When and how does a solution become #"supersaturated"#?
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When it contains greater than an equilibrium quantity of solute. This is an important definition so get it right!
Most solutes have some degree of solubility in aqueous solution, which is the typical solvent. The solubility is typically a function of temperature in that a hot solution can solvate more solute than a cold one.
A #"saturated solution"# is described when there is an equilibrium between dissolved and undissolved solute. We can take such a saturated solution with EXCESS UNDISSOLVED SOLUTE, heat it up, and bring all the solute into solution. When we cool this solution down, sometimes we can get a cold solution WITHOUT any solute precipitating. Such a solution is #"supersaturated"# with respect to the solute because it contains greater than an equilibrium quantity of solute.
A #"supersaturated solution"# is a metastable phenomenon because we could add a seed crystal or scratch the side of the container to crystallize out the solute, and restore saturation, that is restore a solution whose concentration is the same that it would be if the solute were in equilibrium with undissolved solute.
These ideas are very poorly appreciated at A level, so it would be a good idea to test your understanding of the principle.