At equilibrium, the chemical potentials the gas and liquid phases of a solvent in a solution are equal, and foran ideal mixture the following equation holds (x is the mole fraction of the solvent):Pvapour (T, P*) + RTln(P/p*) =solution (T, P) +RTln(x)a) Modify this equation for a real solution by involving the activity coefficient of the solvent in thesolution, using a Raoult's law standard state.b) The vapor pressure of H₂O above a solution that is 40% by mass in ammonium sulfate, (NH4)2SO4, at300K is 21.28 torr.The standard vapor pressure of pure water (P*) is 26.6 torr at this 300K.Calculate the activity and the activity coefficient of water in this solution.c) Are the IMF between the salt and the water attractive or repulsive? Explain your answer.

The partial pressure of a mixture of solutions is equal to the sum of partial pressure by individual gas present in the mixture of solutions on ideal conditions.(a) The activity coefficient of a solvent in the solution using Raoult's law standard state can be defined as: γA=χAPyAP*A where y_A is the function of activity. So, by introducing this relation in our given equation, we get: μvapour(T,P*)+RTln(γAyAXA)=μ*solution(T,P*)+RTln(X(yA)) So, this is the equation in terms of the activity coefficient. (b) Here P=21.28 torr, P*=26.6 torr, X_A= 40%=0.4, and y_A=1, So, the activity function is equal to: γA=χAPyAP*AγA=0.4×21.281×26.6γA=0.32(c) The IMF between salt and water is attractive, that's why salt mix in water. The positive side of water attracts chlorine and the negative side attracts sodium and breaks it into two pieces, in that manner salt mix with water.So, this is the activity coefficient of the solute in a solution.

Answered: At equilibrium, the chemical potentials…