fractional crystallization

Meaning: The mixture is dissolved in a hot solvent and cooled slowly. The solution becomes saturated with the least soluble component first, so that component forms crystals. Slow growth of an ordered lattice tends to leave other molecules in solution. The crystals are filtered off. The leftover solution (mother liquor) can be concentrated or cooled again to give later crops, and each crop can be recrystallized to raise its purity.

On the MCAT: A passage may give a solubility versus temperature graph for two solids and ask which one crystallizes first on cooling, or why slow cooling gives purer crystals. The technique is also the classic way to resolve a racemic mixture. The racemate is reacted with a single enantiomer of a chiral acid or base, which forms a pair of diastereomeric salts. These have different solubilities, so one crystallizes first. The pure enantiomer is then regenerated from the crystals. Questions may ask you to choose between crystallization (solubility), distillation (boiling point), extraction (partitioning between immiscible solvents) and chromatography (differential adsorption or polarity).

Common confusion: Enantiomers have identical solubilities and melting points in an achiral solvent, so crystallization alone does not separate them. Diastereomers have different physical properties, and that difference is what makes the resolution work. Also, rapid cooling traps impurities in the crystals and lowers purity.