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According to numerous sources online, the percentage of oxygen is approximately the same at sea level and 10,000 meters. Since oxygen is heavier than nitrogen, shouldn't the percentage of oxygen decrease with altitude?

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If you were to surround the atmosphere by an adiabatic envelope and allow it to come to equilibrium, it probably would settle into such a state. However, the atmosphere is not a static place. It is actively mixed due to heating of the ground by the sun, and by cooling of the upper atmosphere by radiation into space. This makes the surface air less dense than the air above it, causing highly turbulent convection cells to form. Also significant is the differential heating between the equator and the poles, which also drives convection on a global scale. The mixing effect of all this turbulent convection is much greater than the very slow tendency for the gases to form concentration gradients due to their differing densities.

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I always thought that it had to do with the relative strength of diffusion vs gravity, and that gravity is unimportant until the frequency of intermolecular collisions declines with air density, eg at very high altitude as suggested by @graham. Could you comment, and perhaps provide a reference? –  Abe Aug 21 '12 at 5:50
    
@Abe I hadn't considered that diffusion alone might be enough to prevent a gradient from forming. The mixing due to turbulent convection behaves like diffusion only on a much faster time scale (they call it "eddy diffusion") so it certainly does overwhelm the effect of gravity, but my comment that "If you were to surround the atmosphere by an adiabatic envelope and allow it to come to equilibrium, it probably would settle into such a state" might be wrong. Unfortunately I'm far too busy to look into it right now, but if you can provide a reference I'll happily change or delete the answer. –  Nathaniel Aug 21 '12 at 15:16
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Nathaniel answer is appropriate. At very high altitudes above 100km there is a separation according to molecular weights.

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