# Question e042c

Oct 20, 2017

Here's what I got.

#### Explanation:

Start by picking a sample of this $\text{20% v/v}$ ethanol solution. To make the calculations easier, let's say that this sample has a volume of $\text{100 mL}$.

The solution is said to be $\text{20% v/v}$ ethanol, which implies that it contains $\text{20 mL}$ of ethanol, the solute, for every $\text{100 mL}$ of the solution.

Use the density of the solution to find its mass.

100 color(red)(cancel(color(black)("mL solution"))) * "0.9 g solution"/(1color(red)(cancel(color(black)("mL solution")))) = "90 g solution"

Next, usee the density of ethanol to find the mass of the solute.

20 color(red)(cancel(color(black)("mL ethanol"))) * "0.75 g ethanol"/(1color(red)(cancel(color(black)("mL ethanol")))) = "15 g ethanol"

Now, in order to find the solution's percent concentration by mass, $\text{m/m %}$, you need to figure out the mass of ethanol present in $\text{100 g}$ of this solution.

Since you already know how much ethanol you have in $\text{90 g}$ of the solution, you can say that $\text{100 g}$ will contain

100 color(red)(cancel(color(black)("g solution"))) * "15 g ethanol"/(90color(red)(cancel(color(black)("g solution")))) = "16.667 g ethanol"#

This means that the percent concentration by mass is equal to

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{\text{% m/m = 17% ethanol}}}}$

I'll leave the answer rounded to two sig figs, but keep in mind that you should round it to one significant figure, the number of sig figs you have for the percent concentration by volume.