# Question 46fd6

Oct 26, 2015

$\text{0.233 M}$

#### Explanation:

The idea here is that you can convert the solution's concentration from percent concentration by mass, or %"m/m", to moles per liter, or molar, by picking a sample solution.

To make calculations easier, you can pick a $\text{100-g}$ sample of the "0.750 m/m"% solution

By definition, a solution's percent concentration by mass is defined as the mass of the solute, in this case methanol, divided by the total mass of the solution, and multiplied by $100$.

$\textcolor{b l u e}{\text{%m/m" = "mass of solute"/"mass of solution} \times 100}$

In your case, the $\text{100 g}$ sample will contain $\text{0.750 g}$ of methanol.

To get the number of moles of methanol, use the compound's molar mass

0.750color(red)(cancel(color(black)("g"))) * ("1 mole CH"_3"OH")/(32.042 color(red)(cancel(color(black)("g")))) = "0.02341 moles CH"_3"OH"

Now, to get the volume of the sample, you need to use its density. A 0.750%"m/m" methanol solution will have a density of approximately $\text{0.997 g/mL}$ at room temperature.

https://en.wikipedia.org/wiki/Methanol_%28data_page%29

This means that the sample will have a volume of

100color(red)(cancel(color(black)("g"))) * "1 mL"/(0.997color(red)(cancel(color(black)("g")))) = "100.3 mL"

Molarity is defined as moles of solute per liter of solution

$\textcolor{b l u e}{c = \frac{n}{V}}$

In your case, you would get - do not forget to convert the volume from mililiters to liters!

c = "0.02341 moles"/(100.3 * 10^(-3)"L") = color(green)("0.233 M")#

The answer is rounded to three sig figs.