Lecture 4. Intermolecular Forces Liquids & Solids, Part IV
Blake, Donald R.
UCI Chem 1B is the second quarter of General Chemistry and covers the following topics: properties of gases, liquids, solids; changes of state; properties of solutions; stoichiometry; thermochemistry; and thermodynamics. 
 Okay. I hope I can promise you that this is going to be the worst lecture of the quarter. I'm just saying I hope that I don't do any worse than today because solids are just, I think you guys will do better with it than I because your generation, you know, you guys have these phones that you can make do just about anything. This is my phone. Okay. Yes. Not easy to text with, you know. I got to hit four things to get an S. Okay. Yeah. So I just don't do it very often, okay. So I could literally go two or three days without even opening this phone. Okay. That's how little I use it. You don't like that too, but you probably use it more than I do. And so, but what your generation is good at is this kind of little electronic stuff. Computers, you just have a, it's like a second nature because you play little video games when you're kids and stuff. And so also I think spinning things. I mean, I think you guys had these, these games that you've played that have sort of allowed your brain to expand a bit. So I'm hoping that this solid stuff, packing of, of atoms and molecules together is going to be something that you actually find that you can do because I find I can't, I'm not much better. I'm only a two dimensional kind of guy. So, so we're going to talk about solids no more. I scared a lot of people, I guess, on, on Tuesday with the, all the gas stuff. You know, I had like 20 people come to office hours. I've been getting emails, people worried about stuff. So we're going to go to solids now. I don't want to show you that and I don't want that. Here. Okay. Now, while I do not particularly like the subject of solids, there are certain things you must know. Now solids folks, we're in the intermolecular forces chapter. Okay. So this is still intermolecular forces. It's just that now instead of it being a liquid, like water added with ethanol and it's hydrogen bonding and why they stay liquids and all, now we're going to wire things solids and how do they pack? Okay. Now there's seven different kinds. Okay. Of, of, of crystalline solids. You only need to know one kind. Okay. And it is the cubic. Okay. Because my brain does not, you'll see what the others look like. So this folks is a simple cubic. It's a lot like this table right here. Okay. With an atom, it could be an atom, it could be an ion, it could be a molecule. Something right there. That's called a lattice point. One here, one here, one down there, one there, one here, one here, one here. Eight corners. There's eight corners of a cube. Okay. So you have this one, it is called a simple cubic. Now on a simple cubic, the atom, well let's say it's an atom here, is, its center is right here. Okay. Right on the corner. So how many, how, when we start stacking these things, how many centers or, or corners are there going to be right here? Look at this and tell me, if I start packing stuff all around this point right there, how many cubes can I fit around that point right there? Eight. Okay. You go, wait a minute, it's only got six sides. Got six sides, we've got eight corners. So you can actually pack it if you don't believe me, get some blocks and do it. Okay. So how much of that atom do you think is inside that box? One eighth. Okay. This is called a simple cubic. Okay. It's a simple cubic and it's, it's as simple as it gets, it's as empty as it gets. So how many atoms are, we can add all the eighths up, how many atoms are inside, are inside a simple cubic? It would be, there's eight of them, times one eighth is one. There's one atom in the unit cell for a simple cubic. Folks, that is as easy as it gets. Okay. The next one then is a body centered cubic. That would be like if this was one more atom and I stuck it right here. Okay. Inside, completely inside. See that one right there? There it is right there. It's completely inside this cube. So now how many atoms are there per unit cell? Two. Okay. And then we get down here where there is the same, it always has these eight corner points, but then we're going to put one right here. So it's half in, half out. One here, half in, half out. One here, half in, half out. One here, half in, half out. One here, half in, half out. And one down here. It's got six faces. Okay. And it's half in, half out. So that's going to be six times a half. Okay. So how many atoms are in a face centered cubic unit cell? Four. One for these guys and then you've got one, two, three. You can't see the other three. These are half and so you have four. So folks, on the exam, you're going to be expected to know these numbers. There will be a multiple choice question. It would be something like a body centered cubic has one, two, three or four atoms in the unit cell. That's simple. Is there anybody here who could have missed that? If anybody misses that, I'm going to put up a list of names after the exam and say these people were not in class obviously because I'm too