_{2}than Earth and is colder than Earth so CO

_{2}can't be causing global warming" claim. This one is usually based on the fact that Mars has an atmosphere that is 95.32% CO

_{2}by volume whereas Earth's atmosphere is only 0.04% CO

_{2}. Unfortunately, all that claim reveals is that whoever is making it didn't get very far in a science class.

If Mars and Earth had the same size atmosphere, then a direct comparison between percentages would be valid. They don't. Measurements show that the Martian atmosphere has a mass of 2.5 x 10

^{16}kg whereas Earth's atmosphere has a mass of 5.1 x 10

^{18}kg. That's right—Earth's atmosphere is 204x more massive than the Martian atmosphere. So we must account for that difference in size before comparing the amount of gas in the atmosphere. The way to do this is simple. Convert percentage volume to percentage mass using moles, then multiply the percentage mass by the total mass of the atmosphere. For those who have forgotten what a mole is, you can partially resurrect those long buried nightmares of general chemistry here.

Given the following

1 mole CO

_{2}= 44.0095 g/mole

Mars:

Total atmosphere mass: 2.5 x 10

^{16}kg

Mean molecular mass of atmosphere: 43.34 g/mole

% volume CO

_{2}: 95.32%

The total mass of CO

_{2}in the Martian atmosphere is

95.32% volume x (44.0095/43.34) = 96.79% by mass CO

_{2}

96.79% mass x 2.5 x 10

^{16}kg = 2.383 x 10

^{16}kg CO

_{2}

The equivalent calculation for Earth is

Earth:

Total atmosphere mass: 5.1 x 10

^{18}kg

Mean molecular mass of atmosphere: 28.97 g/mole

% volume CO

_{2}: 0.04%

0.04% volume x (44.0095/28.97) = 0.0608% mass CO

_{2}

0.0608% mass x 5.1 x 10

^{18}kg = 3.101 x 10

^{17}kg CO

_{2}

Last time I checked, 3.101 x 10

^{17}kg is larger than 2.383 x 10

^{16}kg by over 13x.

Now I can hear someone saying "Wait a second. Earth is larger than Mars." Ok. We can normalize the amount by dividing it by the surface area of the respective planet. Given

Martian equatorial radius = 3396.2 km

Earth equatorial radius = 6378.1 km

Surface area of a sphere = 4πr

^{2},

the surface area of Mars is 144,942,710.74 km

^{2}and the surface area of Earth is 511,201,962.3 km

^{2}. Dividing the amount of CO

_{2}by the surface area gives us

Mars: 164,409,785.62 kg CO

_{2}per km

^{2}

Earth: 606,609,565.04 kg CO

_{2}per km

^{2}

Which means Earth has 3.69x more CO

_{2}than Mars, even after accounting for the different sizes of the planets. No matter how you want to look at it, the claim that Mars has more CO

_{2}than Earth should be just plain dead.

So if Earth has 3.69x more CO

_{2}per unit area than Mars, why is CO

_{2}such a large part of the Martian atmosphere and such a small portion of Earth's atmosphere? The answer is nitrogen, oxygen, and argon. Those gases comprise >99.5% of Earth's atmosphere, virtually none of Mars'. Strip away the nitrogen, oxygen, and argon from Earth's atmosphere and of the gases that would be left, CO

_{2}would make up 99% of the atmosphere by volume, an even higher percentage than on Mars.

0.0608% mass x 5.1 x 10^18 kg = 3.101 x 10^15 kg CO2

ReplyDeleteLast time I checked, 3.101 x 10^15 kg is smaller than 2.383 x 10^16 kg about 8x.

10^17 is correct. 10^15 is not.

DeleteDisagreed:

Delete10^15 is correct. 10^17 is not.

Do I need to point out 0.0608%=0.000608?

The whole post is based on a simple arithmetic mistake. What's most funny, is its unintended support for the 'patently false claim'.