### Video Transcript

In this video, we will learn about
formula masses and molecular masses and learn how to calculate them from atomic
masses. We’ll also look at the difference
between masses and relative masses.

Before we can explore formula
masses, we need to recall what an atomic mass is. Atoms really are tiny, so they have
very, very small masses. The smallest atom, an atom of
hydrogen, is composed of a single electron bound to a single proton. If we measure the mass of a
hydrogen atom in grams, the value would be minuscule. Instead, we have a much more
convenient system.

Imagine you’re loading a delivery
van with some fruit. Each type of fruit weighs a
different amount. And you could use grams. So, an apple is 80 grams, a banana
is 120 grams, and a watermelon is 8000 grams or eight kilograms. However, to make things easier to
manage, we could come up with our own special mass unit, which we’ll call “the
apple”, which is 80 grams. Our apple has a mass of one
“apple”, the banana has a mass of 1.5 “apples”, and our watermelon has a mass of 100
“apples”.

These numbers are relative
masses. They are relative to the apple. These numbers are much easier to
compare. We know when we’re loading our van
that each watermelon is going to weigh as much as 100 apples. Instead of using the incredibly
tiny gram masses of individual atoms, we define the apple equivalent for atoms. For complicated reasons that I
won’t go into here, chemists chose their atom apple to be an atom of carbon-12. That’s an atom consisting of six
protons and six neutrons in the nucleus and six electrons in the electron cloud. The full definition is a little bit
more complex, but we’re not going to look at that here.

Using carbon-12, we can start to
talk about the masses of other atoms in more sensible numbers. Here, my examples are atoms of
hydrogen-1 and bromine-79. Now, we could just use the whole of
the carbon atom as our reference point. And on that scale, a carbon-12 atom
would have a mass of one. And our hydrogen and bromine atoms
would have relative masses of about a twelfth and about 6.6.

However, chemists came up with a
more convenient way of doing it. Electrons don’t have much mass
compared to protons and neutrons, but protons and neutrons weigh about the same. So, instead, chemists use a system
where the number of protons plus the number of neutrons is very close to the
relative mass. While it may sound complicated, it
does make things a lot easier. These small, easy to handle numbers
can be used in calculations. And we can measure the mass of a
carbon-12 atom more easily than we can the mass of an individual proton or an
individual neutron.

So, for our purposes, relative mass
is the mass of something on a scale where the mass of a carbon-12 atom is exactly
12. Relative masses in chemistry are
great as long as you remember what they are relative to. To make things easier, there’s a
unit called the unified atomic mass unit with symbol u. It’s very similar to the atomic
mass unit, amu, but I’ll use u throughout.

One unified atomic mass unit is
equal to one twelfth of the mass of the carbon-12 atom. So, it’s defined in a very similar
way to relative mass. Unified atomic mass units are
particularly useful when you want to convert to grams because one unified atomic
mass unit is approximately equal to 1.66 times 10 to the negative 24 grams.

So, how do we use measuring mass in
fractions of a carbon atom into use? If you look at all the atoms and
ions in the universe, you’ll be able to identify many different varieties. We first group them together based
on the number of protons in their nuclei. These are the elements of which
carbon is an example. However, nuclei of an element can
have different numbers of neutrons. So, we have another layer of
grouping, which are the isotopes.

On Earth, we need to know the
average mass of atoms of an element to do calculations. So, we analyze samples and work out
how common each isotope is. You have the benefit of years of
research in the form of the periodic table, where you can see the average atomic
masses of many of the elements.

Let’s look at carbon as an
example. We can read the number at the
bottom as an average atomic mass and add the units of unified atomic mass units. Or we can take it as a relative
atomic mass. We define the average atomic mass
of an element as the average mass of an atom of that element in unified atomic mass
units. The average atomic mass of carbon
is 12.011 unified atomic mass units, a little more on average than a carbon-12 atom
because there is some carbon-13 in samples on Earth.

Of course, you can use relative
atomic mass or RAM instead, which is simply the average mass of the atom on a scale
where an atom of carbon-12 has a mass of 12. Some elements don’t have
standardized atomic masses because they are too rare for accurate measurements to be
made, often because they are unstable and undergo radioactive decay to form other
elements.

