Physics:Cryoscopic constant

Short description: Material property relating molality to freezing point depression

In thermodynamics, the cryoscopic constant, K_f, relates molality to freezing point depression (which is a colligative property). It is the ratio of the latter to the former:

$\mathrm{\Delta }{T}_{\mathrm{f}}=i{K}_{\mathrm{f}}b$

• $\mathrm{\Delta }{T}_{\mathrm{f}}$ is the depression of freezing point, defined as the freezing point $T_{\mathrm{f}}^0$ of the pure solvent minus the freezing point $T_{\mathrm{f}}$ of the solution;
• i is the van ‘t Hoff factor, the number of particles the solute splits into or forms when dissolved;
• b is the molality of the solution.

Through cryoscopy, a known constant can be used to calculate an unknown molar mass. The term "cryoscopy" means "freezing measurement" in Greek. Freezing point depression is a colligative property, so ΔT depends only on the number of solute particles dissolved, not the nature of those particles. Cryoscopy is related to ebullioscopy, which determines the same value from the ebullioscopic constant (of boiling point elevation).

The value of K_f, which depends on the nature of the solvent can be found out by the following equation:

$K_{\text{f}}=\frac{RM{T}_{\text{f}}^2}{1000\mathrm{\Delta }{H}_{\text{fus}}}$

• R is the ideal gas constant.
• M is the molar mass of the solvent.
• T_f is the freezing point of the pure solvent in kelvin.
• ΔH_fus is the molar enthalpy of fusion of the solvent.

The K_f for water is 1.853 K kg mol⁻¹.

See also

• List of boiling and freezing information of solvents