Lesson Video: Moles Chemistry

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 at how to convert between formula masses, masses, and amounts in moles.

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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.

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