Two miscible liquids `A` and `B` having vapour pressure in pure state `P_(A)^(@)` and `P_(B)^(@)` are mixed in mole fraction `chi_(A)` and `chi_(B)` to get a mixtue having total vapour vapour pressure of mixture `P_(M)`. Which of the following relations are correct?

Options

A. `chi_(A)=(P_(M)-P_(B)^(@))/(P_(A)^(@)-P_(B)^(@))`
B. `(chi_(A)(l))/(chi_(A)(V))=P_(M)/P_(A)^(@)`
C. `(chi_(A)(l))/(chi'_(A)(V))=P_(M)/P_(B)^(@)`
D. All of these

Answer

A, B

Explanation

`P_(M)=P_(A)^(@).chi_(A) + P_(B)^(@).chi_(B)`,`P'=P_(M).chi_(A)(V) = P_(A)^(@).chi_(A)(l)`
`=P_(A)^(@).chi_(A) + P_(B)^(@).(1-chi_(A))`
`:. chi_(A)=(P_(M)-P_(B)^(@))/(P_(A)^(@)-P_(B)^(@))`