### Video Transcript

In this video, we will look at percentage
composition, the percentage by mass of each element in a substance. The percentage composition of a substance
is the percentage by mass of each element in the substance. The mass percentage of an element in a
substance is the percentage mass of that element in a sample of that substance. We can calculate the mass percentage by
taking the mass of the element and dividing it by the mass of the substance and multiplying
by 100 percent.

Let’s have a look at water as an
example. Water is a substance made up of the
elements hydrogen and oxygen. We know that water is composed of
molecules made of hydrogen and oxygen atoms and that a single molecule of water consists of
two hydrogen atoms and one oxygen atom. The percentage composition of water is
about eleven percent hydrogen and 89 percent oxygen. Remember that the mass percentages must
sum to 100 percent. So why is it that even though we have
twice as many hydrogen atoms oxygen makes up so much more of the mass? Well, an oxygen atom has a much greater
mass per atom than hydrogen. So even though there’re twice as many
atoms of hydrogen in the molecule of water, the element oxygen makes up a much greater
proportion of the mass.

We can see the relative masses of an
average atom of each element by going to the periodic table. We can see that oxygen has a relative
atomic mass of 15.999. And hydrogen has a relative atomic mass
of 1.008. So an oxygen atom clearly has about 16
times the mass of a hydrogen atom. Now, we need to know the contribution to
the mass of the molecule of each element. For that, we take the relative atomic
mass of each atom and multiply it by the number of atoms per molecule. This means that oxygen contributes 15.999
to the mass of the water molecule. And hydrogen contributes 2.016.

If we add up these contributions, we’re
going to get the relative formula mass of a water molecule which is 18.015. The last thing to do is calculate the
mass percentage for each element. To do that we take the mass contribution
of the element and divide it by the formula mass of the molecule. This will tell us the proportion of mass
that that element is responsible for. And then we multiply it by 100
percent. So we get a value for the mass percentage
of oxygen in a water molecule of 88.8 percent and the value for the mass percentage of
hydrogen of 11.2 percent.

You can see that these numbers were
rounded to give 89 percent and 11 percent originally. This information is useful when we’re
thinking about separating compounds into elements. We know that all the mass in the water
will be converted into the mass of the hydrogen and the oxygen. And 11.2 percent of that mass will be
hydrogen and 88.8 percent of that mass will be oxygen. Percentage compositions are generally
used in two ways, either they are used to determine the ratio of elements in a compound to
help us find the formula or they are used to determine the mass of an element present in a
compound.

Of course, percentage compositions need
to be determined from one of these two things in the first place. So you can think of percentage
composition as a bridge between the elemental composition of a single sample and the
chemical formula. In this case, we say the percentage
composition of water is 88.8 percent oxygen and 11.2 percent hydrogen. Now, let’s move on and think about how we
calculate percentage composition when we know the formula.

Let’s say you have a compound like sodium
chloride and you’re going to separate it into its elements. I’ve chosen sodium chloride here because
sodium chloride is actually separated into its elements in industry. Sodium chloride has the formula NaCl. This means we have one sodium Ion for
every chloride ion. When calculating percentage compositions,
ions are treated like atoms. We don’t pay attention to the mass
differences from having more or fewer electrons. In the case of sodium chloride, we can
identify our elements as sodium and chlorine. The next step is to find the relative
atomic masses of the elements. For sodium, that’s 22.990. And for chlorine. that’s 34.45. If you wanted to, you could also use the
atomic masses in unified atomic mass units, as long as you calculate the formula mass in the
same units.

In the next step, we need to work out the
number of ions in the formula. We have one sodium ion and one chloride
ion per sodium chloride formula. That makes it easy because it means that
the contribution for each element to the mass is the same as the relative atomic mass. If we sum these together, we’ll end up
with a relative formula mass of sodium chloride which is 58.44. Then we calculate the mass percentage for
each element by dividing the contribution by the relative formula mass and multiply by 100
percent. This gives us a mass percentage for
sodium of 39.3 percent and a mass percentage for chlorine of 60.7 percent. If we sum these two percentages together,
we get 100 percent as we should.

This means that if we have a sample of
500 grams of sodium chloride, we can work out the mass of sodium and the mass of chlorine we
get from it. We multiply the mass of our sample by the
mass percentage to get 197 grams for sodium and 303 grams for chlorine. If we started with a different compound
like iron(III) oxide, we would go through exactly the same procedure. For a sample of iron(III) oxide, iron is
responsible for 69.9 percent of the mass. And oxygen is responsible for the
remaining 30.1. The key thing to remember is to include
the number of each element in the mass contribution.

Now that we’ve looked at how to calculate
percentage composition from the formula, let’s have a look at calculating it from
masses. Calculating the percentage composition of
a substance from the masses of each element is actually a lot easier than doing it from the
formula. Let’s imagine we have a sample of methane
with a mass of 120 grams. And let’s for the moment imagine that we
don’t know the formula for methane. All you’ve been told is that the mass due
to hydrogen is 30 grams and the mass due to carbon is 90 grams. So at this point, we haven’t yet
demonstrated whether there are any other elements present. However, if we add up the masses for each
element, we can see that it equals 120 grams. The compound must only contain hydrogen
and carbon because the sum of the individual masses equals the mass of the sample.

