Stratification of gasses by mass [closed]








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Suppose a homogenous mixture of mutually non-reactive gases is isolated in a container so that there are no external kinetic forces (vibration or rotation) that create turbulence or other mixing motion. Will the gases always tend towards a perfect stratification by mass? If not, what factors oppose stratification?


My guess is that temperature imposes a lower bound on stratification: i.e., even starting from a perfect stratification, higher temperatures cause more mixing across layers due to the random kinetic movement of gas molecules.


I'm also wondering if some non-reactive gases can nevertheless exhibit weak interactions that prevent or oppose stratification, similar to the way liquids can form solutions or emulsions that do not separate under gravity.




These questions are addressed well in this 2009 paper by Giovanni Badino: [The Legend of Carbon Dioxide Heaviness](https://caves.org/pub/journal/PDF/v71/cave-71-01-100.pdf).


**Gravitational stratification** does occur, but it is a result of the fact that change in pressure *P* with altitude *z* is a function of the molar mass of the molecules *M* (paper Equation 3):
$$\frac{dP}{P} = -\frac{M g}{R T}dz$$


The paper also notes the important but perhaps counter-intuitive independence of ideal gases: "Gases collaborate to create a final total pressure, but the partial pressure of each gas behaves as if the others did not exist." Hence, the pressure (and therefore relative concentration) of heavy molecules decreases much faster as altitude increases. So gravitational stratification only appears on scales of many meters (or kilometers when considering molecules of very similar mass).


Even if gases are initially stratified or otherwise separated, they will approach an equilibrium mixture through **diffusion**, the chemistry of which is complicated by many factors. Nevertheless, w.r.t. the suggestion in the question: it is true that diffusion rates are proportional to $T^{3/2}$ (see paper Equation 7).


 7

Gases definitely will stratify. It is possible to collect CO2 by upward displacement of air. Chlorine gas spills are incredibly dangerous because they will fill low lying areas for hours or even days. I was familiar with this one: **<https://ebrary.net/131196/health/youngstown_february_1978_train_derailment_with_chlorine_cloud>** Even a lower MW gas such as water vapor at a higher pressure will force all the air from a container such as a boiling teakettle. Once mixed, thermal motion and turbulence resist separation but lighter mass molecules more easily escape the Earth's gravitational field while they seem to have trouble getting away from Jupiter [we'll know more about stratification when we get there, I suspect that there is more H2 near the surface.]. The hexafluorides of U235 and U238 separate in a centrifuge.


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