# Question 48318

##### 1 Answer
Apr 21, 2016

For part (1)

${m}_{\text{solution" = "160. g}}$

${m}_{\text{solvent" = "138 g}}$

#### Explanation:

I'll show you how to solve part (1), and leave part (2) to you as practice.

A solution's percent concentration by mass, $\text{% m/m}$, essentially tells you how many grams of solute you get for every $\text{100 g}$ of solution.

In this case, your solution is said to have a 14.0% concentration by mass, which means that you get $\text{14.0 g}$ of solute for every $\text{100 g}$ of solution.

As you know, the total mass of a solution is given by the mass of solute and the mass of solvent. This means that a solution's percent concentration by mass tells you how many grams of solute you have in $\text{100 g}$ of solute + solvent mixture.

Implicitly, a 14.0% concentration by mass also tells you that you get $\text{86.0 g}$ of solvent for every $\text{100 g}$ of solute + solvent mixture.

So, you know that this first solution contains $\text{22.4 g}$ of solute. Use the percent concentration by mass to find the mass of the solution

$22.4 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{g solute"))) * overbrace("100 g solution"/(14.0color(red)(cancel(color(black)("g solute")))))^(color(purple)("14.0% by mass")) = color(green)(|bar(ul(color(white)(a/a)"160. g solution} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

This means that the mass of the solvent will be

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

m_"solvent" = "160. g" - "22.4 g" = color(green)(|bar(ul(color(white)(a/a)"138 g solvent"color(white)(a/a)|)))#

Both answers are rounded to three sig figs.