Now that we know how to find how
heavy atoms of different elements are on average, we should be able to work out how
much molecules and compounds weigh.

Let’s imagine you want to weigh out
specific amounts of chemicals in the lab, but the atoms are bonded together, like in
a water molecule. A water molecule is made of two
atoms of hydrogen and one atom of oxygen. We don’t know for sure which
isotopes are in this particular molecule. But we do know, on average, that
each atom of hydrogen has a mass of 1.008 unified atomic mass units from the
periodic table and each atom of oxygen has a mass of 15.999 unified atomic mass
units.

To work out the mass of the average
water molecule, all we need to do is add the masses of the atoms together, giving us
18.015 unified atomic mass units. Remember, this is an average for
all water molecules. Some water molecules might be a
little bit lighter because they’re made of lighter isotopes of oxygen and
hydrogen. And, of course, some may be
heavier. We’re not trying to work out the
actual mass of individual molecules. We’re just working out averages so
we can do calculations for the lab.

For water, we call this the formula
mass. This is because we can look at the
chemical formula of water H2O, see there are two hydrogen atoms and one oxygen atom,
and add the average masses of those atoms together. So, the formula mass is simply the
sum of the average atomic masses of the components of a formula. The relative formula mass is simply
the equivalent with relative atomic masses.

Formula mass is a general term. For lattices, the chemical formula
is the simplest ratio of the elements that make it up. For instance, sodium chloride is
made up of alternating sodium ions and chloride ions. Since the crystal could
theoretically go on forever, there isn’t a simple way to write the formula. So, we write the empirical formula
NaCl. And we do the same for metals like
magnesium or covalent lattices like silicon dioxide.

To work out the formula mass for
sodium chloride, we simply take the average atomic mass of sodium and add it to that
of chlorine, giving us 58.44 unified atomic mass units. For magnesium, the formula mass is
exactly the same as the average atomic mass of magnesium.

For molecules, the chemical formula
can be different to the empirical formula. This is a molecule of hydrogen
peroxide made of two oxygen atoms and two hydrogen atoms. The empirical formula of hydrogen
peroxide is just HO because the hydrogen and oxygen atoms are in a ratio of one to
one. But the molecular formula accounts
for all the atoms in a single molecule H2O2. It’s the molecular formula we use
when we’re working out the formula mass for a molecular substance. So, we call that, specifically, the
molecular mass to be clear.

Molecular mass is simply the
formula mass of a molecule based on its molecular formula. Now, we’re going to have a look at
how we’d calculate the formula mass for various types of substance.

For an atom or an ion, the formula
mass is simply the atomic mass of the element. For ions, we generally ignore any
mass changes due to the gain or loss of electrons. For lattices like sodium chloride,
magnesium, or silicon dioxide, we start by separating the formula into the
individual elements, keeping track of how many atoms or ions there are for each
one. Then, we look up the average atomic
masses for those elements on the periodic table. We then multiply those average
atomic masses by the number of atoms or ions in the formula and then add them
altogether.

Molecules can be drawn in a variety
of ways, so you might have to figure out the molecular formula from a diagram. Once you’ve counted up all the
atoms of each element, you then do exactly the same process as with the lattice. Separate out formula, find the
average atomic masses, and multiply and sum them together.

So, we’ve looked at how formula
masses apply to atoms, ions, lattices, and molecules. Let’s have some practice.

The atomic mass unit, u, is defined
as one twelfth of the mass of an atom of carbon-12. What is the mass of a silicon-30
atom in atomic mass units?

Sometimes, you may see unified
dropped from unified atomic mass unit. That’s fine as long as you’re using
the symbol u. The symbol amu is sometimes used
interchangeably, but they’re actually defined slightly differently. But it’s perfectly okay because we
actually have the definition in the question, one twelfth of the mass of an atom of
carbon-12.

Carbon is an element we can find on
the periodic table. The atomic number for carbon is
six. The atomic number of an element is
the number of protons we find in atoms or ions of that element. So, in an atom of carbon-12, we
know that there are six protons in the nucleus. In the naming of isotopes like
carbon-12, we put the mass number at the end. Atomic number tells us the number
of protons in the nucleus. And mass number tells us the number
of protons plus the number of neutrons.

