### Video Transcript

How many moles of atoms are there
in 12 grams of carbon-12?

Carbon-12 is the name for a
specific isotope of the element carbon. We can find the entry for carbon on
the periodic table of elements, which tells us the symbol for carbon is C and that
the atomic number for carbon is six. We can use this information to tell
us a little bit more about what an atom of carbon looks like. As with all atoms, we have a
nucleus surrounded by an electron cloud. The atomic number tells us the
number of protons in atoms of carbon. So, in this nucleus, we have six
protons.

By definition, an atom is neutral
overall. So, we need six electrons to
balance the charge of the six protons. However, there’s one bit of
information we’re missing. An atom of carbon-12 contains a
specific number of neutrons. When we label isotopes, we use the
mass number. In this case, the mass number of
carbon-12 is 12. The mass number of an isotope is
simply the number of protons plus the number of neutrons to be found in nuclei of
that isotope.

To work out the number of neutrons
in our atom of carbon-12, we simply take the atomic number away from the mass
number, giving us six, six neutrons in the nucleus. So, we now know what we’re talking
about, neutral atoms of carbon-12 consisting of six protons, six neutrons, and six
electrons each.

The question tells us that we have
exactly 12 grams of carbon-12. To work out the absolute number of
atoms, we could take our mass and divide it by the mass of each atom. However, this would be the amount
of atoms we have. But the question is asking for the
amount of atoms in moles. One mole of atoms is equivalent to
an Avogadro’s number of atoms, which is an astonishingly big number, about six times
10 to the power of 23. So, to get the number of moles of
atoms not simply the number of atoms, we have to divide our mass by the mass per
mole for carbon-12.

You might see mass per mole
referred to as molar mass. At this point, it’s very easy to
make a mistake and use the atomic mass for the element on the periodic table. For an element, we can take the
number in the periodic table and add the units, unified atomic mass units, to get
the atomic mass and then convert that into the molar mass with units of grams per
mole. However, this value is an average
determined by the amount of each isotope and the mass of each isotope.

To find the molar mass of
carbon-12, we need to do something different. For this, we need to recall the
actual definition of a unified atomic mass unit, one twelfth of the mass of a
carbon-12 atom. This means that the mass of a
carbon-12 atom is exactly 12 unified atomic mass units. Therefore, the mass per mole of
carbon-12 is 12 grams per mole, meaning moles of carbon-12 atoms. We can work out the number of moles
of atoms in 12 grams of carbon-12 by taking the mass and dividing by the molar
mass.

You might see this written as 𝑛 is
equal to 𝑚 divided by capital 𝑀. So, our amount is 12 grams
multiplied by one mole for every 12 grams, giving us our final answer of exactly one
mole of carbon-12 atoms. Therefore, the number of moles of
atoms in 12 grams of carbon-12 is one mole.