it is an ideal gas because the weird forces of attraction and repulsion (Such as hydrogen bonding, diploe-dipole stuff) have very little effect at this temperature, pressure and volume. This is true because the molecules in this gas have enough distance in b/w them at this P,V,T.
Density doesn't really directly have anything to do with this. rho = m/V = (n*MM)/V, the only variable here is V, so density is proportional to the volume, but it as i mentioned above it is the distance b/w the molules that matters, and this of course is related to the density, so that's how the density factors in.
Hope that helps