JEE Main 2024 — Some Basic Concepts Of Chemistry Question with Solution

To calculate the molality $(\mathrm{m})$ of a 3M (molar) aqueous solution of $\mathrm{NaCl}$, we need to follow certain steps, using the given data and understanding the definitions properly.

Molarity (M) is defined as the number of moles of solute per liter of solution. Molality $(\mathrm{m})$, on the other hand, is defined as the number of moles of solute per kilogram of solvent. The given density of the solution is $1.25\mathrm{g}{\mathrm{mL}}^{-1}$ which allows us to calculate the mass of the solvent in a given volume of solution.

We know:

• Molarity (M) of NaCl = $3\mathrm{M}$
• Density of NaCl solution = $1.25\mathrm{g}{\mathrm{mL}}^{-1}$
• Molar mass of $\mathrm{NaCl}=\mathrm{Na}+\mathrm{Cl}=23+35.5=58.5\mathrm{g}{\mathrm{mol}}^{-1}$

First, to find the molality, we need to find the moles of NaCl in a given mass of the solvent. Keeping in mind that $3\mathrm{M}$ means there are $3\mathrm{moles}$ of $\mathrm{NaCl}$ per liter of solution, we consider 1 liter (or 1000 mL) of solution to simplify our calculation, knowing that density can convert volume to mass directly.

The mass of 1 liter of NaCl solution is $1.25\mathrm{g}{\mathrm{mL}}^{-1}\times 1000\mathrm{mL}=1250\mathrm{g}$.

Since we have a 3 M solution of NaCl,

$3\mathrm{moles}=\frac{\text{mass of the solution}-\text{mass of solvent}}{\text{molar mass of NaCl}}$

With 3 moles of NaCl, the mass of NaCl present in 1 L solution $=3\mathrm{moles}\times 58.5g/mol=175.5\mathrm{g}$

The mass of the solvent (water) can be found by subtracting the mass of NaCl from the total mass of the solution.

$\text{Mass of solvent}=1250\mathrm{g}-175.5\mathrm{g}=1074.5\mathrm{g}$

To convert this mass into kilograms (since molality is expressed per kilogram of solvent),

$1074.5\mathrm{g}=1.0745\mathrm{kg}$

Finally, the molality $(\mathrm{m})$,

$\mathrm{m}=\frac{\text{moles of solute}}{\text{kilograms of solvent}}=\frac{3\mathrm{moles}}{1.0745\mathrm{kg}}$

$\mathrm{m}\approx 2.79$

So, the correct answer is

Option D: 2.79 m