# What is the Mole Concept?

Hi, and welcome to this video on the mole, the unit used to describe the amount of particles, atoms, and molecules in chemical reactions. Today, we’ll cover more about what the mole is, where the concept came from, and how to use it in chemical calculations. Let’s get started!

To start, here’s the very simplest explanation of what a mole is and what it’s used for: a mole is a number that allows chemists to count atoms and molecules by using mass instead of counting them individually.

Now, let’s dig into this a bit.

## What is a mole?

By definition, a mole is \(6.02214076 \times 10^{23}\) units of something, which is usually reduced to \(6.022 \times 10^{23}\). It’s a proportionality constant, relating the number of units in a sample to the amount of a sample, which we can write out in this equivalency: 1 mole equals 6.022 times 10 to the 23 units of something.

\(\frac{6.022 \times 10^{23}\text{ units}}{1\text{ mole}}\)

As it turns out, this is a famous number, known as the **Avogadro constant** or Avogadro’s number. This number is named after Amedeo Avogadro, an Italian scientist from the late 1700s who first documented the relationship between the volume of a gas and number of gas particles.

We can apply the concept of a mole to anything, not just molecules or atoms or anything else related to a chemical reaction. I could tell you that I have a mole of marshmallows, which would mean that I have \(6.022 \times 10^{23}\) marshmallows. Now, obviously this is a ridiculous number of marshmallows to have; just look at the number written out:

602,214,076,000,000,000,000,000

That’s a lot of zeros. It’s such a large number that our poor human minds have trouble comprehending it.

Think about a mole of seconds, for example. That’s about 600 sextillion seconds, which ends up being \(2.73 \times 10^{15}\) years.

\((\frac{6.022 \times 10^{23}\text{ seconds}}{1\text{ mole}})(\frac{1\text{ min}}{60\text{ sec}})(\frac{1\text{ hour}}{60\text{ min}})(\frac{1\text{ day}}{24\text{ hours}})(\frac{1\text{ year}}{365\text{ days}})=2.73 \times 10^{15}\text{ years}\)

Some scientists believe the big bang only happened \(13.7 \times 10^9\) years ago, so the universe isn’t even a mole of seconds old. That’s how large this number is. So, why do we need such a ludicrously large number?

Well, it turns out that when you’re dealing with something as small as atoms, Avogadro’s number isn’t that large. One mole of carbon atoms would just be 12 grams of carbon.

If that 12 grams seems oddly precise, that’s because scientists specifically selected the value of the mole so that a substance in grams would be numerically equivalent to the average mass of one molecule of the compound in atomic mass units (AMU).

Okay, let’s unpack that for a second. We need to understand how Avogadro’s number was originally calculated, because, as you may have guessed, scientists didn’t pick \(6.022 \times 10^{23}\) for the way it rolls off the tongue. They picked it because it actually makes calculations easier and more intuitive.

The atomic mass unit is defined as 1/12 of the mass of 1 carbon atom, which is \(1.660 \times 10^{-27}\) kg—a very, very small number. Remember, a carbon atom has 6 protons and 6 neutrons, which make up the vast majority of the atom’s weight, so an AMU is roughly the weight of a single proton or neutron. This was, in a way, by accident. At the time, scientists didn’t even know that protons, neutrons, or electrons existed. They defined carbon as 12 because they wanted the lightest element, hydrogen, to be 1 (which in a way, does acknowledge the existence of subatomic particles, just not intentionally). Regardless, by definition, a carbon atom is 12 AMU.

Because the AMU is such a tiny number and we rarely ever interact with 1 atom or molecule, scientists wanted a unit to describe larger amounts of material while maintaining the intuitiveness of the AMU. After all, it does make sense that carbon should weigh 12 AMU since it has 12 nucleons.

The mole provides us with a very useful concept of molar mass, the mass in grams of one mole for any compound. And, since scientists defined it this way, the molar mass is numerically equivalent to the AMUs in the chemical element or compound. In the case of carbon, the molar mass of carbon is 12.01 g/mol.

You might immediately be wondering, “Why isn’t the molar mass of carbon exactly 12.00 g/mol like we said earlier?” That’s because for the molar mass, we’re taking into account the naturally occurring carbon isotopes that slightly adjust the total mass of a bulk carbon sample. So when we made that calculation earlier, we assumed that every single one of those \(6.022 \times 10^{23}\) carbon atoms were carbon-12 atoms, when in fact, some of them were ^{13}C and ^{14}C. So when we have a naturally occurring sample of carbon, say in a diamond, the weight in grams of one mole is best estimated as 12.01 g/mol, which reflects the natural abundance of the different carbon isotopes.

