Calculation
If the solution is treated as an ideal solution, the extent of freezing point depression depends only on the solute concentration that can be estimated by a simple linear relationship with the cryoscopic constant:
ΔTF = KF · b · i
- ΔTF, the freezing point depression, is defined as TF (pure solvent) - TF (solution).
- KF, the cryoscopic constant, which is dependent on the properties of the solvent, not the solute. Note: When conducting experiments, a higher KF value makes it easier to observe larger drops in the freezing point. For water, KF = 1.853 K·kg/mol.
- b is the molality (mol solute per kg of solvent)
- i is the van 't Hoff factor (number of ion particles per individual molecule of solute, e.g. i = 2 for NaCl, 3 for BaCl2).
This simple relation doesn't include the nature of the solute, so this is only effective in a diluted solution. For a more accurate calculation at a higher concentration, Ge and Wang (2010) proposed a new equation:
ΔTF ={ΔHfusTF - 2RTF·lnaliq - 0.5} /
In the above equation, TF is the normal freezing point of the pure solvent (0oC for water for example); aliq is the activity of the solution (water activity for aqueous solution); ΔHfusTF is the enthalpy change of fusion of the pure solvent at TF, which is 333.6 J/g for water at 0oC; ΔCfusp is the differences of heat capacity between the liquid and solid phases at TF, which is 2.11 J/g/K for water.
The solvent activity can be calculated from Pitzer model or modified TCPC model, which typically requires 3 adjustable parameters. For the TCPC model, these parameters are available at reference for many single salts.
Read more about this topic: Freezing-point Depression
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