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

1 Answer
Oct 5, 2017

Because atoms are ridiculously small.


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.