Boiling Point Elevation and Freezing Point Depression

Dissolving anything in water raises its boiling point and lowers its freezing point. The size of the shift depends only on how many particles are dissolved, not on what they are. This finds where the boiling and freezing points of water move to.

Dissolve anything in water and its boiling point rises above 100 °C while its freezing point falls below 0 °C. The striking part is that the size of the shift hardly depends on what was dissolved. Only the number of dissolved particles matters. Properties that behave this way are called colligative.

\Delta T_b = K_b \, m \, i \qquad \Delta T_f = K_f \, m \, i

$\Delta T_b$ and $\Delta T_f$ are the elevation and the depression
$K_b$ and $K_f$ are water's constants, 0.515 and 1.853
$m$ is the molality, the amount of solute per kilogram of solvent
$i$ is the number of particles each formula unit breaks into

Molality divides by the mass of the solvent, not of the solution. That denominator differs from the familiar molar concentration.

For $i$ , common salt splits into a sodium ion and a chloride ion and counts as 2, calcium chloride counts as 3, and something like sugar that does not split counts as 1.

Example

The default input dissolves 5.85 g of salt in 1000 g of water.

The molality is $5.85 \div 58.44 \div 1$ , about 0.1001 mol/kg. Salt splits in two, so the effective particle count is twice that.

The boiling point rises by about 0.1031 °C and the freezing point falls by about 0.3710 °C, putting them at 100.103 °C and −0.371 °C.

The freezing point moves more

Water's $K_f$ is about 3.6 times its $K_b$ . At the same concentration the freezing point shifts considerably further, which makes it the more precise thing to measure. That difference is why freezing point depression became a classical method for determining molecular mass.

Road salt and antifreeze work on the same principle. Calcium chloride is favoured for de-icing because each formula unit breaks into three particles and so does more work.

Points to watch

Salting pasta water does not meaningfully raise its boiling point. Ten grams in a litre, one percent, lifts it by only about 0.18 °C. The salt is there for flavour and for the surface of the pasta.

This calculator fixes the solvent as water. Other solvents have their own $K_b$ and $K_f$ .

Concentrated solutions depart from the formula. Ions attract one another and stop separating completely, so the effective $i$ falls somewhat below 2. Treat this as an approximation for dilute solutions.