What this tells us is that in our
nucleus of carbon-12, we have six protons and enough neutrons that when you sum them
together, you get 12. 12 minus six is six. So, we have six neutrons. And since we’re dealing with atoms,
which must be neutral, we must have six electrons to balance out the positive charge
of the protons.

The next thing we have to do is
work out the mass of a silicon-30 atom in atomic mass units. Silicon is the element just below
carbon in the periodic table with an atomic number of 14. So, we know in our atom of
silicon-30, there must be 14 protons in the nucleus. But of course, silicon-30 is an
isotope of silicon where the nuclei contain a strict number of neutrons and the
number of protons plus the number of neutrons is 30.

So, our atom of silicon-30 also
contains 16 neutrons. Just like with the atom of carbon,
we’re dealing with a neutral combination of protons and electrons. So, we need 14 electrons to balance
out the charge of the 14 protons. The first thing we need to
understand is that an atom of carbon-12 has a mass of exactly 12 unified atomic mass
units. We know that because from the
definition, we know one unified atomic mass unit is the mass of a carbon-12 atom
divided by 12.

The next thing we need to know is
that the mass of a proton and the mass of a neutron are about the same. And electrons have much less mass
than protons or neutrons. So, for the purposes of this
question, we can ignore them. Protons and neutrons are known
collectively as nucleons. So, the question is, if 12 nucleons
together have a mass of 12 unified atomic mass units, what will be the mass of 30
nucleons? And the answer is 30 unified atomic
mass units.

Now, bear in mind this is only
approximate because when neutrons and protons bond together, there is a slight
change in their mass and things are a bit more complicated. You may have noticed that I steered
clear of the average atomic mass for silicon, which is 32.06. This represents the average mass
for a silicon atom on Earth based on the abundance of different silicon
isotopes.

Our estimate of 30 unified atomic
mass units for an atom of silicon 30 is the best we can do with the figures we have
available.

Now, let’s have a look at a
formula-mass calculation.

A substance has a formula unit
AB2. What is the relative formula mass
of this substance in terms of Ar(A) and Ar(B), the relative atomic masses of A and
B?

This one’s a little bit tricky
because we haven’t been told what elements are involved. We’ve just got one A, whatever that
is, and two of B. We’ve been asked for the relative
formula mass of this substance, which means we need to work out the relative mass on
a scale where an atom of carbon-12 would have a mass of 12.

To make things easier, let’s
actually imagine a number line. We’d read an atom of carbon-12 as
having a mass of 12. And what we’ve been given are some
symbols for the relative atomic masses of A and B. I’m just going to imagine that the
relative atomic mass of A is about four and that the relative atomic mass of B is
about five. These numbers don’t actually
matter. It’s just useful to draw it
out.

To work out the relative formula
mass, what we need to do is sum together the relative atomic masses of the
constituents of the formula. With the formula AB2, we have one
of A and two of B. Therefore, our relative formula
mass, or RFM, is equal to one of the relative atomic mass of A plus two of the
relative atomic mass of B.

We can imagine that on our diagram,
where we’re getting gradually heavier as we move to the right. We have one of the relative atomic
mass of A and two of the relative atomic mass of B. Since we’ll multiply the relative
atomic mass of A by one, we can just remove the one and simplify our answer to the
relative formula mass is equal to the relative atomic mass of A plus two times the
relative atomic mass of B.

Now, it’s time to go over the key
points. Whether we’re doing things
relatively or directly, we’re comparing the masses of atoms, ions, and formulas with
the mass of the carbon-12 atom. The unified atomic mass unit is
equivalent to a twelfth of the mass of a carbon-12 atom. The average atomic mass of an
element is the average mass of one atom of that element in unified atomic mass
units. For carbon, the average atomic mass
is 12.011 unified atomic mass units. If you want the relative atomic
mass, you just have to drop the units of u.

A formula mass is the mass of a
single unit of a formula in unified atomic mass units. We can calculate the formula mass
by summing together the average atomic masses of the constituents. Or we can get the relative formula
mass by summing together the relative atomic masses.

And lastly, the molecular mass is
simply the formula mass as applied to a molecule. So, it’s the mass of a single
molecule in unified atomic mass units. The calculation is identical. And at the end, you can remove the
units of u to produce the relative molecular mass. And you may see these terms
abbreviated.