The formula
ΔT = K · m · i
| Symbol | Quantity | Unit |
|---|---|---|
| ΔT | Change in temperature | °C |
| K | Solvent constant | °C·kg/mol |
| m | Molality | mol/kg |
| i | Van ’t Hoff factor |
What it means
Dissolving something in a liquid changes its phase-change points, and the curious part is that **what matters is not what you dissolve but how many particles you add**. Hence the name colligative properties. The constant K is a property of the solvent — 1.86 for freezing water and 0.512 for boiling it — and the van ’t Hoff factor counts how many pieces the solute breaks into: one for sugar, which does not dissociate, and two for salt, which separates into sodium and chloride.
How to work it out by hand
- Look up the cryoscopic or ebullioscopic constant of the solvent
- Work out the molality of the solution
- Find how many ions the solute dissociates into
- Multiply the three together
What is worth knowing
This is where the explanation for salting icy roads comes from: it does not melt ice with heat, it lowers water’s freezing point so it cannot refreeze. And also its limit, which almost nobody mentions: however much salt you throw down, the maximum depression for brine is around −21 °C, its eutectic point. Below that salt stops working and calcium chloride is needed, which reaches further because it contributes three ions instead of two. In cooking the opposite happens and on a tiny scale: salting pasta water raises the boiling point by mere tenths of a degree, so it does not cook faster; it goes in for flavour.