Freezing-point depression



Freezing-point depression describes the phenomenon that the sea water, which due to its salt content remains liquid at temperatures below 0°C, the freezing point of pure water.

Explanation

 

The freezing point depression is a 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 molal concentration of the solution according to the equation[1]

ΔTf = Kf · mB

where

  • ΔTf, the freezing point depression, is defined as Tf (pure solvent) − Tf (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.
  • Kf, the cryoscopic constant, which is dependent on the properties of the solvent. It can be calculated as Kf = RTf2M/ΔHf, where R is the heat of fusion per kilogram of the solvent.
  • mB 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 mB = msolute · 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 phase diagram of the mixture.

Cryoscopic constants

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

Compound Melts at °C Kf at K·kg/mol
Acetic acid 16.6 3.90
Benzene 5.5 5.12
Camphor 179 39.7
Carbon disulfide −112 3.8
Carbon tetrachloride −23 30
Chloroform 63.5 4.68
Cyclohexane 6.4 20.2
Ethanol −114.6 1.99
Naphthalene 80.2 6.80
Phenol 41 7.27
Water 0 1.86

Uses

The phenomenon of freezing point depression is used in technical application to avoid freezing. In the case of water, 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 glucose.[4]

Together with formula above, freezing-point depression can be used to measure the degree of dissociation or the 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

References

  1. ^ a b P. W. Atkins, Physical Chemistry, 4th Ed., Oxford University Press, Oxford, 1994, ISBN 0-19-269042-6, p. 222-226
  2. ^ P. W. Atkins, Physical Chemistry, 4th Ed., p. C17 (Table 7.2)
  3. ^ Molare Schmelzpunkterniedrigung, article in German Wikipedia
  4. ^ L. Sherwood et al., Animal Physiology - From Genes to Organisms, 2005, Thomson Brooks/Cole, Belmont, CA, ISBN 0-534-55404-0, p. 691-692
  5. ^ Julius B. Cohen Practical Organic Chemistry 1910 Link to online text
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