|Thanks to kinetic energy, there will be no appreciable 'unmixing' - or even partial stratification,- at least under normal g values. That's the case even if one type of molecule is much heavier than the other|
The question in the title was inspired by a comment on a site I visit a lot, one to which I've posted a lot in nigh on three years. More about that later. Suffice it to say that I shall reply to here, rather than there, and attempt to place a link on the other site. There will be no more posting to that site until such time as its moderation policies are given a thorough overhaul! Nuff said for now...
The question was essentially this: given that we all know that petrol fumes sink to the ground at a filling station, why doesn't CO2 - which we also know is denser than air - also settle at ground level? Why are we not suffocated by the stuff - or does it only come up to ankle or knee level?
Imagine one were to trap gases inside balloons - one for hydrogen, one for oxygen, one for nitrogen, one for carbon dioxide - and then release them. The four balloons would behave exactly as the questioner supposes. The hydrogen balloon would quickly ascend, the CO2 balloon would rapidly descend, and the nitrogen and oxygen balloons would probably hover or sink slowly - due mainly to the weight of the balloon rubber - not the contents. The relative densities of hydrogen :nitrogen: oxygen: air::carbon dioxide are approximately 1 : 7 : 8 : 7.2 : 22. Gases lighter than air rise, those heavier than air sink. No surprises there.
When petrol fumes are released, they too sink quickly, at least to start with. A typical molecule in petrol is one of the isomeric octanes, general formula C8H18, with a relative vapour density of 57 - some 4 times greater than air.
But the petrol fumes would not stay for very long at ground level. Convection current carry them upwards, and gaseous diffusion would cause mixing with air even without convection. That's because gas molecules are in a state of constant motion, colliding with other molecules, millions of times a second, causing them gradually to diffuse ("spread") in all directions. The fumes gradually spread into all the space available - which could be a jar, a garage, a hangar, the entire atmosphere. Once the space is evenly occupied, the molecules then show no tendency to unmix. Why not? Answer: because the 1g force that acts on all molecules in air at sea level is insufficient to overcome the kinetic forces due to collision between molecules. Put more simply - a molecule that gets a strong bump from below will be knocked upwards, against the weaker force of gravity.
This is true for g=1, but is not true for progressively higher g forces.
Here's an example - always a a controversial one. Enrichment of the fissile uranium isotope U-235 needed for atomic power stations OR Hiroshima-type A bombs, requires separation from the more abundant U-238. This can be accomplished in gaseous diffusion plants, or in centrifuges that generate an intense g force. Either process requires that solid metallic uranium first be converted to the gaseous uranium hexafluoride (UF6).
There is a well known experiment that is done in schools, at any rate, those that still have a fume cupboard, to demonstrate that dense gases and/or vapours gradually diffuse to fill the space available, and then do not subsequently unmix from air.
One places of few drops of elemental bromine, Br2, a fuming red liquid in the lower jar, which is separated from the upper jar by a glass divider. One waits for the lower jar to fill completely with red-brown fumes. One then removes the separator. The fumes gradually fill both jars evenly, despite bromine vapour being 5 times denser than air.
There's a variant on the experiment that I devised while teaching to demonstrate the petrol vapour effect. One places a jar of bromine on top, and then removes the divider. Most of the bromine fumes sink immediately into the lower jar, behaving as if they were enclosed in a balloon. But the fumes then gradually diffuse back upwards to produce the same end-result as before.
The short term behaviour of the petrol fumes is called a bulk phase effect. It's the temporary behaviour of heavy molecules in close proximity, which behave briefly as if enclosed in a balloon. But once diffusion has caused mixing of heavy molecules with the lighter molecules of nitrogen and oxygen, unmixing does not occur at normal values of g.
Think then of a gas before diffusion and mixing as a kind of ghost fluid, with its own density and buoyancy characteristics. In fact, while the term "fluid" in everyday life is synonymous with "liquid", in physics it applies to both gases and liquids. But a gas loses the distinguishing characteristics of its original 'fluidity' once it's had time to spread sufficient for its own kind of molecules to become separated and irreversibly mixed with other kinds of molecules.
Will mixed gases spontaneously unmix?
Here's another that's quite thought-provoking, once you get past the unpromising preamble
Finally, even if the air were completely and
perfectly still, the carbon dioxide would
not form a pool on the surface. There is a
"dynamic equilibrium" set up between
gravitation -- the tendency for the denser
material to go to the bottom -- and diffusion
– the tendency for a material not to
concentrate in one place, but to spread
itself out. The atmosphere we have contains
roughly 78% nitrogen, 21% oxygen,
0.93% argon, and 0.036% carbon dioxide.
