I do not know about the best way, however if you for orientation consider the ideal gas law to be accurate, you can see that you can relatively easily determine the number of moles of the atoms in your cylinder by some simple measurements (we know what atoms air is composed of and their ratio*)). You could along the same line improve the accuracy of your results by using the virial expansion. For details, you may consult any good textbook on thermodynamics and statistical physics. In particular, you may consult the excellent book Modern Course in Statistical Physics, 2nd edition, by LE Reichl (John Wiley & Sons, New York, 1998); see in particular Sec. 2.C, Some Mechanical Equations of State, herein.

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*) https://en.wikipedia.org/wiki/Atmosphere_of_Earth

You may take the specific volume (m3/kg) of compressed dry air from Table 2-229 entitled "Thermophysical Properties of Compressed Air", or/and that of saturated air from Table 2-228; both at: R.H. Perry, D.W. Green, J.O. Maloney (Eds.), "Perry’s Chemical Engineers’ Handbook", 7th ed., McGraw-Hill, 1997.