`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 fraction of component 1, the total pressure of the solution 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_(1)(P_(1)+P_(2))`
D. `P_(1)+x_(2)(P_(1)+P_(2))`

Answer

c

Explanation

`P_("total")=P_(1)+P_(2)`
=`P_(1)x_(1)+P_(2)x_(2)` `[becausex_(1)+x_(2)=1x_(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))`