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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.)

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Pressure is caused by particles colliding with a surface. The accompanying change in momentum direction contributes to the force per surface unit, or pressure. The particle momentum and energy depends on the temperature. Pressure is also proportional to the number of particles per volume, the density. Fewer particles colliding results in a smaller pressure. This is all described by the ideal gas law.

The low pressure in your example is caused by a low density. For the particles to be gravitationally confined their energy would have to be extremely low and/or the gravity extremely strong. Such conditions are found in galaxies which contain gravitationally bound molecular clouds. A galaxy is gravitationally a very deep "container" and the molecules are at near absolute zero temperature.

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