A solution of 5 g nonvolatile solute in 50 g water decreases its freezing point by 0.2 K . Calculate the molar mass of solute if K _ f of water is 1.86 ~K ~kg ~mol ⁻¹ .

Step-by-step solution

The molar mass is determined using freezing point depression, a colligative property where T_f = K_f m , with m representing molality. Molality is defined as m = w₂ / M₂ w₁ , where w₂ is the solute mass, M₂ is the molar mass, and w₁ is the solvent mass in kg. Substituting into the freezing point equation yields T_f = K_f w₂ M₂ w₁ . Rearranging for molar mass gives M₂ = K_f w₂ T_f w₁ . Using the provided values: w₂ = 5 g , w₁ = 0.050 kg , T_f = 0.2 K , and K_f = 1.86 K kg mol ⁻¹ . M₂ = 1.86 5 0.2 0.050 = 9.3 0.01 =