 Okay, in this video I am going to basically introduce a new term. It might seem like a new concept, but we've already been talking about the concept in the past couple of videos. This is a piece of the periodic table, and we're going to use it for the next bunch of questions. The first question is, what's the mass of one mole of hydrogen atoms? You can pause the video and try to answer that if you unpause. It's this number, but the units are grams. So one mole of hydrogen atoms, which is about 6.02 times 10 to the 23 H atoms, it weighs about one gram. And again, for the purposes of these videos, it's okay to round to the nearest whole number. So one gram of hydrogen is about one mole of hydrogen atoms. And we're going to use these numbers in the periodic table to answer these types of questions. You can't just know them. You have to be able to look them up unless you've committed them to memory, but that's a little bit of a waste of time. This idea of how much does one mole of something weigh, something weigh, or more formally, what's the mass of one mole of something? It has a special name in chemistry. It's called molar mass. So I asked you, what's the mass of one mole of hydrogen atoms? And if you've been following along, you'd say it's one gram. Another way of asking this question is to say, what's the molar mass of hydrogen? I'm asking the same question, but I'm using this new term. That all that is asking is, how much does one mole of hydrogen weigh? But you can ask this question for any of the elements. So what's the mass of one mole of beryllium atoms? You can pause the video and figure this out. Here's beryllium. The mass of one mole of beryllium is about nine grams, because we're looking up this number in the periodic table. Another way of asking this is to say, what's the molar mass of BE, or beryllium? And you'd give the same answer. You'd say nine grams. Or sometimes people say nine grams per mole. But molar mass implies how much does one mole weigh? What's the mass of two moles of oxygen? This is not asking what the molar mass of oxygen is. The molar mass of oxygen is about 16 grams. But I want to know how much two moles of oxygen weighs? So you'd say one mole weighs about 16 grams. So two moles must weigh about twice as much. What's twice as much as 16? It's 32. So the answer to this question is going to be 32 grams. What's the mass of one and a half moles of carbon atoms? Well, here's carbon. Here's the molar mass of carbon if we use grams. So we could say 12 grams of carbon atoms. It is one mole of carbon atoms. Again, all I'm doing is I'm writing a ratio or a fraction. But I don't have, in my question, I don't have one mole of carbon atoms. I have 1.5 moles of carbon atoms. And we can say x grams here. So 12 grams weighs one mole. I'm sorry, one mole of carbon atoms weighs 12 grams. One and a half moles of carbon atoms weighs, I don't know how many grams. We're going to call it x. But now that we have these two fractions set equal to each other, we can cross multiply. We can figure out what x is just by cross multiplying. Before we go rampaging off and doing that, you can conduct a sanity test. You can say, look, is 1.5 bigger or smaller than 1? Well, it's bigger. 1.5 is a bigger number than 1. So x better also be bigger than 12. Because one mole weighs 12, but we have more than one mole. We have one and a half moles. So however much it weighs, it better weigh more than 12. Now, it should weigh one and a half times 12. So if you did that and say 1.5 times 12 is 18 grams. So you could solve your question that way. You could answer the question and the answer is going to be 18 grams. I'm going to do it in a slightly more detailed way, because sometimes you won't necessarily be able to do this in your head. So let's do it the hard way. So here's the setup, just like we had on the PowerPoint slide. We have 12 grams of carbon atoms. It's the same thing as one mole of carbon atoms. But we don't have one mole. We have a little bit more. We have 1.5 moles of carbon atoms. I want to know how much it weighs. We cross multiply and solve for x. So we're going to do 12 grams of carbon atoms. Sorry, let's make this green so that it matches. 12 grams of carbon atoms times 1.5 moles of carbon atoms. That's coming from here. Equals this number, 1 mole of C atoms times x grams of carbon atoms. We want to get this x all by itself, which means we need to get rid of this number here. So if we divide this right side by 1 mole of C atoms, then the mole of C atoms will cancel. That unit will go away. 1 divided by 1 is still 1. So now we have the x all alone. But if we divide this side by 1 mole of carbon atoms, we also have to divide the left side by 1 mole of carbon atoms to keep the sides equal to each other, because there is an equal sign here. And then mole of carbon atoms cancels on the left side as well. The only unit we're left with is grams of carbon atoms on the left, grams of carbon atoms on the right. So 12 grams