The vapour pressure of two liquids A and B in their pure states are in ratio of 1:2. A binary solution of A and B contains A and B in the mole proportion of 1:2. What is the mole fraction of A in the vapour phase of the solution?

0.2

Let vapour pressure of A be p so that vapour pressure of B is 2p.

Mole fraction of A = \(\frac{1}{1+2}\) = \(\frac{1}{3}\)

Mole fraction of B = \(\frac{2}{1+2}\) = \(\frac{2}{3}\)

Total vapour pressure of solution = P^o_AX_A + P^o_BX_B

                                                = p x \(\frac{1}{3}\) + 2p x \(\frac{2}{3}\) = \(\frac{5p}{3}\)

In vapour phase, mole fraction of A is Y_A = \(\frac{p/3}{5p/3}\) = 0.2