# Question b3e94

Jan 31, 2016

That actually depends on the mass / volume of the sample.

#### Explanation:

You know that your solution is $\text{62.02% w/v}$, which represents mass by volume percent concentration.

This type of percent concentration is calculated using the mass of the solute, which in your case is an acid, and the volume of the solution.

You will usually find it expressed in grams per 100 mL.

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

So, in essence, that $\text{62.02% w/v}$ concentration tells you that every $\text{100 mL}$ of solution contain $\text{62.02 g}$ of acid.

For a given volume of solution, let's say $V$ milliliters, you can find the mass of the acid by using the mass by volume percent concentration as a conversion factor

V color(red)(cancel(color(black)("mL"))) * overbrace("62.02 g acid"/(100color(red)(cancel(color(black)("mL")))))^(color(purple)("%w/v")) = (62.02/100 * V)color(white)(a)"g acid"

Now, if you are given the mass of the solution instead, let's say $m$ grams, use its density to find its volume

m color(red)(cancel(color(black)("g solution"))) * overbrace("1 mL solution"/(1.12color(red)(cancel(color(black)("g solution")))))^(color(purple)("density")) = (m/1.12) color(white)(a)"mL solution"

Another interesting thing to do here is use the density of the solution to convert the concentration from mass by volume to mass by mass.

As you know, mass by mass percent concentration is defined as the mass of the solute divided by the mass of the solution, and multiplied by $100$

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

This means that you can write, using the given $\text{% w/v}$ and density

"62.02 g acid"/(100color(red)(cancel(color(black)("mL solution")))) * (1color(red)(cancel(color(black)("mL solution"))))/("1.12 g solution") = "62.02 g acid"/((100 * 1.12)"g solution")

The percent concentration by mass will thus be

"%w/w" = (62.02 color(red)(cancel(color(black)("g"))))/(112color(red)(cancel(color(black)("g")))) xx 100 = 55.375%#

In other words, for every $\text{100 g}$ of solution, you get $\text{55.375 g}$ of acid.