Final answer:
Big crystals form when a hot saturated solution is cooled slowly because the decreased molecular movement and stability allow for orderly alignment and growth into larger crystal structures, relying on the temperature dependence of solubility.
Step-by-step explanation:
The reason big crystals form when a hot saturated solution is cooled slowly is due to the molecular alignment and crystal growth processes. Detailed in the information provided, as a solution cools, the solute's solubility decreases and excess from a supersaturated state begins to crystallize out of the solution. During slow cooling, there is sufficient time for molecules to align properly and grow into a well-ordered and larger crystal structure. In the context of a saturated solution, this means that upon cooling, the dissolved compound starts to come out of the solution as a crystalline solid (a process called recrystallization).
On the other hand, rapid cooling can lead to rapid supersaturation and a rush to form solid crystals without the time needed for the molecules to align properly. This often results in the formation of smaller, less ordered crystals. Using the information on the temperature dependence of solubility, slow cooling allows a gradual shift from a supersaturated to a saturated state, promoting crystal growth in a controlled manner.