`P_1 ` and `P_2` are the vapour pressures of pure liquid components , 1 and 2 respectively of an ideal binary solution if ` x_1` represents the mole Traction of component 1, and the total pressure of the solutions formed by 1 and 2 will be

Options

A. `p _(1) + X _(1) (P_(2) -P_(1))`
B. `P_(2) -x _(1) (P_(2) +P_(1))`
C. `P_(1) -x _(2) (P_(1) -P_(2))`
D. `P _(1) + x_(1) (P_(1) -P_(2))`

Answer

C

Explanation

`P_("total") = P_(1) + P_(2)`
`=P_(1)x_(1) + P_(2) x_(2)" "[because x _(1) +x_(2) =1 x _(1) =1 - x _(2)]`
` = P _(1) (1- x _(2)) + P_(2) x _(2)`
` = P_(1) - P_(1) x _(2) + P _(2) x _(2) = P_(1) -x _(2) (P_(1) -P_(2))`