Density and Molarity to Find Molality JEE Chemistry

 

❓ Question

The density of a 3 M NaCl solution is 1.25 g mL⁻¹. Find the molality of the solution.

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✍️ Solution

Given molarity:

$$M=3\text{ M}$$

Therefore, 1 L of solution contains 3 moles of NaCl.

Mass of 1 L solution:

$$\text{Mass}=\text{Volume}\times\text{Density}$$
$$=1000\times1.25$$
$$=1250\text{ g}$$

Molar mass of NaCl:

$$=23+35.5=58.5\text{ g mol}^{-1}$$

Mass of NaCl:

$$=3\times58.5$$
$$=175.5\text{ g}$$

Mass of solvent:

$$=1250-175.5$$
$$=1074.5\text{ g}=1.0745\text{ kg}$$

Molality:

$$m=\frac{\text{Moles of solute}}{\text{Mass of solvent in kg}}$$
$$m=\frac{3}{1.0745}$$
$$m\approx2.79\text{ mol kg}^{-1}$$

✅ Final Answer

$$\boxed{2.79\text{ m}}$$