Question

The concentration of aqueous methanol is $10\%$ of its mass. What is the mole fraction of methanol?

Answer 1

Given that the concentration of aqueous methanol is $10\%$ of its mass. It is the mass percent which means $10g$ of methanol is dissolved in $90g$ of water. Thus, the moles of methanol and water can be calculated from mass and molar mass. Mole fraction can be calculated from the moles of methanol and water.

Complete answer:
Concentration of solution can be expressed in different units like molarity, molality and mass percent. Given that the concentration of aqueous methanol is $10\%$ of its mass.
Water has chemical formula of ${H_2}O$ and methanol has chemical formula of $C{H_4}$
$10\%$ means $10g$ of methanol is dissolved in $90g$ of water. The molar mass of water is $18gmo{l^{ - 1}}$ and the molar mass of methanol is $32gmo{l^{ - 1}}$
The number of moles can be obtained by dividing the mass of a compound with the molar mass of the compound.
Moles of water is $\dfrac{{90}}{{18}} = 5$
Moles of methanol is $\dfrac{{10}}{{32}} = 0.312$
The mole fraction of a solute can be defined as the ratio of the number of moles of solute to the total number of moles of solute and solvent in the solution.
Mole fraction of methanol is $\dfrac{{0.312}}{{5.0 + 0.312}} = 0.05$
Thus, the mole fraction of methanol is $0.05$ .

Note:
Concentration is the amount of solute dissolved in a solvent. It can be expressed in different units like mass percent, mole fraction and molarity. The mole fraction has no units as it is a ratio of the number of moles of solute and sum of the moles of solute and solvent.