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At a certain temperature pure liquid A a...

At a certain temperature pure liquid `A` and liquid `B` have vapour pressure `10` and `37` torr respectively. For a certain ideal solution of `A` and `B`, the vapours in equilibrium with the liquid has the components `A` and `B` in the partial pressure ratio `P_(A):P_(B) = 1:7`. The mole fraction of `A` in the solution are:

A

(a) `0.346`

B

(b) `0.654`

C

( c) `0.5`

D

(d) `0.8`

Text Solution

Verified by Experts

The correct Answer is:
A
`P'_(A)=(1)/(7)P'_(B)` (Given)
Also `P_(A)^(@)=10 "torr"`
`P_(B)^(@)=37"torr"`
`P'_(A)=P_(A)^(@).X_(A)=10.X_(A)`....(i)
`P'_(B)=P_(B)^(@).X_(B)=37.X_(B)`
or `7P'_(A)=-37.X_(B)`.....(ii)
Thus b y (i) and (ii),
`(X_(A))/(X_(B))=(37)/(10)xx(1)/(7)=(37)/(70)` ,
Also `X_(A)+X_(B)=1`,
`:. (1-X_(B))/(X_(B))=(37)/(70)`
`:. (1)/(X_(B))=(37)/(70)+1`
`:. X_(B)=(70)/(107)`,
Thus `X_(A)=(37)/(107)=0.346`
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