Question

In a solution of 7.8gm benzene ${C_6}{H_6}$and 46.0 gm toluene (${C_6}{H_5}C{H_3}$), the mole fraction of benzene in this solution is :
a.) $\dfrac{1}{6}$
b.) $\dfrac{1}{5}$
c.) $\dfrac{1}{2}$
d.) $\dfrac{1}{3}$

Answer 1

The benzene has molecular mass of 78 g and the toluene has molecular mass of 92 g. From the given mass, the number of moles can be found out and from this, the mole fraction can be calculated by formula as -
$Mole fraction =$ $\dfrac{{Number{\text{ of moles of component}}}}{{Total{\text{ number of moles of all components}}}}$

Complete step by step solution:
First, let us write what is given to us in the question what we need to find out.
Mass of benzene (${C_6}{H_6}$) = 7.8 gm
Mass of toluene (${C_6}{H_5}C{H_3}$) = 46.0 gm
To find : mole fraction of benzene in this solution
Let us first see what is mole fraction.
Mole fraction may be defined as the number of moles of one component divided by the total number of moles of all the components in a solution. It is used to describe the concentration of a species.
Thus, we can write the formulas as -
Mole fraction = $\dfrac{{Number{\text{ of moles of component}}}}{{Total{\text{ number of moles of all components}}}}$
We are given mass of the components. First, we will find its number of moles.
We know number of moles = $\dfrac{{{\text{Given mass}}}}{{{\text{Molar mass}}}}$
Number of moles of benzene = $\dfrac{{7.8}}{{78}}$
Number of moles of benzene = 0.1 moles
Number of moles of toluene = $\dfrac{{{\text{46}}}}{{{\text{92}}}}$
Number of moles of toluene = 0.5 moles
Total number of moles in solution = 0.1 + 0.5
Total number of moles in solution = 0.6 moles
Now, Mole fraction of benzene = $\dfrac{{Number{\text{ of moles of benzene}}}}{{Total{\text{ number of moles of both components}}}}$
Mole fraction of benzene = $\dfrac{{0.1}}{{0.6}}$
Solving the decimals, we get
Mole fraction of benzene = $\dfrac{1}{6}$

Thus, the option a.) is the correct answer.

Note: It must be noted that the total mole fractions of all components of a solution are equal to one. For example - in the above ques, the mole fraction of benzene and mole fraction of toluene will be equal to 1. Further, the molar mass of benzene is 78 and for toluene, it is 92.