Colligative Properties Formulas
Colligative properties depend on solute concentration, not identity.
Learn boiling point elevation and freezing point depression formulas.
The Formulas
ΔT_f = i × K_f × m
Colligative properties are properties of solutions that depend only on the number of dissolved particles, not on what those particles are. The four main colligative properties are boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure.
Boiling point elevation means a solution boils at a higher temperature than the pure solvent. Freezing point depression means a solution freezes at a lower temperature than the pure solvent. This is why salt is spread on icy roads in winter — it lowers the freezing point of water.
The van't Hoff factor (i) accounts for how many particles a solute produces when dissolved. For non-electrolytes like sugar, i = 1. For NaCl, which dissociates into Na⁺ and Cl⁻, i = 2. For CaCl₂, i = 3.
Variables
| Symbol | Meaning |
|---|---|
| ΔT_b | Boiling point elevation (in °C) |
| ΔT_f | Freezing point depression (in °C) |
| i | van't Hoff factor (number of particles per formula unit) |
| K_b | Ebullioscopic constant of the solvent (°C/m). Water: 0.512 °C/m |
| K_f | Cryoscopic constant of the solvent (°C/m). Water: 1.86 °C/m |
| m | Molality of the solution (mol solute / kg solvent) |
Example 1
What is the boiling point of a solution containing 0.5 mol of NaCl dissolved in 1 kg of water? (K_b = 0.512 °C/m, i = 2)
Identify the values: i = 2, K_b = 0.512 °C/m, m = 0.5 mol/kg
ΔT_b = i × K_b × m = 2 × 0.512 × 0.5 = 0.512 °C
New boiling point = 100 + 0.512
Boiling point = 100.512 °C
Example 2
Ethylene glycol (antifreeze, i = 1) is added to 2 kg of water at a concentration of 3 mol/kg. What is the new freezing point? (K_f = 1.86 °C/m)
Identify the values: i = 1, K_f = 1.86 °C/m, m = 3 mol/kg
ΔT_f = i × K_f × m = 1 × 1.86 × 3 = 5.58 °C
New freezing point = 0 - 5.58
Freezing point = -5.58 °C
When to Use It
Colligative property formulas are used whenever you dissolve a substance in a solvent and need to predict how the solution behaves.
- Calculating antifreeze concentrations for car radiators
- Predicting freezing point depression for road de-icing
- Determining molar mass of unknown solutes experimentally
- Food science — controlling freezing and boiling in recipes