Freezing-point depression 607495 216239648 2008-05-31T19:19:22Z Rifleman 82 1255637 Revert to revision 212369069 dated 2008-05-14 15:32:00 by 190.161.172.236 using [[:en:Wikipedia:Tools/Navigation_popups|popups]] '''Freezing-point depression''' describes the phenomenon that the [[Melting point|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. ==Explanation== [[Image:Freezing point depression and boiling point elevation.png|thumb|400px|The change in chemical potential of a solvent when a solute is added explains why freezing point depression takes place.]] 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.){{Fact|date=February 2008}} The freezing point depression happens both when the solute is an [[electrolyte]], such as various salts, and a nonelectrolyte. In [[thermodynamics|thermodynamic]] terms, the origin of the freezing point depression is [[entropy|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.<ref name="Atkins">P. W. Atkins and J. de Paula, ''Atkins' Physical Chemistry'', 7th Ed., Oxford University Press, Oxford, 2002, ISBN 0-19-879285-9, p. 175-177</ref> 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 [[Concentration|molal]] concentration of the solution according to the equation<ref name="Atkins"/> ''ΔT''<sub>f</sub> = ''K''<sub>f</sub> · ''m''<sub>B</sub> where * ''ΔT''<sub>f</sub>, the freezing point depression, is defined as ''T''<sub>f (pure solvent)</sub> − ''T''<sub>f (solution)</sub>, 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''<sub>f</sub>, the [[cryoscopic constants|cryoscopic constant]], which is dependent on the properties of the solvent. It can be calculated as ''K''<sub>f</sub> = ''RT''<sub>m</sub><sup>2</sup>''M''/''ΔH''<sub>f</sub>, where ''R'' is the [[gas constant]], ''T''<sub>m</sub> is the [[melting point]] of the pure solvent in kelvin, ''M'' is the molar mass of the solvent, and ''ΔH''<sub>f</sub> is the [[heat of fusion]] per mole of the solvent. * ''m''<sub>B</sub> is the [[molality]] of the solution, calculated by taking [[Dissociation_%28chemistry%29|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''<sub>B</sub> = ''m''<sub>solute</sub> · ''i''. The factor ''i'' accounts for the number of individual particles (typically ions) formed by a compound in solution. Examples: ** ''i'' = 1 for [[sucrose|sugar]] in water ** ''i'' = 2 for [[sodium chloride]] in water, due to dissociation of NaCl into Na<sup>+</sup> and Cl<sup>-</sup> ** ''i'' = 3 for [[calcium chloride]] in water, due to dissociation of CaCl<sub>2</sub> into Ca<sup>2+</sup> and 2 Cl<sup>-</sup> ** ''i'' = 2 for [[hydrogen chloride]] in water, due to complete dissociation of HCl into H<sup>+</sup> and Cl<sup>-</sup> ** ''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 the approximations used in its derivation and any [[ideal solution#Non-ideality|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 cryoscopic constant ''K''<sub>f</sub> for selected solvents:<ref>P. W. Atkins, ''Physical Chemistry'', 4th Ed., p. C17 (Table 7.2)</ref><ref>[http://de.wikipedia.org/w/index.php?title=Molare_Schmelzpunkterniedrigung&oldid=37163298 ''Molare Schmelzpunkterniedrigung'', article in German Wikipedia]</ref> {| class="wikitable sortable" ! Compound !! Freezes at °C !! ''K''<sub>f</sub> at [[Celsius|°C]]·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 |- | [[Ethyl ether]] || −116.2 || 1.79 |- | [[Naphthalene]] || 80.2 || 6.80 |- | [[Phenol]] || 41 || 7.27 |- | [[Water]] || 0 || 1.86 |} ==Uses== The phenomenon of freezing point depression is used in technical applications 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 [[evolution|evolved]] in some animals that live in very cold environments. This happens through permanently high concentration of [[physiology|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]].<ref>L. Sherwood et al., ''Animal Physiology - From Genes to Organisms'', 2005, Thomson Brooks/Cole, Belmont, CA, ISBN 0-534-55404-0, p. 691-692</ref> Together with formula above, freezing-point depression can be used to measure the degree of [[dissociation (chemistry)|dissociation]] or the [[molar mass]] of the solute. This kind of measurement is called '''cryoscopy''' ([[Ancient Greek|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''<sub>B</sub> and then comparing it to ''m''<sub>solute</sub>. In this case, the molar mass of the solute must be known. The molar mass of a solute is determined by comparing ''m''<sub>B</sub> 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,<ref>Julius B. Cohen ''Practical Organic Chemistry'' '''1910''' [http://archive.org/details/PracticalOrganicChemistry Link to online text]</ref> 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== {{reflist}} {{Chemical solutions}} [[Category:chemical properties]] [[Category:phase changes]] [[de:Molare Gefrierpunktserniedrigung]] [[es:Descenso crioscópico]] [[it:Abbassamento crioscopico]] [[hu:Fagyáspontcsökkenés törvény]] [[nl:Vriespuntsdaling]] [[ja:凝固点降下]] [[sv:Fryspunktssänkning]] [[vi:Sự suy giảm điểm đóng băng]]