Its composition does not vary until
you get above 80 km in height. If the air
were perfectly still,
its composition would be
Ground level: 75% nitrogen, 23% oxygen,
1.3% argon, 0.055% carbon dioxide
10 km high: 79% nitrogen, 20% oxygen, 0.75% argon,
0.026% carbon dioxide
20 km high: 82.5% nitrogen, 17% oxygen, 0.43% argon,
0.012% carbon dioxide
So even in these circumstances, the
heavier gases like carbon dioxide would
have higher concentrations
lower down, but could not form a lethal pool.
So there is an effect (of sorts) that relates to molecular mass ("heaviness"),
even if there is no unmixing as such. Does that contradict anything that precedes
it in this posting? Discuss. :-)
Here's my own interpretation, for what it's worth, of the grading by molecular size/mass with increasing altitude (added September 17 2014)?
As one gets higher, the air thins (this being due to decreasing gravitational pull on everything, gases included, such that most gas is held relatively close to the Earth's surface (a few tens of kilometres). But another effect can then operate that discriminates according to molecular mass. It's to do with the average spacing between molecules and their average speed (best measured we're told as the root mean square velocity). As the molecules become further apart they can travel further using their own intrinsic motion before colliding with another to be deflected off in a different direction, impeding upward progress.
But a light molecule travels faster at a given temperature than a heavier one. It's one of the givens of kinetic molecular theory. It explains why hydrogen gas diffuses faster than carbon dioxide. Thus there is a greater probability that a lighter molecule like hydrogen will be able to cross a given transient empty space faster than a heavier one before the gap, so to speak, closes up. Ipso facto, light molecules have a greater probability of "winning the race" to the top of the Earth's atmosphere. But having got there they will find they are still held by the Earth's gravitational field albeit much weaker than at ground level, unless exceptionally light, like hydrogen and/or helium atoms which we are told can and do escape from the Earth's atmosphere, leaking off into interplanetary space.
Summary: what's operating is not settling out of heavier molecules in response to gravity. It's the speedier motion in an otherwise unfavoured direction (upwards) of molecules that are LIGHTER and thus able to DIFFUSE faster! (They would diffuse anyway, whether or not a gravitational field was present, so gravitation becomes a secondary consideration).
Even further reading: see the excellent wiki entry on 'Atmospheric Escape" which also focuses on differential rates of gaseous diffusion.
Note: I'm pushing the limits of my physics in offering the above interpretation. If folk find it faulty, and/or can offer a better explanation for the sorting-by-size effect with altitude, then please feel free to comment. However, I do not consider the phenomenon is serious enough to challenge the generalization that gases do not spontaneously and efficiently unmix of their own accord, at least in a natural gravitational field around a planet-size object. Random molecular motion with constant collisions always ensures that molecules will never completely unmix, while accepting there can be concentrating effects of the kind described under normal or elevated g forces.
Here's a handy link to 'Physics for Dummies' with a section entitled "Using the Kinetic Energy Formula to Predict Air Molecule Speeds".
The takeaway message is the inverse square law that relates molecular mass to average speed at particular temperatures. A nitrogen molecule, N2, can be calculated to have an average speed of 508 metres per second at 28 degrees C (301K), though it would have to be in a perfect vacuum to be able to traverse that distance. A molecule that was 4 times as heavy would travel at half that speed, a half being the inverse square root of 4. A molecule that was half as heavy would travel at, er, darn, where did I put that pencil? Off the top of my head I think the answer is root 2 times as fast. That's approx 1.4 times as fast, i.e. 40% faster or thereabouts. A hydrogen molecule, H2, has 1/14th the mass of a nitrogen molecule, N2, so would travel (1/root 1/14) i.e. approx 3.75 times faster.
Addendum, 18th September 2014
I'm not sure I've adequately explained the difference between having a gas confined within a balloon or not, especially as regards the 'thought experiment' of taking the balloon away to watch the disappearance of density characteristics, "sinking" etc,
Here's a home-made diagram that will be used to describe my current (and still evolving) thinking on the subject:
Brace yourselves. More to come
First, look at the right-half of the balloon, and imagine the left were the same, i.e. an intact envelope enclosing gas all the way round. In that situation, the normal laws of buoyancy would apply, which as a revision exercise I shall now show in three diagrams (A-C) filched from the internet, of increasing detail and complexity.
Diagram A above shows an object (only) partly immersed in a fluid, which is subject to two forces: gravity, pulling it down, and "buoyancy" pushing it up. But what is the nature of the buoyancy force? The diagram does not explain. Let's look at another which does.
