frac{G^{E}}{R T}=A X_{1} X_{2} (a) Find expressions for Iny₁ and lny 2 at T and P. (b) For a particular binary system to which these activities equations apply, determine the value of A if at the equilibrium: T = 45 °C, Psat = 27.78 kPa, Pat = 29.82 kPa, P = 37 kPa, X₁ =0.398, Y₁ = 0.428. (c) For the same binary system in (b), calculate P and Y₁ for X₁ = 0.5 and T = 45 °C.