Question

The vapour pressure of pure benzene and toluene are 160 and 60 torr respectively. The mole fraction of toluene in the vapour phase in contact with an equimolar solution of benzene and toluene is:
A.0.50
B.0.6
C.0.27
D.0.73

Answer 1

Hint: In this question, we have to calculate the mole fraction of toluene in the vapour phase in contact with an equimolar solution of benzene and toluene. In a liquid, the molecules continue to collide with one another and also with the walls of the container. Thus, the liquid molecules are not associated with the same energy at the given temperature. These molecules at the surface of the liquid which acquire more energy overcome the attractive forces changes into vapour.

Complete step by step answer:
Now we will calculate mole fraction of toluene
Given,
Vapour pressure of pure benzene \[\left( {p_B^0} \right)\]= 160 torr
Vapour pressure of pure toluene \[\left( {p_T^0} \right)\]= 60 torr
Equimolar solution of benzene and toluene means mole fraction of benzene is equal to mole fraction of toluene.
\[{X_B} = {X_T} = 0.5\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {{X_B} + {X_T} = 1} \right)\]
Since benzene and toluene are the ideal solution, they follow Raoult’s law.
According to Raoult’s law – Total pressure of the ideal solution is equal to the partial pressures of the components at that composition.
\[ \Rightarrow {P_{total}} = P{}_B + {P_T}\]
\[ \Rightarrow {P_{total}} = p_B^0 \times {X_B} + p_T^0 \times {X_T}\]
(Partial pressure of a component is equal to the product of the vapour pressure of the component and the mole fraction of the component)
Now putting the given values in the equation to calculate the total pressure of the solution.
\[ \Rightarrow {P_{total}} = 160 \times 0.5 + 60 \times 0.5\]
\[ \Rightarrow {P_{total}} = 110\,\,torr\]
We got the total pressure of the component as 110 torr.
Now, We will find the mole fraction of toluene in vapour phase
\[{Y_T} = \dfrac{{p_T^0 \times {X_T}}}{{{P_T}}}\]
\[ \Rightarrow {Y_T} = \dfrac{{60 \times 0.5}}{{110}}\]
\[ \Rightarrow {Y_T} = 0.27\]
After calculation we get the mole fraction of toluene in vapour phase in contact with an equimolar solution of benzene and toluene.
Thus, the correct option is (C).

Note:
An ideal solution is the one in which no volume exchange and no enthalpy takes place when the components are mixed in any proportion and it obeys Raoult’s law. Examples of ideal solutions are: - Benzene and Toluene, Ethyl bromide and Ethyl iodide and Chlorobenzene and Bromobenzene.