This diagram shows an object fully immersed in the fluid (I wish that Diagram A had too, but beggars/filchers can't be choosers). Note that the fluid exerts pressure on the object, that the pressure acts in all directions, that being the nature of pressure as a result of billions of random molecular collisions per second that have no single directionality. Note the upwards pointing arrow in the middle. Why is the nett force upwards ("buoyancy"). Again, the diagram does not explain. For that we need to go to the next diagram.
What this diagram shows is the imbalance of forces acting on the immersed object. The pressure at the bottom (pressure being force per unit area) is greater than at the top, and indeed greater than at all points between top and bottom. In other words, the nett force is upwards. the nett upwards force is called the UPTHRUST.
For the object to float, the upthrust needs to be greater than the weight of the object in air. For the object to sink, the upthrust must be less than the weight of the object. Upthrust can be measured as the weight of fluid displaced (handy for calculation, while not giving insights into the mechanism of upthrust which as explained is due to increasing pressure with depth producing an imbalance of forces between highest and lowest points).
Now let's return to our sealed/soon to become leaky balloon and compare with the three diagrams above:
Hopefully, dear reader, you can guess what is coming. While that balloon is intact, with the same kind of molecules all packed together, exerting their particular density characteristics, whether smaller or greater than the surrounding air, then the balloon goes up or down, following the laws of buoyancy, the gas behaving just the same as any other fluid.
However, imagine that balloon envelope suddenly becoming permeable, with gas escaping and mixing, then one no longer has a homogeneous fluid of characteristic density and buoyancy. As the escaping molecules begin to mix with the surrounding molecules of air, then the bulk effects disappear, the molecules then behaving more or less independently from their neighbours, now increasingly different. What matters now are not the original bulk properties that respond to gravity, and/or the contingent pressure differences that depend on gravity, but the behaviourof the individual particles comprising the originally-enclosed gas, which is now determined by their intrinsic molecular speed, which is in turn a function of temperature, kinetic energy, mass and velocity, summed up in the term diffusibility.
Interestingly, there's a transition period between release from a confining receptacle and complete mixing (whether by slow diffusion, or aided by air currents etc) when the body of gas is still sufficiently discrete to continue behaving as a fluid. Some of us recall the demo experiment in school chemistry labs where teacher takes a jar full of CO2 gas and "pours" it over a candle or lit Bunsen burner, the flame being instantly extinguished in both cases.
Come to think of it, might the idea that CO2 "sinks and suffocates" be based on reports where the gas has been released from underground, say, or under water (as in the 1986 Lake Nyos disaster in Cameroon) , in both instances in regions of volcanic activity where the gas has vented from subterranean magma, and then flowed as a 'fluid' for a considerable time before there was time for mixing to occur?
|Lake Nyos disaster, 1986|
Update: September 22 2014
I discovered today why this posting attracts far more visitors each day than any of my other postings, despite having been written some 5 years ago. Assuming that most visitors were finding it via their search engines, I tried entering strings of search terms that correspond with the title, and then whittling them down to a core set. To my surprise, I find that one has simply to enter (CO2 heavy) and this posting tops the list of returns! It's clearly achieved that virtuous circle, aka critical mass, where its present prominence helps ensure continuing prominence!
Never one to rest on laurels, I've been making some additions by way of afterthoughts, and picking up on points that others have raised elsewhere, notably on science discussion forums where the content comes chiefly in serial additions from the participants themselves, starting with someone's primer question. In fact there's just such a forum that arrived three years after this one, posing essentially the same question, and is now third in my list of Google returns.
From 'spoogington' some 9 months ago, currently with 109 comments:
If CO2 is heavier than O2, why is our atmosphere not stratified with a layer of CO2 closer to earth?
Looking at the points made, I'm more than ever convinced that I was right to raise the question, since clearly there is some confusion in people's minds (as there was initially in my own) as to the importance or otherwise of bulk density v molecular weight where the behaviour of 'heavy' gases is concerned, before and after mixing in a gravitational field.
At the risk of giving this post an intimidating length, I might try supplying my own answers to some of the points raised. Or there again, it might be wise to create a separate follow-up post so as not to overload this one.
Oh, and here's a link to a climate change sceptic, maybe denialist even, who seems to think that CO2 is too heavy to get into the upper atmosphere. In fact,the faux science gets worse as one reads on, much worse.
Sample: (my italics)
"How mad with power does a group of people become that they now want to control, CO2, a naturally occurring colorless, odorless, incombustible gas formed during respiration, decomposition of organic substances, volcanic emissions, decay of plant and soil organic matter? A gas that was intelligently designed to be heavier than air for a purpose. How crazy is that?
I invite him to read this posting and reconsider.
