Hey guys last night on a phone that was charged through USB the entire day at work my battery had died over night. I used the phone for about 40 mins talk time total after the charge and had Google chat running as a 3rd party application. That is not the first time I had it running it night but since Sunday my battery dies quick. Should I exchange the phone or am I missing something?

Are you sure that Google Chat was the only running 3rd party app? If anything I would see if you could switch out the battery, not the whole device, to test it first.

It looked like the only app that was using an internet connection...When I went to switch application there were a bunch of apps open i.e. address book, calendar, but nothing that seemed to be running in the background. does that make a difference that those apps are open?

You will always have open and running, by the default of the BB OS needing these apps to be running.
-Homescreen
-Phone
-Address Book
-Browser (make sure NOT on an active webpage, only the bookmark page),
-BlackBerry Messenger.

You could have other apps which can't be closed unless you force an exit or delete them, such as:
-BBAlerts
-BeamBerry

And a third category of apps may be running which you should close unless you actively need them running
-JiveTalk
-BBWeather
-GoogeTalk
-various games that eat resources
-Media Player
-Camera
-Opera Mini
etc