Question

How many moles of ${\text{HCl}}$ will be present in 100 mL of a solution of specific gravity $1.08$, containing $20\%$ ${\text{HCl}}$ by mass?
A.${\text{0}}{\text{.50}}$
B.${\text{0}}{\text{.60}}$
C.${\text{0}}{\text{.80}}$
D.${\text{0}}{\text{.12}}$

Answer 1

From the given density of solution we can calculate the mass of solution and hence with the mass percentage will get the mass of ${\text{HCl}}$ in the solution. Number of moles can be calculated using the formula.
Formula used:
${\text{n}} = \dfrac{{\text{m}}}{{\text{M}}}$
here n is the number of moles, m is the mass of substance and M is the molar mass.
${\text{D}} = \dfrac{{\text{m}}}{{\text{V}}}$
Here, D is density, m is mass and V is volume.

Complete step by step answer:
${\text{HCl}}$ is hydrochloric acid. Specific gravity is the ratio of the density of the substance to the density of the reference material on whose basis the specific gravity or relative density is calculated. We generally use water as a reference so we can consider specific gravity and density are the same
in this question.
We know the density of the solution and the volume of the solution from the question. Using the formula will calculate the mass of the solution as:
${\text{mass of solution}} = 1.08{\text{ g}}/{\text{ml}} \times 100{\text{ ml}} = 108{\text{ g}}$
Now ${\text{HCl}}$ is contained $20\%$ by mass in the solution. So calculating $20\%$ of the mass of the solution will give us the mass of ${\text{HCl}}$ as: $\dfrac{{20}}{{100}} \times 108 = 21.6{\text{ g}}$
Now we have mass of ${\text{HCl}}$ the molar mass of ${\text{HCl}}$ is $1 + 35.5 = 36.5$.
So the number of moles of ${\text{HCl}}$ will be: $\dfrac{{21.6}}{{36.5}} = 0.59{\text{ moles}}$
Hence the numbers of moles are approximately equal to ${\text{0}}{\text{.60}}$.

So the correct option is B.

Note:
Hydrochloric acid is an inorganic acid also known as mineral acid. It is a corrosive acid. There are enormous uses of hydrochloric acid such as it is used in pickling of Steel and in synthesis of many organic and inorganic compounds.