Question

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?

Answer 1

`"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 `"150 mL"` of this hydrochloric acid solution.

The density of the solution is said to be equal to `"1.1 g mL"^(-1)`, so right from the start, you know that every `"1 mL"` of solution will have a mass of `"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, `"% m/m"`, you need to figure out the mass of hydrochloric acid present in `"100 g"` of this solution.

Since you know that `"165 g"` of solution contain `"30. g"` of hydrochloric acid, you can say that `"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

`color(darkgreen)(ul(color(black)("% m/m = 18% HCl")))`

The answer is rounded to two sig figs.