 Okay, just to recap what was covered in the previous video, these numbers, the way they were introduced in the beginning of the course is, I said these were a measure of average atomic mass, and I said the units were AMU. And what I'm telling you is that people reuse these numbers, chemists reuse these numbers. They swapped out this unit and they said look, we can reuse this number and every once in a while if we need to, we can use the unit of grams. People know that one gram is about the weight of one paperclip. And we can say that 1.0079 grams of hydrogen atoms is this many hydrogen atoms, 4.0026 grams of helium is that many helium atoms. So there's a way of converting between grams and how many of an atom you have. And it's not just hydrogen and helium you can do this with. You can use these numbers in any of the 118 elements in the periodic table. So you can do it for any of them. I realize that at least for a lot of you, this is a difficult idea. This is a weird number. This has a different name. It's called the one mole of things. Because it's weird enough, we're going to sort of do drills on it. We're going to talk about this. That's what this video is about. It's to just practice. So again, here's a little bit of practice. If I have 10.811 grams of boron atoms, then I have 6.02 times 10 to the 23 boron atoms. If I have 6.02 times 10 to the 23 carbon atoms, how much does it weigh? It weighs 12.011 grams. So these numbers and this number are inter-convertible. But you have to be able to look up these numbers in the periodic table to do the conversion. One mole is 6.02 times 10 to the 23 things. We're going to do some drills. Here we go. Chemistry does not use the dozen because 12 atoms of something is just not enough to be usable by humans. It's not enough to weigh out on a scale. It's just not useful. Instead of the dozen, chemistry uses this weird term called the mole. That's 6.02 times 10 to the 23 group, 6.02 times 10 to the 23 of something. It's about equal to this number. As I mentioned, there are other digits here. Some of the digits are known, but it's not known. We don't know all of the digits, actually. There are people who, for whatever reason, still work on this, trying to find out the extra digits. But it's taken a long time just to get three or four more digits. As far as we're concerned, it's just going to be about 6.02 times 10 to the 23. Mole does not refer to the furry creature under your lawn. It comes from the German word for molecule, which is shown there. So here comes the drill. I went to the store and I bought a mole of jelly beans. How many jelly beans did I buy? Well, you can pause and think about that. But it's going to be 6.02 times 10 to the 23 jelly beans. Now this may seem silly, and it kind of is, but I'm just trying to get you accustomed to this number. I went to the store and I bought one mole of sodium atoms. How many sodium atoms did I buy? Well, I bought 6.02 times 10 to the 23 sodium atoms. Don't worry, it's going to get more difficult. I went to the store and I bought a dozen Toyota Corollas. And I actually want to ask two questions. How many cars did I buy? And the second question is written. How many wheels did I buy? How many wheels did I buy? I bought a dozen of them. So I bought 12 cars. I bought 12 Corollas. How many wheels did I buy? Assuming that there's no spare, it's going to be 12 times 4 because there's 4 wheels per car, and that's 48 wheels. Again, this might not seem too difficult to you because, well, 12 is a reasonable number to wrap your head around. 4 is a reasonable number to wrap your head around. But this type of question is going to show up with moles in a little bit. So I'm trying again to get you in the right frame of mind. I've thought a lot about this probably more than I should have as far as why. The idea behind moles is difficult. And I can come up with three reasons. One, it's a weird number that people don't think about very often. It's a huge number, right? And it's almost always written in scientific notation because it's too big to write in conventional form. Because it's in scientific notation, this tends to confuse people in calculations. But it's just a number like any other number. Sometimes I feel like the questions are phrased poorly with respect to mole questions. I will do my best to phrase them as clearly as possible. But again, nobody's perfect. So I'm shooting for perfection, but probably going to miss. And the other thing is that putting these numbers into your calculator is not always the easiest thing to do. And so you have to be able to type this number into your calculator and use it in calculations to get the correct answers. In addition to it being a weird number, you actually have to use it. So that's another thing that makes it difficult. So if you can tackle those three things, or at least if I can help you tackle the second point and you tackle the first and third, maybe we make some progress. OK. More drills. I have one mole of hydrogen atoms. How many atoms do I have? Well, I have 6.02 times 10 to the 23 H atoms. I have two moles of hydrogen atoms. Well, something changed here. And everything I asked you before with respect to moles was one mole. Now I have two moles of hydrogen atoms. How many hydrogen atoms do I have? Well, I have this number times 2 because I have two sets of this number. So it's going to be 2 times 6.02 times 10 to the 23 H atoms. Unfortunately, you're not going to see the answer written this way. You have to be able to multiply this out, either in your head or on a piece of paper or on a calculator and come up with the answer