[eru]

Air molecules are large and massive, so their de Broglie wavelength is actually much smaller than their physical size (and that's much smaller than the hole needs to be to let in one at a time at ambient pressure and temperature), and you don't need to know their speeds all that well, eg if you just want to 'pump' all the air from one chamber into another.

So all in all, a classic description would work reasonably well. (Remember that quantum uncertainty is related more to de Boglie wavelength than physical size.)

[n4r9]

I'm not sure I understand - why is the wavelength size relevant? In my understanding, the standard deviations of position and momentum are at least some constant multiple of Plank's constant.

[eru]

Sorry, I meant to say that for particles (or collections of particles) with a short de Broglie wavelength classical effects dominate quantum effects.

The typical scale at which quantum effects dominate for a system is roughly equivalent to the de Broglie wavelength of the relevant parts.

Does that make sense?