What Are Colligative Properties?
Colligative properties are physical properties of solutions that depend on the number of solute particles dissolved, not on the chemical identity of the solute. This counterintuitive fact means that dissolving one mole of glucose (a molecular solid) and one mole of NaCl (which dissociates into two ions) produce very different effects — even though both are "one mole of solute."
The four colligative properties are: vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure. All arise from the thermodynamic effect of solute particles on the solvent's chemical potential.
Vapor Pressure Lowering
When a nonvolatile solute is dissolved in a solvent, the vapor pressure of the solution is lower than that of the pure solvent. Solute particles occupy the surface, reducing the rate at which solvent molecules escape into the vapor phase.
Raoult's Law quantifies this:
P_solution = χ_solvent × P°_solvent
Where χ_solvent is the mole fraction of the solvent and P°_solvent is the vapor pressure of the pure solvent. The vapor pressure lowering is:
ΔP = P°_solvent − P_solution = χ_solute × P°_solvent
Example: A solution containing 0.1 mol glucose in 0.9 mol water has χ_water = 0.9, so the vapor pressure is 90% of that of pure water.
Boiling Point Elevation
Because the vapor pressure of a solution is lower than that of pure solvent, the solution must be heated to a higher temperature to reach an atmospheric pressure of 1 atm and boil. The boiling point elevation is:
ΔT_b = K_b × m × i
Where: - K_b = ebullioscopic (boiling point elevation) constant of the solvent (K·kg/mol) - m = molality of the solution (mol solute per kg solvent) - i = van 't Hoff factor (number of particles per formula unit in solution)
For water: K_b = 0.512 °C·kg/mol.
The van 't Hoff factor (i) accounts for dissociation: - Glucose (molecular): i = 1 - NaCl → Na⁺ + Cl⁻: i ≈ 2 - CaCl₂ → Ca²⁺ + 2Cl⁻: i ≈ 3 (ideal)
Example: 1.0 molal NaCl solution: ΔT_b = 0.512 × 1.0 × 2 ≈ 1.02°C. The solution boils at ~101°C.
Freezing Point Depression
Dissolving a solute also lowers the freezing point of the solution — it must be cooled to a lower temperature before the solvent begins to crystallize. The formula is:
ΔT_f = K_f × m × i
Where K_f is the cryoscopic constant.
For water: K_f = 1.86 °C·kg/mol (notably larger than K_b, making freezing point depression easier to measure precisely).
ΔT_f is defined as a positive quantity: the new freezing point = T_f(pure) − ΔT_f.
Example: 1.0 molal NaCl solution: ΔT_f = 1.86 × 1.0 × 2 ≈ 3.72°C. The solution freezes at approximately −3.72°C.
Why Does Salt Melt Ice?
Road salt (NaCl or CaCl₂) sprinkled on ice lowers the freezing point of the water film on the ice surface. The brine formed has a freezing point below ambient temperature, so ice melts instead of forming. CaCl₂ (i ≈ 3) is more effective per mole than NaCl (i ≈ 2) but also more expensive.
Osmotic Pressure
Osmosis is the net flow of solvent through a semipermeable membrane from a region of lower solute concentration (higher solvent concentration) to higher solute concentration (lower solvent concentration). The membrane allows solvent molecules to pass but blocks solute particles.
The osmotic pressure (Π) required to halt osmotic flow is given by the van 't Hoff equation:
Π = iMRT
Where M is molarity, R is the gas constant (0.08206 L·atm/mol·K), and T is temperature in Kelvin.
Even dilute solutions can generate surprisingly large osmotic pressures. A 1 M NaCl solution at 25°C: Π = 2 × 1 × 0.08206 × 298 ≈ 48.9 atm — powerful enough to support a column of water ~500 meters tall.
Reverse Osmosis
Applying external pressure greater than the osmotic pressure forces solvent to flow from the concentrated to the dilute side — against the natural direction. This is reverse osmosis (RO), the principle behind modern desalination plants and water purification systems.
Biological Significance of Osmosis
Osmosis is fundamental to biology: - Cell membranes are semipermeable; cells placed in hypotonic solution (lower solute concentration) swell as water flows in; in hypertonic solution, cells shrink (crenation) - Blood plasma must be maintained at approximately 0.9% NaCl (isotonic saline) for safe IV administration - Marine fish actively regulate internal salt concentration against the osmotic gradient of seawater - Plant turgor pressure — the rigidity of plant cells — arises from osmotic water uptake into vacuoles
Determining Molar Mass
Freezing point depression and osmotic pressure are used to determine the molar mass of unknown solutes, particularly macromolecules (polymers, proteins) that require osmotic pressure due to its greater sensitivity at low concentrations.
Example: 10 g of a polymer dissolved in 1 kg water lowers the freezing point by 0.0186°C. Molar mass = K_f × m_solute / ΔT_f = 1.86 × 10 / 0.0186 = 1,000 g/mol.
Summary
Colligative properties are a direct manifestation of the thermodynamics of mixing. They depend only on particle count, not identity — making them powerful tools for measuring molar masses, explaining de-icing, designing semipermeable membranes, and understanding biological fluid balance. The van 't Hoff factor bridges the idealized equations with the reality of electrolyte dissociation.