Tank

I was checking my car out today while getting gas and i noticed that one of my hoses connected to my airram was ripped where it connected. Its the closet one to the throttle body by the 3 on the bottom of the image. I taped it up, but was wondering what it went to? I saw where it lead but i don't know what it's for. It doesn't seem to be causing any huge problems but i haven noticed some weird idle issues, so i thought this may be the cause.