Question

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

Answer 1

Hint: First of all we need to use the density of the solution to determine the mass of $ 150\,mL $ of this hydrochloric acid.
We need to convert this given value i.e.
 $\Rightarrow 150\,mL $ into $ g $ .
After this we will use the unitary method to solve this question.

Complete Step By Step Answer:
We know that the density of the solution is said to be equal to
  $\Rightarrow 1.1\,gm{L^{ - 1}} $ .
It can also be written as
  $\Rightarrow \dfrac{{1.1g}}{{1\,mL}} $ . $ 150\,mL $
We will now apply the unitary method to solve this question.
We know that every $ 1\,mL $ of solution will have a mass of
 $\Rightarrow 1.1\,g $ .
So for $ 150\,mL $ , we will have a mass of
  $\Rightarrow 150\,mL \times \dfrac{{1.1\,g}}{{1\,mL}} $ .
On simplifying we have
 $\Rightarrow \dfrac{{150 \times 11}}{{10}}\,g $
It gives us
 $\Rightarrow 165\,g $ .
Now in order to find the solution’s percent concentration by mass i.e.
 $ \% m/m $ , we need to figure out the mass of hydrochloric acid present in $ 100\,g $ of this solution.
Since we know that $ 165\,g $ of solution contains $ 30\,g $ of hydrochloric acid.
So for $ 1\,g $ of solution, it gives us $ \dfrac{{30\,g}}{{165\,g}} $ of hydrochloric acid.
Similarly, for $ 100\,g $ of solution, we have
  $\Rightarrow 100\,g \times \dfrac{{30\,g}}{{165\,g}} $
On simplifying it gives us
 $\Rightarrow 18.18\,g\,HCl $ .
Hence we can say that the solution has a percent concentration by mass equal to $ \% m/m = 18\% \,\,HCl $ .
Or, it can be written as
  $\Rightarrow 18\% m/m $ .

Note:
We should know that density is the compactness of a substance in solid, liquid or gas. It is the
ratio of mass and volume of the substance. So more density of a substance less will be the volume and vice versa.
The density of water is given by
 $ 1\,gm/mL $ .