Relation between Raoults law and Daltons Law

Relation between Raoult’s Law and Dalton’s Law :-

If the mole fractions of solute(A) and solvent(B) in liquid phase are X_A and X_B , and their vapour pressures in pure state are P⁰_A and P⁰_B respectively. Vapour pressure of the solution is P.

 If the mole fractions of solute and solvent in Vapour Phase are Y_A and Y_B respectively than-

According to Raoult’s Law P_A = P⁰_A . X_A

And according to Dalton’s Law P_A = Y_A . P

Then                                      P⁰_A . X_A = Y_A . P   and  P⁰_B . X_B = Y_B . P

ð    Y_A = (P⁰_A . X_A )/P , similarly for B  Y_B = (P⁰_B . X_B )/P

Now using                           X_A + X_B = 1

Substituting X_A and X_B,

                                                (Y_A .P) / P⁰_A  + (Y_B .P) / P⁰_B   = 1

ð                                              Y_A/P⁰_A  + Y_B/P⁰_B  = 1/P