Solutions and Colligative Properties
This section covers Solutions and Colligative Properties: Raoult's law, ideal and non-ideal solutions, azeotropes, relative lowering of vapour pressure, boiling-point elevation, freezing-point depression and osmotic pressure. Numerical questions often use colligative data to find molar mass.
Core rules
- Raoult's law: for a volatile component, p_A = x_A p_A°. Ideal solutions obey Raoult's law over the whole range; positive deviations weaken A–B interactions, negative deviations strengthen them.
- Colligative properties depend on the number of solute particles: Δp/p° = x_solute; ΔTb = iKb m; ΔTf = iKf m; π = iCRT.
- Van't Hoff factor i is greater than 1 for dissociation, less than 1 for association, and 1 for non-electrolytes.
Worked example
1.00 g of a non-electrolyte in 100 g water depresses the freezing point by 0.186 K. Kf for water = 1.86 K kg mol⁻¹. Molality = ΔTf/Kf = 0.186/1.86 = 0.100 mol kg⁻¹. Moles of solute in 0.100 kg water = 0.0100 mol. Molar mass = 1.00/0.0100 = 100 g mol⁻¹. Using molality avoids the temperature dependence of molarity.
Traps
Use molality in ΔTf and ΔTb, not molarity; include i for electrolytes; do not ignore association of solutes such as benzoic acid in benzene; remember that osmotic pressure uses molarity and must use kelvin temperature; volatile solutes change the treatment of Raoult's law.