Question

Concentrated hydrochloric acid is $36.5\% $ by weight. What is the molality of the solution?
A. 1.575 molal
B. 15.75 molal
C. 157.5 molal
D. 1575 molal

Answer 1

Hint: The mass percentage and molality are both a measure of concentration of the solute. The composition of the solution can be described in mass percentage. It is the mass of solute present in each mass of solution. The total moles of a solute contained in a kilogram of a solvent is the molality.

Complete step by step answer:
The atomic mass of an element is the mass of one atom of the element in terms of atomic mass units (amu). It gives an average value to the mass of one atom of the element.
The molar mass of a substance is the total mass of one mole of the substance. It is expressed as ‘grams per mole \[\left( {{{g/mol}}} \right)\]. The gram atomic mass (GAM) of an element is the mass of one mole of that element and the gram molecular mass (GMM) of a compound refers to the mass of one mole of the compound.
The molality can be calculated by dividing the number of moles of solute, ${{n}}$ by mass of solvent in kilograms, ${{{m}}_{{s}}}$.
Molality, \[{{m = }}\dfrac{{{n}}}{{{{{m}}_{{s}}}}}\]
Number of moles of solute, ${{n}}$ can be calculated by dividing the given mass of solute, ${{{m}}_{{{sol}}}}$ by molecular mass of solute, ${{{M}}_{{{sol}}}}$.
In the above question,
Mass of HCl, \[{{{m}}_{{{HCl}}}}{{ = 36}}{{.5\;g}}\]
Mass of ${{{H}}_2}{{O}}$, \[{{{m}}_{{{{H}}_2}{{O}}}}{{ = 63}}{{.5\;g}}\]
Number of moles of HCl, \[{{{n}}_{{{HCl}}}}\] \[{{ = }}\dfrac{{{{36}}{{.5}}}}{{{{36}}{{.5}}}}\,{{ = 1\;mol}}\]
Molality \[{{ = }}\dfrac{{{{{n}}_{{{HCl}}}}}}{{{{{m}}_{{s}}}}}{{ = }}\dfrac{{{1}}}{{{{63}}{{.5/1000}}}}\,\,{{ = }}\dfrac{{{{1000}}}}{{{{63}}{{.5}}}}\,\,{{ = 15}}{{.75\;m}}\]

So, the correct answer is Option B.

Note: Molarity and molality is also a measure of concentration of a solution. Molarity is the number of moles of solute per litre of solution. It is denoted by the symbol ${{M}}$. Molality can be defined as the number of moles of solute in one kilogram of solvent. It is denoted by the symbol ${{m}}$.