Editing Colligative properties (section)

=== Freezing point depression (cryoscopy)===
{{Main|Freezing point depression}}
The freezing point (<math>T_{\rm f}</math>) of a pure solvent is lowered by the addition of a solute which is insoluble in the solid solvent, and the measurement of this difference is called ''cryoscopy''. It is found that 
    
:<math>\Delta T_{\rm f} = T_{\rm f,\text{solution}} - T_{\rm f,\text{pure solvent}} = - i\cdot K_f \cdot m </math><ref name=":0" /> (which can also be written as <math>\Delta T_{\rm f} = T_{\rm f,\text{pure solvent}} - T_{\rm f,\text{solution}} = i\cdot K_f \cdot m </math>)

Here ''K<sub>f</sub>'' is the [[cryoscopic constant]] (equal to 1.86&nbsp;°C kg/mol for the freezing point of water), ''i'' is the van 't Hoff factor, and ''m'' the molality (in mol/kg). This predicts the melting of ice by [[road salt]].

In the liquid solution, the solvent is diluted by the addition of a solute, so that fewer molecules are available to freeze. Re-establishment of equilibrium is achieved at a lower temperature at which the rate of freezing becomes equal to the rate of liquefying. At the lower freezing point, the vapor pressure of the liquid is equal to the vapor pressure of the corresponding solid, and the chemical potentials of the two phases are equal as well. The equality of chemical potentials permits the evaluation of the cryoscopic constant as <math>K_f = RMT_f^2/\Delta_{\mathrm{fus}}H</math>,  where Δ<sub>fus</sub>''H'' is the solvent molar [[enthalpy of fusion]].<ref name=Engel/>