# Atomic units and moles

Transcript

#### Content Reviewers:

Rishi Desai, MD, MPH

#### Contributors:

Atomic mass units and moles are units of measurement in chemistry, which allow us to easily work with very small and very large numbers.

For example, the mass of a hydrogen atom is 1.6735 times 10 raised to the negative 24th grams.

It is inconvenient to work with numbers like this for such small objects, and so chemists use the atomic mass scale instead.

One atomic mass unit is equal to 1.66054 times 10 raised to the negative 24 grams.

So in order to find the mass of a hydrogen atom in atomic mass units, we multiply the mass by the conversion factor consisting of one atomic mass unit divided by 1.66054 times 10 raised to the negative 24 grams.

The grams cancel out, and we end up finding that one hydrogen atom has a mass of 1.0078 atomic mass units, or a.m.u.

A hydrogen atom consists of a proton and an electron.

Electrons have a mass that is negligibly small compared to a proton.

As a result, we generally round the mass of an electron down to zero, and just estimate that the mass of a hydrogen atom is equal to the mass of one proton inside the atom’s nucleus.

So one proton has a mass of about one a.m.u.

For atoms containing neutrons, the mass of a neutron is almost identical to the mass of a proton, and so we say that a neutron also has a mass of about one a.m.u.

So we can estimate the mass of a given atom by counting the total number of utrons in the atom’s nucleus, which gives us the mass in a.m.u.

For example, let’s take an atom of carbon-12.

Carbon-12 has a mass number of 12 which tells us that carbon has a total of 12 protons and neutrons combined.

Since each proton and neutron has a mass of about 1 a.m.u., we would estimate the mass of the carbon-12 atom to be 12 a.m.u.

Actually, the atomic mass unit is currently defined as assigning a mass of exactly 12 amu to a carbon-12 atom.

But many elements exist in different isotopes, which have the same number of protons but different numbers of neutrons.

As a result, these isotopes have different total atomic masses.

For this reason, when we look up the atomic mass of a given element, we are actually looking up its atomic mass averaged over all of its isotopes found in nature.

For example, in the universe, the majority of hydrogen atoms have a nucleus consisting of just a single proton and no neutrons, corresponding to a mass of about one 1 a.m.u.

But there are also cases of hydrogen isotopes that have one or even two neutrons in the nucleus.

These cases are extremely rare in nature, though, and so they contribute negligibly to the average atomic mass for hydrogen.

Let’s do another example. 98.93% of all of the carbon atoms in the universe are carbon-12, and only about 1.07% of all the atoms in the universe are carbon-13.

Since carbon-13 has one more neutron than carbon 12, we would expect the mass of carbon-13 to be about 13 a.m.u.

Carbon-14 isotopes also exist, but in negligibly small quantities.

To find the average atomic mass for carbon, we convert the percent abundances into decimals, so that’s 0.9893 for carbon-12 and 0.0107 for carbon-13.

We then multiply the mass of each isotope by its respective mass, and then add these numbers.

So that would be 0.9893 times 12 a.m.u. plus 0.0107 times 13.00335 a.m.u..

This results in a weighted average value of the atomic mass of carbon, and it equals 12.01.

This weighted average is referred to as the average atomic mass or the “atomic weight” of carbon.

Note that if all of the carbon in the universe was carbon-12, then the atomic weight of carbon would be exactly 12 a.m.u.

But because there is a tiny fraction of carbon-13 in the universe, and this fraction has greater mass, there is an extra 0.01 in the atomic weight.

If carbon-13 were even more abundant, then the atomic weight would be even closer to 13 a.m.u.

The atomic weight is shown with the element symbols on most periodic tables.

Since the atomic weight is on the periodic table, you can use it to find the masses of molecules.

For example, H2O consistents of two hydrogen atoms, which each have a mass of 1 a.m.u. according to the periodic table.

One oxygen atom has a mass of about 16 a.m.u.

So 1 times 16 plus 2 times 1 gives a total mass of 18 a.m.u. for one water molecule.

We can call this the molecular mass or the molecular weight.

H2O is a covalently bonded compound, so we can call it a molecule.