Tutorial: Calculating the Concentration of Rare Trace Gases in the Atmosphere

The concentration of rare trace gases in the atmosphere in parts per million by volume (ppmv), parts per billion by volume (ppbv) and parts per trillion by volume (pptv) have been reported from several sources. Sustainability, chemistry, and physics students can benefit from understanding how to calculate the concentrations of rare trace gases in the atmosphere. Noting that it is the concentration of a substance which influences the chemical and physical properties of a mixture of the substance not the quantity. Here the calculations are shown from first principles and then applied to carbon dioxide (CO2), methane (CH4), nitrous oxide (N2O), sulphur hexafluoride (SF6) and carbon monoxide (CO). The masses equivalent to 1ppmv of each gas in the atmosphere are calculated and can be used in a spreadsheet or calculation to arrive at the concentration of these gases in a dry well-mixed atmosphere. This method can also be used for teaching and tutorial work with students in physics, chemistry, botany, environmental science and sustainability courses. Some worked example calculations are used to illustrate how the method can inform policymakers. It is expected that such calculations may be incorporated into models of the atmosphere or climate.