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. 500 mm, 500 mm

Answer

D

Explanation

Given that, `n_(x)=n_(y)=1 or (n_(x))/(n_(y))=1`
`thereforechi_(x)=(1)/(1+1)=(1)/(2)=0.5`
`chi_(y)=(1)/(2)=0.5`
`P=p_(x)^(o)x_(x)+p_(y)^(o)x_(y)=400`
or `P=0.5p_(x)^(o)+0.5p_(y)^(o)=400`
When `n_(x^(1))/(n_(y^(1)))=(1)/(2)` at same temperature
then `x_(x^(1))=(1)/(3)&x_(y^(1))=(2)/(3)`
`therefore P=(1)/(3)p_(x)^(o)+(2)/(3)p_(y)^(o)=350`
Solving equation (i) and (ii), we get
`p_(x)^(o)=550 and p_(y)^(o)=250`.