Do gas molecules align with gravity?

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Loren Booda
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In a gas, do the molecular centers of gravity align significantly toward the dominant source of gravity? E. g., do atmospheric water vapor molecules tend to have their oxygen atoms facing Earth's center?
 
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It's interesting to consider the energy penalty of a water molecule being "upside down"; that is, with the oxygen atom on top. When I multiply the mass of an oxygen molecule by the force of gravity by the difference in height between the two configurations, I get about 10-35 J. I'll leave it to you to compare that with the average rotational energy of a water molecule to determine if gravity has any considerable influence on orientation.
 
My initial guess is that such a molecule would have the average rotational energy of kT/2=10-35 J. So T=10-12 K, about the current limit of cryogenic technology. The influence is negligible.