Question

Why is 1 gram = 6.02 x 10^23 amus?

Answer 1

For convenience. That way when you get together 6.02 x 10^23 things that each weigh 1 amu (like a hydrogen atom), they will weigh 1 g. That's a convenient way to measure out how many things you have, when the things are very small.

Of course, we could easily have made Avogadro's Number a nice even number, but only at the cost of redefining all the atomic weights. For example, if Avogadro's number were exactly 1 x 10^23, and the weight of a single hydrogen atom were still 1 amu, then the molar mass of hydrogen would have to become 0.16605 g. With which would you label the Periodic Table? The mass of a hydrogen atom (1 amu) or the mass of 1 mole of hydrogen atoms (0.16605 g)?

There's nothing special or mysterious about Avogadro's Number. The only reason it's not some nice even number is because we defined the gram before we knew about atoms. Presumably, if we'd discovered atoms first, and had a way to count them, we could have defined the gram to be the weight of some large even exact number of some particular atom. For example, we could've defined Avogadro's Number as exactly 1 x 10^23, and the gram as the mass of exactly 1 x 10^23 hydrogen atoms. (That would give us a "new" gram equal to about 0.16605 "old" grams.) Then the mass of the atoms would be nice even numbers (H = 1, He = 4, et cetera) *and* the molar masses of the elements would be nice even numbers *and* the Avogadro Number would be a nice even number.

But of course every *other* weight would have to be recomputed and relearned, because the definition of the gram would've changed. Good luck getting people to agree to that!

Answer 2

Hhahaha thanks that really helped.