cryoscopic constant
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In thermodynamics, the cryoscopic constant, , relates
molality Molality is a measure of the number of moles of solute in a solution corresponding to 1 kg or 1000 g of solvent. This contrasts with the definition of molarity which is based on a specified volume of solution. A commonly used unit for molali ...
to freezing point depression (which is a colligative property). It is the ratio of the latter to the former: :\Delta T_f = -i \cdot K_f \cdot b * is the van ‘t Hoff factor, the number of particles the solute splits into or forms when dissolved. * is the
molality Molality is a measure of the number of moles of solute in a solution corresponding to 1 kg or 1000 g of solvent. This contrasts with the definition of molarity which is based on a specified volume of solution. A commonly used unit for molali ...
of the solution. Through
cryoscopy Freezing-point depression is a drop in the minimum temperature at which a substance freezes, caused when a smaller amount of another, non- volatile substance is added. Examples include adding salt into water (used in ice cream makers and for ...
, a known constant can be used to calculate an unknown
molar mass In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance which is the number of moles in that sample, measured in moles. The molar mass is a bulk, not molecular, ...
. The term "cryoscopy" comes from
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and means "freezing measurement." Freezing point depression is a colligative property, so depends only on the number of solute particles dissolved, not the nature of those particles. Cryoscopy is related to ebullioscopy, which determines the same value from the
ebullioscopic constant In thermodynamics, the ebullioscopic constant relates molality to boiling point elevation. It is the ratio of the latter to the former: :\Delta T = iK_\text b * is the van 't Hoff factor, the number of particles the solute splits into or form ...
(of
boiling point elevation Boiling-point elevation describes the phenomenon that the boiling point of a liquid (a solvent) will be higher when another compound is added, meaning that a solution has a higher boiling point than a pure solvent. This happens whenever a non-volat ...
). The value of , which depends on the nature of the solvent can be found out by the following equation: :K_ = \frac * is the ideal gas constant * is the
molar mass In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance which is the number of moles in that sample, measured in moles. The molar mass is a bulk, not molecular, ...
of the solvent in kg mol−1 * is the
freezing point The melting point (or, rarely, liquefaction point) of a substance is the temperature at which it changes state from solid to liquid. At the melting point the solid and liquid phase exist in equilibrium. The melting point of a substance depend ...
of the pure solvent in kelvins * represents the molar
enthalpy of fusion In thermodynamics, the enthalpy of fusion of a substance, also known as (latent) heat of fusion, is the change in its enthalpy resulting from providing energy, typically heat, to a specific quantity of the substance to change its state from a s ...
of the solvent in J mol−1. The for water is 1.853  K kg mol−1.


See also

*
List of boiling and freezing information of solvents See also *Freezing-point depression Freezing-point depression is a drop in the minimum temperature at which a substance freezes, caused when a smaller amount of another, non- volatile substance is added. Examples include adding salt into w ...


References

Phase transitions Thermodynamic properties {{Thermodynamics-stub