# Lesson Video: Units of Energy Chemistry

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.

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### 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.