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If left undisturbed, CO2 does sink lower to the ground than oxygen, although they both form separate exponential profiles (it's not like the bottom half of a volume is 100% CO2 while the top half is 100% oxygen - they both have distributions that tail off exponentially with height - it's just that the CO2 /oxygen density ratio is higher at the bottom of a large undisturbed container than at the top). For example, in large grain silos where CO2 can chemically build up, the CO2 sinks more to the bottom. A worker who walks directly into the bottom of the silo may find that he has too much CO2/not enough oxygen and can't breath properly. From the Penn State agricultural website:
"Like carbon dioxide, nitrogen dioxide is heavier than air so the highest concentration of gas is typically located at the silage surface, which is the area where a person will be going if they need to enter the silo for any reason."
Out in the open atmosphere, there is enough motion in the air to keep the oxygen and carbon dioxide mixed up. This motion of the air mostly comes from convection currents (i.e. wind) caused by temperature differences. But if you go up high enough in the atmosphere, the temperature differences even out enough that the vertical mixing becomes insignificant. The higher part of the atmosphere does indeed have the different molecules settle out to different altitudes depending on their density. The altitude that marks the point separating the part of the atmosphere that is mixed and the higher part of the atmosphere that is not mixed is called the turbopause. In the region above the turbopause, hydrogen and helium are the lightest and form the highest parts of the atmosphere. Oxygen is heavier and is farther down in this region. The turbopause is at about 13 km above Earth's surface, which is above the highest mountain, but below where many airplanes fly.
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