hello my friends, i didnt post any instructable latly because i am in school and end is near.... but now i am working on few projects, and for one of them i need capacitor 1f 5.5 v.
so my question is how long can this capacitor power the single white LED?

Depends on the materials the cap uses but in general not for very long. Capacitors are not very good at letting out power at a slow rate. If it is a super capacitor it may give you a few seconds to a minute.