We work out the mass percentage of each
element by dividing the element mass by the sample mass and multiplying by 100 percent. 30 grams divided by 120 grams times 100
percent is 25 percent. And 90 grams divided by 120 grams times
100 percent is 75 percent. So the percentage composition of methane
is hydrogen 25 percent and carbon 75 percent. So we’ve looked at percentage composition
and different ways to calculate it. Now, let’s have some practice.

A compound contains only the elements 𝑋
and 𝑌. A sample of the compound with a mass of
12.5 grams is found to contain 6.50 grams of 𝑋. What is the percentage composition of the
compound?

Percentage composition is a list of mass
percentages for each element in the compound. So we’re looking for an answer with this
kind of format where we have the mass percentage of 𝑋 and the mass percentage of 𝑌. We start off knowing that we have a
sample mass of 12.5 grams and knowing that the only elements in our compound are 𝑋 and
𝑌. Thankfully, we’ve also been told that the
mass of 𝑋 in the sample is 6.50 grams. But we don’t know the mass of 𝑌. However, that won’t stop us calculating
the mass percentage of 𝑋 which is the mass of element 𝑋 divided by the mass of sample
multiplied by 100 percent. This means we take 6.50 grams divided by
12.5 grams and then multiplied by 100 percent giving us 52.0 percent.

But we still don’t know the mass
percentage for 𝑌. We can get the mass percentage in one of
two ways. We know the mass percentages must sum to
100 percent. So we can take away the mass percentage
of 𝑋 to get the mass percentage of 𝑌. Or we can work out the mass of 𝑌 by
taking away the mass of 𝑋 from the mass of the sample and then dividing by the mass of the
sample and multiplying by 100 percent. For this question, it isn’t actually
necessary to work out the mass of 𝑌. So I’ve skipped it. Instead, we’ve worked out the mass
percentage of 𝑌 by taking away the mass percentage of 𝑋 from 100 percent.

However, just in case you’re interested,
it should be six grams. All that remains for our answer is to
write the percentage composition which is a list of the elements and their mass
percentages. A compound containing only the elements
𝑋 and 𝑌 having a sample mass of 12.5 grams will have a percentage composition of 52
percent 𝑋 and 48 percent 𝑌 if 6.50 grams of the sample is 𝑋. So our first example dealt with
calculating mass percentages from sample masses and element masses.

Now, let’s do a question that uses a
chemical formula.

Ethanol has the formula C₂H₅OH. a) As a percentage by mass, what is the
oxygen content of the ethanol molecule to two significant figures? b) As a percentage by mass, what is the
carbon content of the ethanol molecule to two significant figures? And c) As a percentage by mass, what is
the hydrogen content of the ethanol molecule to two significant figures?

On the surface, it looks like this
question isn’t looking for percentage composition. But it does ask for the mass percentage
of all the elements in our formula. The first thing we should do is condense
down the formula into its chemical formula listing the number of atoms of each element
only. From the formula, we can see that an
ethanol molecule contains only carbon, hydrogen, and oxygen. And each molecule contains two carbon
atoms, six hydrogen atoms, and one oxygen atom. The percentage by mass or mass percentage
is equal to the mass of the element divided by the mass of the sample all multiplied by 100
percent.

In this case, the sample is one molecule
of ethanol. And the mass of the element is the mass
of either two carbon atoms, six hydrogen atoms, or one oxygen atom. We can work out the mass of an atom of
each element by looking up the relative atomic mass on our periodic table. The relative atomic mass of carbon is
12.011. The relative atomic mass of hydrogen is
1.008. And the relative atomic mass of oxygen is
15.999. By multiplying the number of atoms of
each element per molecule by the relative atomic mass of that element, we’ll get the mass of
each element in the molecule. This means that for a molecule of
ethanol, carbon contributes 24.022 to the mass, hydrogen contributes 6.048, and oxygen
contributes 15.999. If we sum all these contributions
together, we’ll get the relative formula mass of an ethanol molecule.

We now have all the information we need
to answer all three questions. For part a), we take the contribution for
oxygen per molecule of ethanol as 15.999 and divide it by the relative formula mass of
ethanol 46.069 and then multiply everything by 100 percent. This gets us 34.7283 percent which we
round to 35 percent as our answer to two significant figures. Doing the same working for carbon where
we use it’s mass contribution of 24.022, we get a mass percentage of 52 percent to two
significant figures. And lastly for hydrogen, we get a mass
percentage of 13 percent. To find the mass percentage for hydrogen,
we could’ve taken away the percentage for oxygen and carbon from 100 percent. However, that would mean that any mistake
in our oxygen or carbon calculation would make our hydrogen calculation incorrect. Doing it this way gives us better odds of
a correct answer.

So using the process for figuring out the
percentage composition of ethanol, we’ve demonstrated that oxygen has a mass percentage of
35 percent. Carbon has a mass percentage of 52
percent. And hydrogen has a mass percentage of 13
percent in the ethanol molecule.

Since we’ve learned all about percentage
composition and done a couple of practice questions, let’s look at the key points. Percentage composition is a list of the
mass percentages of all the elements in a substance. The mass percentage of an element in a
substance is the percentage of the mass of that substance that particular element is
responsible for. Percentage compositions can be determined
from chemical formulas and atomic masses or from masses of samples and the elements
inside.