that I'm going to show you. If you do this on your calculator, and if you do it correctly on your calculator, you should get 1.204 times 10 to the 24. And the unit would be hydrogen atoms. So 2 times this number, 2 times Avogadra's number, is 1.204 times 10 to the 24. So if I told you I have two moles of hydrogen atoms, how many hydrogen atoms do I have? The correct answer would be 1.204 times 10 to the 24 hydrogen atoms. So, again, we're sort of changing things a little bit. I'm varying the number of moles now. For those of you who are connoisseurs of significant digits, this is not correctly rounded, but I don't give a crap. So let's keep going. That's good enough. I will not mark you wrong if you do not round correctly. I have 3.2 moles of hydrogen atoms. How many hydrogen atoms do I have? Well, I have to have 3.2 times as much as 6.02 times 10 to the 23 H atoms. In other words, I have 3.2 sets of 6.02 times 10 to the 23 H atoms. What this is in scientific notation if you punch it out is some other number. So I'm going to punch this out on my calculator just so that you can sort of play along at home. And I get 1.9264 times 10 to the 24 H atoms. So you're going to have to be able to do this. You're going to have to be able to take 3.2 and multiply it by this number, which is sometimes called Avogadra's number. And this would be your answer. This would be waiting for you on a quiz or a test where I would expect you to be able to write it out this way. If you wrote it out this way, if it was a fill in the blank or something like that, I would probably give you credit. But if it's multiple choice, you're definitely not going to see this as a possible answer. You're going to see this as a possible answer. Here's a very different question. I have 1 times 10 to the 23 H atoms. How many moles of H atoms do I have? This question is basically phrased backwards from all of the others. Up here, I gave you moles. Gave moles asked how many. Down here, I give you how many and ask for moles. So you can pause and try to figure this out. I tend to do it this way. So if you unpause, I will show you what I would do. I would say 6.02 times 10 to the 23 H atoms is one mole of H atoms. So I'm writing this as a ratio or a fraction if you want. But I don't have 6.02 times 10 to the 23 H atoms in my question. I only have 1 times 10 to the 23 H atoms. So I want to know how many moles of H atoms I have. And I set these two fractions equal to each other. I can cross multiply. I can multiply these two things together. And set them equal to these two things. So let me do that on a different slide or let me do that somewhere else. Okay, this setup here is the same as what I had on the slide earlier. So what we're going to do is we're going to cross multiply and solve for X. So let's cross these two first. One mole of H atoms times 1 times 10 to the 23 H atoms equals these two numbers multiplied together. 6.02 times 10 to the 23 H atoms times X moles of H atoms. And what we want to do is we want to figure out what this X is all by itself. We want to get rid of this ugly number that's attached to it. And so what we're going to do is we're going to divide this side by 6.02 times 10 to the 23 H atoms. And if we do that, the H atoms unit goes away. 6.02 times 10 to the 23 on top, 6.02 times 10 to the 23 on the bottom. That reduces down to 1. So we have the X all by itself. However, if we divide this side by 6.02 times 10 to the 23 H atoms and we want to keep both sides equal, we have to do the same thing to the left side. So we also have to divide this side by 6.02 times 10 to the 23 H atoms. H atom unit in the top, H atom unit in the bottom, they cancel away. The only unit we're left with is moles of H atoms. Here it is. And the only thing we have on the right is X moles of H atoms. So 1 mole of H atoms, it's coming from there, times 1 times 10 to the 23. This unit went away, divided by 6.02 times 10 to the 23 is equal to X moles of H atoms. And if you do this out, if you multiply and divide everything out there you're going to get 0.166 moles of H atoms. Has, and I'm just going to write this extra stuff, has 1 times 10 to the 23 H atoms. So that was not the most elegantly phrased statement, but what this is saying is if I have 1 times 10 to the 23 H atoms, I have 0.166 moles of H atoms. And hopefully this makes a little bit of sense. This number here, it's less than 1 mole of stuff. This number here, 1 times 10 to the 23, which is what we're trying to convert to moles. This number is less than 6.02 times 10 to the 23, which means whatever this answer was going to be in moles it had to be less than 1 mole. And we got a number that was less than a mole, we got 0.166 moles. So the reason I point this out is we did this very complicated calculation, or this complicated looking calculation. But if you came out with a number that was bigger than a mole you should at least conduct what I call a sanity test. See if you went insane, because we know that this number, weird as it is, is smaller than this number. So this x, it better be smaller than 1. And we got less than 1. We got 0.166, so at least by that measure we did not go insane. So just to summarize, 1 times 10 to the 23 H atoms is 0.166 moles of H atoms. And that's the answer here. Approximately 0.166 moles of H atoms. So that's about it. That's probably enough to digest for the moment. We might do one more page of drills in a little bit, but you know, go have a beer. Or not. Have you heard the story of the hot rod race with the forwards and the legacy was set in the past? That story is true. I'm here to say I was driving that model A.