Colligative properties
Dissolving a solute in a solvent lowers its freezing point and raises its boiling point. These changes, called colligative properties, depend on the number of dissolved particles, not on what they are. That is why salt melts ice on roads, why antifreeze protects car engines and why seawater freezes at about −1.9 °C instead of 0 °C.
The formulas
- Freezing point depression: ΔTf = i × Kf × m
- Boiling point elevation: ΔTb = i × Kb × m
- Molality: m = moles of solute ÷ kg of solvent
Kf and Kb are constants of the solvent, in °C·kg/mol, and i is the van ’t Hoff factor, the number of particles each formula unit releases in solution.
Worked example
Dissolve 58.44 g of sodium chloride (1 mol) in 1 kg of water. NaCl splits into Na⁺ and Cl⁻, so i = 2.
- m = 1.00 mol ÷ 1.00 kg = 1.00 mol/kg.
- ΔTf = 2 × 1.86 × 1.00 = 3.72 °C: the water now freezes at −3.72 °C (25.3 °F).
- ΔTb = 2 × 0.512 × 1.00 = 1.024 °C: it boils at 101.02 °C.
Freezing point at other amounts of salt (1 kg of water)
| NaCl added | Freezing point | Boiling point |
|---|---|---|
| 10 g | −0.64 °C | 100.18 °C |
| 50 g | −3.18 °C | 100.88 °C |
| 100 g | −6.37 °C | 101.75 °C |
| 200 g | −12.73 °C | 103.50 °C |
At high concentrations, the real depression is somewhat smaller, because ions pair up and the ideal formula no longer holds exactly. A saturated brine bottoms out at about −21 °C.
Solvent constants
| Solvent | Freezing point | Kf | Boiling point | Kb |
|---|---|---|---|---|
| Water | 0 °C | 1.86 | 100 °C | 0.512 |
| Benzene | 5.5 °C | 5.12 | 80.1 °C | 2.53 |
| Cyclohexane | 6.5 °C | 20.0 | 80.7 °C | 2.79 |
| Ethanol | −114.1 °C | 1.99 | 78.4 °C | 1.22 |
| Acetic acid | 16.6 °C | 3.90 | 118.1 °C | 3.07 |
Measuring molar mass
Before mass spectrometry, chemists found molar masses by cryoscopy: dissolve a known mass in a solvent with a large Kf, such as cyclohexane or camphor, measure ΔTf, and solve for the number of moles.
Road salt and antifreeze
Rock salt works well down to about 15 °F (−9 °C) on roads; below that, calcium chloride (i = 3) is used. Car antifreeze uses ethylene glycol, a molecular solute (i = 1): a 50/50 mix with water protects to about −37 °C, more than the simple formula predicts for such a concentrated solution, which is outside its ideal range.