Cryoscopic constant

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:

\Delta T_{\mathrm {f} }=iK_{\mathrm {f} }b

$\Delta T_{\mathrm {f} }$ 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 $Δ T$ 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 {RMT_{\text{f}}^{2}}{1000\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.
$Δ H fus$ is the molar enthalpy of fusion of the solvent.

The $K f$ for water is 1.853 K kg mol⁻¹.^[1]

^ Aylward, Gordon; Findlay, Tristan (2002), SI Chemical Data (5 ed.), Sweden: John Wiley & Sons, p. 202, ISBN 0-470-80044-5

[1] Aylward, Gordon; Findlay, Tristan (2002), SI Chemical Data (5 ed.), Sweden: John Wiley & Sons, p. 202, ISBN 0-470-80044-5

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