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The plots of (1)/(X(A))vs.(1)/(Y(A)) (wh...

The plots of `(1)/(X_(A))vs.(1)/(Y_(A))` (where `X_(A)` and `Y_(A)` are the mole fraction of liquid `A` in liquid and vapour phase respectively) is linear with slope and intercept respctively are given as:

A

`P_(A)^(@)/P_(B)^(@),((P_(A)^(@)-P_(B)^(@)))/(P_(B)^(@))`

B

`P_(A)^(@)/P_(B)^(@),((P_(B)^(@)-P_(A)^(@)))/(P_(B)^(@))`

C

`P_(B)^(@)/P_(A)^(@),((P_(A)^(@)-P_(B)^(@)))/(P_(B)^(@))`

D

`P_(B)^(@)/P_(A)^(@),((P_(B)^(@)-P_(A)^(@)))/(P_(B)^(@))`

Text Solution

Verified by Experts

The correct Answer is:
b
According to Raoult's Law
`P_(A)=X_(A)P_(A)^(@),P_(B)=X_(B)P_(S)^(@)`
`Y_(A)P_(A)/(P_(A)+P_(B))=(x_(B)P_(S)^(@))/(X_(A)P_(A)^(@)+X_(B)P_(B)^(@))`
`or 1/Y_(A)=(P_(A)^(@)-P_(B)^(@))/P_(A)^(@)+P_(B)^(@)/P_(A)^(@)xx1/X_(A)`
`or P_(B)^(@)/(X_(A)P_(A)^(@))=1/Y_(A)-[(P_(A)^(@)-P_(B)^(@)]/P_(A)]`
`1/X_(A)=P_(A)^(@)/P_(B)^(@)[1/Y_(A)+((P_(B)^(@)-P_(B)^(@)))/P_(A)^(@)]`
`=P_(A)^(@)/P_(B)^(@)xx1/Y_(A)+((P_(B)^(@)-P_(A)^(@)))/P_(B)^(@)`
Hence plot of `1/X_(A)vs1/Y_(A)` will be liner with slope =`P_(A)^(@)/P_(B)^(@)"and intercept"=((P_(B)^(@)-P_(A)^(@)))/P_(B)^(@)`
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