Wakefulness is a condition of being alert, rather than sleepy. Last night's wakefulness might catch up with you later and make it hard to keep your eyes open during chemistry class.
A new baby's wakefulness, keeping them wide awake all night, usually results in exhausted parents. You can also use this noun for a kind of vigilance or alertness, sort of a figurative way of being awake: "The teacher's wakefulness meant that she noticed immediately if a student was falling behind or being bullied." The original meaning of wakeful, in fact, was "diligent," from an Old English root meaning "night watch."