Several days ago, I was reading comments from individuals highly distressed that even if we managed to stop all CO2 emissions immediately, it wouldn't save the planet because all the CO2 we'd emitted since the Industrial Revolution would still be. One even used the analogy of a bath tub filled with water.
It was a strange analogy of course, as a bath tub has a drain, which can be used to empty of reduce the amount of water in the tub, though I didn't pursue that line of reasoning because the analogy is all wrong anyway.
Instead, I mentioned that the average residence time of a CO2 molecule in the atmosphere was around 100 years, and so future lower levels of the gas were inevitable.
Then a second commentator jumped in, claiming that the cycle time for CO2 was in the millions of years. At that time, I didn't know what to say, and left things hanging this way with open ignorance.
Delightfully, it turns out this is an interesting problem in physical and chemical equilibrium, and that both myself and the second commentator were right!
First, a little background on the subject. The following is from a set of notes on atmosphere-ocean of
various gasses from a general chemistry course taught by Professor Shapley (university unknown), the entire paper at http://butane.chem.uiuc.edu/pshapley/GenChem1/L23/web-L23.pdf:
Equilibrium is a state in chemical or phsysical reactions in which the rates of the "forward" reaction and of the "backward" reaction are the same. To rehash some of the above material, we would write [CO2](g) <=> [CO2](aq), where the brackets mean concentration (in appropriate units) and (g) and (aq) main air phase and aqueous (i.e., water) phase respectively.
However, the entire system is much more complicated than this. We should at least say
1. [CO2](g) <=> [CO2](aq)
2. [H2O] + [CO2](aq) <=> [H2CO3](aq)
3. [H2CO3](aq) <=> [HCO3-] + [H+](aq)
4. [HCO3-](aq) <=> [CO3--](aq) + [H+](aq)
where [H+] is the source of CO2's acidity in water. Incidentally, reactions 2. through 4. proceed only to a slight degree under normal conditions, and so the resulting acidity ([H+](aq), remember) is quite weak; this is why the oceans have been able to absorb as much CO2 as they have without lowering the pH of sea water significantly, at least as of yet (~0.1 pH units from 8.+). Oh, I won't describe what pH means here, except to say that pH = 7 is neutral, and reducing pH means increasing acidity; thus, the oceans today are mildly basic, yet are slowly acidifying due to anthropogenic CO2 emissions, with possibly unpleasant consequences for many forms of sea life.
There is another, important, equilibrium to be considered here:
y[CO3--](aq) + x[M(++...)](aqueous] => M(x)CO3(y)(ppt)
where (ppt) means the compound isn't soluble in water and so "drops" out of the aqueous phase into a solid phase (this is called precipitation, hence the ppt abbreviation), and falls, perhaps all the way to the ocean floor. M(++...) can be one of several, some fairly common, metals, such as magnesium, calcium, iron, and others.
This is important because -- well, notice how in this reaction I've used => instead of the usual <=>. This is an important concept in chemistry (and other sciences): by precipitating out of solution, [M(x)CO3(y)](aq) remains very close to or at zero no matter much the forward reaction runs. It is one way to "drive" a reaction to completion.
But if this is happening, then the effects trickle up back the line. CO3--(aq) and M++>(aq) keep being consumed, and we keep going back to [CO2](g) <=> [CO2](aq) constantly being driven forward; until, hypothetically all of the atmosphere'and s CO2 is consumed, down to ~[0].
This is where my second commentor's concern comes into play. Actually [CO2] wouldn't be completely depleted, because the CO3-- compounds on the ocean floor are subject to further reactions, this time geological: a lot of the oceans' floors are subject to forces (tectnonic) which drive them deep into the Earth's crust then emit them as CO2 in volcanic eruptions.
Now, if that were the whole story, we would be in serious trouble -- or all our troubles would be over, if you prefer looking at it that way -- because the CO2 emitted by volcanic activity is fairly small, and there wouldn't be enough of the gas in the atmosphere to support serious plant life, meaning there wouldn't be any (with a few exceptions) animals either, including us. Fortunately, there is a second set of equilibria as we all know, and that is the cycling of CO2 through living things:
[CO2](atm) => [CO2](plants] => [CO2](animals) => [CO2](atm) => repeat
This is largely what sustains sufficient carbon dioxide in the atmosphere, as well as keeping oxygen levels high enough for us animals. (This accounts for some 2000 gigatons of CO2.) Actually, CO2 seems to be slowly decreasing over geologic time, resulting in the Earth gradually cooling, so there may come a time when our planet, ironically, becomes a dead, frozen wasteland, but that won't happen for a long so don't worry about it -- we have much larger problems right now, in the opposite direction.
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Back to residence time of CO2 in air. The most widely accepted accepted value for this seems to be around 100 years. By the way, a better term than residence time is half-life; for it means that, if we start with 128 molecules of CO2 in air, then in a hundred years there will be 64, then 32 in another centurey, followed by 16, 8, 4, etc., in subsequent centuries As for the total CO2 and derived species (mentioned above), there is about 50 times as much of the gas in the oceans as in the air.
Given that some 70% of the anthropogenically generated CO2 over the last some 200 years (oh: approximately 2 trillion tons is in biological sources) has been absorbed by the seas, and that over 700 billion tons remain in the atmosphere. That's about one third of the total we've generated. Since the great majority of that has been produced only recently, then given the half-life of 100 years, quite a bit must have gone unabsorbed yet; that is, not reached equibrium. (Since the equibrium is affected by temperature, the slightly warmer world of today will favor [CO2](g), but the difference is not very large.) Therefor, projecting out another one or two hundred years we might expect 2/3 of what we've added, about 200 billion tons, will also be absorbed, That would bring current 400 ppm levels,down to around 300, which would be a safe level. Admittedly, this is a bit of guesswork on my part.
