Freezing Point Depression Calculator

The solvent counts particles and cannot tell what they are — which is why calcium chloride beats table salt on ice.

Freezing point depression3.72 °C2 × 1.86 × 1 — Water now freezes at -3.72 °C

Boiling point elevation1.024 °Cboiling now at 101.024 °C. NOTE how much smaller this is than the freezing effect — Kb is a fifth of Kf for water

THE SOLVENT COUNTS PARTICLESit cannot tell what they area mole of sugar gives one particle and a mole of NaCl gives two, so the salt has twice the effect at the same molality. That is the whole phenomenon

With a non-electrolyte instead1.86 °Ci = 1 for sugar or urea. Your factor of 2 multiplies that

Constants for WaterKf 1.86, Kb 0.512 °C·kg/molfreezing point 0 °C, boiling point 100 °C

Osmotic pressure4.8931 atm (495.8 kPa)iMRT at 25 °C. Osmotic pressure is ENORMOUS compared with the temperature effects — a tenth-molar solution pushes several atmospheres

Why camphor was used for molar massesKf of 39.7, twenty times watera large constant gives a large, easily measured depression from a small sample. That is what made the Rast method practical before spectrometry

Molality, not molaritybecause these are temperature experimentsthe solution volume changes as you cool it and the solvent mass does not. Using molarity here would introduce an error that grows as the measurement proceeds

The formula

ΔTf = i·Kf·m; ΔTb = i·Kb·m; Π = iMRT

The solvent is counting

Freezing point depression, boiling point elevation and osmotic pressure all depend on how many dissolved particles there are and not at all on what they are.

A mole of sodium chloride splits into two moles of ions and has twice the effect of a mole of sugar. Calcium chloride gives three and has three times the effect, which is why it outperforms table salt on icy roads.

Freezing is a much bigger lever than boiling

Water's cryoscopic constant is 1.86 and its ebullioscopic constant is 0.512.

So the same solution depresses the freezing point nearly four times as far as it raises the boiling point. Adding salt to pasta water raises the boiling point by a fraction of a degree and does nothing useful to the cooking time.

Osmotic pressure is the violent one

A tenth-molar salt solution depresses freezing by about a third of a degree and generates nearly five atmospheres of osmotic pressure.

The same particle count produces a barely measurable temperature change and a pressure that will burst a cell. This is why osmosis dominates biology and the temperature effects do not.

Camphor and the Rast method

A cryoscopic constant of 39.7 means a milligram of unknown produces a depression you can read on an ordinary thermometer.

Before mass spectrometry that was how molar masses of small organic samples were determined, and camphor was chosen precisely for the size of its constant.

Ideal behaviour is an approximation

The colligative and gas relations here assume dilute solutions and ideal gases, which real systems approach and do not reach.

At high concentration or high pressure the deviations become large, and the corrections are substance-specific. These figures are right where the assumptions hold and approximate where they do not.