`p_(A)` and `p_(B)` are the vapour pressure of pure liquid components, A and 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) + x_(A)(p_(B)-p_(A))`
B. `P_(A)+ x_(A)(p_(A)-p_(B))`
C. `p_(B)+x_(A)(p_(B)-p_(A))`
D. `p_(B)+x_(A)(p_(A)-p_(B))`

Answer

D

Explanation

According to Raoult.s law
`p=x_(A)p_(A)+x_(B)p_(B)`
For binary solution, `x_(A)+x_(B)=1` or `[x_(B)=1-x_(A)]`
`p=x_(A)p_(A)+(1-x_(A))p_(B)`
`=x_(A)p_(A)+p_(B)-x_(A)p_(B)`
or `=p_(B)+x_(A)(p_(A)-p_(B))`