Two liquids A and B have vapour pressure in the ratio `P_A^@: P_B^@ = 1:2` at a certain temperature. Suppose that we have an ideal solution of A and B in the mole fraction ratio A : B = 1:2, the mole fraction of A in the vapour in equilibrium with the solution at the given temperature is

Options

A. 0.25
B. 0.2
C. 0.5
D. 0.33

Answer

B

Explanation

Since the ratio of `P_A^@ and P_B^@` is 1 : 2 and mole fraction is 1 : 2 therefore,
partial pressure of `A (P._A) = P_A^@ x_A` and
partial pressure of `B (P._B) = P_B^@ x_B` are related as
`P._B = 4P._A`
`P= P._A + P._B=P._A+4P._A=5P._A`
The mole fraction of A in the vapour in equilibrium with solution (according to Dalton.s law of partial pressure) is
`x._A = (P._A)/P = (P._A)/(5P._A) = 1/5 =0.2`