colligative

Colligative properties are a group of physical properties of solutions that depend on the number of solute particles in a given amount of solvent, rather than on their chemical identity. This dependence becomes evident for dilute solutions of nonvolatile solutes and is independent of solute–solvent interactions in the ideal case. The term is used to describe several closely related phenomena.

The major colligative properties are boiling-point elevation, freezing-point depression, vapor-pressure lowering, and osmotic pressure. Boiling-point elevation means the solution boils at a higher temperature than the pure solvent; for dilute solutions, ΔTb = i Kb m, where i is the van't Hoff factor, Kb is the solvent's ebullioscopic constant, and m is molality. Freezing-point depression is the lowering of the freezing point, ΔTf = i Kf m, with Kf the cryoscopic constant. Vapor-pressure lowering follows Raoult's law: P_solution = X_solvent P° solvent, so the decrease in vapor pressure is approximately ΔP ≈ P° solvent X_solute for dilute solutions. Osmotic pressure is the pressure required to stop osmosis, given by π = i M R T for dilute solutions, with M the molarity.

The factor i reflects solute dissociation; non-electrolytes have i ≈ 1, while electrolytes may have i > 1 (or less than expected due to ion pairing). At higher concentrations, deviations from ideality occur due to solute–solute and solute–solvent interactions; activity coefficients provide a more accurate description.

Applications include antifreeze formulations, salt solutions for de-icing, and osmotic processes in biology and medicine. The concept originated from work on osmosis and the idea that properties are governed by particle number; the term colligative derives from Latin colligare, to assemble or bind together.