good of a teacher to not have you understand this. Okay. One, two, four. Okay. Now you can only remember and memorize that but the real important thing folks is that you are able to conceptually see this in three dimensions. Okay. So any questions on these? And then what happens is the unit cell folks is the smallest part that allows you to then duplicate that exact entity. What I mean by that is like an atom. If you break an atom, a sodium atom is the smallest unit, you start pulling off a neutron or a proton or electron, it's no longer sodium. So a whole atom is the smallest you can be. Then you can have a whole bunch of atoms and make a mole of atoms if you want. The unit cell, it's the same thing. That is the smallest thing that defines what it looks like. You have one of these and you start stacking them together. One of these you start stacking together. This is what it looks like when you've got eight unit cells together, eight unit cells, eight unit cells. Okay. So once again it's the smallest piece that you can have and still recognize it as one of these things here. Okay. Does that make sense? And once again folks it's important for you to understand that we can have, they say this is gold. Okay. So I guess gold, polonium and uranium. That's how they stack. All right. Then it can be an atom, it can be an ion, it can be a molecule like water. You can have water at each one of these points. Okay. So once again, simple cubic, body centered cubic, face centered cubic. Same thing. Okay. This is what I'm talking about. The unit cell looks like this. Now is this, would you call this a cubic? No. It's not a cubic. This is something else. Some other shape. Maybe like a rhombus or a, yeah, probably a rhombus. What is this? Who can tell me what is that? What is that shape, that geometric shape? Rhombus? Oh, good. Parallelogram. Parallelogram. Okay. Well, I think a parallelogram is also a square cube, I think. But anyway, okay. What is that? Parallelopiped? Oh, I see. Okay. Well, thank you for that comment. That will not be on the exam. But this is how they pack, okay. Once you have this shape, then you can put them together and make the big thing. It's like blocks. If you cut a block in half, it doesn't do any good. You can't tell what the block look like. You need the whole block and then you can build a bunch of stuff. So, what does this thing say? Crystalline solids. Okay. So there are some general things. Unfortunately, they're not that specific. Okay. So, possessed rigid, long range order. That is true. Crystalline solid. Adams molecules or ions can occupy. That is absolutely true. And an amorphous is not possessed well defined arrangements and long range molecular order. So what I'm going to use, I'm going to use this classroom as an example. Okay. If every seat were filled today, every seat, then we would say we are a crystalline solid. But there's a seat right there, empty in one there, in one there, and there's a bunch of them. So these holes tend to make it a little bit less perfect. And these holes can cause destruction or distortion in how things look and all. So that would be more of an amorphous. This is still too ordered for amorphous, but still. Amorphous can have some order to it, then it's got a hole, or it's got some weird kind of bonding going on. So the amorphous, once again, does not have this well defined lattice structure. And once again, the unit cell is the basic repeating structure. Lattice point, lattice point I said it can be either atoms, molecules, or ions. Okay. We already did this. It just looks a little bit different now. This is what it would look like once again. It's harder to see. I will not ask you to draw these. Okay. Because if we do, all the females, almost all the females will do a much better job than the males. It's a stereotype that I probably shouldn't have, or it's a bias, but I have two sons and a daughter. And I've had female students. Who's writing can you not read downstairs, Josette, in the lab book? Brent. Yes, yes. Can you read Gloria? Yes, perfect. Okay. So I can't draw these very well. You're not going to have to draw them either, but I want you to understand the basic structure. Okay. That's the main point. Okay. So simple cubic. You can see there's nothing stuck inside there. Okay. Body centered cubic. There's one inside. It's easier to see right there for me. That one's a little confusing down there. And then this one. Okay. This just sort of shows how on this side there's four sides here, and then there's one that cuts it in half, and then there's four more. Okay. So this is the one that's got the eight, and then this is, I think that's right. Corner out of here. And this is one just cut in half. Okay. More of the same. This looks like the exact same one I just showed. Okay. We're doing the math now. You don't have to do the math on the exam. You just need to know. But you know, I don't want you to memorize it. I want you to remember what does this thing look like? Okay. The cubic means you always have those little ones out there on the corners. You've got an eighth times eight. Okay. Face centered. Can't get any more obvious than that. That means it's on the