At 40 deg. C, the vapor pressure of benzene is 180 torr and that of toluene is 60 torr.What mole percent...?

Question

...of benzene and toluene are needed to prepare a solution that has a total vapor pressure of 96 torr at 40 deg C?

Answer 1

let pb = vapor pressure solution of benzene = p° Xb

let pt = vapor pressure solution toluene = p° Xt

p° Xb + p° Xa = 96

180 Xb + 60 Xt = 96

Xb + Xt = 1

Xt = 1 - Xb

solving this system

180 Xb + 60 ( 1 - Xb ) = 96

180 Xb + 60 - 60 Xb  = 96

120 Xb = 36

X b = 0.3  => mole fraction benzene

and X t = 0.7 => mole fraction toluene