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We need some facts about dry air. But the bottom line seems to be molecular weight of dry air M = 0.0289644 kg/mol, with some room for adjustments in the last two digits. This is quite adequate for the purpose. My best calculation gives M = 0.0289652 kg/mol.

Roughly, considering only nitrogen and oxygen and using 80%/20% instead of 78%/21%, the average molecular weight of air is about 0.8 * 0.028 + 0.2 * 0.032 = 0.0288 kg/mol.

By volume, the earth's atmosphere contains:

  • Molecular weight of N2 is 2*14.0067 g/mol, 78.084% of air
  • Molecular weight of O2 is 2*15.9994 g/mol, 20.946% of air
  • Molecular weight of Ar is 39.948 g/mol, 0.9340% of air
  • Molecular weight of CO2 is 44.01 g/mol, 365 ppmv of air

From the NASA page cited by the above link:

Atmospheric composition (by volume, dry air): 
    Major      : 78.084% Nitrogen (N2), 20.946% Oxygen (O2), 
    Minor (ppm): Argon (Ar) - 9340; Carbon Dioxide (CO2) - 350
                 Neon (Ne) - 18.18; Helium (He) - 5.24; CH4 - 1.7
                 Krypton (Kr) - 1.14; Hydrogen (H2) - 0.55 

Wikipedia adjusted the CO2 and the CH4 values.

      NASA        Normalized  difference  Wikipedia   Normalized  difference
N2    780840.000  780826.874 13.126       780840.000  780815.127 24.873
O2    209460.000  209456.479  3.521       209460.000  209453.328  6.672
Ar      9340.000    9339.843  0.157         9340.000    9339.702  0.298
CO2      350.000     349.994  0.006          365.000     364.988  0.012
Ne        18.180      18.180  0.000           18.180      18.179  0.001
He         5.240       5.240  0.000            5.240       5.240  0.000
CH4        1.700       1.700  0.000            1.745       1.745  0.000
Kr         1.140       1.140  0.000            1.140       1.140  0.000
H2         0.550       0.550  0.000            0.550       0.550  0.000
     1000016.810 1000000.000             1000031.855 1000000.000

Using the normalized Wikipedia values I get 28.9652 as the average molecular weight of dry air, very close to the value quoted in Wikipedia:Density of air:

Gas  M.W.        NASA ppm    Normalized  avg M.W.   Adjust ppm  Normalized  avg M.W.
N2   28.0134     780840.000  780826.874  21.8736156  780840.000  780815.127  21.8732865
O2   31.9988     209460.000  209456.479   6.7023560  209460.000  209453.328   6.7022552
Ar   39.948        9340.000    9339.843   0.3731080    9340.000    9339.702   0.3731024
CO2  44.0095        350.000     349.994   0.0154031     365.000     364.988   0.0160629
Ne   20.1797         18.180      18.180   0.0003669      18.180      18.179   0.0003668
He    4.002602        5.240       5.240   0.0000210       5.240       5.240   0.0000210
CH4  16.04246         1.700       1.700   0.0000273       1.745       1.745   0.0000280
Kr   83.798           1.140       1.140   0.0000955       1.140       1.140   0.0000955
H2    1.00794         0.550       0.550   0.0000006       0.550       0.550   0.0000006
                                         28.9649938                          28.9652189

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