Two components A and B form an ideal solution. The mole fractions of A and B in solution are `X_(A) and X_(B)`, while that in vapour phase are `Y_(A) and Y_(B)`. The slope and intercept of plot of `(1)/(Y_(A)) " vs " (1)/(X_(A))` will be

Options

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

Answer

B

Explanation

`P_(A) = P_(A)^(@)X_(A), P_(B)= P_(B)^(@) X_(B)` (`P_(A)^(@) and P_(B)^(@)` = v.pr. Of pure A and B) and `Y_(A)= (P_(A))/(P_(A) + P_(B)) rArr (P_(A)^(@)X_(A))/(P_(A)^(@)X_(A) + P_(B)^(@) (1-X_(A)))`
`(P_(A)^(@) X_(A))/(P_(A)^(@) X_(A) + P_(B)^(@) (1- X_(A))) rArr Y_(A) = (P_(A)^(@)X_(A))/(X_(A) (P_(A)^(@) - P_(B)^(@)) + P_(B)^(@))`
`rArr (1)/(Y_(A))= ((P_(A)^(@)-P_(B)^(@))/(P_(A)^(@)))+ (P_(B)^(@))/(P_(A)^(@)).(1)/(X_(A))`