Wednesday, June 07, 2017

0.04% Is a Lot of Molecules

An evergreen in the denial crowd is that CO2 is only a very small part of the atmosphere so how could it make a difference.

ADDED: In the comments Mark B points out that

The silliness is that it is precisely because CO2 is a very small part of atmosphere that humans are able to meaningfully change it's concentration. For example we are depleting O2 at the same rate as we are adding CO2, but the change is a negligible percentage of the normal content so only the most pedantic would dwell on it. That is, we've changed the CO2 concentration by about 45% and the O2 concentration by about 0.06%.
The short answer is that the atmosphere is very big.   Eli has a nice BOE (back of the envelope, not quite a Fermi problem but Eli would be quite pleased if others thought it in the neighborhood of same) answer

"... the estimation of rough but quantitative answers to unexpected questions about many aspects of the natural world. The method was the common and frequently amusing practice of Enrico Fermi, perhaps the most widely creative physicist of our times. Fermi delighted to think up and at once to discuss and to answer questions which drew upon deep understanding of the world, upon everyday experience, and upon the ability to make rough approximations, inspired guesses, and statistical estimates from very little data." 
 It starts by estimating the number of molecules in a m3 of air.  Well a Bunny who knew Loschmidt's number 2.7 x 1019 cm-3 or 2.7 x 1025 m-3  (which is the same thing since 1 m3 is 106 cm3 ) could start there or you could rearrange the ideal gas law
pV = nRT to n/V = p/RT
Since 1 atm is 101, 325 N/m², the gas constant R is  8.314 J K-1mol-1 and 0 C is 273 K
n/V = 101 325 N/m² /(8.314 J K-1mol-1 x 273.15 K) = 44.64 mol m-3 
which is a little surprising, since the average weight of a molecule of air is ~ 29 g or 0.029 kg so a cubic meter would weigh 1.3 kg but that is another direction.  In any case since there are 6.02 x 1023 molecules per mole that gives us Loschmidt's number again, in case a bunny has forgotten it or 2.69 x 1025 m-3.

If 400 ppm or 0.04% of that is CO2 there are  1.07 x 10 21 CO2 molecule in a cubic meter.  A useful estimate of the average distance between CO2 molecules is the inverse of the cube root. of the number density.  That is 4.5 x 10-8 m.

So how does that compare to the wavelength of light at which CO2 absorbs light in the IR.  Hmm, that's about 14 microns.  A micron is a millionth of a meter, So how many CO2 molecules are there along one wavelength of IR light where it is capable of absorbing.

About 300.

That's enough


CapitalistImperialistPig said...


Nick Stokes said...

The way I think about it is that it is about 6 kg/m2 CO2. If it condensed to a liquid of density like water, it would be 6mm thick. It's pretty easy to imagine that being totally opaque.

Bernard J. said...

Nick, I made a similar point at HotWhopper:

Fernando Leanme said...

Imagine how hard we would have to huff and puff if oxygen content were 400 ppm?

Bernard J. said...

Your point, El non sequitur?

Florifulgurator said...

My answer to that evergreen: "Put 250 microgram of LSD in 250g of unchlorinated water. That's 1ppm LSD. You sure will swallow that glass of water. Report back what you have seen."

Mark B said...

The silliness is that it is precisely because CO2 is a very small part of atmosphere that humans are able to meaningfully change it's concentration. For example (to Fernando's comment) we are depleting O2 at the same rate as we are adding CO2, but the change is a negligible percentage of the normal content so only the most pedantic would dwell on it. That is, we've changed the CO2 concentration by about 45% and the O2 concentration by about 0.06%.

EliRabett said...

Well said Mark B

Jim Eager said...

