In a mixture of liquids A and B, if the mole fractions of component A in vapour phase and liquid mixture are \(x_1\) and \(x_2\) respectively, then the total vapour pressure of liquid mixture is (where P\(_A^0\) and P\(_B^0\) are the vapour pressures of pure A and B)
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For ideal binary solutions, remember the key connection between liquid phase mole fraction (X) and vapor phase mole fraction (Y) for a component A:
\(P_A = Y_A P_{Total}\) (Dalton's Law) and \(P_A = X_A P_A^0\) (Raoult's Law).
Equating these gives \(Y_A P_{Total} = X_A P_A^0\). This allows you to solve for any of the four variables if the others are known.