What this calculator does
Dissolving anything in a solvent lowers its freezing point, by an amount proportional to the particle concentration rather than to what the particles are. This is why salt melts ice and why antifreeze works.
The particle count is what matters, which is where the van t Hoff factor enters. Sodium chloride splits into two ions, so it depresses the freezing point twice as much per mole as sugar does. One hundred grams of salt in a kilogram of water gives a depression of 6.37 °C, which is roughly the practical limit of road salting.
The formula
The depression is the van t Hoff factor multiplied by the cryoscopic constant of the solvent and the molality of the solution. The cryoscopic constant is a property of the solvent alone, 1.86 °C·kg/mol for water. The relationship is reliable for dilute solutions and drifts at high concentration as ion pairing reduces the effective particle count.
| Term | Meaning |
|---|---|
| Cryoscopic constant (Kf) | A solvent property. Water is 1.86, benzene 5.12, camphor 37.7. |
| van t Hoff factor (i) | Particles per formula unit. 1 for sugar, about 2 for NaCl. |
| Molality | Moles of solute per kilogram of solvent, the correct concentration measure here. |
| Colligative | Depending on particle count rather than particle identity. |
The inputs explained
| Field | What to enter |
|---|---|
| Mass of solute (g) | Mass of solute in grams. |
| Molar mass of solute (g/mol) | Molar mass of the solute. |
| Mass of solvent (kg) | Mass of solvent in kilograms. |
| Cryoscopic constant Kf (water 1.86) (°C·kg/mol) | Cryoscopic constant of the solvent. Water is 1.86. |
| Van’t Hoff factor i | van t Hoff factor. Use 1 for sugar or ethylene glycol, about 2 for NaCl. |
| Freezing point of pure solvent (°C) | Freezing point of the pure solvent. Water is 0 °C. |
When to use it
Road salting
How much salt is needed to keep a road above its freezing point at a given temperature.
Antifreeze formulation
Ethylene glycol does not dissociate, so it works by sheer concentration rather than by ion count.
Determining molar mass
Measuring the depression from a known mass gives the molar mass of an unknown, which is the classical cryoscopic method.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How much does salt lower the freezing point?
A range of salt masses in the same quantity of water.
| Mass of NaCl | New freezing point | Freezing point depression ΔTf | Molality |
|---|---|---|---|
| 10 g | -0.64 °C | 0.637 °C | 0.1711 mol/kg |
| 50 g | -3.18 °C | 3.183 °C | 0.8556 mol/kg |
| 100 g | -6.37 °C | 6.366 °C | 1.711 mol/kg |
| 200 g | -12.73 °C | 12.731 °C | 3.422 mol/kg |
Questions
Why does salt melt ice?
It lowers the freezing point of the water film on the ice surface below the ambient temperature, so the ice cannot remain solid. It does not generate heat; it changes the temperature at which the phase boundary sits. Below about −10 °C the effect becomes too small to be practical.
Why does salt work better than sugar?
Because it dissociates. One mole of sodium chloride produces close to two moles of particles while one mole of sugar produces one, so salt is roughly twice as effective per mole. Salt is also far cheaper and has a lower molar mass, which compounds the advantage per kilogram.
Does the identity of the solute matter?
Only through its particle count and molar mass. Colligative properties depend on how many particles are dissolved, not what they are. Two solutions with the same particle molality depress the freezing point identically regardless of the chemistry.
Why does the calculation overestimate at high concentration?
Because the van t Hoff factor drifts below its ideal value as ions begin to associate into pairs, reducing the effective particle count. At 1 molal, sodium chloride behaves as about 1.87 particles rather than 2, so the real depression falls short of the calculated one.
For the opposite effect at the other end, see the boiling point elevation calculator. For the concentration measure used, see the molality calculator.