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Name: R. Casao
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Date: 1999 


Question:
A student asked me how it was determined that one mole of any gas at STP occupies a volume of 22.4 L. I was initially at a loss. An interesting question! I explained Avogadro's Law and figured it was an experimental determination, because if you use the Ideal Gas Law 22.4 L would be the given answer for any gas at STP. I believe that I satisfied her curiosity. Is there anything I can add?



Replies:
Dunno if it means you want to add something, but I have two comments. First, the fact that *all* gases have nearly the same molar volume occurs because the molecules in a gas are so far apart on average that they almost never affect each other. If they do not affect each other, then the properties of the gas are determined just by how fast they are going, (i.e. the temperature) and how many of them you've got. It doesn't matter what shape or size they are. This can be proved.

Secondly, the ideal gas law is not empirical, that is the figure of 22.4 does not need to be measured. *Given* the assumption that the molecules do not interact, you can derive the ideal gas law, and given the definitions of the units of mass, energy and temperature you may derive the 22.4 mathematically. The only reason the number is not known precisely is because the mole is defined arbitrarily not as exactly 6.022 x 10^23 atoms --- which it certainly could be --- but rather as equal to *whatever* number of atoms there are in exactly 12 grams of carbon-12. And *that* number is not known precisely. (It's not empirical either, though; you could calculate the density of carbon from first principles, but measurement is a lot easier and more accurate way to go at the moment.)

christopher grayce



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