of carbon atoms times 1.5 divided by 1 is equal to x grams of carbon atoms. If you do 12 times 1.5 divided by 1, you're going to come out with 18 grams of carbon atoms, which is what we did on the PowerPoint slide as well. So we did it the hard way. You don't necessarily have to do it this way, but sometimes the questions will be more complicated and complicated enough that maybe it's worth it to set up these two fractions the way that they're set up here. So you should be able to do the types of calculations that we just did. If I tell you how many moles of something you have, you should be able to use the periodic table to figure out how much that many moles weighs. You should also know what molar mass means. In other words, you should know the definition of molar mass. So here's a summary of the mole before we make things even more slightly more complicated. Mole is just an easier way of saying this number. Mole means one group of 6.02 times 10 to the 23 things. And this gets its own bigger print. One mole of an atom weighs equals shouldn't be here. Ways should be in quotes. Ways, the atomic mass number, the average atomic mass number, but in units of grams. This number, 6.02 times 10 to the 23, is sometimes known as Avogadro's number. In other words, if someone asks you what Avogadro's number is, please do not say it's 1-800 Avogadro. That is a horrible joke that I made up. I'm pretty sure I invented it. Anyway, so let me summarize again. What we have been doing in the past couple of videos is interconverting between counting number of atoms, counting number of moles, which is just groups of numbers of atoms, and then taking number of moles and using the periodic table to convert that into how much some number of atoms weighs. So if I tell you how many atoms you have and I give you a periodic table, you should be able to figure out how much it weighs. If I tell you how much some pile of atoms weighs and I give you the periodic table, you should be able to convert and tell me how many atoms there actually are. And on your way there, the easiest thing to do is to convert to moles. So if I tell you how many atoms, if you convert to moles and then use the periodic table, you can figure out how much it weighs. If I tell you you have a pile of atoms and it weighs a certain amount, you can use the periodic table to convert this information to moles and then you can use moles to convert to how many atoms you actually have. Some examples of that. If I tell you that you have this many carbon atoms, 6.02 times 10 to the 23, you should, this number should ring a bell in your head and you should say, well, that's one mole of carbon atoms. And I say, well, I have one mole of carbon atoms, let me look up carbon in the periodic table. I've got this 12.011. So one mole, if I have this many carbon atoms, it must weigh about 12 grams. And you can do this in reverse. If I hid this information from you and this information and I said that I had 12 grams of carbon, you could look up this number in the periodic table and you could say, well, that's about, these numbers just about match, so I must have, must have one mole of carbon atoms. And if I have one mole of carbon atoms, that's 6.02 times 10 to the 23 of them. So you can go in either direction. And you can do this for any of the elements. You can do it for hydrogen, 6.02 times 10 to the 23 hydrogens is one mole of hydrogens. One mole of hydrogens weighs about one gram or in reverse. So you should be able to do those types of calculations as well. So this, to summarize what I just showed you on the previous slide, this slide gets its own sort of special couple of bullets that reiterates what was on the previous slide. If you know the number of moles of some material and you know its formula, you can figure out how much it weighs. You can figure out how many grams you have. And you can do this in reverse. If you know how many grams of something you have and you know its formula, you can figure out how many moles of the material you have. You can go in either direction, which is what the previous slide said. And we are going to do this an awful lot for the rest of the semester. So this is something that you really sort of need to become comfortable with. If I have one mole of hydrogen, it weighs one gram. If I have one gram of hydrogen, I must have one mole. If I have two moles of H, then it must weigh about two grams. So you should be able to interconvert like that. I give you a simple one because one mole of hydrogen weighs one gram, but it won't always be that way. Carbon, one mole of carbon is about 12 grams. And you can look that up in the periodic table. But there the conversion is one mole is 12 grams. Two moles of carbon is 24 grams, et cetera, et cetera. So it will be a different conversion for different elements and that's why you need the periodic table. So that's it for this. There will be another drill in a little bit and maybe a new concept too. So, all right, see you later.