Freezing-point depression

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Freezing-point depression is the difference between the freezing points of a pure solvent and a solution mixed with a solute. It is directly proportional to the molal concentration of the solution, or more precisely, to the solute activity, according to the equation:

ΔT_f = i · K_f · activity

activity is in units of mol/kg, and is equal to an activity coefficient times the molality
ΔT_f, the freezing point depression is defined as T - T_f, where T is the freezing point of the solution and T_f is the freezing point of the pure solvent.
K_f, the cryoscopic constant, is a colligative property, given by RT_f²/ΔH_f, where R is the gas constant, and T_f is the normal freezing point of the solvent and ΔH_f is the heat of fusion per kilogram of the solvent
- K_f for water is 1.858 K·kg/mol (or more commonly used, 1.858 C/m) which means that per mole of solute dissolved in a kilogram of water the freezing point depression is 1.858 kelvins.
i is the i factor or the van 't Hoff factor (see van 't Hoff), accounts for the number of individual ions formed by a compound in solution.

Examples:

i = 1 for sugar in water.
i = 2 for NaCl in water.
i = 3 for CaCl₂ in water.
i = 2 for HCl in water. (complete dissociation)
i = 1 for HCl in benzene. (no dissociation)

Freezing point depression can be used to measure the degree of dissociation of a solute or to measure its activity or to determine molar mass of the solute.

In Cohen's Practical Organic Chemistry of 1910 ^[1] the molar mass of napthalene is determined in a so-called Beckmann freezing apparatus at 128 g/mole.