### Video Transcript

In this video, we will learn about
one of the most important units in chemistry, the mole. We’ll look at why it’s useful, how
it’s defined, and look how to convert between formula masses, masses, and amounts in
moles.

Once chemists discovered the atom,
they faced a problem. Atoms are so small and weigh so
little that it’s really unhelpful to think of weighing individual atoms. There have been many units of mass
over the centuries, but the one most familiar to chemists at the moment is the
gram. I’m not going to go into how the
gram is officially defined, but you can remember easily that one milliliter of
water, that’s enough water to fill a cube that’s one centimeter by one centimeter by
one centimeter, has a mass of about one gram.

Rather than weigh out individual
atoms, chemists invented a unit. Just like using a dozen to group up
eggs, this unit would help group up atoms, ions, molecules, and so forth into groups
that we can weigh. Here’s an atom of hydrogen-1. It has one proton in the nucleus,
no neutrons, and one electron. An atom of hydrogen-1 has a mass of
about one unified atomic mass unit. One unified atomic mass unit,
symbol u, is equivalent to the twelfth of the mass of a carbon-12 atom. This is just how we define masses
on the atomic scale.

Here’s one gram of hydrogen-1 atoms
contained in a gas jar. If we counted all these atoms, we’d
end up with about six times 10 to the power of 23 atoms. That’s six hundred thousand billion
billion atoms. Theoretically, if you could count
an atom per second, it would take 80 million times the lifetime of the known
universe to complete. That’s 80 million times 13.8
billion years. Bluntly speaking, chemists don’t
have that kind of time.

To keep things simple, chemists
came up with a strict amount of things and called it Avogadro’s number after the
Italian scientist Amedeo Avogadro. Avogadro’s number is exactly
6.02214076 times 10 to the power of 23. That’s about 602 thousand billion
billion. The old definition of Avogadro’s
number derived from the number of carbon-12 atoms in a strict amount of
carbon-12. But during the 2010s, Avogadro’s
number was defined as a strict number of things. So, we can actually say that
Avogadro’s number is a strict number of things exactly. However, you’re much more likely to
see it in scientific notation than written out in full.

Now, all this seems pretty round
about. All we’ve got is a massive
number. But what’s it useful for? Truth be told, Avogadro’s number is
an awkward necessity for converting between unified atomic mass units and grams. So, an Avogadro’s number of things,
each weighing one unified atomic mass unit, has a combined mass of one gram.

Now that we’ve done the complicated
stuff, let’s take a step back and see how it would be useful. If you think about a brick, it’ll
have a property which we call mass. But this is just one of many of the
properties of a given brick. But there’s a special property that
can be applied to bricks and many other things. And that is the amount. A single brick has an amount of
one. But if I’ve got 10 bricks, then the
amount of bricks I have is 10.

When we talk about chemicals, we
often talk about the amount of that chemical we have. What we mean by this is the amount
of units we have. So, if we have one hydrogen atom,
the amount of atoms is one. Let’s have a look at a water
molecule to see how amount can change depending on what we’re talking about. A water molecule consists of two
hydrogen atoms bonded to an oxygen atom. So, we have three atoms in
total. But we can also talk about the
amount of water molecules. So, if we have one water molecule,
the amount of molecules we have is one.

But we can’t say that we have an
amount of molecules if we only have a hydrogen atom. An atom is not a molecule, so it
simply doesn’t make sense. Some measures of amount of
substance apply to some substances and not others. Avogadro’s number comes in useful
when we’re talking about large amounts. An Avogadro’s number of hydrogen-1
atom has the mass of about one gram. And chemists invented a new unit
for amount of substance, which is called the mole. One Avogadro’s number of things is
equal to one mole of things. A mole is simply a group of
things. It’s an Avogadro’s number of atoms,
ions, molecules, any kind of chemical or particle.

When we talk about these things in
general, we call them entities. The abbreviation for a mole is
mol. Just like we said earlier, we can
think of a mole as a group, just like a dozen. One dozen eggs is the same as 12
eggs. One mole of X is equal to an
Avogadro’s number of X. The nice thing about the mole is
that it’s a convenient way to convert between atomic scale masses, like unified
atomic mass units, and human scale masses, like grams.

An atom of carbon-12, that’s an
atom with six protons, six neutrons, and six electrons, has a mass of 12 unified
atomic mass units exactly. You can express unified atomic mass
units in grams if you want to, but one unified atomic mass unit is only about 1.66
times 10 to the negative 24 grams. So, to keep things simple, we can
use unified atomic mass units and say that the mass for carbon-12 is 12 u per
atom. One mole’s worth of carbon-12 has a
mass of 12 grams. So, we can say that the mass per
mole of carbon-12 atoms is 12 grams per mole of atoms. We call this the molar mass of
carbon-12.

We can look inside the mole of
carbon atoms and be sure there are about six times 10 to the 23 atoms. And we can even tell how many
protons, neutrons, and electrons are inside because there’s six protons, six
neutrons, and six electrons per atom. But using moles is much easier. We have one molar of atoms
consisting of six moles of protons, six moles of neutrons, and six moles of
electrons.

