### Video Transcript

In this video, we will learn about
a few common units of energy and units of energy per chemical bond or amount of
chemical substance. And we’ll also practice converting
between them. Before we dive in, there are a few
things we need to know. Firstly, there are many types of
energy, for instance, chemical potential energy, gravitational energy, electrical
energy, and so on. We use the generic word “energy”
when we’re not sure about which type we’re dealing with or for a mix of different
types of energy. Regardless of the type, the
internationally recognized unit of energy is the joule, with symbol J.

The full definition of one joule is
quite sophisticated. It’s equal to the work done by a
force of one newton when its point of application moves one meter in the direction
of action of the force. This is an appropriate example, an
object sitting on the surface being pushed. It would take one joule of energy
to move that object one meter if the friction force was one newton. However, as chemists, since we
don’t deal with forces or distances often on this level, we can come up with a
different way of remembering it. It takes about 4.2 joules of
thermal energy to warm one milliliter of one of our favorite substances, water, by
one degree Celsius. And if we need larger or smaller
units to deal with a particular problem, we can use standard prefixes.

For instance, we could have
microjoules, which are millions of joules indicated by the letter 𝜇. Or we could have millijoules, which
are thousands of joules or kilojoules, which are thousands of joules. In chemistry, one of the most
helpful units of energy is the kilojoule, but we’ll come to that later. The other key item of information
we need is to know the mole, the SI unit of amount of substance. Officially, one mole of an atom ion
or molecule is exactly 6.02214076 times 10 to the power of 23 of those atoms, ions,
or molecules and so forth. We can compare this to one dozen of
something being 12 of something. You’ll generally see this very
precise number rounded to four or three significant figures.

This number is known as Avogadro’s
number. And it represents our best estimate
of the number of carbon-12 atoms in 12 grams of carbon-12. It’s a unit that helps us talk
about amounts of substance on a human scale. If we want to convert between
numbers of things and amounts of things in moles, we can use Avogadro’s constant,
which is just Avogadro’s number with units of per mole. This just tells us the number of
things per mole. Using Avogadro’s constant, we can
convert between number of 𝑋 and amount of 𝑋 in moles.

Next, we’re going to look at an
area where a lot of this information crops up. Bond energy is the amount of energy
that’s converted between chemical potential energy and other forms of energy, like
heat and light when a bond is formed or broken. The formation of one bond releases
a minuscule amount of energy. For instance, when two nitrogen
atoms come together and form one of the strongest covalent bonds, the
nitrogen-nitrogen triple bond, the energy released is 0.00000000000000000156 joules
likely as thermal energy. In scientific notation, this is
1.56 times 10 to the power of negative 18 joules per nitrogen-nitrogen triple
bond.

Because these energies are so
small, it’s much more common to talk about bond energies per mole of bonds. In one mole of nitrogen gas, we
have about 6.022 times 10 to the power of 23 nitrogen-nitrogen triple bonds. The energy converted during the
formation or destruction of all these bonds would be about 942000 joules. So we can say the molar bond energy
of the nitrogen-nitrogen triple bond is about 942000 joules per mole. To clean things up, we usually use
kilojoules per mole instead of joules per mole. So the molar bond energy is 942
kilojoules per mole.

Next, we’re going to take a look at
doing conversions between different units of energy. To do conversions, you probably
need to know the meaning of the standard prefixes. And you may need to convert between
a familiar and an unfamiliar unit. Here, we’re going to look at how to
convert between microjoules, millijoules, joules, kilojoules, and megajoules. If you have one joule of energy,
that’s equivalent to 1000 millijoules. And a single millijoule is
equivalent to one one thousandth of a Joule. 10 to the sixth or one million
microjoules is also equivalent to a joule. And one microjoule is equivalent to
a millionth or 10 to the negative six of a joule.

Going in the other direction, one
joule is 1000 times smaller than a kilojoule. And one kilojoule is 1000 times
bigger than a joule. And finally, one joule is
equivalent to 10 to the negative sixth megajoules, while one megajoule is equivalent
to one million joules. From here, it’s easy to see what
the prefixes mean. However, if you’re not comfortable
with prefixes, you can always come back to the table to do your conversions. To start with, you want to find the
unit you’re in on the left, then find the unit you’re converting to on the top, and
then find the equivalents in the table. For instance, let’s say we’re
looking to convert between joules and millijoules. From the table, one Joule is
equivalent to 1000 millijoules. We start off with a certain number
of joules labeled 𝑥, and then we multiply by our conversion ratio, 1000 millijoules
per joule.

