Colligative properties are properties of solutions that depend only on the number of solute particles dissolved, not on what those particles are. Dissolving 1 mole of glucose in 1 kg of water has the same effect on freezing point as dissolving 1 mole of urea in 1 kg of water, even though the two solutes are completely different chemicals. This counterintuitive result follows from the fact that colligative properties arise from the solute particles disrupting the solvent's normal behavior.
Freezing Point Depression
When you dissolve a solute in a solvent, the freezing point of the solution is lower than that of the pure solvent. The relationship is delta Tf = i x Kf x m, where i is the van't Hoff factor (the number of particles the solute dissociates into), Kf is the cryoscopic constant (specific to each solvent), and m is the molality. This is why we salt roads in winter: the salt dissolves in the thin layer of water on the ice, lowering its freezing point and preventing it from refreezing. For water, Kf = 1.86 C kg/mol.
Boiling Point Elevation
Similarly, adding solute raises the boiling point: delta Tb = i x Kb x m, where Kb is the ebullioscopic constant (0.512 C kg/mol for water). This is why adding salt to cooking water raises its boiling point slightly, though the effect is small in the kitchen. The Freezing and Boiling Point Calculator computes both effects for water, benzene, and camphor.
Osmotic Pressure
Osmotic pressure is the pressure that must be applied to a solution to prevent the flow of solvent across a semipermeable membrane. It is given by the equation pi = iMRT, where M is molarity, R is the gas constant, and T is temperature in Kelvin. Osmotic pressure is biologically critical: it drives water transport across cell membranes, and imbalances can cause cells to shrink (crenation) or swell and burst (lysis). The Osmotic Pressure Calculator makes quick work of these calculations.
The Van't Hoff Factor
The van't Hoff factor (i) accounts for the number of particles a solute produces in solution. For non-electrolytes like glucose, i = 1. For NaCl, which dissociates into Na+ and Cl-, i = 2 (in dilute solutions). For CaCl2, i = 3. In reality, ion pairing in concentrated solutions can make i slightly less than the theoretical maximum, but for introductory chemistry, you can use the theoretical values. When comparing colligative properties, remember that a 1 m solution of NaCl (i = 2) has twice the effect of a 1 m solution of glucose (i = 1).