# How many more molecules of CO2 are there in the atmosphere now than 150 years ago?

A noted global warming denier made the following observation/question:

"CO2 has increased 100ppm over the last 100 [actually 150] years.

That's just 1ppm per year, or just one co2 molecule for every million molecules of air per year.

How can anyone believe one molecule of co2 can cause any change in climate?"

So let's examine this question.

1) Approximately how many molecules are there in the Earth's atmosphere?

2) Based on this number, approximately how many more molecules of CO2 are there in the atmosphere now than 150 years ago, when there was 100 parts per million less CO2?

3) Does this number make you question whether the increase in CO2 can cause a change in the Earth's climate?

A few numbers which may be useful for this calculation:

According to the National Center for Atmospheric Research, the total mean mass of the atmosphere is 5.1480 × 10^18 kg.

The density of air at sea level is about 1.2 kg/m³.

Update:

Carl E - with regards to CO2 saturation, I suggest you read the response to comment #10 here:

http://www.realclimate.org/index.php/archives/2006...

Also 250 years ago we were in the middle of the Little Ice Age.

Update 2:

250 million years ago is irrelevant to today's climate. There was more CO2 in the atmosphere and thus a higher temperature, and a completely different set of species inhabiting the planet.

Update 3:

Carl - I don't want to go into this discussion because it doesn't apply to this question. If you'd like to discuss these issues you can ask a seperate question or email me. And check out the link above.

Update 4:

Carl - if you're going to dismiss a physical discussion written by a physicist as equivalent to political propaganda, then I don't know what to tell you. I suppose you probably think all scientists are liberally biased.

Update 5:

evans - that has to be a first!

Update 6:

Relevance

Interesting to see how numerate people are. Lets take a wild guess and say 1.07 x 10^40 more molecules of CO2 with an absorption cross section of 5.35 x 10^12 km^2 at 14 microns.

A trivial solution using grade 10 chemistry is

n = N(sub A)*f(sub v)*M(sub a)/m

where

N(subA)= Avagadro's number = 6.022 E23

f(sub v ) is the volume fraction of CO2 =100 ppm

M(sub a) is the mass of the atmosphere = 5.148E18 kg

m = average molar mass of air =2.9E-2 kg

and the absorption cross section of CO2 is 5E-18 cm^2

This solution assumes that the mass of the atmosphere is constant, the average molar mass of air is constant and that the atmosphere behaves like an ideal gas. These are good approximations, but not valid in a more detailed analysis.

Why would a 1/e barrier 10,500 times the size of the earth's surface have any effect on climate? Or put another way, how could an infrared photon passing through 10,500 gates with a 1/e probability of getting through each one possibly effect the photon's path? To a physicist, the answer is obvious: CO2 has an effect on radiative transfer. The same problem, aside from scaling, is a very important part of the physics of photon propagation in tissue used for medical imaging. For references search " photon diffusion theory".

• 7 years ago

I know this is a bit belated. I took this approach to solve. I assumed that CO2 acts like an ideal gas. The temperature of the atmosphere today is 1.5 K higher than it was 150 years ago. So Today if the temp. is 288 K then 150 years ago it was 286.5 K. The Atmospheric pressure I will use is 1 Atm, although the pressure goes down as we increase altitude. To k.i.s.s. I did not adjust for a changing pressure with altitude. I calculated the spherical volume of the solid earth with a mean volumetric radius of 6371 km and then the volume of the sphere using that same radius + 8.5 km of atmosphere we are focused on (higher altitudes have an insignificant amount of CO2). I took the difference of the larger volume with the atmosphere and the smaller volume of just the solid earth, for a volume of 4.34 x 10^9 km^3 of air in the atmosphere we are going to focus on. Convert that to liters for use in our gas law equation; you should get 4.34 x 10^21 L. Using Pv=nRT, where Pressure is 1 atm. and Volume for the 2 different scenarios of today's concentration of CO2 and the concentration of CO2 150 years ago, would be (.000400 x 4.34 x 10^21 L ) and(.000250 x 4.34 x 10^21 L), if today there are 400ppm of CO2 and 100 years ago there were 250 ppm. Now the volume is 1.74 x 10^18L for the current atmosphere and 1.09 x 10^18 L for the atmosphere 150 years ago. Plug the correct values in the Ideal Gas Law equation for each scenario: 1 Atm (1.74 x 10^18L) = n (.0821 L.atm/mol.K)(288K) = 7.34 x 10^16 moles of CO2 1 Atm (1.09 x 10^18L) = n (.0821 L.atm/mol.K)(286.5K) = 4.61 x 10^16 moles of CO2

