Posted by eric on Saturday, July 24, 2010 at 1:38pm.
Eric, there are a lot of ifs, ands, and buts, in this problem but here is a somewhat simplified approach.
"Air" is composed of several gases; therefore, when we talk about the distance between "air" molecules, one wonders if we are to consider just A molecule of one of the constituents or if we are to consider air as a non-mixture. I will approach it, because it's simpler, to talk about A molecule of air and assume it is NOT composed of essentailly 4 gases (N2, O2, CO2, Ar).
The molar mass of air is about 29. A mole of air is 22.4 L at STP, if we assume 25 C and 1 atm pressure, this 22.4 L would occupy 22.4 x (298/273) = about 24.5 L so 1 L of air at room T and P will contain 6.02 x 10^23 x (1/24.5) = 2.4 x 10^22 molecules. A L container is 10 cm x 10 cm x 10 cm; therefore, if we lined molecules up along the edges of a cube we would have them cube root(2.4 x 10^22) = about 2.9 x 10^7 molecules along the 10 cm edge and that makes them about (10 cm/2.9 x 10^7) = 3.4 x 10^-7 cm from one to the other. Note however, that this considers air as as one molecule of something and not the four kinds of molecules in air.