Colligative Properties
Van 't Hoff factor, freezing/boiling shifts, Raoult's law, osmotic pressure, and molar-mass back-calculation.
Van 't Hoff factor i
REFERENCE| Solute | i (predicted) |
|---|---|
| nonelectrolyte (glucose, urea) | 1 |
| NaCl, HCl, KBr | 2 |
| CaCl₂, Na₂SO₄ | 3 |
| AlCl₃, Na₃PO₄ | 4 |
| Al₂(SO₄)₃ | 5 |
i = particles per formula unit on full dissociation. Use the predicted (integer) i for forward calculations; measured i runs a bit lower at real concentrations (ion pairing).
Strong-electrolyte dissociation
CORE RULEEach ion's concentration = compound concentration × its coefficient. Total dissolved particles = i × compound concentration. CaCl₂ → Ca²⁺ + 2Cl⁻ gives total = 3 × [CaCl₂].
Freezing-point depression
CORE RULEΔTf = Kf·m·i (m = molality). New FP = pure FP − ΔTf. For water (FP 0 °C) the depressed FP = −ΔTf. Kf is solvent-specific (supplied).
Boiling-point elevation
CORE RULEΔTb = Kb·m·i. New BP = pure BP + ΔTb. For water (BP 100 °C) the elevated BP = 100 + ΔTb. Kb is solvent-specific (supplied).
Common constants (°C·kg/mol)
REFERENCE| Solvent | Kf | Kb |
|---|---|---|
| water | 1.86 | 0.512 |
| benzene | 5.12 | 2.53 |
| chloroform | 4.68 | 3.63 |
| camphor | 37.7 | n/a |
Raoult's law (vapor pressure)
CORE RULENonvolatile solute: ΔP = X_solute·P°_solvent, or P_solution = X_solvent·P°_solvent. Use particle-based mole fraction (i × n_solute) for electrolytes. Two volatile components: P_total = X_A·P°_A + X_B·P°_B.
Osmotic pressure
CORE RULEπ = i·M·R·T with MOLARITY (not molality), R = 0.0821 L·atm/(mol·K), T in K; π in atm. Given in molality/mass? You need density to convert to molarity.
Kelvin vs °C
WATCH OUTOsmotic pressure needs T in Kelvin. But ΔTf and ΔTb are the same magnitude in °C or K, so apply K constants directly. Report final FP/BP in °C.
Molar mass from ΔT
METHODn_solute = ΔT / (K·kg_solvent·i), K = Kf or Kb, i = 1 for a nonelectrolyte (the usual MW case). Then MW = mass_solute / n_solute.
Molar mass from osmotic pressure
METHODn_solute = π·V / (R·T·i), i = 1 for biomolecules (lysozyme, hemoglobin). Then MW = mass_solute / n_solute. π is often tiny, so convert torr/mmHg to atm first.
Molecular formula protocol
METHODBack-calc MW from ΔT or π; get the empirical formula from % composition; n = MW / empirical-formula mass (round to an integer); molecular formula = empirical × n. Single-element (Sₙ): n = MW / atomic mass.