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In a solution of $7.8gm$ benzene ${C_6}{H_6}$and $46gm$ 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)$\dfrac{1}{3}$

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Last updated date: 14th Jul 2024
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Answer
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Hint: The mole fraction can be defined as the number of moles of a component divided by the total number of moles of a solution. It is a unit of concentration. It does not have any units because it is ratio. The sum of mole fraction of all the components in the solution is equal to one.

Complete answer:
The number of moles of any substance is the ratio of the given mass of the substance by the molar mass of the given substance.
Molar mass of benzene$ = 78$
Molar mass of toluene$ = 92$
The number of moles of benzene$ = \dfrac{{7.8}}{{78}}$$ = 0.1{\text{ moles}}$
The number of moles of toluene$ = \dfrac{{46}}{{92}} = 0.5{\text{ moles}}$
So, the mole fraction of benzene$ = \dfrac{{0.1}}{{0.5 + 0.1}} = \dfrac{1}{6}$
Therefore option A is the correct answer.

Note:
Mole is the standard scientific unit to measure large quantities of smaller entities such as molecules, atoms, etc. Remember that a mole and a molecule are two different words in chemistry. To find the mole fraction, first convert the given grams of solute and solvent to moles of solute and solvent, then calculate the mole fraction by dividing the moles of solute by the total number of moles of substances present in the given solution.