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The mole and Avogadro's number

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Let's talk about a concept that probably confuses chemistry students the most on some level. But on some level it's also one of the simplest concepts. And that's the idea of a mole, which in chemistry is different that the thing digging up your backyard, or the thing you want to get removed from your left eye. A mole in chemistry is just a number. It's just a number, and the number is 6.02 times 10 to the 23. So it's a very huge number. And this is also called Avogadro's number. Maybe I will do a video on Avogadro. Avogadro's number But that's all you need to know. A mole is just a number. There are kind of more Byzantine definitions of a mole. This actually is not -- actually, let me copy and paste it from Wikipedia. This is Wikipedia's definition of a mole. And you hopefully at the end of this video you'll see that they're equivalent. But if you're just getting exposed to the concept, this to me, it's just not an easy concept. Basically, "a mole is defined as the amount of substance of a system that contains as many elemental entities as there are atoms in 12 grams of carbon 12." Well, I just told you that a mole is 6.02 times 10 to the 23. So if you just take the last part, atoms in 12 grams of carbon 12. So that means that there are 1 mole of carbon 12 -- let me write it like that -- carbon 12. There are 1 mole of carbon 12 atoms in 12 grams of carbon. And so that's why a mole is useful. So I could have just instead of writing 1 mole, I could have replaced this as there's 6.02 times 10 to the 23 carbon atoms, carbon 12 atoms in 12 grams of carbon. How do you figure that out? Or I guess, what else does this mean? I mean, we just added in carbon, they said it's the amount of substance of any molecule, if you convert between atomic mass units and grams. This I find very confusing. How can we apply this in other places? So the first thing to realize is a mole is just a way of translating between grams and atomic mass units. One carbon 12 atom is what? What's its mass number? It's 12. That's why it's called carbon 12 instead of carbon 14. So its mass is 12 atomic mass units. So if you have something that has a mass of 12 atomic mass units and you have a mole of them, or you have 6.02 times 10 to the 23 of them, all of those atoms combined will have a mass of 12 grams. So another way to think about it is 1 gram is equal to 1 mole of atomic mass units. I'll write amu's like that. Or you can write 1 gram is equal to 6.02 times 10 to the 23 atomic mass units. And the reason why this is useful -- and it's kind of addressed in this Wikipedia definition there -- is it helps us translate between the atomic world -- where we deal with atomic mass units and we deal with, oh, we've got an extra neutron now, let's add one to our atomic mass number -- and translating between that atomic world and our everyday world where we deal in grams. And just so you know, a gram is still a pretty small amount of mass. It's 1/1,000 of a kilogram. A kilogram is about 2 pounds. So this is about 1/500 of a pound. So this is not much. So there's a ton of atoms in a very small amount of -- in 1 gram of carbon, or at least in 12 grams of carbon, you have a ton of atoms. You have 6.02 times 10 to the 23. And just to hit the point home, I probably should have talked about this in the atom. This is a huge number. To maybe visualize it, if you think of -- I was told that in the diameter of a hair, if this is a hair and this is diameter of the hair, if you go this way there 1 million carbon atoms. 1 million carbon atoms that way. Or if you were to take an apple and you were to try to figure out what fraction, if you were to make one of the atoms of an apple -- and obviously, an apple has a bunch of different types of atoms in it -- but if you were to take one of the atoms and make it the size of the apple, then the apple would be the size of the earth. So an apple atom is to an apple as an apple is to the earth. So these are obviously-- it's hard for us to even process things of this size. When you just have one gram of -- well, let's say you have 1 gram of hydrogen. 1 gram of hydrogen. 1 gram of hydrogen. If you have 1 gram of hydrogen, that means you have 1 mole of hydrogen. How do I know that? Because hydrogen's atomic mass number is 1. So in general, if you just take any element -- so what is the mass of, let me just pick, 1 mole of aluminum? So if I were to take 6.02 times 10 to the 23 aluminum atoms, what is the mass of that collection? Well, each of them have an atomic mass number of 13. So it's 13 amu's-- I don't have to put the s there -- times six point -- well, I won't write that way, actually. That'll probably just confuse you. The easy way to think about is if you have a mole of an atom, you take its mass-- I was taking its atomic number, that's not good-- you take its mass number. In this case let's say it's 27. So we're dealing with aluminum 27. You take its mass number, and if you have 1 mole of it, then the mass of that will be 27 grams. So that literally, when you have one mole of an atom it's a direct translation between its mass number and grams. 1 mole of iron, let's say iron 56-- there's obviously many isotopes or iron -- let's say we're dealing with iron 56. You normally don't hear it like that, but let's say we're dealing with the isotope of iron that has a mass number of 56. So if I have 1 mole of this, 1 mole of this atom right here, that's going to have a mass of -- the math isn't difficult here -- 56 grams. Right? And if you think about it, how many atomic mass units is this? Well, this is 56 atomic mass units per atom. Then you have a mole of those, so you have 6.02 times 10 to the 23 times 56 atomic mass units. And then you divide it by the number of atomic mass units per gram. And you end up with 56 grams. But the easy way to think about it is you just take whatever the mass number is. If you have silicon, if you have a mole of silicon, a mole of silicon will have a mass -- I don't want to say weight because this should apply to any planet -- of 28 grams. What about 2 moles of silicon? 2 moles of silicon. And I'll write its mass number. Let's say silicon has a mass number of 28. Two moles of silicon. Well, 1 more would have a mass of 28 grams, so 2 moles is going to have a mass of 56 grams. If I were to say, let's say I had 4 moles of oxygen, which has a mass number of 16. What is the mass of that? This is a huge number of oxygen atoms -- what would be the mass of that? Well, it would be 4 times-- 1 mole of oxygen would have a mass of 16 grams, so 4 moles has 64 grams. It's confusing because we're not used to using a word like moles as a number, but all it is, is a number. And the easy way to think about is that it lets us translate between this atomic mass unit number and grams. And you say, well, how do I get that many grams? Well, I have to have 6.02 times 10 to the 23 carbon atoms for that collection of carbon to have a mass of 12 grams. That's all that mole means. It's just a number. And I encourage you to kind of play around with a lot of what we talked about. Because it's super important to have the intuition behind moles, otherwise, you'll get confused later on when we start getting into energies in terms of it requires kilojoules per mole, and what is the energy of this reaction and all that type of stuff. So just really try to make sure you digest this as well as possible. And let me know if you don't and I'll maybe make another video on this because it's so important.