Astudent was given a pale blue transparent liquid in a beaker. the student gently heated the solution until the liquid had vaporized. some blue crystals remained on the bottom of the beaker, why.

This is so as the liquid you are heating is copper (II) sulfate (I think so) so when you heat it to saturation, there will still be some water molecules left behind, which will allow copper (II) sulfate crystals to be formed since there is water of crystallisation. so the formula is (CuSO4.5H2O).

Hence, if you heat it for a longer period of time when all the water has evaporated, you will obtain a white powder (CuSO4) as crystals cannot form without water of crystallisation