`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_(1))/(x_(2))`
B. `(p_(A)^(@)-x_(2))/(x_(1))`
C. `(p_(B)^(@)x_(1))/(x_(2))`
D. `(p_(B)^(@)x_(2))/(x_(1))`

Answer

B

Explanation

Mole fraction in the vapour phase `(x_(1))=(p_(A))/(P_("total"))`
But `p_(A)=x_(A)xxp_(A)^(@)=x_(2)xxp_(A)^(@)`
Hence, `x_(1)=(x_(2)p_(A)^(@))/(P_("total"))or P_("total")=(p_(A)^(@)x_(2))/(x_(1))`