face. There's six faces. You can only, if you've got one, two sides, you mean you have to share half with each. So you've got a half of an atom in the face centered. Body centered just one stuff in the middle. Okay. So you don't need to do this math, but you very well may need to on an exam say that, you know, a body centered cubic has two atoms. This is just an example of different types of crystals. This is an atomic solid, an ionic solid. This is just sodium chloride here. Molecular solid is with water at each point. Okay. So once again, you can have any. You can have an atom. You can just have a bunch of copper. Okay. Copper is something that we use. It's, those kinds of metals are very good at conducting electricity in heat. That's why we have copper wires, all of your computers. And if you are, we had an infinite amount of gold, we have gold instead or gold something because gold conducts even better. Okay. But so again, three different, four different things here. Now what I want you to, well, I think we'll come back to this, but this is a diamond. Diamonds are kind of interesting because it's just carbon. It's just like you're, the lead in your pencil, it is just carbon. It's like a chunk of coal. That's what a diamond is. Okay. And we will learn maybe next chapter or the chapter after that in thermodynamics that there's just a tiny energy difference between a, you know, one pound diamond and a one pound piece of coal. But huge difference in price. Okay. Turns out that for a diamond, it has four bonds. Okay. And you got a carbon and it's, it's the unit cell. I'm not sure what the unit cell looks like there, but it's bonded to four things. For your lead in your pencil, which is graphite, it's got these layers where they're bonded together, but there's only three bonds and then their inner, their, their intermolecular forces are what keep these layers together. That's why when you drag your pencil across a piece of paper, stuff just slides right off and goes right on the paper. Okay. That bond is not nearly as strong as diamond. Diamond is like one of the hardest things in the world. Okay. Seven types. So, I would say, huh. Now, do you think this is a tri-clinic and a monoclinic? Okay. Well, I'm not even going to, you guys, that would be on the exam. This entire page would be on the exam. Like, I'm lying. Okay. You need to know there are seven though. You need to know that there are seven different kinds of unit cells. This is the only one for which you need to know how they pack in. Okay. Because it's the only one that my mind will allow me to understand and, and, and remember. Okay. These other ones, obviously, you're going to put points, you know, you're going to still have a, a, a, a last point right there. You can have eight of them here, eight of them here, eight of them here. This one looks like it's got a little bit more than eight. But they just get too complicated for me. Okay. So feel free to learn all this. You do need to know that there are seven, seven types of unit cells. You can get an exam question. Number of unit cells. One, three, five, seven, eight. Okay. Okay. This is where I start having problems. Okay. So metals have high thermal and electric conductivity. I said that about so, or about copper. If you, I, I actually, I don't wear my wedding ring anymore because I got too fat and plus, plus, that's probably the word I can't say. I put on some weight. But I have some arthritis in my finger joint here. So my wedding ring doesn't quite fit. But I remember one day about 10 years ago, I walked out of this room and the door didn't have the resistance that I was expecting. The spring was broken or something like this. And when I opened the door, I pulled kind of hard and the door just went open really fast like this. And it turns out that my, the handle was like this and my hand sort of slammed into the wall. Not hard. I wasn't hurt. But my ring was smashed. I mean, it literally just got like bent in and that's because gold is very malleable. It says that's right there, right there. Okay. Very, I mean, if you have really good gold, I mean like 24 karat kind of stuff, I mean, it's like soft. Okay. So it is very much like, and that's why we can have wires, wires that are copper wires that actually bend. Okay. So, but, but, but these properties folks, all of these properties are related to their atomic interactions within the lattice. So this is a few things here. So this is how they pack stuff. Okay. I can, I'm good to write there. Okay. You got yellow ones and then you got blue ones. They're going to put some blue ones on top now. Okay. Top view, side view. I'm not sure where they came up with the extra yellows there, but anyway, this is the closest packing. Okay. Look at that. You guys understand that? It's like making a sandwich. Okay. One layer on top, one layer on top, one layer. It's just that they're balls and stuff and round things or whatever and they pack on top of each other. And nature kind of folks doesn't like empty space. So what that means is that there's not as many of the simple cubics as there are body centered cubics or face centered cubics. I mean, it's just, I think there's something