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Freezing Point Depression Calculator

Enter Kf, molality and the van ’t Hoff factor to get the depression.

Result

5.58 °C

How it is calculated

The tool multiplies three numbers: ΔTf = i × Kf × m. Kf is the cryoscopic constant of the solvent in °C·kg/mol, m is the molality of the solution in mol of solute per kg of solvent, and i is the van 't Hoff factor, roughly the number of particles one formula unit gives in solution. If i is left empty it is taken as 1. The answer is the size of the drop in freezing point in °C, shown with two decimals, not the new freezing point itself; subtract it from the pure solvent's freezing point. Negative inputs give no result. The simple linear formula assumes a dilute, ideal solution, and the tool applies no correction for strong ion interactions.

Worked example

Dissolve salt in water to make a 1.5 mol/kg solution. Water has Kf = 1.86 °C·kg/mol, and sodium chloride splits into two ions, so i = 2. Multiply: 2 × 1.86 × 1.5 = 5.58 °C. With water freezing at 0 °C, the solution would start to freeze near −5.58 °C under this ideal model. If the same amount of a non-electrolyte such as sugar were used, i = 1 and the drop would be only 2.79 °C, which is why salt lowers the freezing point about twice as much.

Try this example →

Common mistakes

  • Using molarity (mol/L) instead of molality (mol/kg solvent). The formula needs mass of solvent, not volume of solution.
  • Leaving out the van 't Hoff factor for a salt. Without i = 2 for NaCl, the tool uses 1 and gives half the drop.
  • Reading the answer as the new freezing point. The result is the drop, so water at 0 °C freezes at 0 − 5.58 = −5.58 °C here.
  • Using the water value of Kf for another solvent. Kf is specific to the solvent, so use the value for your own solvent.
  • Applying it to concentrated solutions. Real brines and antifreeze mixes deviate from the straight-line result, so treat the number as an ideal-case estimate.

About this calculator

Freezing point depression is a colligative property: dissolving a solute lowers a solvent's freezing point in proportion to the concentration of dissolved particles, via ΔTf = i·Kf·m, where Kf is the solvent's cryoscopic constant (1.86 °C·kg/mol for water), m is molality, and i is the van 't Hoff factor accounting for how many particles each solute unit dissociates into (i≈2 for NaCl, i≈1 for a non-electrolyte like sugar).

Chemists use this relationship in cryoscopy to determine an unknown solute's molar mass from a measured ΔTf, while it's also the physics behind salting icy roads and antifreeze/coolant formulation, both of which work by depressing the freezing point of water below the ambient temperature.

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