# Density of air using ideal gas law

I need to find the density of air using (I think) the ideal gas law. I have calculated $V$ of an ideal gas at s.t.p. to be $.0224m^3$. I am asked to find the density of air knowing it's temperature ($20^\circ$) and atmospheric pressure. I have looked up online however I feel the methods I find are skipping steps from where I am currently. Where do I go from here? $$pV = nRT$$

• number density, or mass density? – anon01 Apr 22 '16 at 12:06
• Solving for n after you input p V and T seems like a good next step. – pentane Apr 22 '16 at 13:06

The ideal gas law says you something about $p$, $V$ and $T$ in terms of the number of particles. That's nice, because it holds approximately for all gases. For a given $p$ and $T$ you know the number per volume - it is independent of the type of gas!
So now you have to rewrite your equation: the $n$ has to go, you want to have $m$ instead, and the molar mass. And then you can bring $m/V$ to one side, and there you are. Do you see the way now?
• I have the molar mass of air, $M_{air}$ = 28.8x$10^{-3}$, and I divided that by $N_A$ to get $m$ = 4.78x$10^{-26}$. Do I then use the ideal gas law to get a volume for this or what V do I use? – davkav9 Apr 22 '16 at 11:59
• the ideal gas law is still valid; you have just to replace the $n$ and bring the desired $m/V$ on one side. – Ilja Apr 22 '16 at 12:13
• as to your calculation: no, M is not 28g, it 28 g/mole... and you need just this to replace the $n$ (which is the number of moles). You calculated the mass of one particle; which is interesting to have a feeling for the magnitude, but you don't need it. – Ilja Apr 22 '16 at 12:14