Solutions

Colligative properties depend only on the number of solute particles, not their identity. Four properties:

1. Relative lowering of vapour pressure (Raoult's law).
Δp / p° = x_solute (mole fraction of solute).

For a non-volatile solute: p_solution = x_solvent × p°_solvent.

2. Boiling point elevation.
ΔT_b = K_b × m, where K_b is the ebullioscopic constant (water: 0.512 K·kg/mol) and m is molality.

3. Freezing point depression.
ΔT_f = K_f × m, where K_f is the cryoscopic constant (water: 1.86 K·kg/mol).

4. Osmotic pressure.
π = MRT (where M is molarity, R is gas constant, T is in Kelvin).

Van't Hoff factor (i) corrects for solutes that dissociate or associate:

i = (observed colligative effect) / (expected for non-electrolyte)

Examples:

• Sugar (non-electrolyte): i = 1
• NaCl (full dissociation): i = 2 (Na⁺ + Cl⁻)
• BaCl₂ (full dissociation): i = 3
• Acetic acid (partial dissociation, ionizes ~1% in water): i ≈ 1
• Benzoic acid in benzene (dimerizes): i ≈ 0.5

For dissociation: i = 1 + α(n − 1), where α = degree of dissociation, n = number of ions.
For association: i = 1 − α(1 − 1/n), where n = molecules associating.

Modified colligative formulas with i:

• ΔT_b = i K_b m
• ΔT_f = i K_f m
• π = i MRT

Worked example. Find ΔT_f when 11.7 g NaCl is dissolved in 200 g water. (K_f = 1.86, assume i = 2)

Moles NaCl = 11.7 / 58.5 = 0.2. Molality = 0.2 / 0.2 kg = 1 m.
ΔT_f = 2 × 1.86 × 1 = 3.72 K.

Freezing point drops from 0°C to −3.72°C — this is why salt is spread on icy roads.

Worked example: osmotic pressure for blood IV solutions. 0.9% saline (NaCl) at 310 K (body temp):
M = 9 g/L ÷ 58.5 = 0.154 M. With i = 2: π = 2 × 0.154 × 0.0821 × 310 = 7.84 atm. This matches blood osmotic pressure — that's why 0.9% is "isotonic".