I like to use the easy to grasp visual analogy of mixing pure carbon black into a swimming pool. Let’s say the pool holds 1,000,000 liters and has a sloped bottom, i.e. it has a shallow end and a deep end. Remove the filter but leave the circulation pump running, then remove 300 liters of water from the pool and add 300 liters of carbon black and let the pump mix it throughout the pool. Let's say that at the shallow end you can still see bottom, but as you head toward the deep end at some point you will no longer be able to. Mark that point. Now remove another 100 liters of water and mix in 100 more liters of carbon black. What happens to the point at which you can no longer see the bottom? That's the power of a few hundred parts per million. Just as carbon black blocks visible light in the pool, CO2 blocks certain wavelengths of infrared light in the atmosphere, rendering the atmosphere as opaque at those wavelengths as carbon black does in the pool.

Fernando Leanme said...

Caracas air is running 150 ppm CS tear gas at ground level. Its so bad the tropical birds are moving up from the trees onto rooftops. Today I heard some kids debate whether a parrot would go over well on rice.

Howard said...

I think you are off by an order of magnitude
ppmv to mg/m3 = (ppmv * MW)/24.45
MW CO2 = 44.01 grams per mole
400ppmv CO2 = 721mg/m3 = 0.721grams/m3
0.721/44.01 = 0.0164-moles per m3
0.0164M/m3 * 6.022e23molecules/M= 9.9e21molecules/m3

Russell Seitz / Bright Water said...

Nick, as long ago remarked to Eli, it is fortunate that liquified ozone is a dark midnight blue that appears almost metallic

If condensed, the ozone layer would be dark as the ink on a printed page.- never mind that the O3 would set fire to it - considered as as sunscreen, the UV SPF is huge.

EliRabett said...

It also has the habit of taking out labs and anybunny who is near a lab doing ozone kinetics set up can tell you from sad experience

magmacc said...

But what about all those sophisticated skeptics who developed their own models of a convecting radiating/absorbing gray atmosphere as a simple sanity check on the Great Global Warming Conspiracy?

(You know, in between shouting that CO2 is plant food and that Algore lives in a big house within view of an ocean.)

Bob Loblaw said...

To follow on the LSD example: "Put 250 microgram of LSD in 250g of unchlorinated water"

...would the result be different if you put the same amount of LSD in 5g of water, or diluted it in 1000g of water? Or is it the absolute amount of LSD that matters?

Or the ink in the swimming pool. If you put the same amount of ink an a half-full pool, would it be easier or harder to see the bottom - or the same?

Russell Seitz / Bright Water said...

Eli is right about O3 and concentrated hydrogen peroxide being at the top of the SOGZ list
( Substances Of Great Zorch )

When, post Oklahoma bombing , ammonium nitrate & nitroanything became not-so-easy to get
over the counter, many suicide vest wearers joined the ranks of the Illegally Blonde :
Sales of hair bleach and nail polish remover have yet to return to normal.

Jim Eager said...

For Bob Loblaw,
Putting the same weight of LSD in less water would change the mixing ratio, but not the absolute dosage, so it would not matter.

Putting the same qty of carbon black in a half-full pool would increase the density per unit volume and would consequently shorten the mean free path, making the point at which you could not see bottom much more shallow, if you could see it at all.

Bob Loblaw said...


The questions were largely rhetorical...

For the LSD, the fact that the effect is the same illustrates that concentration (g LSD/g water) is not the factor of concern. Just as the ppm CO2 is not the issue, it's the absolute amount of CO2.

As for the swimming pool: if it did not have a shallow and deep end, then the same amount of carbon black in half the amount of water would have an identical screening effect. In the case where the pool changes depth from one end to the other, the point at which you cannot see the bottom will be the point at which the pool is half the depth from before. At this point, the total carbon black will be the same as it was for the full pool:

--- same carbon black (entire pool) * half the water = twice the concentration

---twice the concentration * half the depth = same visibility reduction.

I think we are on the same page.

Russell Seitz / Bright Water said...

Jim & Bob:

Allow me to introduce the Mie Integral, which will answer your swimming pool questions about particles & asperities of all sorts

E. Swanson said...

FL, given that you have frequently expressed doubt about AGW, here's a view of the latest efforts by the denialist camp to create FUD, efforts which may have formed your opinions.

