Avogadro's constant is not itself a heavily-used value in chemistry. Its derivation is obvious if you think in a different way:
You need to convert from mass to numbers of molecules, which means you need to divide it by the mass of a molecule. The mass of a molecule is determined by the sum of the weights of each of the atoms, themselves the weights of their constituent nucleons [1]. If you fix the weight of a nucleon to be 1 (that is, we measure in daltons), then computing the weight of a molecule such as glucose (aka C₆H₁₂O₆) in daltons is a trivial formula. All you need is a periodic table that lists atomic weights, which is every copy you find a chemist using. It's worth noting that the resulting molecular weights are going to be independent of whatever measuring system you want to use [2], whether it be grams, ounces, alien flits, what have you.
Now you need to convert the mass of your substance into a count of "stuff-loads" of molecules. The simplest and most idiotic thing to do is to define a "stuff-load" to be the amount of molecules in a unit mass if it weighs 1 dalton--in other words, you make this formula be exactly one. In SI, the unit mass for this equation is grams and the "stuff-load" is the mole. If we were using US ounces as the unit mass, we'd define an ounce-mole and use that instead of SI moles.
Put another way: we define a mole such that the constant in the computation of moles from molecular weight and mass is exactly 1. Avogrado's constant itself is merely the inverse of the mass of a nucleon when expressed in grams.
[1] Okay, there's a lot more that goes on into the computation of mass. In terms of the mathematical error, though, other sources of error (e.g., wrong isotopic ratio) are going to matter before these come up.
[2] Up to the slight adjustment (about ±1%) of what you consider the weight of a nucleon to actually be.
An Avogadro's constant number of molecules is one mole. One mole of hydrogen has much less mass than one mole of iron. You have to choose an arbitrary mass of a single element as the base quantity. Hydrogen might be the best theoretically, it's just a proton and an electron, but it is tricky to work with because it's a gas at room temperature. So instead the mole has been defined as the number of molecules in a specific mass of carbon-12.
I think this is exactly the rationale. But, from a more practical perspective...
If instead of g/mol, we referred to molecules/g -- we would end up populating tables and charts with really big numbers. This would make lookup tables hard to read, difficult to publish, and hard to work with. Imagine if you had to do math with a bunch of 10^23 exponents all of the time.
Instead, it was agreed to effectively pull out a constant value from each of those to make the math significantly easier. Now, instead of dealing with a lot of big numbers, all of the lookup tables could now list smaller g/mol values. And we would be left with just the one single large (Avogadro's) number in the equations.
Honestly, we don't need a set mole constant, but it makes chemistry significantly easier to do so. Unlike the other constants mentioned in the OP, Avogadro's number is completely arbitrary. It could be '1' as the parent suggested, except then it makes the rest of the math more difficult.
Even for this SI overhaul, we didn't really even need to redefine the mole, except for the fact that it was previously defined in terms of the old kg. This was just "fixing a glitch".
> Even for this SI overhaul, we didn't really even need to redefine the mole, except for the fact that it was previously defined in terms of the old kg. This was just "fixing a glitch".
I came to complain about the article calling the mole a "base unit of the SI", and this seems like an appropriate thread.
Why is the mole a defined unit at all? As far as I understand things, "one mole" is the same thing as Avogadro's number -- neither can be a unit, because they're both dimensionless constants (well, they're both one and the same dimensionless constant). Applying actual units, "one mole of water molecules" is the same thing as "Avogadro's number of water molecules". Avogadro's number, and therefore the mole, is the conversion factor between atomic mass units and grams. Similarly, 3 is the conversion factor between feet and yards, but nobody thinks 3 is a fundamental base unit of the imperial system. The foot is a base unit of the imperial system, measuring length, the yard is a non-base unit also measuring length, and 3 is a number with no special relationship to the system at all. It would be total nonsense to say that yards are defined by reference to 3. How is Avogadro's number different?
Wouldn't "fixing the glitch" be abandoning the idea of calling the mole a unit in the first place?
I'm pretty sure the mole is not defined as 6 * 10^23 mol^{-1}.
There is a concept of "the Avogadro constant", which is defined to have units of mol^{-1} (at least, according to a cited statement on wikipedia), but that is not a coherent concept -- since mol is dimensionless, mol^{-1} is also dimensionless.
> Since its adoption into the International System of Units in 1971, numerous criticisms of the concept of the mole as a unit like the metre or the second have arisen:
> the number of molecules, etc. in a given amount of material is a fixed dimensionless quantity
> the mole is not a true metric (i.e. measuring) unit
> One unified atomic mass unit is approximately the mass of one nucleon (either a single proton or neutron) and is numerically equivalent to 1 g/mol.
amu and g are both units of mass, so 1 amu = 1 g/mol is an explicit statement that mol is dimensionless.
Calling mol a unit won't accomplish anything except corrupting your dimensional analysis. mol is not analogous to the SI units meter, second, ampere, gram, kelvin, etc. -- it is analogous to the SI prefixes kilo-, mega-, milli-, micro-, nano-, etc.
> Imagine if you had to do math with a bunch of 10^23 exponents all of the time.
What if it was just set to 10^24 then? Much easier to remember and serves the same purpose.
If it was 1 it would work too, since the SI system already has a way to deal with large numbers: prefixes. So we might wrote Ymol for yotta mole = 10^24 mol.
Why does it need to be based on the mass of an arbitrary molecule? Can't it just be 10^23 or 10^24? Most of the time, you're going to have to look up constants to convert moles to mass anyways.
Yeah, I think that's his idea. So, instead of tables of molar mass in g/mol, you would have tables in terms of "amount of substance"/g. E.g. number of atoms or number of molecules.
