Why does the air we breath float on Earth?

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themadquark
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Why does air on Earth float? Obviously, lighter gases such as Helium and even hot air will float due to having a lowed density than the air around it. Why is it though that the base higher density gases that we breath float rather than sink to the ground? My belief is that gravity is simply too weak to hold the O2 and the other gases completely to the ground.
 
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Air does sink to the ground. Put your head near the ground and breathe in - it still works down there!

Think of a swimming pool. Down at the bottom there's some water, and at the top there's water too. The water at the top of the pool isn't "floating", there's just not enough room for it all to be at the bottom.

On Earth, we're swimming around in a bunch of gases. Some gas at ground level, some is up higher, all in one giant pile. There isn't enough room for it all to be exactly 0 cm from the ground, so it piles up.
 
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Gasses mix due to turbulence below 100 km and diffusion at high altitudes. A NOAA study of composition of the atmosphere versus altitude can be found in http://ruc.noaa.gov/AMB_Publications_bj/2009%20Schlatter_Atmospheric%20Composition%20and%20Vertical%20Structure_eae319MS-1.pdf
 
Air doesn't all sink to the ground for the same reason you don't. Gravity on Earth isn't strong enough to compact it that much. The layer of atmosphere we live in is made up of gasses that weigh more than those in higer layers. If Earth's gravity was that strong the Earth would be a star instead of a planet.