# A solution of HCl in water has a density of 1.1 g/mL. What is the mass% of HCl in the solution if 150 mL of the solution contains 30. g of HCl?

Sep 16, 2017

$\text{18% m/m}$

#### Explanation:

The first thing that you need to do here is to use the density of the solution to determine the mass of $\text{150 mL}$ of this hydrochloric acid solution.

The density of the solution is said to be equal to ${\text{1.1 g mL}}^{- 1}$, so right from the start, you know that every $\text{1 mL}$ of solution will have a mass of $\text{1.1 g}$.

This means that your sample will have a mass of

150 color(red)(cancel(color(black)("mL"))) * "1.1 g"/(1color(red)(cancel(color(black)("mL")))) = "165 g"

Now, in order to find the solution's percent concentration by mass, $\text{% m/m}$, you need to figure out the mass of hydrochloric acid present in $\text{100 g}$ of this solution.

Since you know that $\text{165 g}$ of solution contain $\text{30. g}$ of hydrochloric acid, you can say that $\text{100 g}$ of this solution will contain

100 color(red)(cancel(color(black)("g solution"))) * "30. g HCl"/(165color(red)(cancel(color(black)("g solution")))) = "18.18 g HCl"

You can thus say that the solution has a percent concentration by mass equal to

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{\text{% m/m = 18% HCl}}}}$

The answer is rounded to two sig figs.