Liquids `X` and `Y` form an ideal solution. The vapour pressure of `X` and `Y` at `100^(@)C` are `300` and `100 mm` of `Hg`, respectively. Suppose that a solution composed of `1 mol` of `X` and `1 mol` of `Y` at `100^(@)C` is collected and condensed. This condensate is then heated at `100@C` and vapour is again condensed to form a liquid `A`. What is the mole fraction of `X` in `A` ?

Explanation

In vessel `A`
`p_(x)@ = 300 ,p_(y)@ = 100 mm`
`chi_(x) = 1/2,chi_(y) = 1/2`
`p_(x) =300 xx 1/2 = 150 , p_(y) =100 xx 1/2 = 50`
`chi_(x)^(v) = 150 /200 = 3/4`
`chi_(y)^(v) = 1-3/4 = 1/4`
In vessel `B`
(`chi_(x)` in `B` = `3/4`
`chi_(y)` in `B` = `1/4`)]
`p_(x) = chi_(x) xx (p_(x)@)`
`p_(x) =3/4 xx 300 =225`
`p_(y) = chi_(y) xx (p_(y)@)`
`p_(y) = chi_(y) xx (p_(y)@)`
`p_(y) = 1/4 xx 100 = 25`
` (p_(x)) + (p_(y)) = 225 + 25 = 250`
`chi_(x)^(v)` in B = `225/250 =0.9`
`{:(( :' chi_(X)("liquid")=chiX^(vv) "in B"),("in C Vessel Vessel")):}`