Consider a liquid solution of species a and b. the chemical potentials of a and b are the following functions of t, p, and composition: a() + rtln(xa) + w x hacls) , hb(ls) = fab(l) + rtln(xb) w x^ where a( and flb(l) are the chemical potentials of the pure liquids at the same t and p as the solution and wis a constant, proportional to 2ea-(e+) where is a molecular interaction energy term. assuming convention i, derive expressions for the activity coefficients y4 and yg, in terms (a) of tand solution composition. prove that as x1, y1 and as x1, yb> 1. also, prove that the derived expressions for the activity coefficients satisfy the duhem-margules equations. consider a dilute liquid solution of solute b to solvent a. assuming convention ii, derive (b) an expression for /, in terms of tand p. does h, depend on solvent properties? explain. (c) for the previous dilute solution, derive expressions for the convention ii activity coefficients y and y, in terms of t and solution composition. prove that as x-1, r^-*1 and as xg-> 0, y»-*1. also, prove that the derived expressions for the activity coefficients satisfy the duhem-margules equations. (d) for the previous dilute solution, derive an expression for henry's law constant, kg, for solute b in solvent a in terms of the vapor pressure of the pure solute, p», and the parameter w. does henry's law constant depend on solvent properties?