Question

What is the composition of the vapour which is in equilibrium at 30 degree centigrade with a bun with a benzene toluene solution with the mole fraction of benzene of. 40?

Answer 1

The idea here is that the vapor pressures of benzene and toluene will contribute to the total vapor pressure of the solution proportionally to their respective mole fraction - this is known as Raoult's Law.

Mathematically, you can express this by the following equation

P
sol
=
χ
benzene
⋅
P
∘
benzene
+
χ
toluene
⋅
P
∘
toluene
, where

P
sol
- the vapor pressure of the solution
χ
benzene
- the mole fraction of benzene
P
∘
benzene
- the vapor pressure of pure benzene

Now, mole fraction is defined as the ratio between the number of moles of a component of a solution and the total number of moles present in the solution.

Since you only have two components to this solution, benzene and toluene, you can say that

χ
benzene
+
χ
toluene
=
1

Let's say that the mole fraction of benzene is
x
and that of toluene is
y
. You can say that

x
=
1
−
y

and

P
total
=
x
⋅
P
∘
benzne
+
(
1
−
x
)
⋅
P
∘
toluene

40
.
torr
=
x
⋅
75
torr
+
(
1
−
x
)
⋅
22
torr

40
.
=
75
x
+
22
−
22
x

40
−
22
=
53
x
⇒
x
=
18
53
=
0.3396

This means that you have

y = 1 - 0.3396 = 0.6604#

The mole fractions of benzene and toluene in the solution will thus be - rounded to two sig figs

χ
benzene
=
0.34

and

χ
toluene
=
0.66