thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...

, the cryoscopic constant, , relates

molality In chemistry, molality is a measure of the amount of solute in a solution relative to a given mass of solvent. This contrasts with the definition of '' molarity'' which is based on a given volume of solution. A commonly used unit for molality ...

to freezing point depression (which is a colligative property). It is the ratio of the latter to the former: :

\Delta T_\mathrm = iK_\mathrm b

\Delta T_\mathrm

is the depression of

freezing point The melting point (or, rarely, liquefaction point) of a substance is the temperature at which it changes state of matter, state from solid to liquid. At the melting point the solid and liquid phase (matter), phase exist in Thermodynamic equilib ...

, defined as the freezing point

T_\mathrm^0

of the pure solvent minus the freezing point

T_\mathrm

of the solution; * is the van ‘t Hoff factor, the number of particles the solute splits into or forms when dissolved; * is the

of the solution. Through cryoscopy, a known constant can be used to calculate an unknown

molar mass In chemistry, the molar mass () (sometimes called molecular weight or formula weight, but see related quantities for usage) of a chemical substance ( element or compound) is defined as the ratio between the mass () and the amount of substance ...

. The term "cryoscopy" means "freezing measurement" in

Greek Greek may refer to: Anything of, from, or related to Greece, a country in Southern Europe: *Greeks, an ethnic group *Greek language, a branch of the Indo-European language family **Proto-Greek language, the assumed last common ancestor of all kno ...

. 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_\text = iK_\text b * is the van 't Hoff factor, the number of particles the solute splits into ...

(of boiling point elevation). The value of , which depends on the nature of the solvent can be found out by the following equation: :

K_\text = \frac

* is the ideal gas constant. * is the

of the solvent. * is the

of the pure solvent in

kelvin The kelvin (symbol: K) is the base unit for temperature in the International System of Units (SI). The Kelvin scale is an absolute temperature scale that starts at the lowest possible temperature (absolute zero), taken to be 0 K. By de ...

. * is the molar enthalpy of fusion of the solvent. The for water is 1.853 K kg mol⁻¹.

References

Phase transitions Thermodynamic properties {{Thermodynamics-stub

See also

References