What would happen to the volume and pressure of the gas if it reached absolute zero?

Firstly you can't reach absolute zero in equilibrium, you can get very close though.

 

If we just consider an ideal gas:

 

PV=nRT

 

Where:

P = pressure

V = volume

n = number of moles (I think)

R = Gas constant

T = pressure

 

Most gases will suffer a phase transition to something else at very low temperatures.

 

Although this isn't really correct as if you look at this as T->0 the PV->0 so if you hold pressure constant then V->0 this cannot happen due to statistical physics, I'm a bit tired right now so can't really explain this...

 

http://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_statistics

 

Would be a worthwhile read...

The equations for the gas law are macroscopic equations, which are based on statistics. At temperatures near 0 K these approximations do not apply anymore, the equations only are good approximations of reality over a certain interval of temperatures.