# Question fbe14

Apr 8, 2017

$\text{1.8% NaCl}$

#### Explanation:

The trick here is to realize that a solution's mass by mass percent concentration, $\text{% m/m}$, expresses the number of grams of solute present for every $\text{100 g}$ of solution.

The mass of the solution will be equal to the sum of the mass of the solute and of the mass of the solvent

$\text{mass of solution = mass of solute + mass of solvent}$

In your case, you will have

$\text{mass of solution" = "4.6 g" + "250 g" = "254.6 g}$

Now, you know that this solution contains $\text{4.6 g}$ of sodium chloride, the solute, in $\text{254.6 g}$ of solution. Your goal now is to figure out the number of grams of solute present in $\text{100 g}$ 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 of the solution as a conversion factor

100 color(red)(cancel(color(black)("g solution"))) * overbrace("4.6 g NaCl"/(254.6 color(red)(cancel(color(black)("g solution")))))^(color(blue)("the composition of the solution")) = "1.807 g NaCl"#

You can thus say that the solution's mass by mass percent concentration is equal to

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{\text{% m/m = 1.8% NaCl}}}}$

The answer is rounded to two sig figs, the number of sig figs you have for the mass of sodium chloride and for the mass of water.