Question

Concentrated hydrochloric acid is $36.5\% $ by weight. What is the molarity of solution?
A. $11.8{{M}}$
B. $15.7{{M}}$
C. \[{{51}}{{.5M}}\]
D. None of these

Answer 1

Hint: There are several units for measuring concentration. Some of them are molarity, normality, molality etc. We may confuse molality and molarity. But both of them are different. Molarity can be calculated by dividing the number of moles of solute by volume of solution in litres.

Complete step by step answer:
Concentration is the amount of solute dissolved in a given amount of solution. There are different types of concentration units. Formula and molecular mass deal with individual atoms and molecules. Mole is the unit that relates the number of particles and mass.
One mole of an element contains $6.022 \times {10^{23}}$ particles. This absolute number is called Avogadro’s number. Mass of one mole of substance is called molar mass. Or molar mass of an element is equal to the molecular weight.
It is given that the weight percentage of ${{HCl}}$ is $36.5\% $. Thus we can say that the solution contains ${{HCl}}$ and water, ${{{H}}_2}{{O}}$.
Density of ${{HCl}}$, $\rho = 1180{{g}}.{{{L}}^{ - 1}}$.
Now we can calculate the molarity by using the following formula:
Molarity, \[{{M = }}\dfrac{{\% \times \rho }}{{{{{M}}_{{{HCl}}}} \times 100}}\], where ${{{M}}_{{{HCl}}}}$ is the molecular weight of ${{HCl}}$.
Molecular weight of ${{HCl}}$ can be calculated by adding the atomic weights of hydrogen and chlorine atoms.
i.e. ${{{M}}_{{{HCl}}}} = 1 + 35.5 = 36.5{{g}}.{{mo}}{{{l}}^{ - 1}}$
Substituting the value of molecular weight of ${{HCl}}$, we get
\[{{M = }}\dfrac{{36.5 \times 1180{{g}}.{{{L}}^{ - 1}}}}{{{{36}}{{.5g}}{{.mo}}{{{l}}^{ - 1}} \times 100}}\]
On simplification, we get
\[{{M = }}11.8{{M}}\]
i.e. the molarity of solution is $11.8{{M}}$.

So, the correct answer is Option A.

Note: Molar mass is the collective name for atomic mass and molecular mass. We use moles to calculate the number of particles, molecules, concentrations, etc. It represents a very large quantity of items. Moles relate the mass of a single atom in ${{amu}}$ to the mass in grams. Moles to atoms or molecules conversions can be done by multiplying with Avogadro number. Atoms or molecules to moles conversions can be done by dividing by Avogadro number. Moles to grams conversion is moles times molar mass.