why does rapid cooling of a saturated solution produce small crystals , but slow cooling produce large crystals?
A solute when dissoved in a solvent produces a solution. For example, grain sugar dissolves in water at room temperature to produce a sugar solution. The maximum amount of sugar that dissolves in water at room temperature produces what is known as a saturated sugar solution. Beyond this stage, if the solution is warmed it will dissolve more sugar to produce what is known as a supersaturated sugar solution.
When a supersaturated sugar solution is cooled, it cannot hold the excess sugar. This is thrown out of the solution in the form of crystals i.e. recrystallization takes place. This is principle for manufacture of sugar crystals from sugar cane or sugar beet juice.
The size of sugar crystals depends on the number of nuclei present (i.e. graining stage). The lesser the number of nuclei and the longer the cooling time will lead to production of larger sugar crystals.