Solutions of benzene and toluene obey Raoult’s law. The vapor pressures at 20°C are: benzene, 76 torr; toluene, 21 torr. 53. What is the mole fraction of benzene in a benzene-toluene solution whose vapor pressure is 51 torr at 20°C? A) 0.26 B) 0.45 C) 0.55 D) 0.67 E) 0.74
Answers
Answer:
Explanation:
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
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