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In thermodynamics, the cryoscopic constant, K_f, relates molality to freezing point depression (which is a colligative property). It is the ratio of the latter to the former:

ΔTf=i⋅Kf⋅b{displaystyle Delta T_{f}=icdot K_{f}cdot b}

• 
  i{displaystyle i} is the van 't Hoff factor, the number of particles the solute splits into or forms when dissolved.


• 
  b{displaystyle b} is the molality of the solution.

Through cryoscopy, a known constant can be used to calculate an unknown molar mass. The term "cryoscopy" comes from Greek and means "freezing measurement." Freezing point depression is a colligative property, so ΔT{displaystyle Delta T} 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 (of boiling point elevation).

The value of Kf{displaystyle K_{f}}, which depends on the nature of the solvent can be found out by the following equation:

Kf=R⋅M⋅Tf2ΔfusH{displaystyle K_{f}={frac {Rcdot Mcdot T_{f}^{2}}{Delta _{fus}H}}}

• 
  R{displaystyle R} is the Universal Gas Constant
  


• 
  M{displaystyle M} is the Molar mass of the solvent in kg mol−1{displaystyle kg mol^{-1}}
  


• 
  Tf{displaystyle T_{f}} is the freezing point of the pure solvent in kelvin


• 
  ΔfusH{displaystyle Delta _{fus}H} represents the molar enthalpy of fusion of the solvent in Joules per mole.

The K_f for water is 1.853 K·kg/mol.^[1]

See also

• List of boiling and freezing information of solvents

References

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