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Physics/Avogadro's Law


Hi Mr. Nelson,

One of my peeves when I learned chemistry in college was that you always had to bang your head against the wall trying the understand the theory, only to eventually "get it" and ask "why didn't they just say that?". However, there is one question that I have never fully understood since it seems very counter intuitive. If I tell someone that I can stuff the same number of marbles into a car as I can bowling balls, they would probably laugh at me because that is naturally impossible; each bowling ball would take up far too much space, and the number would be minuscule compared to the number of marbles that I could put in the car. This is what is so counter intuitive about Avogadro's Law. According to his theory, as long as the material is a gas, size doesn't matter. You could have gaseous Hydrogen, or gaseous Octane fill up the car, and assuming the temperature and pressure doesn't change, you would have the same number particles in that car. How can that possibly make any sense? Octane is clearly a larger species, and, like the bowling ball, should take up more space, right?

Thanks for your help

Stuffing a car with marbles or bowling balls is like making a supersolid.  We're talking about something over a thousand times less dense if you consider the gas phase.  So his theory is sound in that phase, because the space between the atoms/molecules is far larger than the space they occupy.  Also consider that it was developed for "ideal" (zero-size) monatomic gases like helium or argon.  All atoms are, within a certain factor, about the same size.  You'd think that Argon would be huge compared to helium, but the electrical attraction between all those protons and all those electrons keeps their sizes at about 1 Angstrom.  But even with molecules, you're talking about something hundreds of times less dense than the liquid phase.

Nowadays, Avogadro's number is more precisely defined, so perhaps it's best not to dwell on older but really close theories and concentrate on modern definitions.  12g of carbon = 1 mole now. But basically there are modern gas theories that account for the size of the's just that the ideal gas law is still close because the atomic volume is hundreds to thousands of times smaller than the volume those molecules occupy as they fly around in space.  So ignore your intuition and draw all your molecules in a diagram where the space between them is somewhere around 10x the diameter of any of the atoms.  It'll make more sense that way.

Excellent question, though.


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Dr. Stephen O. Nelson


I can answer most basic physics questions, physics questions about science fiction and everyday observations of physics, etc. I'm also usually good for science fair advice (I'm the regional science fair director). I do not answer homework problems. I will occasionally point out where a homework solution went wrong, though. I'm usually good at explaining odd observations that seem counterintuitive, energy science, nuclear physics, nuclear astrophysics, and alternative theories of physics are my specialties.


I was a physics professor at the University of Texas of the Permian Basin, research in nuclear technology and nuclear astrophysics. My travelling science show saw over 20,000 students of all ages. I taught physics, nuclear chemistry, radiation safety, vacuum technology, and answer tons of questions as I tour schools encouraging students to consider careers in science. I moved on to a non-academic job with more research just recently.

Ph. D. from Duke University in physics, research in nuclear astrophysics reactions, gamma-ray astronomy technology, and advanced nuclear reactors.

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