Filtration is a technique used to separate a mixture of insoluble solids and liquid. It expoloits the size difference between the two by passing the mixture over a surface with lots of tiny holes. The smaller liquid molecules can pass through but the larger solid particles cannot, separating them.
Crystallisation is the formation of crystals from a saturated solution, it allows the separation of a dissolved solid from its liquid. The solution is slowly heated until all the liquid evaporates, left behind is the solid, precipitated as highly organised crystals.
Distillation is a technique which separates a mixture of liquids by their boiling point. As the mixture is heated, the liquid with the lowest boiling point will evaporate and travel up the glassware. When it reach the cold environment of the distillation column, the gas will condense and be collected as pure liquid. This is repeated until all the liquids are separated.
Liquid chromatography is a technique which separates liquids and solutions by their affinity to two distinct phases, the mobile phase and stationary phase. The stationary phase is usually a solid which remains unmoved throughout the experiment. The mobile phase is usually a liquid or a gas that moves over and through the stationary phase, carrying different compounds with it. The extent a compound travels depends on its affinity for the mobile phase, a high affinity substance will move further.
There are lots of separation techniques and it's important to know which work best to separate certain mixtures. Filtration works for insolible solid/liquid mixtures. Crystallisation is best for separating dissolved solids from a liquid. Distillation separates a mixture of liquids, with preferably low and distinct boiling points. Chromatography can be used to separate a mixture of gases, liquids or solutions.
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