Ordinarily, we assume that a gas expands to fill it's container, however, I've had the thought that at low enough densities, this may not be possible, because the force from pressure would not be enough to overcome gravity. Put another way, the particles of gas would not be fast enough to reach the top of the container. I have this idea that in such a situation, the gas would pool at the bottom of it's container, or at least be significantly more dense near the bottom.
I also think I might be entirely mistaken. I strongly suspect that I'm just describing a liquid.
Am I mistaken? If not, how low would the pressure/density need to be to observe this pooling effect, or a significant density gradient?
I understand that this effect is apparent in large containers, such as the Earth, which is why we have different pressures at different altitudes. I was more interested to know if there is a similar effect in small containers, due to extremely low pressures. (No bigger than say, a room in your house.)