The 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 of 1: 1 and a vapour pressure of 350 mm when mixed in the molar ratio of 1:2 at the same temperature . The vapour pressures of the two pure liquids X and Y respectively are

Options

A. a) 250 mm , 550 mm
B. b) 350 mm , 450 mm
C. c) 350 mm , 700 mm
D. d) 550 mm , 250 mm

Explanation

In Ist case ,
When two liquids X and Y are mixed in the molar ratio `1:1`
Moles of X=1
Moles of Y =1
Mole fraction of `(X_(X))=(1)/(2)`
Mole fraction , of `Y(X_(Y))=(1)/(2)`
We know that
`p=p_(X)^(@)X_(X)+p_(Y)^(@)X_(Y)` (p= total pressure of mixture)
`400=(1)/(2)p_(X)^(@)+(1)/(2)p_(Y)^(@)`
`400xx2=p_(X)^(@)+p_(Y)^(@)` ... (i)
For case `II^(nd)` ,
When liquids are mixed in the molar ratio of `1:2`
Moles of X=1
Moles of Y=2
Mole fraction of X `(X_(X))=(1)/(3)`
Mole fraction of Y `(X_(X))=(2)/(3)`
`p=p_(X)^(@)X_(X)+p_(Y)^(@)X_(Y)`
`350=(1)/(3)p_(X)^(@)+(2)/(3)p_(Y)^(@)`
`350xx3=p_(X)^(@)+2p_(Y)^(@)`
From Eqs (i) and (ii) , we get
`p_(X)^(@)=550mm`
`p_(Y)^(@)=250` mm