Freezing Point Depression Calculator

Dissolve anything in a liquid and that liquid freezes at a lower temperature than before. Salt keeps icy roads slushy, glycol keeps a radiator from freezing, and the sugar in ice cream is the reason a scoop stays scoopable. This effect — freezing point depression — depends only on how many dissolved particles are present, not on what they are, and this calculator works it in both directions: give it a concentration and it returns the freezing temperature, give it a freezing temperature you measured and it returns the concentration that produces it.

The concentration input is molality, in moles of solute per kilogram of solvent, and the effect is scaled by the solvent's own freezing point depression constant. Seven solvents are built in — water, benzene, ethanol, chloroform, ether, nitrobenzene and acetic acid (listed as hydrogen acetate) — each with a tabulated constant and melting point. A van't Hoff factor handles solutes that split into several particles, and switching the solvent menu to Custom hands you every box, including the two that are normally locked.

Worked example: 0.4 molal antifreeze in water

A 0.4 molal solution of ethylene glycol in water, with the default van't Hoff factor of 1. First the depression, then the temperature it lands on:

One equation does all the work. The depression — how far the freezing point drops below the pure solvent — grows in proportion to the concentration:

and the solution's freezing point is the solvent's own, minus that drop:

Every direction it solves

• Forward: concentration to freezing point, as in the example above.
• Back to the van't Hoff factor: $i = \Delta T_{\mathrm{f}}\,/\,(K_{\mathrm{f}}\,m)$ — the standard way to extract a measured particle count from a lab freezing point.
• Back to the molality: $m = \Delta T_{\mathrm{f}}\,/\,(i\,K_{\mathrm{f}})$ — "what concentration do I need for a target freezing point?"
• Under Custom only: back to the constant $K_{\mathrm{f}} = \Delta T_{\mathrm{f}}\,/\,(i\,m)$ or back to the solvent's own freezing point $T_{\mathrm{solvent}} = T_{\mathrm{solution}} + \Delta T_{\mathrm{f}}$, which is how you calibrate an unknown solvent from two measurements.

The constants belong to the solvent

Each built-in solvent carries its tabulated constant and melting point. The values follow the usual handbook figures; for a cross-check, the NIST Chemistry WebBook page for acetic acid lists its melting point as 289.6 K — about 16.5 °C, matching the 16.6 °C this calculator uses for that entry:

Two kinds of temperature share the form

The two freezing-point boxes hold levels — 0 °C for water, −114.6 °C for ethanol — and each carries its scale's offset, so kelvin, Celsius and Fahrenheit all agree on the same physical temperature. The constant, though, is a difference per molal: it counts degrees of drop, where an offset makes no sense. That is why benzene's constant reads 5.12 on the Celsius and kelvin scales but 9.216 on the Fahrenheit scale ($5.12 \times \tfrac{9}{5}$), while its melting point stays 5.5 °C however you display it. The same distinction explains the opposite effect on the boiling side, which the boiling point elevation calculator handles; both are colligative effects rooted in the solvent's vapour pressure, which you can explore further with the Raoult's law calculator.

Three situations that use different parts of the calculator. Every result below is the value the calculator itself produces for those inputs.

Road salt: why one mole of salt behaves like almost two

Sodium chloride splits into a sodium ion and a chloride ion, so each formula unit contributes roughly two particles — in practice the measured van't Hoff factor lands near 1.9, slightly under the ideal 2 because some ion pairs re-associate. A 1 molal brine with $i = 1.9$:

Nearly double the drop of a 1 molal sugar solution, for the same moles of solute — that doubling is the whole reason salt works on roads, and the same effect at larger scale is what makes calcium chloride (three ions, $i \approx 3$) even more aggressive per mole.

Designing backwards: how much solute for a −10 °C target?

A technician wants a water-based solution that stays liquid down to −10 °C. Leave the van't Hoff factor at 1, keep water as the solvent, and type −10 into the solution freezing point instead of a concentration:

To order that by mass, multiply by the solute's molar mass — for ethylene glycol, 62.07 g/mol:

Same concentration, different solvent

A 1 molal solution in water freezes at −1.86 °C. Switch the solvent to benzene — same molality, same van't Hoff factor — and the answer moves to the other side of zero:

Benzene freezes at 5.5 °C on its own, and its constant of 5.12 is nearly three times water's, so a molal of solute eats almost the entire gap. The particle count is identical in both cases — only the solvent changed. That is the practical lesson: when you compare two solutions, check which solvent's constant is doing the scaling.