'Boiling Away' Questions

about Molecular Components

of Earth's Atmosphere


(unanswered by physicists?)


(Atomic weights rounded to integers.)

(2017 Feb blog post)

Paragraphs or web-links or images may be added (or changed),
if I ever get back to this page.

Home > Blog menu > This page posing questions on 'boiling away' of atmospheric gas molecules.

Introduction :

With all the talk about

  • carbon-dioxide levels in the atmosphere
  • ozone layer depletion
  • chloro-fluoro-carbon levels in the atmosphere
  • what happened to the atmosphere of Mars?
  • etc. etc.

I am motivated to ask some questions about the dynamics of the concentration levels of molecules of various gases in the Earth's atmosphere --- especially in relation to their possible 'escape' from the atmosphere --- an apparent 'boiling off'.

Since I have long been interested in math and physics (and mathematical physics), I am prone to thinking about the atmosphere as being this huge, on-going, raucous, 3-dimensional 'billiard balls game' ---- of molecules of various weights crashing into each other --- and rebounding with higher or lower velocities, related to their relative weights.

In this scenario, it seems that the heavier molecules could dominate over the lighter molecules, in the sense that the lighter molecules, when they are headed away from Earth, could be more likely to exit the Earth's 'sphere of influence'.

The lighter molecules could be more likely to head for outer space (or the moon's gravitational field --- or the sun's gravitational field --- or some planet's gravitational field) --- for example, whenever a molecular collision causes a molecule to exceed 'escape velocity' --- and the molecule manages to avoid a collision 'on its way out'.

In thinking about these issues, it helps to consider the molecular composition of the atmosphere and the percentages of those components.

A quick web search reveals that:

By volume, dry air contains 78.09% nitrogen, 20.95% oxygen, 0.93% argon, 0.04% carbon dioxide, and small amounts of other gases. Air also contains a variable amount of water vapor, on average around 1% at sea level, and 0.4% over the entire atmosphere.

However, to assure that this does not give a skewed view of the components of the atmosphere, it seems advisable to ask for the composition by weight.

A web search on keywords such as

      nitrogen oxygen carbon dioxide percentage in the atmosphere "by weight"

yields sites such as EngineeringToolbox.com, which shows the percentages by weight. Here is a re-ordering of the table there --- with the largest percentages listed first.

      Gas         ------ Percent ------    Molecular  Chemical   Boiling
                  By volume   By weight       Mass      Symbol    Point (C)
                  ---------   ---------    ---------  --------   ---------
      Nitrogen        78.09     75.47        28.02       N2      -195.79
      Oxygen          20.95     23.20        32.00       O2      -182.95
      Argon            0.933     1.28        39.94       Ar      -186.
      Carbon Dioxide   0.03      0.046       44.01       CO2      -78.5
      Neon             0.0018    0.0012      20.18       Ne      -246.
      Helium           0.0005    0.00007      4.00       He      -269.
      Krypton          0.0001    0.0003      83.8        Kr      -153.4
      Hydrogen         0.00005   ~ 0          2.02       H2      -252.87
      Xenon            9 10-6    0.000044   131.29       Xe      -108.1

Note that the percents result in almost the same sort order, whether we use volume or weight percents.

If my conjecture that the lighter molecules might be more likely to 'escape' from the Earth (i.e. in greater numbers per unit of time) is true, then it looks like Nitrogen (according to the 'Molecular Mass' column) might be 'the first to go' --- among the 'top 4'.

Oxygen might be the next most 'likely to escape' --- with Carbon Dioxide being the least likely of the 'top 4'.

    Could this tend to favor a (very slow) relative-build-up of Carbon Dioxide --- even if there were not the (very fast) factors of fossil-fuel burning and the destruction of CO2-consuming plant life adding to the build-up? And would there be a slow 'escaping' of oxygen --- relative to heavier CO2 and Argon?

Futhermore, hydrogen and helium molecules (in the upper atmosphere, unhindered by further collisions) might be really likely to be accelerated to escape velocity.

---

After getting a handle on the molecular composition of the atmosphere, it then becomes a question of what is the (relative) mass of the 'molecules of interest' --- in order to support a quantitative study of their collisions ...

and some 'molecules of interest' may not be in the brief table above.

Here is one table of molecular weights --- with some 'molecules of interest' marked with a red dot. (If one were concerned with the dynamics of the petroleum-related and man-made-pollution-related molecules, one might be interested in benzene, ethylene, ethane, propane, etc.)

    I have marked hydrogen (H2) and helium, because they are the most common molecules in the known universe.

    I have marked methane (CH4) and 'natural gas', because they are often the subject of localized or large-volume pollution concerns.

