When you dissolve something in a liquid, it freezes at a lower temperature than the pure solvent. This freezing point depression is one of the four colligative properties, and it underpins everything from de-icing roads to formulating isotonic eye drops and protecting cells during cryopreservation.
How it works
The depression is proportional to the concentration of dissolved particles:
delta Tf = i × Kf × m
new fp = normal fp − delta Tf
osmolality = i × mHere Kf is the cryoscopic constant of the solvent (for water: 1.86 °C·kg/mol), m is the molality in moles of solute per kilogram of solvent, and i is the van’t Hoff factor counting how many particles each formula unit releases. The osmolality, the total particle concentration, follows directly as i times molality.
Worked example
A one-molal solution of sodium chloride in water, with i near 2 (Na⁺ and Cl⁻), depresses the freezing point by about 3.7 °C, giving a freezing point near −3.7 °C, and has an osmolality of roughly 2 osmol/kg. For glucose (i = 1, a non-electrolyte), the same 1 molal solution depresses the freezing point by only 1.86 °C — half as much, because each formula unit releases only one particle.
Cryoscopic constants for common solvents
| Solvent | Kf (°C·kg/mol) | Normal freezing point (°C) |
|---|---|---|
| Water | 1.86 | 0.00 |
| Benzene | 5.12 | 5.53 |
| Cyclohexane | 20.2 | 6.54 |
| Acetic acid | 3.90 | 16.60 |
| Camphor | 37.7 | 178.8 |
Camphor’s exceptionally large Kf makes it useful in molecular weight determination: even small amounts of solute produce a measurable depression.
Practical applications
Road de-icing. Rock salt (NaCl) is effective because it dissociates into two ions, doubling the particle count and thus the depression per mole. Calcium chloride (CaCl₂, i ≈ 3) is more effective still on a per-mole basis and works at lower temperatures.
Pharmaceutical formulation. Isotonic solutions for intravenous fluids and eye drops target an osmolality close to blood plasma (approximately 285–295 osmol/kg). Formulators use freezing-point depression calculations to verify tonicity before production.
Food science. Ice cream and frozen desserts use sugars and salts to control the freezing point, keeping the product scoopable at typical freezer temperatures.
Cryopreservation. Cryoprotectants such as glycerol or DMSO are added to cell suspensions partly to depress the freezing point and slow ice crystal formation, protecting cell membranes.
When the formula deviates from measurement
At higher concentrations, ion pairing reduces the effective i below the theoretical value, so the measured depression is smaller than calculated. Activity coefficients correct for this, but the ideal formula is adequate for dilute solutions (molality below about 0.5 for electrolytes). For biological osmometry — measuring actual osmolality from freezing-point depression — dedicated osmometers measure the value directly rather than relying on the formula.
Notes
The formula is most accurate in dilute solutions. Use the Custom solvent option to enter any cryoscopic constant and freezing point not in the built-in list. All calculations run locally in your browser.