Thermodynamics Stupidisation - Ideal Gases

i hate this topic...yucks. its so heaty...when i think i know it, i don't...
lets see if i can put the big chunks in order...we have ideal gases, macro and micro behaviour...then we've got the actual thermodynamics that deals with gases (ideal and non-ideal) and their processes...then we have "thermal properties of materials", which really is a pretentious cover for "heat capacity, latent heat and their measurement"...hmm i think i can get started now:

Ideal Gases
Gases are one of three commonly observed states of matter (you don't see Bose-Einstein Condensates everyday do you?) i suppose its hard to define a gas, i guess (pun!! not intended...) i could say that if the particles which constitute some "thing" aren't clumped together, then its a gas i suppose.

So lots of things could be gases, if we could give them the energy to become a gas...and the particles could be complex molecules, ions...so to start out simple, and then by extrapolation deepen our understanding of gases, we start with the notion of the "idea gas"...

So here goes...An Ideal Gas is:
1. composed to infinitesimal point particles, which actually have mass! i.e. point masses
2. NO forces of attraction between gas particles, or between gas particles and any container which holds the gas. In fact, ZERO potential energy exists in the whole system.
3. the gas particles obey Newton's laws! (argh i hate Newton's laws!)

in addition, we also assume that the gas particles undergo perfectly elastic collisions with the container walls, of zero duration, and that the container is totally rigid and of infinite mass (otherwise we won't get a change-in-direction-with-no-change-in-speed particle-wall collision condition)

So, gas particles like to move around. And when they hit the walls of a container, they exert forces on those walls. This would be the pressure of the gas. So how do we figure out the pressure exerted on a container by N gas particles?

[oh well too lazy to type the derivation...i suppose i remember it..hehe]

Some problems with the theory
I think there're some problems...maybe the problem is really me, but i say that there's some incompleteness in the theory that was printed in our notes. i'll list them here:

1. It was said that the particles are in constant, random motion. However, the derivation given does not seem to be consistent with this claim. Instead, we have taken one particle, assumed it to be moving from one wall to the opposite wall, and back, and forth...and assumed that (probably by thinking this implied random motion...i beg to differ) 1/3 of the particles will oscillate between one of 3 pairs of opposite walls.
the point is that random motion really implies that the particles could travel in oblique angles such that they strike the wall at oblique angles. In such a case, the time taken to travel between consecutive walls would differ...

2. Look at the equation: P = 1/3(rho)(mean sq. speed) [darn i can't insert Greek!]
again, i say that this was based on the assumption that 1/3 of all the particles are oscillating between one of 3 pairs of opposite walls. But doesn't this only happen when all 1/3 of the particles are striking the wall simultaneously? If that does not happen, the pressure would be lower than calculated right? Well we could say that since everything happens so quickly, it would seem as if all 1/3 strike at any one time. BUT the problem with this is that, there are so many possibilities of combinations of particles striking the wall, that having all 1/3 striking simultaneously is a highly improbable event? Well, suppose we forget abt the 1st point i made above, so that the particles' motion is truly random. even so, even though we can claim that statistically, all walls get hit by the same no. of particles at almost any instant, we can't expect all the particles to be hitting the walls at the same time...i.e. there's gotta be some particles which don't touch the wall at some instant, and i've pointed out that the probability should be quite high shouldn't it? So the pressure should really be lower than what
P = 1/3(rho)(mean sq. speed) gives us...right?