`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_(B)+x_(A)(P_(B)-P_(A))`
B. `P_(A)+x_(A)(P_(A)-P_(B))`
C. `P_(A)+x_(A)(P_(B)-P_(A))`
D. `P_(B)+x_(A)(P_(A)-P_(B))`

Answer

D

Explanation

`P_(M)=P'_(A)+P'_(B)`
`=P_(A).x_(A)+P_(B).x_(B)( :.P'_(A)=P_(A).x_(A))`
`=P_(A).x_(A)+P_(B)(1-x_(A))( because x_(A)+x_(B)=1)`
`=P_(B)+x_(A)(P_(A)-P_(B))`