If you do something purposely, you mean to do it. It is not an accident. You purposely sat in the front. You purposely didn't answer the phone. This is the ordinary word for on purpose, just a little more dressed-up. Parents, teachers, and news writing all use it. It does not have to sound nasty: you can purposely leave a light on so someone finds their way. Though actually, this is the word students mix with purposefully their whole lives. Purposely = you chose to. Purposefully = you did it with a clear aim, in a sure, determined way. You walk purposefully into a room when you look like you have a job to do. You purposely walk into a room when going in was the plan, not a mistake. You cannot really swap them.