Solutions are homogeneous mixtures in which one component (the solvent) is present in excess and another (the solute) is dissolved in it. The physical behaviour of solutions underlies a rich set of measurable phenomena known as colligative properties — properties that depend solely on the number of dissolved particles per unit of solvent, not on their chemical identity or molecular size.

Henry's Law governs the solubility of gases in liquids. It states that the partial pressure of a gas above a solution (p) is proportional to its mole fraction in the solution (x): p = K_H × x. The Henry's law constant K_H is characteristic of each gas-solvent pair at a given temperature. A critical feature is that K_H increases with temperature, meaning gas solubility decreases as the liquid is warmed. This explains why carbonated beverages effervesce when warmed or when the bottle is opened (pressure drops, solubility falls, $CO_{2}$ escapes). It also explains decompression sickness ("the bends") in deep-sea divers: dissolved $N_{2}$, highly soluble under the elevated pressures at depth, forms dangerous bubbles when a diver ascends too rapidly and pressure drops.

Raoult's Law describes the vapour pressure behaviour of liquid solutions. For a volatile binary mixture, the partial vapour pressure of each component equals its mole fraction in the liquid multiplied by its pure component vapour pressure: P_A = x_A·P°_A, giving P_total = x_A·P°_A + x_B·P°_B. For a solution containing a non-volatile solute, vapour pressure is simply lowered: P = x_solvent·P°, yielding the relative lowering $\Delta P$/P° = x_solute. This is the first colligative property.

Ideal solutions obey Raoult's law perfectly at all compositions. They are characterised by $\Delta H$_mix = 0 and $\Delta V$_mix = 0, arising when A-B, A-A, and B-B intermolecular interactions are indistinguishable. Classic examples are benzene + toluene and n-hexane + n-heptane — structurally similar non-polar pairs.

Non-ideal solutions deviate from Raoult's law in two directions. Positive deviation (P_obs > P_Raoult) arises when A-B interactions are weaker than A-A and B-B — molecules escape the solution more easily than expected. The enthalpy of mixing is positive (endothermic) and volume increases ($\Delta V$_mix > 0). The resulting higher vapour pressure creates a maximum in the P-x diagram, corresponding to a minimum boiling azeotrope — a constant-composition mixture that distils at a lower temperature than either pure component. Ethanol + water (azeotrope at 95.6% ethanol, 78.1°C) is the definitive example.

Negative deviation (P_obs < P_Raoult) arises when A-B interactions are stronger than A-A and B-B — molecules are held more tightly and escape less readily. $\Delta H$_mix < 0 (exothermic) and $\Delta V$_mix < 0 (volume contraction). The P-x curve passes through a minimum, corresponding to a maximum boiling azeotrope. Chloroform + acetone is the canonical example (strong C–H···O=C hydrogen bond between $CHCl_{3}$ and acetone). HCl + water and $HNO_{3}$ + water also belong here.

The four colligative properties all depend on the number (not nature) of solute particles: (1) Relative lowering of vapour pressure: $\Delta P$/P° = x_solute. (2) Boiling point elevation: $\Delta Tb$ = Kb·m, where Kb is the ebullioscopic constant (water Kb = 0.52 K·kg/mol). (3) Freezing point depression: $\Delta Tf$ = Kf·m, where Kf is the cryoscopic constant (water Kf = 1.86 K·kg/mol). (4) Osmotic pressure: π = CRT, where C is molar concentration and R = 0.0821 L·atm/(mol·K). Note that Kf > Kb for water because the enthalpy of fusion is smaller than the enthalpy of vaporisation.

Molar mass determination exploits all four properties, most practically via cryoscopy ($\Delta Tf$) and osmometry. The formula $M_{2}$ = Kb × w_{2} × 1000 / ($\Delta Tb$ × w_{1}) rearranges directly from the molality definition. Osmotic pressure is most sensitive for macromolecules: even a 10^{-4} M protein gives π ≈ 0.0025 atm (measurable), while the corresponding $\Delta Tf$ ≈ 0.0002 K is far below the detection limit of any thermometer. Camphor (Kf = 40 K·kg/mol) is favoured for organic compounds by cryoscopy because of its very large constant.

The van't Hoff factor (i) is the ratio of observed colligative property to the theoretical value for a non-electrolyte: i = observed / theoretical. For electrolytes that dissociate, i > 1: the formula i = 1 + (n−1)α connects i to the degree of dissociation α and the number of ions n per formula unit (NaCl: n=2, i≈2; $CaCl_{2}$: n=3, i≈3; $AlCl_{3}$: n=4, i≈4). For solutes that associate (dimerize), i < 1: i = 1 − α/2 for dimerization (n=2). Acetic acid and benzoic acid in benzene dimerize through intermolecular –COOH hydrogen bonds, giving i ≈ 0.5. When association occurs, the apparent molar mass calculated from colligative data is larger than the true molar mass — because fewer particles produce a smaller colligative effect, causing the denominator in the $M_{2}$ formula to be smaller than expected.

Reverse osmosis applies external pressure greater than the osmotic pressure to force solvent from the solution side through a semipermeable membrane, used in desalination and home water purifiers. Biomedically, isotonic saline (0.9% NaCl, π ≈ 7.7 atm at 37°C) is used intravenously to avoid haemolysis (hypotonic) or crenation (hypertonic) of red blood cells.