When dealing with moles, it’s vital
to identify which entity you’re talking about. So, with carbon-12, we’re talking
about atoms. And we know already that one mole
of carbon-12 contains one mole’s worth of carbon-12 atoms and six moles each of
protons, neutrons, and electrons. But we can apply this principle to
other entities. Carbon dioxide is a molecular
substance. The molecules consist of two oxygen
atoms and one carbon atom. So, a mole of carbon dioxide
consists of a mole of carbon dioxide molecules. But we can look inside those
molecules and see that we have one mole of carbon atoms and two moles of oxygen
atoms.

But we can also apply the mole to
things like ions and ionic units in ionic substances. The substance sodium chloride has
the simple unit NaCl. So, one mole of sodium chloride
contains one mole’s worth of sodium chloride units, which consists of one mole of
Na+ ions and one mole of Cl- ions. Be careful with ionic substances
because how you define the unit will change the amount of things you’re looking
for.

The next thing we’re going to look
at is something that’s like Avogadro’s number but slightly different. When converting back and forth
between the amount of entities in moles and the number of those entities, it’s
useful to use something called Avogadro’s constant. Avogadro’s constant is Avogadro’s
number with units of per mole. And it’s a useful tool to remind us
how many things there are per mole of something. Technically, Avogadro’s constant
should be written like this. However, only the most accurate
instruments would need Avogadro’s constant to such extreme precision. So, you’ll probably see Avogadro’s
constant rounded to four significant figures, which is 6.022 times 10 to the 23 per
mole. Rounding to three or even two
significant figures often doesn’t present any problems, either.

Now, let’s apply Avogadro’s
constant to a problem. Let’s imagine we have 24 grams of
carbon-12 atoms. We know that the molar mass of
carbon-12 is 12 grams per mole of carbon-12 atoms. We can divide the 24 grams by 12
grams per mole and find that we have two moles of carbon-12 atoms. To convert the amount in moles of
carbon atoms to the actual number of carbon atoms, all we need to do is multiply by
the number of entities per mole, which is Avogadro’s constant. Avogadro’s constant is commonly
given the symbol N subscript A. What we get out is about 1.2 times
10 to the 24 atoms of carbon-12.

Avogadro’s constant makes it easier
to remove the units of moles from equations or add them in. The last thing we need to do is put
this all together. One of the most important skills in
chemistry is converting between mass and amount of substance in moles. Every substance will have a
chemical formula. For instance, sodium chloride has
the formula NaCl. From a formula, we can determine
the formula mass. For sodium chloride, the formula
mass is 58.44 unified atomic mass units because that’s what one atom of sodium and
one atom of chlorine weigh. If you prefer, you can use relative
atomic masses to calculate the relative formula mass.

The last thing you need to do with
any new substance that you’re trying to weigh out is work out the molar mass. This is really easy because the
molar mass has the same numerical value in grams per mole as the formula mass does
in unified atomic mass units. Once you’ve got as far as the molar
mass, you can start analyzing samples.

In this example, we’ve got about
120 grams of sodium chloride. If we take the mass and dissolve it
by the molar mass, we’ll get the amount in moles, in this case, two moles of
NaCl. We can easily convert between mass
and amount by dividing or multiplying by the molar mass, which is given the symbol
M. You can use the formula 𝑛, as in
amount, is equal to 𝑚, as in the mass in grams, divided by capital 𝑀, which is the
molar mass in grams per mole. To get this properly embedded,
let’s do some practice.

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.

Now, it’s time to wrap up with the
key points. Firstly, the unit of mass we use on
the atomic scale is the unified atomic mass unit, which is about 1.66 times 10 to
the negative 24 grams. A unified atomic mass unit is
defined as one twelfth of the mass of a carbon-12 atom.

The special number called
Avogadro’s number is simply the number of these much smaller unified atomic mass
units that’s equivalent to a gram. Avogadro’s number has now been
defined as 6.02214076 times 10 to the 23. Avogadro’s number used to be
defined relative to a specific amount of carbon-12. The new definition is simply our
best estimate of that number.

The amount of a substance is
typically measured in units called moles. One mole of any species, be that
atom, molecule, a unit, or an ion, is equivalent to an Avogadro’s number of that
particular entity. Avogadro’s constant is a useful
term for equations. And it gives us the number of
entities per mole. It’s sometimes simplified to about
6.022 times 10 to the 23 per mole.

We can convert between an amount in
moles, a mass in grams, and molar mass in grams per mole using this formula. And you may see it in the form 𝑛
equals 𝑚 divided by capital 𝑀. We can easily convert between
relative atomic mass, atomic mass in unified atomic mass units, and molar mass in
grams per mole because the number will be exactly the same. We just swap out the units. For instance, for carbon-12, the
relative atomic mass is 12, the atomic mass is 12 unified atomic mass units, and the
molar mass is 12 grams per mole.