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:

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

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

$\overline{){{\mathbf{\Delta T}}}_{{\mathbf{f}}}{\mathbf{=}}{{\mathbf{imK}}}_{{\mathbf{f}}}}$

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.

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 K_{fp} of the solvent is 2.4 K/m, calculate the molar mass of the unknown solute.