Freezing Point Depression Calculator Formula

Understand the math behind the freezing point depression calculator. Each variable explained with a worked example.

Formulas Used

Freezing Point Depression

delta_tf = vant_hoff * kf_const * molality

New Freezing Point

new_fp = fp_pure - vant_hoff * kf_const * molality

Variable	Description	Default
`kf_const`	Cryoscopic Constant (Kf)(C-kg/mol)	1.86
`molality`	Molality(m)	0.5
`vant_hoff`	Van't Hoff Factor (i)	2
`fp_pure`	Freezing Point of Pure Solvent(C)	0

delta_Tf = i × Kf × m

For water, Kf = 1.86 C-kg/mol. New FP = pure FP - delta_Tf.

0.5 m NaCl (i=2) in water.

kf_const = 1.86molality = 0.5vant_hoff = 2fp_pure = 0

Determining the right concentration of road salt (NaCl or CaCl2) needed to keep roads ice-free at a target temperature below 0 °C.
Formulating antifreeze mixtures for car radiators by calculating how much ethylene glycol is needed to prevent freezing at the expected winter low.
Estimating the molar mass of an unknown solute from the measured freezing point depression of a known solvent — a classic lab technique called cryoscopy.
Predicting whether a homemade ice cream mixture will freeze properly in a standard freezer by checking how much the sugar and salt depress the freezing point.
Choosing between different de-icing salts by comparing their van 't Hoff factors — CaCl2 (i ≈ 3) depresses the freezing point more per mole than NaCl (i ≈ 2).

Neglecting the van 't Hoff factor (i) — ionic solutes dissociate in solution, so NaCl produces roughly twice the freezing point depression of a non-electrolyte at the same molality, and CaCl2 roughly three times.
Confusing molality with molarity — the formula ΔTf = Kf × m × i uses molality (mol solute / kg solvent), not molarity. Using molarity introduces errors because solution volume changes with temperature and concentration.
Using the Kf constant for the wrong solvent — water's cryoscopic constant is 1.86 °C·kg/mol, but benzene's is 5.12. Plugging in the wrong constant gives a proportionally wrong result.
Applying the formula beyond the dilute solution range — at high concentrations, solute-solute interactions cause the actual depression to deviate significantly from the linear prediction.
Forgetting that ΔTf is a positive number representing a decrease — the new freezing point is the normal freezing point minus ΔTf, not plus.

A colligative property where dissolving a solute lowers the freezing point. This is why salt is spread on icy roads.

The enthalpy of fusion is smaller than the enthalpy of vaporization, making freezing point more sensitive to solute.

Yes, but each has its own Kf. Cyclohexane Kf = 20.0, making it useful for precise molar mass determinations.

Ready to run the numbers?