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Evaporation removes the solvent to get a solid solute — preferred when the solute is stable on heating and you do not need the solvent back (e.g. getting salt from salt water).
Crystallization forms pure crystals by cooling a saturated solution — preferred when you need a pure solid and want to leave impurities behind (e.g. purifying copper sulfate).
Distillation boils and condenses — preferred when you want to recover the solvent, or separate two miscible liquids with different boiling points (e.g. acetone and water).
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