`P_(A)and P_(B)` are the vapour pressure of pure liquid components ,Aand B respectively of an ideal binary solution,If `x_(A)` represents the mole fraction of component A, the total pressure of the solution will be

Options

A. `P_(A)^(@)+chi_(A)(P_(B)^(@)-P_(A)^(@))`
B. `P_(A)^(@)+chi_(A)(P_(A)^(@)-P_(B)^(@))`
C. `P_(B)^(@)+chi_(A)(P_(B)^(@)-P_(A)^(@))`
D. `P_(B)^(@)+chi_(A)(P_(A)^(@)-P_(B)^(@))`

Answer

4

Explanation

`P_("total")=P_(A)+P_(B)` (Dalton's law)
`=P_(A)^(0)chi_(B)`(Ranoult's law)
since `chi_(A)+chi_(B)=1`
`=P_(A)^(0)chi_(A)+P_(B)^(0)(1-chi_(A))`
`=P_(A)^(0)chi_(A)+P_(B)^(0)-P_(B)^(0)chi_(A)`
`=P_(B)^(0)+(P_(A)^(0)-P_(B)^(0))chi_(A)`