Multiply each mole calculation by Avogadro's number: you get 4.42 x 10^40 molecules of CO2 today and

2.78 x 10^40 molecules of CO2 150 years ago. The difference is a scant (jk) 1.64 x 10^40 more CO2 molecules today in the atmosphere than there was 150 years ago. Any change in vegetation consumption of CO2 and rate of ocean limestone uptake of CO2 may actually change the value a bit, and

• gcnp58
Lv 7

Carl:

If you cook a turkey for 3 hours and then take the turkey out of the oven, it is cooler inside two minutes later. That is a better analogy than yours since the oven doesn't cool immediately, it stays warm, radiating heat to the turkey.

Skeptics love to talk about "thermal flywheels" etc. but none of them can really provide realistic mechanisms by which such things would work. Heat isn't stored anywhere for release years later. Even "mode" water isn't really all that much warmer than surface water, and it never makes it back to the surface anyway (which is why it gets called mode water).

Rising levels of CO2 affect radiative transfer. Just agree with that premise and call it a day.

I suppose nobody wants me to point out that if hydrogen cyanide or hydrogen sulfide were increasing in concentration by the same amounts as CO2 over the same time span, we would all be dead now. Clearly 1 ppm per year increase of CO2 would have no effect on anything.

TC: Last time I checked, it was a thermodynamic law or something that heat goes from hot things to cold things. Most of the ocean is relatively cold, about 277 K. The average temperature of the atmosphere at the surface is somewhat warmer at around 300 K. So if the ocean is storing heat and then releasing it years later back to the atmosphere, which is what a flywheel mechanism must do, it is doing it in a very bizarre way since you need to move heat from a mostly cold body to a mostly warmer body. Even if you want to think outside the box, you still have to remain in the larger box of known physical laws.

• J S
Lv 5

If Dr. Jello says it's one molecule, and he's a Dr...

Nah, I'll go with the scientists and the short cut answer of 35% increase.

If greenhouse gases are responsible for about 22 degrees of warming (I don't know of anyone who disputes that), even if CO2 isn't responsible for a lot of it the CO2 increases already may have us on hook for a few degrees of warming. The process may be slow and take a while as additional CO2 outgassing from the ocean due to the initial warming takes several hundred years, and that additional CO2 provides additional feedback and warming.

Having worked in a lab that measured PCBs, PAHs, and dioxins at the ppm detection level...I know first hand how much a few ppm can affect the environment. The argument as stated doesn't hold water. (Mark this one down Dana, I'm in agreement with you).

• Tomcat
Lv 5

Not enough to matter.

http://en.wikipedia.org/wiki/Image:Atmospheric_Tra...

Psssst.... GCNP58

It's not how warm the surface of the ocean is, it is how cold it is that plays the most important part of regulating the climate, try to think outside the box every once and awhile. everything that is above absolute zero contains heat and thermal equilibrium is the throttle for all engines.

.

• Ken
Lv 5

Carl - comparing co2science with realclimate is a complete apples and oranges thing. co2science has a bunch of policy advisers, a family (Idso's) with some science (but no climate research training or experience) running it, and some known funding from the energy industry. realclimate is a group of active climate scientists currently involved in climate research working mainly for government research facilities, and they are not paid for their efforts. A better comparison would be co2science and the Sierra club, but not realclimate.

I could answer you Dana, but I'll wait and see if any of the doubters can do math.

• Bob
Lv 7

Carl E - the change in temperature 250 years ago was probably due to a change in solar radiation.

We know it's not that now because (duh) we measure the Sun.

"Recent oppositely directed trends in solar

climate forcings and the global mean surface

air temperature", Lockwood and Frolich (2007), Proc. R. Soc. A

doi:10.1098/rspa.2007.1880

http://www.pubs.royalsoc.ac.uk/media/proceedings_a...

News article at:

http://news.bbc.co.uk/1/hi/uk/6290228.stm

Thousands of independent climatologists all over the world agree that the present warming is mostly caused by greenhouse gases, mostly CO2.

Against that, you have a few skeptics disagreeing with the mainstream theory, AND with each other.