Problem: When 1.38 g of an unknown non-electrolyte is dissolved in 50.0 g of acetone, the freezing point decreased by 0.52 degrees C. If the Kfp of the solvent is 2.4 K/m, calculate the molar mass of the unknown solute.

We’re being asked to calculate the molar mass of the unknown solute.

Recall that the freezing point of a solution is lower than that of the pure solvent and the change in freezing point (ΔT­_f) is given by:

$\boxed{{\mathbf{\Delta T}}_{\mathbf{f}}\mathbf{=}{\mathbf{T}}_{\mathbf{f}\mathbf{,}\mathbf{ }\mathbf{pure}\mathbf{ }\mathbf{solvent}}\mathbf{-}{\mathbf{T}}_{\mathbf{f}\mathbf{,}\mathbf{ }\mathbf{solution}}}$

The change in freezing point is also related to the molality of the solution:

$\boxed{{\mathbf{\Delta T}}_{\mathbf{f}}\mathbf{=}{\mathbf{imK}}_{\mathbf{f}}}$

where:

i = van’t Hoff factor

m = molality of the solution (in m or mol/kg)

K_f = freezing point depression constant (in ˚C/m) of the solvent

We go through the following steps to solve the problem: 

Step 1. Calculate the molality of the solution

Step 2. Calculate the moles solute

Step 3. Calculate the molar mass of the solute.