Freezing Point Depression Calculator

Freezing point depression is the decrease in the freezing point of a solvent when a solute is dissolved in it. It is a colligative property, meaning it depends on the number of dissolved particles, not their chemical identity. The more solute particles present, the lower the freezing point of the solution compared to the pure solvent.

The formula is ΔTf = i × Kf × m, where ΔTf is the freezing point depression, i is the van't Hoff factor (number of particles the solute produces), Kf is the molal freezing point depression constant of the solvent, and m is the molality of the solution (moles of solute per kg of solvent). The new freezing point is then: FP(solution) = FP(pure solvent) − ΔTf.

The van't Hoff factor (i) represents how many particles a solute dissociates into when dissolved. For non-electrolytes like glucose or sugar, i = 1. For ionic compounds like NaCl, i ≈ 2 (Na⁺ and Cl⁻), and for CaCl₂, i ≈ 3 (Ca²⁺ and 2 Cl⁻). In practice, i is slightly less than the theoretical value due to ion pairing in solution.

In an ideal solution, NaCl would fully dissociate into Na⁺ and Cl⁻, giving i = 2. However, in real solutions, oppositely charged ions attract each other and briefly associate, reducing the effective number of independent particles. This ion-pairing effect causes the measured van't Hoff factor to be slightly below the theoretical value, typically around 1.85–1.9 for NaCl.

The cryoscopic constant for water is 1.86 °C·kg/mol. This means that dissolving 1 mole of a non-dissociating solute in 1 kg of water lowers the freezing point by 1.86 °C. Other solvents have different Kf values — for example, benzene has Kf = 5.12 °C·kg/mol and camphor has a very high Kf of about 37.7 °C·kg/mol.

When salt (NaCl or CaCl₂) dissolves in water, it dissociates into ions, increasing the total number of dissolved particles. This colligative effect lowers the freezing point of the water below 0 °C, so ice melts at the new lower temperature even when the ambient temperature is slightly below freezing. CaCl₂ is often preferred in very cold climates because its i ≈ 3 gives a larger depression than NaCl.

You can rearrange the freezing point depression formula to find molality (m = ΔTf / (i × Kf)), then use molality = moles of solute / kg of solvent to find moles of solute. Dividing the mass of solute by the moles gives the molar mass. This technique, called cryoscopy, is a classic experimental method for identifying unknown substances.

Molality (mol/kg) is used in freezing point depression calculations because it is independent of temperature — it is based on the mass of solvent, which does not change with temperature. Molarity (mol/L) depends on the volume of solution, which can vary with temperature. Using molality ensures the cryoscopic constant Kf remains accurate across different conditions.