Colligative Properties
High-Yield Summary
- Colligative properties depend on the NUMBER of dissolved solute particles, not their identity: vapor pressure lowering, boiling point elevation, freezing point depression, osmotic pressure.
- Van't Hoff factor (i) = particles produced per formula unit: i=1 nonelectrolytes (glucose), i=2 for 1:1 electrolytes (NaCl), i=3 for 1:2 electrolytes (CaCl₂).
- Raoult's Law: P₁ = χ₁P°₁ — solution vapor pressure proportional to solvent mole fraction.
- Boiling point elevation: ΔTb = iKbm. Freezing point depression: ΔTf = iKfm (Kf here unrelated to formation constant Kf).
- Osmotic pressure: Π = iMRT — pressure needed to stop net solvent flow across a semipermeable membrane.
Key Terms
- Colligative property
- A solution property depending on the number of solute particles, not their chemical identity.
- Van't Hoff factor (i)
- Number of particles one formula unit of solute produces in solution.
- Ebullioscopic constant (Kb)
- Solvent-specific constant relating molality to boiling point elevation; for water, 0.512 °C·kg/mol.
- Cryoscopic constant (Kf)
- Solvent-specific constant relating molality to freezing point depression; for water, 1.86 °C·kg/mol.
- Osmotic pressure (Π)
- Pressure required to stop net solvent flow across a semipermeable membrane from lower to higher solute concentration.
Raoult's Law
P₁ = χ₁P°₁
- P₁ = vapor pressure of the solution
- χ₁ = mole fraction of the solvent
- P°₁ = vapor pressure of the pure solvent
- Worked example: pure water P°=23.8 mmHg at 25°C, 1 mol glucose in 9 mol water → χ(water)=0.9 → P₁=21.4 mmHg.
Boiling Point Elevation
ΔTb = iKbm
- i = van't Hoff factor
- Kb = ebullioscopic constant (water: 0.512 °C·kg/mol)
- m = molality
- Worked example: 1.0 m NaCl (i=2) → ΔTb=2×0.512×1.0=1.024°C → new BP=101.0°C.
Freezing Point Depression
ΔTf = iKfm
- Kf = cryoscopic constant (water: 1.86 °C·kg/mol) — different quantity from the Kf formation constant
- Worked example: 0.50 m CaCl₂ (i=3) → ΔTf=3×1.86×0.50=2.79°C → new FP=−2.79°C.
Osmotic Pressure
Π = iMRT
- M = molarity
- R = 0.0821 L·atm/(mol·K)
- T = absolute temperature (K)
- Worked example: 0.15 M NaCl (i=2) at 310 K → Π=2×0.15×0.0821×310≈7.6 atm — close to human blood plasma's actual osmotic pressure.
Must-Know Points
- Solute particles disrupt solvent-solvent interactions the same way across all four properties — occupying surface area, interfering with ordered solid formation, or creating a concentration imbalance.
- Vapor pressure lowering is the underlying cause of BOTH boiling point elevation and freezing point depression.
- All 3 formulas with i apply only to NON-VOLATILE solutes — a volatile solute would contribute its own vapor pressure, breaking Raoult's law assumption.
Common MCAT Trap
- Forgetting the van't Hoff factor for electrolytes is the #1 colligative-properties mistake — NaCl needs i=2, not i=1, in ΔTb/ΔTf/Π formulas.
- CaCl₂ is a 1:2 electrolyte → i=3 (one Ca²⁺ + two Cl⁻), NOT i=2. Count total ions per formula unit, not just cation+anion pairs.
- The freezing-point-depression Kf and the complex-ion formation constant Kf share a symbol by pure convention — they have zero chemical relationship. Context (colligative properties vs. equilibrium) tells you which is meant.
Quick Recall
What is the van't Hoff factor for CaCl₂?
Why doesn't the identity of the solute matter for colligative properties?
What pressure stops net solvent flow across a semipermeable membrane?