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

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
$1\,gm/mL$ .