AIIMS 2018 Chemistry Colligative Properties MCQ Question

To find the molar mass of the solute, we use the formula for freezing point depression: ΔT_f = k_f * m, where ΔT_f is the change in freezing point (2.2 K), k_f is the cryoscopic constant (1.86 K kg mol⁻¹), and m is the molality of the solution. First, we calculate the molality: m = ΔT_f / k_f = 2.2 K / 1.86 K kg mol⁻¹ ≈ 1.18 mol/kg. Since molality (m) is defined as moles of solute per kg of solvent, we have 1.18 mol/kg = n / 0.6 kg, leading to n ≈ 0.708 moles of solute. The molar mass (M) is then calculated as M = mass of solute / n = 45 g / 0.708 mol ≈ 63.4 g/mol, confirming option A.

Options B (80 g/mol), C (90 g/mol), and D (21 g/mol) do not satisfy the calculations based on the given freezing point depression and the mass of solute, indicating they do not correspond to the correct molar mass derived from the data provided.