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:

Options

A. `(P_(A)^(@))/(P_(B)^(@))` and `((P_(A)^(@)-P_(B)^(@)))/(P_(B)^(@))`
B. `(P_(A)^(@))/(P_(B)^(@))` and `((P_(B)^(@)-P_(A)^(@)))/(P_(B)^(@))`
C. `(P_(B)^(@))/(P_(A)^(@))` and `((P_(A)^(@)-P_(B)^(@)))/(P_(B)^(@))`
D. `(P_(B)^(@))/(P_(A)^(@))` and `((P_(B)^(@)-P_(A)^(@)))/(P_(B)^(@))`

Answer

B

Explanation

`P'_(A)=P_(A^(@))X_(A)"and"P'_(B)=P_(B)^(@)xxX_(B)`
`P'_(A)=P_(M).Y_(A)"and"P'_(B)=P_(M).Y_(B)`
`therefore (P'_(A))/(Y_(A))=(P'_(B))/(Y_(B))`
or `(P_(A)^(@)X_(A))/(Y_(A))=(P_(B)^(@)X_(B))/(Y_(B))=(P_(B)^(@)(1-X_(A)))/((1+Y_(A))) "or" (P_(A)^(@)X_(A))/(Y_(A))(1-Y_(A))=P_(B)^(@)-X_(A)`
or `(P_(B)^(@))/(X_(A))=(P_(A)^(@))/(Y_(A))+(P_(B)^(@)-P_(A)^(@)) "or" (1)/(X_(A))=(1)/(Y_(A)).(P_(A)^(@))/(P_(B)^(@))+((P_(B)^(@)-P_(A)^(@)))/(P_(B)^(@))`
or `y="mix"+C therefore` Slope `=m=(P_(A)^(@))/(P_(B)^(@))` and intercept `C=((P_(B)^(@)-P_(A)^(@)))/(P_(B)^(@))`