wheel spacing
 

I just replaced my rear wheel with a new one and now that I've already thrown the old one away(trust me it was trashed)I notice that it sits closer to one chainstay than the other.Is that normal?

No.
Either the wheel isn't installed properly, the wheel isn't dished properly, or your frame is bent.

Or all 3

+1 Bent frame.

^ No, not normal, unless you have a weird frame design that I've never heard of.

First make sure the hub axle is fully and symmetrically seated in the dropouts (particularly important if you have horizontal dropouts.) Still off-centre? Next, install the wheel backwards from normal -- ignore the chain -- and observe whether it is now a) closer to the same chainstay or b) closer to the opposite one. If a), the frame is bent. If b), the rim is not centred over the hub axle. Because of the width of the gear cluster on the right side, most rear wheels have to be asymmetric: the rim has to be off-centre relative to the flanges and spokes in order to be centred between the axle ends (and the chainstays)

If you know how to true a wheel, then you can re-centre the rim; otherwise take it back to the seller (with the bike so you can show him) for diagnosis and correction.

If this is a "boutique" wheel that is not made of standard user-serviceable hub, rim, and spokes, I am stumped. Post a pic?

Thanks a million guy! Ijust ran through it with a spoke wrench and corrected the dishing.It's almost perfect now.