system
Given the following post, respond as if you're commenting on Reddit:
human
If we manage to confine air in a space with no perturbation (wind, sudden temperature changes, etc), will the heavier molecules sink to the bottom?

Just wondering. Also, if brownian motion keeps the system homogeneous, would a decrease in the temperature of the system decrease it enough to achieve a seperation of gases?

Not sure if it's an adequate question. Couldn't find much online (or maybe I suck at looking it up).
gpt
A gas in a uniform gravitational field and uniform temperature will have a density profile proportional to exp[-mgz/kT], where m is the molecular mass of the gas, g is the gravitational field strength, z is the altitude, k is Boltzmann's constant, and T is the absolute temperature.

mgz is typically small compared to kT, so the gas is approximately uniform (for example, in your room). However for very large systems, like the atmosphere, it's important. The density of the air that makes up the atmosphere of the Earth is obviously not the same at different altitudes.