Question

The mole fraction of benzene in a solution containing 39% by mass in an organic
the solvent of molecular mass 122 is
(A) 0.5
(B) 0.6
(C) 0.4
(D) 0.35

Answer 1

We are supposed to find the mole fraction of solute. It can be found by dividing the number of moles of solute by the sum of the number of moles of solute and the number of moles of solvent.

Complete step by step solution:
Let’s start with the idea of what mole fraction is. Mole fraction is nothing but the number of moles of a particular component in a mixture divided by the total number of moles in the given mixture. It’s also a way of expressing the concentration of a solution. It can be represented as follows:
Mole fraction of solute
= $\dfrac{Number\quad of\quad Moles\quad of\quad solute}{Number\quad of\quad moles\quad of\quad solute+Number\quad of\quad moles\quad of\quad solvent\quad }$
This can also be represented as: $\dfrac{nA}{nA+nB}$
where, $nA$ is the number of moles of solute
$nB$ is the number of moles of solvent

Mole fraction can also be expressed in terms of solvent as follows:
Mole fraction of solvent
=$\dfrac{Number\quad of\quad moles\quad of\quad solvent}{Number\quad of\quad moles\quad of\quad solute+Number\quad of\quad moles\quad of\quad solvent}$
Or also as $\dfrac{nB}{nA+nB}$
Here we are asked to find the mole fraction of benzene. In the given question benzene acts as the solute which gets dissolved in an organic solvent. Let’s assume that the total mass of the solution is 100 g.
Therefore, the mass of the benzene can be calculated by subtracting the mass of organic solvent from the mass of the total solution.
Mass of benzene = 100−39
= 61 g
The molar mass of benzene is $78gmo{{l}^{-1}}$
Therefore, the number of moles of benzene is given by,
= $\dfrac{Given\quad Mass}{Molar\quad Mass}$
= $\dfrac{61\quad g}{78\quad gmo{{l}^{-1}}}$
The molar mass of organic solvent is given as 122 $gmo{{l}^{-1}}$
Therefore, the number of moles of organic solvent
= $\dfrac{39\quad g}{122gmo{{l}^{-1}}}$

From the above details, we got the values to find the mole fraction of benzene and let’s substitute these values on the equation of mole fraction as follows

Mole fraction of benzene
= $\dfrac{nA}{nA+nB}$
= $\dfrac{\left( \dfrac{61}{78} \right)}{\left( \dfrac{61}{78} \right)+\left( \dfrac{39}{122} \right)}$
= 0.6

Therefore, the answer to the given question that is, the mole fraction of benzene is option (B) 0.6.

Note: By combining the equations of mole fractions of solute and solvent, the sum of mole fractions of all components would be equal to one. Another important thing to note down is that mole fraction represents a fraction of molecules and since different molecules have different masses, the mole fraction is different from mass fraction.