Do too many molecules make a gas non-ideal? Now, by this I don't mean the effect when pressure is too high such that the molecules are taking up a significant amount of space, however, I think it might be a different angle to approach the pressure problem from.
Pressure exerted by a gas on the wall of a container can only be through the elastic collision between the gas molecule and the wall. If there was just a low amount of particles it would make sense that $P \propto \frac{n}{V}$ because every single molecule would bounce against the wall exerting pressure.
But this doesn't feel like it should work if we had a lot of particles. For example, there may be one unlucky molecule that keeps bouncing against other molecules molecules but itself never gets to hit the wall. This would mean that this particle never exerts pressure on the wall. Thus the proportionality is no longer true.
My question is, is this a real effect and if so why doesn't it affect the equation? Is this just another reason why high pressure doesn't work for the ideal gas assumption?
 A: Indeed, the ideal gas must be sufficiently sparse that we can neglect the collision between the molecules, apart from the fact that these collisions lead to the establishment of thermal equilibrium. When the density of molecules is too high, we deal with a non-ideal gas or even a liquid. The first approximation for non-ideal gases is van der Waals equation
$$\left(P + a\frac{n^2}{V^2}\right)\left(V - nb\right) = nRT,$$
as an alternative to the ideal gas equation
$$PV = nRT.$$
Here $a$ and $b$ are phenomenological coefficients describing the intermolecular attraction and the finite volume occupied by the molecules. In particular, the pressure of this gas on the walls of a container would be different that that of an ideal gas (for the same $V,T$).
A: Why would there be a single "unlucky" molecule? How would that be singled out?
One of the assumptions behind an ideal gas (and statistical mechanics in general) is that there are many (many many) constituents that are essentialy equivalent. Hence, they all have the same probability of hitting a wall in a given time, i.e. a hitting rate. 
Note that properties such as pressure etc. are averaged over many molecules and many collisions in the gas and with the walls, so even if a given molecule stays in the interior of the gas for some time, it will be near the walls at some other time.
