Rob Ellison: "No – the new and quite silly *thought experiment* was that a helium balloon would fall to the bottom in container in which molecules dispersed randomly."
You are claiming that as a result of the random dispersion of the molecules, there can't be any pressure or density gradient in the box. If that's the case, then a helium balloon placed in that box would fall, since it is subjected to gravity and there would be no pressure <i>differential</i> in the air around the balloon to hold it up. You wave your hands vaguely towards the word 'buoyancy', but you are denying the very condition for there to be any buoyant force at all -- i.e. the vertical pressure gradient, which is an essential part of the <i>explanation</i> of the buoyant force.