Question

Calculate the molarity of the 3.3 molal solution of KCl whose density is 1.28 g/ mL.
A. 3.7 M
B. 5.0 M
C. 3.4 M
D. 2.5 M

Answer 1

Hint: Mol/kg is a typical molality measurement unit in chemistry. One molal is another way to refer to a solution with a concentration of 1 mol/kg. Molar mass must be represented in kg/mol rather than the more common g/mol or kg/kmol when using the unit mol/kg.

Complete Step by Step Solution:
The number of moles of solute in a solution equal to 1 kg or 1000 g of solvent is referred to as its molality.

Mole per kilogram of solvent is the SI unit for molality. Since molality solely depends on the masses of the solute and solvent, which are unaffected by changes in temperature and pressure, it is a particularly advantageous way to estimate concentration. As temperature and pressure fluctuate, however, solutions produced volumetrically (such as those with a molar concentration or mass concentration) are likely to change. This is a huge benefit in many applications where the mass, or quantity, of a substance is frequently more essential than its volume (e.g. in a limiting reagent problem).
Given,
Molality = 3.3 m
Density = 1.28 g / mL

By using the formula,
Molality $(\mathrm{m})=\mathrm{M} \times 1000 / 1000 \times \mathrm{d}-\mathrm{M} \times \mathrm{M}_{\text {solute }}$
$3.3=\mathrm{M} \times 1000 / 1000 \times 1.28-\mathrm{M} \times 74.5$
$4224-245.85 \mathrm{M}=1000 \mathrm{M}$
$1245.85 \mathrm{M}=4224$
$\mathrm{M}=4224 / 1245.85=3.39 \approx 3.4 \mathrm{M}$
Hence option c is correct.

Note: The substance that will be used as the "solvent" in an arbitrary mixture determines the combination's molality. The choice is obvious if there is only one pure liquid substance present in the mixture, but not all solutions are so cut-and-dry. For example, either alcohol or water could be referred to as the solvent in an alcohol-water solution; in an alloy or solid solution, there is no clear winner and all constituents may be treated equally. The preferred compositional specification in these circumstances is mass or mole fraction.