`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) + 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 solutions, `x_(A) + x_(B) = 1, x_(B) = 1 - x_(A)`
Putting value of `x_(B)` from eqn. (ii) to eqn.(i)
`P = x_(A)P_(A) + (1 - x_(A)) P_(B) = x_(A) P_(A) + P_(B) - x_(A)P_(B)`
`P = P_(B) + x_(A) (P_(A) - P_(B))`