Freezing Point Depression

The freezing point for a solution goes down compared to the pure solvent for the same reason the boiling point goes up: the solution is more stable (it has a lower free energy) compared to the pure solvent. Since it is relatively more stable it exists over a wider temperature range. This can be easily seen again on a phase diagram where the solution is depicted with the "larger" liquid region.

Quantitatively, the change in freezing point can be calculated again in an approximate formula based on the molality of the solution.

Freezing Point depression

\[ \Delta T = -iK_f \; m\]

Again \(K_f\) is a constant that depends on the solvent and m is the total solute concentration in molality. K_f is called the freezing point depression constant or cryoscopic constant.

Sometimes this formula doesn't have the negative sign and you simply need to remember that freezing point goes down. i is the vant' Hoff factor and for ionic solutes accounts for the total number of ions the solute breaks up into.

The effect of freezing point depression is generally larger than that of boiling point elevation as values of K_f are typically larger than those of K_b. They range from around 1.5 to as much as 40 °C molal^-1. For water, K_b = 1.8 °C molal^-1. So a 1 M NaCl solution should freeze at -3.6 °C. (i=2 since there are two ions) sFor water 1 M = 1m. ΔT = -(2)(1.8 °C m^-1)(1 m) = -3.6 °C)

Here is video about Freezing Point Depression using a molecular solute thus making the van't Hoff factor equal to one (i = 1).

Here is video about Freezing Point Depression using an ionic solute where the van't Hoff factor is equal to three (i = 3).