Boiling & Freezing Point Calculator (Colligative)

Road salt. 100 g of NaCl ÷ 58.44 g/mol = 1.711 mol, in 1 kg of water: m = 1.711 mol/kg. Each NaCl gives two ions, so ΔTf = 2 × 1.86 × 1.711 = 6.37 °C, and the brine freezes at about −6.37 °C. Gram for gram, calcium chloride does less by this ideal count: 100 g of CaCl₂ is 0.9011 mol, and 3 × 1.86 × 0.9011 = 5.03 °C. (Its real advantage on roads is that it dissolves with heat and keeps working at lower temperatures.)

Antifreeze. To protect water down to −10 °C with ethylene glycol (i = 1): m = 10 ÷ 1.86 = 5.376 mol/kg, so each kilogram of water needs 5.376 × 62.068 = 333.7 g of glycol, a 25.0 % mixture. At this strength real mixtures are far from ideal, so treat it as an estimate.

The common mistake: forgetting the van ’t Hoff factor. Using i = 1 for the road salt gives 1.86 × 1.711 = 3.18 °C, half the right answer of 6.37 °C, because each NaCl releases two particles and colligative properties count particles, not formula units. A close second is dividing by the mass of the solution (1.1 kg) instead of the solvent (1 kg) when working out the molality.

In 1788 Charles Blagden reported to the Royal Society that the freezing point of salt water falls in proportion to the amount of salt dissolved. A century later François-Marie Raoult measured freezing points of many organic substances in the 1880s and found that equal numbers of moles in the same solvent lowered the freezing point by the same amount, whatever the substance. He went on to state the vapour pressure law that carries his name (1887). Ernst Beckmann’s thermometer, which reads small temperature differences to 0.01 °C or better, turned freezing point measurements into a routine way of finding molar masses.

Jacobus van ’t Hoff showed in 1886 that dilute solutes behave like a gas: the osmotic pressure Wilhelm Pfeffer had measured with porous-pot membranes in 1877 obeys Π = cRT, the ideal gas law with concentration in place of n/V. Salts gave values that were too large, and van ’t Hoff simply multiplied by a correction factor, i. Svante Arrhenius explained it in 1887: salts split into ions in water, so NaCl really does supply about twice as many particles. Van ’t Hoff received the first Nobel Prize in Chemistry in 1901, and Arrhenius the third, in 1903.

The constants here are standard textbook values: water K_f 1.86 and K_b 0.512 °C·kg/mol, benzene K_f 5.12 and K_b 2.53 °C·kg/mol, with water freezing at 0 °C and boiling at 100 °C, benzene at 5.5 °C and 80.1 °C. Use Custom to enter values from a data book for other solvents.

This calculator covers the four colligative properties, the ones that depend only on how many particles are dissolved: freezing point depression, boiling point elevation, osmotic pressure and vapour pressure lowering. It also runs the freezing point law backwards, to find the molar mass of an unknown from a measured drop, or to find how much salt or glycol is needed to reach a target freezing point.

Type a formula and it fills in the molar mass and the ideal van ’t Hoff factor (2 for NaCl, 3 for CaCl₂, 1 for sugars), or type your own i. It warns when a solution is too concentrated for the ideal formulas, and when salt is asked to go below the −21.1 °C brine limit. Everything runs in your browser.

It is aimed at chemistry students, and at anyone curious about road salt, antifreeze, saline drips or why salted water barely boils hotter.

Related tools: Concentration Converter, Molarity Calculator, and Molar Mass Calculator.