2006 Kawasaki ZX6R loss of traction question!?

I recently bought a 2006 Kawasaki zx6r. When I open the throttle in second gear about ten to thirteen thousand RPMs my back wheel loses traction and tends to skip. Its hard to explains, but the back wheel just loses traction off the ground and skips. When i change gears to third, it runs fine. I am not sure if its the tires or not. The tires were worned out when i bought the bike, even when i replaced the front and back tires i still have the problem. Does anyone know what the proplem is?