Atmospheric CO2 concentrations have increased from 280 ppmv in preindustrial times to 365 ppmv today. What is the corresponding increase in the mass of atmospheric carbon? Assume CO2 to be well mixed in the atmosphere.

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Solution

We need to relate the mixing ratio of CO2 to the corresponding mass of carbon in the atmosphere. We use the definition of the mixing ratio from the equation where NC and Na are the total numbers of moles of carbon (as CO2) and air in the atmosphere, and mC and ma are the corresponding total atmospheric masses. The second equality reflects the assumption that the CO2 mixing ratio is uniform throughout the atmosphere, and the third equality reflects the relationship N = m/M. The change DmC in the mass of carbon in the atmosphere since preindustrial times can then be related to the change DCCO2 in the mixing ratio of CO2. Again, always use SI units when doing numerical calculations (this is your last reminder!):

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