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

Mar 5, 2017

$\text{3.13% w/v NaCl}$

#### Explanation:

A solution's weight by volume percent concentration, $\text{% w/v}$, sometimes called mass by volume percent concentration, $\text{% m/v}$, is simply a measure of the mass of solute present in $\text{100 mL}$ of solution.

This implies that in order to determine a solution's weight by volume percent concentration, all you have to do is to figure out the number of grams of solute you get for every $\text{100 mL}$ of solution.

In your case, you know that you have $\text{3.60 g}$ of sodium chloride dissolved in enough water to make for $\text{115 mL}$ of solution.

As you know, solutions are homogeneous mixtures, which implies that they have the same composition throughout. This allows you to use the known composition as a conversion factor to scale the mass of the solute to a volume of $\text{100 mL}$ of solution.

In other words, you will have

100 color(red)(cancel(color(black)("mL solution"))) * overbrace("3.60 g NaCl"/(115color(red)(cancel(color(black)("mL solution")))))^(color(blue)("known composition")) = "3.13 g NaCl"

Since this represents the mass of solute present in $\text{100 mL}$ of solution, you can say the solution has a weight by volume percent concentration of

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{\text{% w/v = 3.13% NaCl}}}}$

The answer is rounded to three sig figs.