How much carbon is there in the atmosphere?

The surface area of Earth is 510 x 1012 m2, while the scale height of the atmosphere is around 8800 m (see the section on Boltzmann's law in Chapter 2). Consequently, the volume of air (all of it compressed to 1 atmosphere pressure) is 510 x 1012 x 8800 = 4.5 x 1018 m3.

Present-day atmospheric CO2 concentration is 13.5 x 10~6 kmol/ m3. The atmosphere contains 13.5 x 10~6 x 4.5 x 1018 =61 x 1012 kmol of CO2 and, therefore, 61 x 1012 kmol of carbon. Since the atomic mass of carbon is 12 daltons, the mass of carbon in the atmosphere is 0.73 x 1015 kg. Compare with the 0.825 x 1015 kg of the table.

A simpler way to achieve about the same result is to consider that the atmospheric pressure at sea level is 1 kg/cm2 or 104 kg/m2. Consequently, the total mass of the atmosphere is 510 x 1012 x 104 = 510 x 1016. Of this, 360 x 10~6 is carbon dioxide and 12/44 is carbon. The carbon content of the atmosphere is 510 x 1016 x 365 x 10~6 x 12/44 = 0.51 x 1015 kg, a result comparable with the previous one.

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