    I have marked ozone (O3), because it is often the subject of ultra-violet shielding concerns.

Here is a re-ordering of part of that table, with the heavier molecules ('billiard balls') shown first.

                                Molecular
      Gas or Vapor                Weight
      ----------------------  -------------
      Ozone, O3                    47.998
      Carbon Dioxide, CO2          44.010           *4
      Argon, Ar                    39.948           *3
      Oxygen, O2                   31.999           *2
      Air (mixture)                28.966 (average)
      Nitrogen, N2                 28.013           *1
      Carbon Monoxide, CO          28.011
      Natural Gas                  19.00
      WaterVapor/Steam, H2O        18.020
      Methane, CH4                 16.044
      Helium, He                    4.020
      Hydrogen, H2                  2.016

I have indicated (with asterisks) the 4 most copious molecular components in Earth's atmosphere.

It looks like Ozone might be less likely to 'escape' --- but it might be depleted by chemical means.

It looks like Methane and Natural Gas (being lighter than Argon, Oxygen, Nitrogen, and Carbon Dioxide) might be more likely to be 'forced to escape' --- by collisions with heavier molecules.


How to best simulate Earth's atmospheric molecular-dynamics at the molecular level?

Astrophysicists have been using super-computers for many years now (2017) to simulate the motion of celestial bodies such as the hundreds of thousands of bodies in a spiral galaxy --- via N-body simulations.

And, using the inverse-square-law of gravitational attraction and systems of differential equations describing the forces between all the bodies, they have been performing simulations of how a huge mass of separate particles/bodies distributed in 3-dimensional space might evolve into a planetary system such as our solar system.

And, on an even grander scale, they have modeled how millions of bodies distributed in a model of our early universe might cluster together into galaxies --- and continue to evolve, perhaps to the point of forming 'black holes'.

It seems that such methods might be used in simulating a mixture of molecules (distributed in an initial configuration around Earth, and with randomized initial velocities) --- to see how they might evolve --- in particular, to see if certain molecules could acquire velocities exceeding 'escape velocity' --- and to see if the remaining mixture of molecules (percentages) would be changed.

    Perhaps one could reduce the size of the problem somewhat by considering a 'column' of atmospheric gas, extending above a small patch of the Earth's surface.

Such simulations may involve some new considerations in formulating the equations of motion. There would be Earth's gravitational effects on the molecules, but, also, there would need to be modeling of the collisions --- perhaps using algebraic methods --- combined with differential equation methods for modeling the gravitational effects.

A hint of the algebraic methods that might be employed is indicated by the treatment of a 1-D Collision of 2 Rigid Masses - a numerical (and graphical) simulation.

It seems that one could get a 'small-sized' start on simulating the problem, by considering a few hundred molecules --- of just 2 species --- say nitrogen and oxygen --- and seeing how that would proceed in a scaled-down environment --- say, a box or cylinder with a one-directional gravity-like force involved, along with the collisions.

    In such a simplified simulation, we would be ignoring temperature difference effects (assume temperature remains constant throughout --- a 'spatially constant' randomization of the initial molecular velocities) and assume that there are not molecule-generating and molecule-consuming effects (as in conservation of mass).

    We would also assume there are no wind currents --- no 'jet stream' --- no hurricanes, tornadoes, rain storms, etc.

    In fact, in large-scale simulations, we would (at least initially) want to make such assumptions to make the mathematical modelling less complex.

---

On the other hand, to avoid the massive numbers of equations to be 'integrated', there may be a way to get some answers by using the methods of 'statistical mechanics'.

I have done almost no study of statistical mechanics, so I do not know (at this time) how to proceed using those methods.

---

There may be a way to get some answers by proceeding on a 'macro' level --- using pressure, density, volume considerations --- and not going down to the level of simulating individual molecular trajectories.

---

At this point, I am about out of ideas on the best way to proceed. I retire until another day --- when I might have more to add on these matters.


Conclusion

There may be no conclusion to this web page, unless I find a comprehensive treatment of 'atmospheric evolution' questions, for Mother Earth.

If I find no such super-answer, I hope to continue adding observations and notes and links to this page --- until my ashes are spread to mix with the atoms of the universe.


For further information :

For further information on atmosphere-dynamics questions, here are some links to Google web searches on keywords related to this topic.

After the search window appears with an intial page of 'hits', you can change or add keywords to hone the search to what you are looking for.

In 2017 Feb, I see many 'hits' that might answer some of my questions or, at least, give me some more information that should be added to this page. I may be examining 'hits' from these searches as time permits.

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Page was posted 2017 Feb 21.
Page was changed 2017 Feb 23. (Added a pressure/density/volume search link.)