What hose is this ?

[velvettspiderz]

I can't seem to find out the name of this very small hose to replace it. The engine runs very poorly as it is torn.

2009 Cobalt

 

[YelloEye]

That's your PCV hose, it creates a negative pressure in the crank case of the car by pulling through the intake. Any hose rated for negative pressure will work.