Mixing ratios, concentrations and different units:
Amounts of gases are often given in different units:
concentrations: molecules cm-2 or µmol m-3
or mixing ratios: ppt (pmol mol-1), ppb (nmol mol-1), ppm (µmol mol-1), % (10 mmol mol-1)
Mixing ratios are often more helpful for scientists. When air rises, it expands in volume and, as a result, the concentration of the gas changes. The mixing ratio (relative proportion of the gas to the total number of air molecules), however, remains the same.
Conversion from one unit to the other depends on the pressure (= the altitude) and the molecular weight of the compound. If we do the calculation for the surface of the Earth at a normal pressure of about 1 bar we can express the total molecules per volume of air in the following way:
1 mol = 22.4 L = 6x1023 molecules =>
1 cm3 = 2.7 x 1019 molecules
1 dm3 = 1 L = 2.7 x 1022 molecules
1 m3 = 2.7 x 1025 molecules
A rough estimate:
2 µg m-3 = 2 x 10-6 g m-3 NO2 is a typical value for nitrogen dioxide in a non-urban area.
the molecular weight of NO2 = 46 g mol-1
This means: 2 x 10-6 g m-3 = 4.3 x 10-8 mol m-3 = 2.6 x 1016 molecules m-3
So the mixing ratio is about 2.7 x 1016 / 2.7 x 1025 = 10-9 = 1 ppb
Since ozone has a similar molecular weight, M(O3) = 48 g mol-1, we can also say roughly that;
2 µg m-3 of ozone = 1 ppb
This calculation is valid only for surface of the Earth where we live. So for ozone smog events in urban areas we can now calculate:
120 µg m-3 = 60 ppb -> high levels
240 µg m-3 = 120 ppb -> very high levels, no sports, risky for health
360 µg m-3 = 180 ppb -> extremely high levels, very unhealthy for the lungs, stay at home!
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