I had this part come loose off of the underside of my car. It hooks into a tube and leads into one of the catalytic converters I believe. It has since been removed and now need a new one, I just need help figuring out what it is so I can buy it.

 

you should have an exuast as well .... the fatter end is the air pump check valve

 

this pipe allows the air control valve to divert fresh air to the main converter to clean up the emissions and to assist in cooling the internal element. this pipe should be used if you are running a main converter.

 

So what will my car be doing without this pipe? And my main concern is it passing PA inspection

 

without the pipe, the main converter can possibly overheat. there is an extremely minimal chance of this though. i would reccomend replaing the pipe if you have to pass an emissions test as the air from the air control valve is diverted down this pipe to the main cat for helping to clean up the emissions with fresh air generated by the air pump.