What is the %m/m of 75.0 g of ethanol dissolved in 500.0 g of water?

Feb 23, 2018

13.0%

Explanation:

By definition, a solution's percent concentration by mass, $\text{% m/m}$, tells you the number of grams of solute present for every $\text{100 g}$ of the solution.

This means that if you know the number of grams of ethanol dissolved in exactly $\text{100 g}$ of this solution, you know the solution's percent concentration by mass.

Now, you know that your solution contains $\text{75.0 g}$ of ethanol and $\text{500.0 g}$ of water. The total mass of the solution is equal to

$\text{75.0 g " + " 500.0 g" = "575.0 g}$

So you can say your $\text{575.0-g}$ sample of this solution contains $\text{75.0 g}$ of ethanol, the solute.

This means that $\text{100 g}$ of this solution will contain

100 color(red)(cancel(color(black)("g solution"))) * "75.0 g ethanol"/(575.0 color(red)(cancel(color(black)("g solution")))) = "13.043 g ethanol"

Since this represents the number of grams of ethanol present per $\text{100 g}$ of the solution, you can say that the solution's percent concentration by mass is equal to

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{\text{% m/m = 13.0% ethanol}}}}$

The answer is rounded to three sig figs, the number of sig figs you have for the mass of ethanol.