The unit we’re converting to is on
the top of the fraction, and the unit we’re converting from is on the bottom. So it cancels. After canceling units, we can see
we have 1000 times as many millijoules as we had joules. Now we can fill in the rest of the
table. We can see a pattern in the
table. A millijoules, a joule, a
kilojoule, and a megajoule are all 1000 times bigger than the unit above. So we can follow the pattern to
fill in the rest of the table, which leads us to the extremes where 10 to 12, that’s
one thousand billion microjoules, is equivalent to a megajoule and one microjoule is
equivalent to 10 to the negative 12 megajoules. Now let’s practice converting 5.2
megajoules to joules.

We can see from the table that one
megajoule is equivalent to 10 to the power of six joules. So to do a conversion, we can
multiply 5.2 megajoules by 10 to the six joules per megajoule. After canceling units and
multiplying through, we get 5200000 joules. But what if we have 0.2 microjoules
and, for some implausible reason, we want to convert it to kilojoules? It may be more comfortable to
convert to joules first. Here, we’re multiplying by 10 to
the negative six joules per microjoule. And then we can convert to
kilojoules by multiplying by 10 to the negative three kilojoules per joule. But you can see you could actually
combine these two together into one operation where we multiply by 10 to the
negative nine kilojoules per microjoule.

There’s an alternate method we can
use which involves the prefixes. 0.2 microjoules can be expressed as
0.2 times 10 to the negative six joules simply by expanding the prefix. And we can do the same with our
target kilojoules, turning the k into 10 to the power of three. From here, it’s easy to see that
we’re moving from a very small lump of energy to a very big lump of energy and the
difference in size is 10 to the power of nine. Since we’re converting to a bigger
energy unit, we need fewer of them. So we can multiply by 10 to the
negative nine to make sure it’s equivalent. So we can write this 0.2 times 10
to the negative nine or two times 10 to the negative eight kilojoules.

So there are a few ways of getting
there. What matters is we understand why
it works. It works because we’re always
dealing with equivalent amounts of energy. The nice thing about knowing how
different energy units are equivalent is that you can convert between familiar and
unfamiliar units. For example, the non-SI unit
calorie doesn’t convert to joules quite as easily as kilojoules or millijoules. Historically, one calorie was
defined as the energy needed to heat one millimeter of water by one degree
Celsius. However, that’s no longer the case;
the calorie is now defined relative to the joule. One calorie is now precisely 4.184
joules.

The actual amount of energy
represented by calorie hasn’t really changed. It’s just the way we define it. Since one calorie is equivalent to
4.184 joules, then one joule is roughly equivalent to 0.239 calories, which is one
divided by 4.184. The calorie is a fairly popular
unit, but you may hear the word calorie referring to something slightly
different. As you might expect, if we put kilo
in front of calorie, we get the kilocalorie, which is equivalent to 1000 calories,
which means that one kilocalorie is equivalent to 4184 joules. And one calorie is equivalent to
one one thousandth of a kilocalorie. And if you wanted to do the
conversion between joules and kilocalories directly, one joule is roughly equivalent
to 2.39 times 10 to the negative four kilocalories.

But the problem arises because the
word calorie also refers to a calorie with a capital C, which is equivalent to one
kilocalorie. The calorie equivalent to 4.184
joules is known as the small calorie. And the calorie equivalent to 4184
joules is known as the large Calorie. It’s easy to remember which way
around they are because the small calorie uses a lowercase c and the large Calorie
uses an uppercase C. It’s generally recommended that
people eat enough food to provide about 2000 large Calories per day. And we can easily convert that into
small calories, giving us about two million small calories, which is also equivalent
to two mega small calories. But perhaps that’s a step too
far. The vital lesson here is to make
sure when you hear the word calorie, you know which calorie, the small or the large,
is being referred to.

