The main requirement for the hole is that it's small enough that (with high enough probability) only at most one or a handful of molecules will make its way through.
And that size is completely independent of the size of your molecules, and only depends on how many there are per unit volume. There's a lot of 'empty space' between molecules in a gas.
Good question. I was going off the linked article which states:
> In the middle of the divider was a tiny gate, just large enough to admit one molecule of gas.
Still, that's quite a small hole relatively speaking. So you'd have to be fairly precise about both position and velocity. Potentially more than is allowed by Plank's constant. I dunno though, this isn't one of the counterarguments in the Wikipedia page, so probably you're right.
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.)
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.
The main requirement for the hole is that it's small enough that (with high enough probability) only at most one or a handful of molecules will make its way through.
And that size is completely independent of the size of your molecules, and only depends on how many there are per unit volume. There's a lot of 'empty space' between molecules in a gas.