Breitbart misrepresents research from 58 scientific papers to falsely claim that they disprove human-caused global warming

Jim Eager said...

"I think we are on the same page.”

Perhaps, but halving the volume while leaving carbon black (or CO2) the same has no analog to what is happening in the atmosphere. As the paraphrase goes, all analogies are wrong, but some are useful. Which of course means others are not at all usefull.

EliRabett said... pretty much answers the ink in the pool question. 280 and 560 ppm in the water

Bob Loblaw said...

"has no analog to what is happening in the atmosphere"

The point is that the concentration is not the important factor - it is the amount. Adding or subtracting from the inert ingredients does not change the radiative transfer process.

If the 560ppm beaker in Eli's video link was twice as wide and half as deep as the 280ppm beaker, then it would look the same darkness, because it would have the same absolute amount of ink between the camera and the paper background. And if you had two beakers of different diameters, both with 280ppmm the larger beaker would look darker - because more water * 280ppm ink means more ink in total.

Jim Eager said...

"The point is that the concentration is not the important factor - it is the amount."

Agreed, Bob, but concentration isn't a "factor," it's simply a measurement of the amount and how much it has changed. It's like saying inches or meters aren't important, it's the distance that counts, but you have to measure the distance to measure any change in it. For CO2 in the atmosphere we do that by measuring ppmv over time.

"Adding or subtracting from the inert ingredients does not change the radiative transfer process."

Again, agreed, but talk of adding or subtracting the inert ingredients (O2 and N2) is a distraction here since we are not doing that with O2* and N2. (Actually we are through combustion, but it's negligible since the change is very small and the reservoir is very large.) The only reason to remove 3 and then 1 liter of water from the pool is simply to keep the total volume the same and make the ink concentration 300 ppmv and then 400 ppmv. And the sloping bottom of the pool just provides a handy measurement of how adding more ink will shorten the mean free path of visible light through the water.

Jim Eager said...

Seen it, Eli, and it's a nice, simple illustration that won't upset the pool maintenance staff.

Bernard J. said...

"...the average weight of a molecule of air is ~ 29 g...

Are we suddenly orbiting a black hole?

Russell Seitz / Bright Water said...


Delingpole's response to that critique is a geM:

Bob Loblaw said...


Yes, ppm tracks the the changes in atmospheric CO2, but only because the total air mass is staying constant. For a radiative transfer calculation, you aren't going to want CO2 measured in ppm - you will need it in some absolute units.

The inert ingredients become a distraction when they are included as the denominator in the calculation of ppm (=quantity we really want/inert ingredients that don't matter). That's one of the main points of Eli's post: when you look at what is actually in the numerator and ignore the denominator, it turns out there is a lot of CO2 floating around.

Fernando Leanme said...

Swanson, I never expressed doubts about the CO2 absorption spectrum or its ability to absorb outgoing infrared. Neither do I question the fact that the energy level in the biosphere is increasing, or that surface temperature increases. I started studying the subject in the early 1990's when I was working as a supervisor in an Arctic project. My job included establishing the methods we would use to set the design basis for ice capable vessels and ports (I'm a published author in the subject in Russian). Later after I retired I started reading about the subject, and it seemed to me it was being mishandled.

I gave the typical doubts about TCR because a couple of friends who worked with me in the 1990's told me they felt it was closer to 1.6. These guys are hard core professionals who worked for me and I don't think they have an axe to grind. I also have very sound objections to the "business as usual" RCP8.5, which I found to be a very trashable piece of work (my team started doing system dynamics around 1991, so I'm familiar with the way those IAMs are built).

I'm also doing adhoc research on the link between global warming and the international communist Mafia. And it sure looks like they are linked. Every time I scratch a "Warmist" I get a red coating under the green surface. For example, over the last couple of days I scratched Willard and out popped out a raging red defending communism and quoting all sorts of provenezuelan dictatorship trash. Talking about Venezuela, yesterday was a big day, General Attorney Luisa Ortega declared the designation of over a dozen Supreme Court judges by the Maduristas in December 2015 was spurious and invalid. The Maduro dictatorship has relied on the fake Supreme Court judges to execute the self coup and install a tyranny. These are now disarmed, and it looks like the risk of civil war is increasing every day as the dictatorship elite fractures into at least two factions. Maduro's push into full dictatorship mode was encouraged by Obama when he acted so chummy with Raúl Castro.

