How to use it
- Choose whether to find the new boiling and freezing points or the molar mass of a solute.
- Pick the solvent, or Custom constants.
- Enter the van ’t Hoff factor i (1 for non-electrolytes such as sugar).
- Enter the solute as masses (solute mass, its molar mass, solvent mass) or as molality, or, for the molar mass, the masses and the measured ΔT.
Formulas
- ΔTb = i × Kb × m and ΔTf = i × Kf × m, m = mol of solute ÷ kg of solvent.
- New boiling point = Tb + ΔTb; new freezing point = Tf − ΔTf.
- Molar mass from a measurement: m = ΔT ÷ (i × K), moles = m × kg of solvent, M = grams of solute ÷ moles.
The solvent constants are typical textbook values in °C·kg/mol; tables differ slightly. Water: Kb 0.512, Kf 1.86, boils at 100 °C and freezes at 0 °C.
Worked example
58.44 g of NaCl (1 mol) in 1 kg of water, i = 2: m = 1 mol/kg, ΔTb = 2 × 0.512 × 1 = 1.024 °C, so the solution boils at 101.024 °C, and ΔTf = 2 × 1.86 × 1 = 3.72 °C, so it freezes at −3.72 °C.
An unknown non-electrolyte: 5 g dissolved in 100 g of water freezes 0.93 °C lower. m = 0.93 ÷ 1.86 = 0.5 mol/kg, moles = 0.5 × 0.1 = 0.05 mol, M = 5 ÷ 0.05 = 100 g/mol.
Tips
- Colligative properties depend on the number of particles, not on what they are.
- The formulas hold for dilute solutions. At high concentrations the measured change is smaller than calculated.
- Camphor has a large Kf, so small amounts of solute give a measurable change; it is used in the Rast method for molar mass.