Avodadro's number

I probably should be able to remember this from college/high school, but I can’t.
In this column Son of Dex explains Avogadro’s number pretty well, but I got confused when he said:

It sounds circular to me. If a mole were defined as half of what it is now, then H[sub]2[/sub] would weigh 1 g/mol and 1 mole would weigh 1 gram and everything would still work out, right? (I assume not, but don’t know why.)

Uh, what do you mean by “working out”? What possible use would it be to have a number that gives you half of the gram-molecular weight? Avogadro’s number is a measurement, the number of particles in a mole. The definition of a mole is one of convenience, so that you can convert from molecular weights to mass without arithmetic.

There’s the problem, right there. Hydrogen has a molar weight of 2 g/mol. It has a molecular weight of 2 amu/molecule. An amu is (approximately) the mass of a proton or neutron. In other words, there are two nucleons in a molecule of hydrogen, so a mole of hydrogen is two grams. There are 32 nucleons in a molecule of normal oxygen, so a mole of oxygen is 32 grams, etc.

Chronos has gotten to the gist of it: one mole of protons and/or neutrons (nucleons) weighs one gram – or close enough for government work.

Think of Avogadro’s number as a wonderful convenience: it allows mass and the number of nucleons in an atom/molecule to be numerically interchangeable.

Thanks. I understand now. :slight_smile:


Follow-up question: why the word “mole”? where does it come from? :confused: (and, how much would a mole of moles weigh? :eek: )

From the word “molecule”.

To put it most simply, it comes from Latin: moles, “mass” (molecule is the diminutive of moles). However, the word “mole” is actually short for molekulargewicht, German for “molecular weight.”

Properly defined, it’s “the amount of pure substance containing the same number of elementary entities as there atoms in 12 grams of carbon-12.” Since there is no “elementary entity” called a mole, there can be no such thing as a mole of moles. If what you mean is “how much would Avogadro’s number, squared, of something mass?”, all I can say is, it masses 6 x 10[sup]23[/sup] times the molar mass of whatever it is. Hydrogen, f’rinstance, would be 6 x 10[sup]20[/sup] kilograms; everything else would mass even more.

I understood NP’s question to be “how much would one mole (chemist definition) of moles (the little animals) be?” In that case, the answer would be that a mole of moles would fill up a box with each side being 84 million moles long, which works out to be about the size of the Earth.

I assumed that if NP had meant those kind of moles, he’d’ve specified the eastern mole, hairy-tailed mole, star-nosed mole, broad-footed mole, Townsend’s mole, or one of the others.

Y’know, “African or European” and all that.

I can’t believe nobody has fixed the thread title yet. Shouldn’t that be Avacado’s Number? :wink:

We only bother to fix thread titles if they’re misleading or enormously unclear (like a threat title “My Question”, say).

:: Singing (to tune of “Oklahoma”)::

It’s the finest fruit that’s known to man!
It’s so bright and clean,
So nice and green;
And it’s fresh, not taken from a can!

Chronos wrote:

Actually, it’s worse than that.

Hydrogen gas, H[sub]2[/sub], has a molar weight of 2.0158 g/mol, and a molecular weight of 2.0158 amu/molecule.

And this little difference, this little deviation from exactly 2.00000000 g/mol, isn’t due to the 2 electrons. They only contribute about 0.001 g/mol. The difference is because, despite the fact that a [sup]12[/sup]carbon nucleus is made up of six protons and six neutrons, it weighs slightly less than six protons and six neutrons taken separately. And our mole/amu system is based around [sup]12[/sup]carbon.

Why is a [sup]12[/sup]carbon nculeus lighter than the sum of its parts, I hear you cry? Why, because of binding energy! Lots and lots of binding energy! If you take six protons and six neutrons and slam them together to make a [sup]12[/sup]carbon nucleus*, you release a tremendous amount of energy in the process. It’s called nuclear fusion. You release so much energy, in fact, that it lowers the mass of what’s left over. E = mc[sup]2[/sup] and all that. Thus, the [sup]12[/sup]carbon nucleus, which is essentially the “ashes” of a 6-proton-6-neutron fusion reaction, weighs a little bit less than 6 protons and 6 neutrons.

[sub]*) Well, okay, you can’t form a [sup]12[/sup]carbon nucleus directly by slamming 6 protons and 6 neutrons into each other. For one, bare neutrons only have a half-life of 15 minutes. You can, however, bash 2 protons into each other to form a deuteron (a heavy hydrogen nucleus), then smash another proton into the deuteron to form a [sup]3[/sup]helium nucleus, then smash this into another [sup]3[/sup]helium nucleus to form an alpha particle (a [sup]4[/sup]helium nucleus) and release a couple of protons as by-products, then you can slam three of those alpha particles together to form your [sup]12[/sup]carbon nucleus.[/sub]

not quite =)

2 protons won’t smash into eachother. There is simply too much of what relativity has come to call “the strong force” or “nuclear force” I think this is just semantics - you probably meant to say:

“bash a proton into a NEUTRON to form a deuteron (a heavy hydrogen nucleus)”

From here on out, your chemistry is a little off. Atomic number, and thus the element, is defined by the proton count. So smashing protons together DOESN’T make the “heavy” version of that element; the heavy version has additional NEUTRONS.

H has 1 proton, 1 electron
Deuterium has 1 proton, 1 neutron, 1 electron
Tritium has 1 proton, 2 neutrons, 1 electron
Helium has 2 protons, 2 neutrons, 2 electrons
Alpha Particles are 2 protons, 2 neutrons, no electrons.

you can do the theoretical atom smashing from here, ad nauseum. But ask a rocket scientist how often smashing two particles actually yields what they are looking for =)