Meanwhile in Cuba the resistance sent out a series of messages describing how Raúl Castro was extremely ill, and his eldest son was maneuvering to keep the Castro Dinasty in power. Their plan is to have Diaz Canel, who is married to Raul's granddaughter, take over as nominal head of state but have Raul's eldest son Alejandro in charge of all security and intelligence services. Raul's grandson Raulito would be in charge of the body guards who defend the nomenklatura from the people, as well as the special medical service reserved for the dictatorship's upper caste.

magmacc said...

I gave the typical doubts about TCR because a couple of friends who worked with me in the 1990's told me they felt it was closer to 1.6. These guys are hard core professionals who worked for me and I don't think they have an axe to grind. -- Fernando Leanme

No, Fernando, not good enough. Two anonymous anecdotal friends with phantom credential are far too little and far too late to wash away the memory of your hundreds (or thousands) of climate change denial comments.

E. Swanson said...

FL, I got interested in air pollution back in the '70's when I found I could not tolerate the smog in N. California. By the 1973 Arab Oil Embargo, I had already done work with wind energy systems and moved back into a University environment studying energy. At the time, the US electric system was growing at around 7% a year, an exponential rate which gives a doubling time of 10 years. At that rate of growth, the entire US electric system was being duplicated over a 10 year period and over the next 10 years, the whole mess would need to be doubled again. The conventional thinking was that that rate would continue, thus there was a scramble for energy sources to meet the expected demand. There were serious projections that by the year 2000, there would be 1000 nukes in operation. Of course, things didn't turn out that way, which just shows how difficult it is to look forward. One major problem with the AGW situation is the future projections of emissions, as you note. I think the RCP 8.5 scenario isn't likely, but it does represent what could happen if the rest of the world were to follow the developed world's path going forward, given that there are still a couple of billion people who have no access to electricity while the population is set to reach 10 billion by 2050. We can only hope things don't turn out that way because the resources aren't likely to be available and the environment is already in serious trouble on many measures.

There are those of us who think humanity is headed for a dieoff because our governments aren't willing to face the reality of finite limits. Both the liberal, free market systems and the few remaining centrally planned (aka: communist) economies are failures in this regard. If humanity can't put the brakes on population growth, neither type of government can solve the problem except by unleashing the same 4 horsemen which have appeared throughout history as civilizations collapsed...

jon said...

The argument about few molecules is really poor. We can suggest them to pour 100 ng (10^{-10} kg) of botox (Median Lethal Dosis 1 ng/kg) over a 1 kg steak and hand it over to a 100 kg person. He will very likely die even if he is just eating 1 part per trillion of botox.

Barton Paul Levenson said...

FL: Every time I scratch a "Warmist" I get a red coating under the green surface.

BPL: I had relatives die in the fucking GULAG, you pig. If you want to call me a Commie, do it to my face. You'll only do it once.

David B Benson said...

Barton, Fernando is less than fully sane. He has a bad habit of just Making Stuff Up.

James White said...

If 400 ppm or 0.04% of that is CO2 there are 1.07 x 10 21 CO2 molecule in a cubic meter.

Isn't it 1.07 x 10 22 ? 2.69 x 10 25 * .0004 = 1.07 x 10 22, unless I've missed a step.

Dan Riley said...

Related to Bernard's comment at HotWhopper where he wrote "If all the CO2 in the atmosphere was brought to ground level at standard temperature and pressure, it would form a gaseous layer 3.04 metres (~10 feet) thick", a useful exercise is to actually shine some absorption-band IR through 3m of pure CO2 and see what happens. Spread that over the entire depth of the atmosphere and there's your ppm.