The concentration of aqueous methanol is 10% of its mass. What is the molar fraction of methanol?

Jan 14, 2018

$0.05$

Explanation:

The problem wants you to find the mole fraction of methanol, $\text{CH"_3"OH}$, by using the fact that its solution has a percent concentration by mass equal to 10%.

This means that if you take $\text{100 g}$ of this solution, the sample will contain $\text{10 g}$ of methanol, the solute, and $\text{90 g}$ of water, the solvent.

Now, the mole fraction of methanol is defined as the ratio between the number of moles of methanol and the total number of moles present in the solution.

To make the calculations easier, let's work with a $\text{100-g}$ sample of this solution. Use the molar mass of water to find the number of moles of water present in the sample.

100 color(red)(cancel(color(black)("g"))) * ("1 mole H"_2"O")/(18.015color(red)(cancel(color(black)("g")))) = "5.551 moles H"_2"O"

Next, use the molar mass of methanol to find the number of moles of methanol present in the sample.

10 color(red)(cancel(color(black)("g"))) * ("1 mole CH"_3"OH")/(32.04color(red)(cancel(color(black)("g")))) = "0.312 moles CH"_3"OH"

This means that the mole fraction of methanol, which we'll label ${\chi}_{\text{methanol}}$, is equal to

chi_"methanol" = (0.312 color(red)(cancel(color(black)("moles"))))/((5.551 + 0.312)color(red)(cancel(color(black)("moles")))) = color(darkgreen)(ul(color(black)(0.05)))

The answer is rounded to one significant figure, the number of sig figs you have for the percent concentration of the solution.