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?
 
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.