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

Oct 5, 2017

Because atoms are ridiculously small.

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

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

$= \underline{2.326 \times {10}^{- 23} \text{g}}$

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 $\text{1.000 g}$ or $\text{12.50 g}$.

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")

$= \underline{4.299 \times {10}^{22} \text{N atoms}}$

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

$= \underline{5.374 \times {10}^{23} \text{N atoms}}$

You can clearly tell that this number of atoms is impossible to count. And so Avogadro's number, $6.022 \times {10}^{23} {\text{mol}}^{- 1}$, was invented to describe this many particles...

$4.299 \times {10}^{22}$ "N atoms" xx ("1 mol")/(6.022 xx 10^23)

$=$ $\underline{\text{0.0714 mols N}}$

$5.374 \times {10}^{23}$ "N atoms" xx ("1 mol")/(6.022 xx 10^23)

$=$ $\underline{\text{0.8924 mols N}}$

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