A solution is made by dissolving 3.60g of sodium chloride to a final volume of 115mL solution. What is the weight/volume % of the solute?

Jun 26, 2016

3.13%

Explanation:

The idea here is that a solution's mass by volume percent concentration, $\text{% m/v}$, sometimes called weight by volume, tells you how many grams of solute you get per $\text{100 mL}$ of solution.

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \text{% m/v" = "grams of solute"/"100 mL of solution} \times 100 \textcolor{w h i t e}{\frac{a}{a}} |}}}$

This means that in order to determine a solution's mass by volume percent concentration, all you have to do is figure out how many grams of solute you have in $\text{100 mL}$ of solution.

In your case, you know that you're dissolving $\text{3.60 g}$ of sodium chloride, $\text{NaCl}$, which is your solute, to get a final volume of $\text{115 mL}$ of solution.

Right from the start, you can say that the solution's mass by volume percent concentration will be lower than 3.60% because $\text{100 mL}$ will contain less than $\text{360 g}$ of sodium chloride.

More specifically, $\text{100 mL}$ of solution will contain

100 color(red)(cancel(color(black)("mL solution"))) * "3.60 g NaCl"/(115color(red)(cancel(color(black)("mL solution")))) = "3.13 g NaCl"

So, if $\text{100 mL}$ of solution contain $\text{3.13 g}$ of solute, it follows that the solution's $\text{% m/v}$ will be

$\textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\text{% m/v " = " 3.13 %}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

The answer is rounded to three sig figs.