The earth’s atmosphere is gaining mass due to fossil fuel burning. When we burn coal we add extra carbon atoms to the atmosphere in the form of CO2. For every O2 molecule that we take out of the atmosphere we simply release back an extra carbon atom tacked on. The net effect of this is to increase the total mass of the atmosphere, resulting in a net increase in atmospheric pressure. How large is this effect and are there any long term consequences? I decided to look into this after a twitter exchange. All estimates and any errors are all my own fault. First some facts.

- Molar mass of CO2 is
~~41~~44g/mol - Molar mass of O2 is 32g/mol
- Mean molar mass of air is 29g/mol

CO2 levels have increased by about 43% since 1750. This means that about 0.14% of atmospheric oxygen has been converted to CO2. This is also confirmed by measurements.

So the net fractional increase in mass for the oxygen component is 0.0014*(44-32)/32 = 0.0005. Oxygen is 20% of the atmosphere but makes up 28% of its mass. Therefore the increase in atmospheric mass caused so far by fossil fuel burning is ~~0.0011~~ 0.0014%. This works out at ~ ~~5.7~~ 7.2 x 10^14 kg

This figure is nearly half of the annual variation in atmospheric mass of 1.5 x 10^15 kg due to water vapor (1.5 x 10^15 kg). So it is certainly not negligible. This increase in mass m implies a proportional increase in surface pressure through the hydrostatic relationship

Therefore average surface pressure has increased by ~ 0.011 mb. Does such a small increase matter? What effects if any will this extra mass have?

- Firstly the slight increase in surface pressure combined with a 40% increase in CO2 density will increase the absorption of CO2 in the world’s oceans.
- Secondly the extra CO2 molecules will lead to an enhancement in the dissociation of CO2 by UV to CO and O2 in the stratosphere.
- Thirdly a higher concentration of CO2 will lead to enhanced rock weathering through the dissolving of CO2 in rainwater.

All these tend to increase the natural sinks that remove CO2 from the atmosphere over the long term. The retention of CO2 emissions is stable at about 42%, so about half of the excess is absorbed each year. This fraction has not noticeably changed for several decades. More subtle effects I can think of are as follows.

- Barometric pressure falls as There has been a very small increase in M_a (molecular weight of air) which therefore will slightly decrease the scale height. The troposphere shrinks a little.
- There would also be a very small increase in the Dry adiabatic lapse rate because for CO2 is 16% smaller than ‘air’.

The first effect would tend to offset the enhanced CO2 greenhouse effect, whereas the second would enhance it further, although this lapse rate change (1 part in a thousand) is essentially negligible. In any case, I doubt whether any of this is included in any climate model.

**Update:** corrected for Molar mass of CO2 (44 not 41)