Two liquids X and Y form an ideal solution. The mixture has a vapour pressure of 400 mm at 300 K when mixed in the molar ratio 1:1. when mixed in the molar ratio of 1:2 at the same temperatre the vapour pressure of the mixture is 350 mm. The vapour pressure of the two pure liquids X and Y respectively are

Options

A. 250 mm, 550 mm
B. 350 mm, 450 mm
C. 350 mm, 700 mm
D. 550 mm , 250 mm

Explanation

`n_(X) = n_(Y) = 1 or (n_(X))/(n_(Y)) = 1`
`x_(X) = (1)/(1+1) =(1)/(2),X_(Y) = (1)/(1+1) = (1)/(2) `
`p = p_(X)^(@) xx x_(X) + p_(Y)^(@) xx x_(Y) = 400 mm`
` or (1)/(2) p_(X)^(@) + (1)/(2)p_(Y)^(@) = 400 mm " "…..(i)`
When `(n_(X))/(n_(Y)) = (1)/(2)` at the same temperature .
`x_(x) = (1)/(3)` and `x_(Y) = (2)/(3)`
`therefore " "p. = p_(X)^(@) xx x_(X) + p_(Y)^(@) xx x_(Y) = 350 mm`
or `(1)/(3) p_(X)^(@) + (2)/(3) p_(Y)^(@) = 350 mm" ".....(ii)`
Solving (i) and (ii) `p_(X)^(@) = 5500, p_(y)^(@) = 250 mm`