Alright, now that we’ve established what the mole is and how it was originally calculated, let’s turn to why it’s so useful when dealing with chemical reactions.

Consider the successful combustion of methane with oxygen. Say you have 100.0 grams of methane. How much oxygen do you need to react with it? To know that, we have to know about the chemistry of the reaction, which is done on a particle basis. What we mean by this is that we can’t think about reaction chemistry in grams; we have to think about it in terms of the molecules reacting with each other. In other words, the number of methane molecules in 100.0 grams of methane is different than the number of oxygen molecules in 100.0 grams of oxygen. So we can’t simply say that 100.0 grams of oxygen should react with 100.0 grams of methane because there are actually more molecules of methane in 100.0 grams than oxygen molecules in 100.0 grams of oxygen.

If we look at the combustion of methane, you see we need 2 molecules of oxygen for every molecule of methane.

On a large scale, we could say that we need 2 moles of oxygen for every mole of methane. Now, we need to figure out just how many moles of methane are in 100 grams.

\(100.0\text{ g }CH_4(\frac{mol}{16.04\text{ g}})=6.23\text{ mol }CH_4\)

So, using the molar mass of methane, 16.04 grams per mole of methane, we show that 100 grams of methane is 6.23 moles, which means we need 12.46 moles of oxygen to completely react with the methane.

To sum up, the mole provides us with a unit to convert from the microscopic world, where there are billions upon billions of particles, to our macroscopic world, where we don’t often deal with numbers that large or small. Scientists conveniently defined it so that the molar mass, the grams of one mole of substance, is relatively intuitive in that it is roughly numerically equivalent to the number of nucleons in the compound.

Alright, with that, let’s wrap up with a couple of practice questions. If you’d like to work these out on your own, feel free to pause the video after I read the question.

- If we estimate the world population at 8 billion people, what is the world population in moles?

To convert the world population to moles, we use the following calculation

\(8 \times 10^9\text{ people}\frac{1\text{ mole}}{6.022 \times 10^{23}\text{ people}}=1.33 \times 10^{-14}\text{ mole of people}\)

to find that there are only \(1.33 \times 10^{-14}\) moles of people on earth—that’s a really small number and makes the global population also seem small. But, of course, we know that it’s actually quite a lot of people. So, while we can use moles to describe anything, it doesn’t always make sense to use them—this is one of those cases.

- This question is really two related questions. How many moles are in an 8 ounce cup of water? How many hydrogen atoms are there in the 8 ounces of pure water?

(1 ounce = 29.6 mL, 1 mL H_{2}O = 1 g H_{2}O, and molar mass of water = 18.02 g/mol)

To calculate the number of moles in 8 ounces of water, we need to convert ounces to milliliters then to grams, which we can then convert to moles using the molar mass of water, which is approximately 18.02 g/mol (which makes sense since oxygen has 16 nucleons and each hydrogen has 1, which makes 18). Then, it’s just simple multiplication.

\(8\text{ ounces }H_2O(\frac{29.6\text{ mL}}{1\text{ ounce}})(\frac{1\text{ g}}{1\text{ mL}})(\frac{1\text{ mole}}{18.02\text{ grams }H_2O})=13.14\text{ moles of water}\)

This shows that 8 ounces of water is 13.14 moles of water, which means that when you drank that cup of water, you put \(7.9 \times 10^{24}\) molecules of water into your body!

Now, to calculate the number of hydrogen atoms in that cup of water, we simply need to multiply the number of moles by \(6.022 \times 10^{23}\) and then multiply by 2 since there are 2 hydrogen atoms for every mole of water.

\(13.14\text{ moles }H_2O(\frac{6.022 \times 10^{23} H_2O\text{ molecules}}{1\text{ mole}})(\frac{2\text{ H atoms}}{H_2O\text{ molecule}})=1.58 \times 10^{25}H\text{ atoms}\)

This gives us \(1.58 \times 10^{25}\) hydrogen atoms, which is a lot of atoms! Best to stick with moles for this.

All right! That’s it for today’s video on the mole. Thanks for watching, and happy studying!