Question

Why is the atomic mass unit (amu), rather than the gram, used to express atomic mass?

Answer 1

Because atoms are ridiculously small.

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And the `"amu"` is numerically equivalent to the `"g/mol"`. For instance, if I were to be so lucky as to isolate `"1 atom"` of `"N"`, it would have a mass of

`14.007 cancel"amu" xx (1.6605 xx 10^(-24) "g")/(cancel"1 amu")`

`= ul(2.326 xx 10^(-23) "g")`

which is immeasurably small. We don't care for masses that small because we physically can't see or measure it. Instead, we care for masses we can touch, like `"1.000 g"` or `"12.50 g"`.

And that involves:

`1.000 cancel"g N" xx cancel"1 mol N"/(14.007 cancel"g N") xx (6.022 xx 10^23)/(cancel"1 mol")`

`= ul(4.299 xx 10^22 "N atoms")`

`12.50 cancel"g N" xx cancel"1 mol N"/(14.007 cancel"g N") xx (6.022 xx 10^23)/(cancel"1 mol")`

`= ul(5.374 xx 10^23 "N atoms")`

You can clearly tell that this number of atoms is impossible to count. And so Avogadro's number, `6.022 xx 10^23 "mol"^(-1)`, was invented to describe this many particles...

`4.299 xx 10^22` `"N atoms" xx ("1 mol")/(6.022 xx 10^23)`

`=` `ul"0.0714 mols N"`

`5.374 xx 10^23` `"N atoms" xx ("1 mol")/(6.022 xx 10^23)`

`=` `ul"0.8924 mols N"`

And as you can see, these numbers look much nicer and more physically useful.