October 5, 2014:
Have just come across this blog, with a brief mention at the end of a delightful reductio ad absurdum argument. Look for the term "layer cake atmosphere".
October 6, 2014
And here's a must-see paper from a kindred spirit (an Italian caver at Turin University) who unlike myself has the maths to support the theory. The title says it all. Click to enlarge if you wish to read the abstract.
It's available as a pdf:
Note the date of first publication: April, 2009, i.e. some 9 months before I penned this posting. But I'm not a plagiarizer, honest, no, really, HONEST, not having spotted this paper until just a few days ago.
November 8th 2014
Here's an additional 'thought experiment' using CO2 and helium filled balloons to demonstrate that once mixed, gases do not unmix.
I composed it yesterday as a new blog posting, and intended to add a brief summary here. Being somewhat busy right now, here's a cut-and-paste of the entire posting, which I shall endeavour to prune when I've some fee time.
Still they keep coming, to a posting I did nearly 5 years ago.
|Posted on this site, Jan 12, 2010|
It was provoked as I recall by a barmy comment to the effect that CO2 had been made "heavy" by a Benign Presence (Gaia? Guardian angel in attendance?) so as to stay at lower altitudes, feeding our plants, not reaching higher altitudes where it might cause mischief!!!
Here's a snapshot from my sitemeter, showing that 11 of the last 20 visits have been to that posting (13 is a more typical average).
|The red tags are mine, pointing to the CO2 posting|
Quite why it still gets all the attention I haven't a clue. Maybe it's because
To be honest, I've been somewhat embarrassed that a instant tutorial should now be seen as the first or second stop on a simple non-technical web search. So much so that I gave it a spring clean this last September, adding bits here and there to strengthen the case (as I'm only 99.9% certain about my conviction that normal g forces - from the Earth's own pull - are insufficient to cause unmixing of CO2 and stratification, ONCE THE GAS has diffused and mixed with the nitrogen and oxygen of air).
With that as preamble, folk should perhaps understand why I'm back again, still fine-tuning, still whittling down that stubborn 0.1% of doubt.
What I wish to describe now is a thought experiment. (Yes, I know it should or could have been a real one, but if thought experiments were good enough for Albert Einstein then they are good enough for me - that's my story and I'm sticking to it).
It's a development of the 'teaching aid' in the original posting, which began with a brief look at the behaviour of gases trapped inside balloons, where they do indeed show their heavier or lighter-than-air characteristics. That's before the gases have escaped from their balloons, then diffused and mixed with air and lost their ability to "sink", settle out, stratify, call it what you wish.
Last night I had a brainwave. Why not keep the gases trapped inside their balloons, and allow them to mix by diffusion (which may take a few minutes, possibly a lot of minutes for totally even and homogeneous mixing, but mix they will, such is the nature of gaseous diffusion).
How might the behaviour of the balloons compare before and after mixing? Let's do that thought experiment.
Before opening the valve: the two attached balloons may ascend, descend, or stay put, depending on the relative size of the two balloons, and the average density of the two gases compared to that of the surrounding air. If the average density is less, the system ascends etc. (And it won't matter a jot whether the gases are separate or pre-mixed or post-mixed for that to be true - important for what follows).
But one thing's for certain. The two balloons will remain oriented with respect to each other, as in the diagram, with the blue helium balloon on top. That's because it always experiences more upthrust than the red balloon, displacing a greater volume of air for a given weight of enclosed gas. If one attempts to alter the stacking geometry, the system will self-correct when released.
Now let's picture what happens if the valve is opened, or the fusible wax plug is melted, allowing the two gases to mix. One could allow mixing by diffusion only, which means a lot of waiting. Alternatively one can speed up mixing by inverting the balloons as shown below.
What happens when one releases the two (still attached) after mixing?
If the original system ascended, so will the new one.
If the original system descended, so will the new one.
If the original system was perfectly balanced, neither ascending nor descending, so will the new one.
But there will be a difference. Both balloons are now equally buoyant (or non-buoyant, depending on the proportions of the two gases). So there will be no tendency for one balloon to be above the other. In other words, the two balloons can adopt any configuration through 360 degrees (with a slight tendency maybe for the smaller balloon to 'lead the way' if rising or sinking, due to aerodynamic differences).
So the two attached balloons might go up, go down, or stay put, looking like this:
or like this:
or any angles of rotation in between.
One thing's for certain. Restoring the original configuration to blue on top, red underneath will not cause reversion to the original self-correcting orientation, since that would require that the gases unmix, with CO2 going back into the red balloon, helium going back on top.That as we've seen. simply does NOT happen at normal values of g. Which is where we came in...