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, the activity, or the molar mass of the solute, although this particular process, called cryoscopy (Greek "freeze-viewing"), is not as common as it once was. It was still taught as a useful analytic procedure in Cohen's Practical Organic Chemistry of 1910,^[1] in which the molar mass of napthalene is determined in a so-called Beckmann freezing apparatus.

Freezing-point depressions occur whenever a solute is added to a pure solution, such as water. This is due to solute molecules disrupting the ability of the solvent to form crystals during the freezing process. Because of this, the liquid range of solvent is increased resulting in a freezing point depression.