posted by eric on .
On average, how far is a molecule of air in the room in which you're sitting from the nearest molecule of air to it, assuming it is an ideal gas. Make appropriate assumptions about the temperature and pressure.
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.