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)
  • i is the factor that takes into account the presence of ions in a solution, it indicates the number of particles formed.

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 Julius B. Cohen Practical Organic Chemistry 1910 Link to online text the molar mass of napthalene is determined in a so-called Beckmann freezing apparatus at 128 g/mole.

See also

• Boiling-point elevation
• Eutectic point

References