A vessel is separated into two halves. On the right is an ideal solution (of a single solute and single solvent) and on the ledt is a the pure solvent. If the solution is separated from the pure solvent by a membrane which is permeable only to the solvent molecules the net effect is for solvent molecules to diffuse into the solution aa there is greater concentration of these molecules in the pure solvent than in the solutionn. This pressure is called the osmotic pressure of the solution and given the symbol Y.
Thus the pressure of the components on the ledt is P where as the pressure on the components on the right is P+Y. To make this clear I will write the chemical potentials as a function of the pressure (eg u1* (P) for the pure solvent on the left)
A) write the chemical potential of the solution at pressure P+Y (I.e. u soln(P+Y)) in terms of of the liquid chemical potential at the pressure P+Y (I.e. u1*(P+Y)) And the mole fraction of the solvent component of the solution x and RT
B) at equilibrium the pure solvent at pressure P will be in equilibrium with the solution at pressure P+Y. Write the equation relating the chemical potentials describing this b
C) insert your equation for the solution chemical potential above and put the pure liquid chemical potentials on one side. Your equation should no longer have any terms involving the solution chemical potential u soln.