The next question is, does any of
this change when we look at bond energy? Not really. All we need to add is that one mole
of anything is equivalent to an Avogadro’s number of that thing. And that Avogadro’s constant tells
us how many things there are per mole. Naturally, a bond energy of one
joule per mole is equivalent to one joule per mole or 0.001 kilojoules per mole. And that arises because one
kilojoule is equivalent to 1000 joules. But what if we’re not dealing with
joules per mole of bonds but Joules per bond? To convert joules per mole to
joules per bond, we need to divide by Avogadro’s constant. When we divide by Avogadro’s
constant, we’re using it to tell us how many moles there are per number of
things.

Dividing by Avogadro’s constant is
equivalent to multiplying by one mole per 6.022 times 10 to 23 of something. You can check you’ve got it the
right way up because you should be dividing by a big number because the energy
released per bond is going to be significantly less than the energy released per
mole of bonds. Here are the conversion factors
between joules per mole, kilojoules per mole, and joules per bond. However, this may not be the best
way to remember how to do this. If we want to convert between units
of joules per bond to joules per mole of bonds, we multiply by Avogadro’s
constant. And to convert the other way, we
simply divide by Avogadro’s constant.

Then to convert between joules per
mole and kilojoules per mole, our typical unit for bond energies, we multiply by 10
to the negative three kilojoules per joule. This is exactly how we convert
between joules and kilojoules. And to go in the other direction,
we simply multiply by 1000 joules per kilojoule. If you wanted to, you could jump
directly between joules per bond and kilojoules per mole. All we need to do is follow the
path between joules per bond and kilojoules per mole and combine the
conversions. So we’d multiply by Avogadro’s
constant and then multiply by 10 to the negative three kilojoules per joule.

However, in practice, it may be
better to do it as two steps to reduce the likelihood of mistakes. So, for example, with the
nitrogen-nitrogen triple bond, the bond energy is 1.56 times 10 to the negative 18
joules per bond. Converting to joules per mole by
multiplying by Avogadro’s constant gives us 942000 joules per mole. And lastly, we convert the joules
to kilojoules by multiplying by 10 to the negative three kilojoules per joule,
giving us 942 kilojoules per mole. Now that we’ve looked at unit
convergence and bond energy convergence, let’s have some practice.

It is estimated that the average
adult should consume around 2000 kilocalories per day to maintain a healthy
lifestyle. What is this value in units of
kilojoules?

2000 kilocalories is an amount of
energy, and kilojoules is another unit of energy. So we can ignore the per day. We can break down a kcal into k and
cal. The k corresponds to kilo, which
means 1000 of something, and cal stands for calorie or small calorie. So kilocalorie refers to 1000
calories. Meanwhile, the symbol for
kilojoules is kJ. The J corresponds to joule. Our starting unit and our final
unit both have kilo in them, so we don’t need to focus in on that. What we do need to remember is the
relationship between calories and joules. It takes about one calorie to warm
one milliliter of water one degree Celsius. But officially, one calorie is
defined as 4.184 joules. If we scale both sides by 1000, we
end up with the same numerical relationship between kilocalories and kilojoules.

Now we have all the information we
need to convert our kilocalories to kilojoules. We start by multiplying our 2000
kilocalories by 4.184 kilojoules per kilocalorie. So our answer is 8368
kilojoules. Alternatively, you could have done
it in steps, first, by converting from kilocalories to calories by multiplying by
1000 calories per kilocalorie, then convert it to joules by multiplying by 4.184
joules per calorie, and then finally convert it to kilojoules by multiplying by 10
to negative three kilojoules per joule. If we cancel common terms along
this route, we end up with exactly the same conversion factor. So regardless of the route, 2000
kilocalories is the equivalent of 8368 kilojoules.

Let’s finish up with the key
points. Energy is measured in joules
regardless of the type. We can use standard prefixes to
make larger or smaller units of energy like microjoules, millijoules, kilojoules,
and megajoules. The non-SI unit, the calorie, the
small calorie, is equivalent to 4.184 joules. The related unit, the large Calorie
with capital C, is equivalent to a kilo small calorie or 4184 joules. When we discussed bond energies, we
typically expressed them in kilojoules per mole. But we can convert those values to
joules per mole by multiplying by 1000 joules per kilojoule. And lastly, we can convert between
joules per mole of bonds and joules per individual bond by dividing by Avogadro’s
constant.