# Question d80bb

Nov 8, 2016

Here's how you can do that.

#### Explanation:

The idea here is that you need to work with the solution's percent concentration by mass, $\text{%m/m}$, to figure out how much solute you have in your sample.

So, the solution's percent concentration by mass is a measure of how many grams of solute you get in $\text{100 g}$ of solution. Indirectly, this can help you figure out how many grams of solvent you have in $\text{100 g}$ of solution, since

$\textcolor{p u r p \le}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{m}_{\text{solution" = m_"solute" + m_"solvent}}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

In your case, a $\text{17.3% m/m}$ solution will contain $\text{17.3 g}$ of solute for every $\text{100 g}$ of solution. This is, of course, equivalent to saying that $\text{100 g}$ of this solution contains

${m}_{\text{solvent" = overbrace("100 g")^(color(blue)("mass of solution")) - overbrace("17.3 g")^(color(darkgreen)("mass of solute")) = "82.7 g solvent}}$

Now all you have to do is scale up this proportion to figure out how many grams of solution would contain $\text{355.2 g}$ of solvent

355.2 color(red)(cancel(color(black)("g solvent"))) * "100 g solution"/(82.7 color(red)(cancel(color(black)("g solvent")))) = color(green)(bar(ul(|color(white)(a/a)color(black)("429.5 g solution")color(white)(a/a)|)))

Therefore, the mass of solute must be

m_"solute" = "429.5 g" - "355.2 g" = color(green)(bar(ul(|color(white)(a/a)color(black)("74.3 g solute")color(white)(a/a)|)))#