# How can freezing point depression determine purity?

Mar 19, 2014

If the freezing point depression constant is known you can calculate the molal concentration of solute from a measured freezing point depression, assuming the concentration is dilute enough to be considered an ideal solution.

Example:

For water, the freezing point depression constant is
K_F = 1.853 (°C*kg)/(mol)

If an aqueous solution has a measured freezing point of
\DeltaT = -0.07 °C
then the molal concentration of solute is given by

$c = \frac{- \setminus \Delta T}{K} _ F = 0.0378 \frac{m o l}{k g}$ (moles of solute per kg of solvent)

Note that for dilute aqueous solutions, molality and molarity have very similar values, but for other solvents this is not true.

Freezing point depression does not depend on which solute is present, only on the total concentration of dissolved species. If the solute is dissociated (e.g. $N {a}^{+} \mathmr{and} C {l}^{-}$) you must add up the concentrations of all solutes.