Freezing-point depression

Freezing-point depression describes the phenomenon that the freezing point of a liquid (a solvent) is depressed when another compound is added, meaning that a solution has a lower freezing point than a pure solvent. This happens whenever a solute is added to a pure solvent, such as water. The phenomenon may be observed in sea water, which due to its salt content remains liquid at temperatures below 0°C, the freezing point of pure water.

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Explanation

The freezing point depression is a colligative property, which means that it is dependent on the presence of dissolved particles and their number, but not their identity. It is an effect of the dilution of the solvent in the presence of a solute. It is a phenomenon that happens for all solutes in all solutions, even in ideal solutions, and does not depend on any specific solute-solvent interactions. (Explanations claiming that the solute molecules somehow "prevent" the solvent molecules from forming a solid are thus wrong.) The freezing point depression happens both when the solute is an electrolyte, such as various salts, and a nonelectrolyte. In thermodynamic terms, the origin of the freezing point depression is entropic and is most easily explained in terms of the chemical potential of the solvent.

At the freezing (or melting) point, the solid phase and the liquid phase have the same chemical potential meaning that they are energetically equivalent. The chemical potential is dependent on the temperature, and at other temperatures either the solid or the liquid phase has a lower chemical potential and is more energetically favourable than the other phase. In many cases, a solute does only dissolve in the liquid solvent and not in the solid solvent. This means that when such a solute is added, the chemical potential of the solvent in the liquid phase is decreased by dilution, but the chemical potential of the solvent in the solid phase is not affected. This means in turn that the equilibrium between the solid and liquid phase is established at another temperature for a solution than a pure liquid; i.e., the freezing point is depressed.^[1]

The phenomenon of boiling point elevation is analogous to freezing point depression. However, the magnitude of the freezing point depression is larger than the boiling point elevation for the same solvent and the same concentration of a solute. Because of these two phenomena, the liquid range of a solvent is increased in the presence of a solute.

Calculations

The extent of freezing-point depression can be calculated by applying Clausius-Clapeyron relation and Raoult's law together with the assumption of the non-solubility of the solute in the solid solvent. The result is that in dilute ideal solutions, the extent of freezing-point depression is directly proportional to the molal concentration of the solution according to the equation^[1]

ΔT_f = K_f · m_B

where

• ΔT_f, the freezing point depression, is defined as T_{f (pure solvent)} − T_{f (solution)}, the difference between the freezing point of the pure solvent and the solution. It is defined to assume positive values when the freezing point depression takes place.
• K_f, the cryoscopic constant, which is dependent on the properties of the solvent. It can be calculated as K_f = RT_f²M/ΔH_f, where R is the gas constant, T_f is the freezing point of the pure solvent, M is the molar mass of the solvent, and ΔH_f is the heat of fusion per kilogram of the solvent.
• m_B is the molality of the solution, calculated by taking dissociation into account since the freezing point depression is a colligative property, dependent on the number of particles in solution. This is most easily done by using the van 't Hoff factor i as m_B = m_solute · i. The factor i accounts for the number of individual particles (typically ions) formed by a compound in solution. Examples:
  • i = 1 for sugar in water
  • i = 2 for sodium chloride in water, due to dissociation of NaCl into Na⁺ and Cl^-
  • i = 3 for calcium chloride in water, due to dissociation of CaCl₂ into Ca²⁺ and Cl^-
  • i = 2 for hydrogen chloride in water, due to complete dissociation of HCl into H⁺ and Cl^-
  • i = 1 for hydrogen chloride in benzene, due to no dissociation of HCl in a non-polar solvent

At high concentrations, the above formula is less precise due to nonideality of the solution. If the solute is highly soluble in the solid solvent, one of the key assumptions used in deriving the formula is not true. In this case the effect of the solute on the freezing point must be determined from the phase diagram of the mixture.

Cryoscopic constants

Values of the cryscopic constant K_f for selected solvents:^[2][3]

Uses

The phenomenon of freezing point depression is used in technical application to avoid freezing. In the case of water, ethylene glycol or other forms of antifreeze is added to cooling water in internal combustion engines, making the water stay a liquid at temperatures below its normal freezing point.

The use of freezing-point depression through "freeze avoidance" has also evolved in some animals that live in very cold environment. This happens through permanently high concentration of physiologically rather inert substances such as sorbitol or glycerol to increase the molality of fluids in cells and tissues, and thus decrease the freezing point. Examples include some species of arctic-living fish, such as rainbow smelt, which need to be able to survive in freezing temperatures for a long time. In other animals, such as the peeper frog (Pseudacris crucifer), the molality is increased temporarily as a reaction to cold temperatures. In the case of the peeper frog, this happens by massive breakdown of glycogen in the frog's liver and subsequent release of massive amounts of glucose.^[4]

Together with formula above, freezing-point depression can be used to measure the degree of dissociation or the molar mass of the solute. This kind of measurement is called cryoscopy (Greek "chillawatchsts") and relies on exact measurement of the freezing point. The degree of dissociation is measured by determining the van 't Hoff factor i by first determining m_B and then comparing it to m_solute. In this case, the molar mass of the solute must be known. The molar mass of a solute is determined by comparing m_B with the amount of solute dissolved. In this case, i must be known, and the procedure is primarily useful for organic compounds using a nonpolar solvent. Cryoscopy is no longer as common a measurement method as it once was. As an example, it was still taught as a useful analytic procedure in Cohen's Practical Organic Chemistry of 1910,^[5] in which the molar mass of napthalene is determined in a so-called Beckmann freezing apparatus.

In principle, the boiling point elevation and the freezing point depression could be used interchangeably for this purpose. However, the cryoscopic constant is larger than the ebullioscopic constant and the freezing point is often easier to measure with precision, which means measurements using the freezing point depression are more precise.

See also

• Boiling-point elevation
• Eutectic point
• Colligative properties
• List of boiling and freezing information of solvents

References