I have a 2001 f4i and I need to know what size socket you need to loosen the back wheel nut so i can adjust the chain.

 

Is it not in your tool kit?

I just looked up the wrenches in your tool kit. You have a 22mm and a 27mm. I'm guessing it's the 27mm. If you have the tool kit, compare it then go buy the size you need. The one in the kit is ok for an emergency, but I like having the real tools around so I can make sure I have the right torque when I'm working on my bike at home.