that says nature adores a vacuum. Is that something you've ever heard? Okay. Has anybody ever heard that? Okay. Well, maybe somebody made it up. Okay. So things tend to pack so that you cram as much stuff in as possible. Be like this room. Be nice if there were much bigger lounge chairs, right? But then you'd sleep. But then you'd be more comfortable, but right now they got you packed in like on an airplane. Okay. So hexagonal close packed structure. Okay. But so this one on top of this one, here's the unit cell. Top view like this unit cell looks like that. What does that look like? Okay. The problem is when they draw these drawings is this thing, this blue thing is actually, I guess there's three of them inside, isn't there? Okay. Hold on. Let's see what it says. Oh, great. See, it just gets complicated. Josette, do you understand this stuff at all? Okay. Good. Good. Office hours. Go to, I mean, this stuff to me. Anyway, those cubic, or cubic close packed. Okay. That's what that's called. You're going to have to know that in a minute. I'll show you why. Okay. Note, cubic close packed is face centered cubic. That you need to know. Okay. Because there's different terminology. And so if you get something that says you've got a cubic close packed structure, how many atoms are in it in the unit cell? You say, oh, well, I know that it's a face centered cubic, so there must be four. So, types. Okay. Look at this first one. Okay. What would you say this is? Would you call that body centered? I'd call it body centered. Now, the zinc one looks like it's face centered. Okay. Because I see a face right here. Anyway, I think it's face centered and it's got these other, um, um, sulfurs in here. Eh. Who wants to take a guess at this? Well, maybe it's going to tell us. I don't know. You know the answer to that? Sulfur. Okay. The holes. We're going to get to the whole stuff later. Yes, thank you. Okay. So before it was just a face centered, but that was too empty. Okay. So, sulfurs end up going in there and jumping in those holes. Okay. That makes sense. Ion and crystal. So what would a molecular crystal be? It's got a molecule. What would an atomic crystal be? It's got an atom. Okay. So, ionic crystal. I want you people to sort of be able to visualize something. Can somebody give me an example of an ionic crystal? It's something I talked about in class. Salt. Thank you. Okay. So if I had a block of salt right here, would you say that it's hard? Brittle. If I drop the salt, it would just shatter. Okay. And you wouldn't know it had a high melting point, but trust me, you can take some heat and put it to it and it just sits there and it's just salt. So those are general characteristics of an ionic crystal. Okay. Think of salt. And you wouldn't know this, but if we had this block of salt and we put an electric charge on one side and something on the other side, it wouldn't conduct very well. Okay. You just don't have the electron flow that you need. Okay. So we're going to do a problem. Okay. Why are we going to do a problem? We're going to do a problem because you're worried about this and you don't know what kind of questions I can ask on an exam. Okay. This question right here, folks, goes back to Chem1A. For those of you who have not had Chem1A in a while, I know there are some of you who took AP chemistry in high school and have passed out of Chem1A. So for those of you who, that's the case, you're going to want to pay close attention. This is a very simple question. Okay. But last night when I went over it in class, people were freaking out. They're going, how am I supposed to know this? How am I supposed to know that? So while I'm trying not to draw too heavily on what you learned in Chem1A, I do expect you to know what a mole is. Okay. I expect you to know how many molecules or particles or atoms there are in a mole. And I expect you to know what the molecular weight of something means. If something has a molecular weight of 18, okay, then that means that there's 18 grams per mole. That's what the molecular weight means. If something's got a molecular weight of 165, you need 165 grams to come up with 6 times 10 to the 23rd pieces. Okay. So you have to, you know, I don't want to have those of you who either didn't do well in Chem1A or haven't had it in a while be at a disadvantage. But this is a class that builds on the previous quarter. So looking at this, okay, the element copper, okay, copper has a CCP packing, okay, with a face centered, now they didn't have to tell you that, they could have just told you this. So I told you, I had to know this CCP was face centered cubic. Okay. How many atoms in a face centered cubic? Four. Okay. So if I were giving this on an exam, and I were taking this exam, I would just write down four atoms per unicell. I would just write that down. Okay. It says the density of copper is 8,920 kilograms per meter cubed. Calculate the volume of the unit cell. Now, you might look at that and go, what the heck? Okay. It's actually quite simple. Okay. It's quite simple. Density is usually given in grams per CC. I tell you that the density of water, we did the water the other day, water was at four degrees was 1.0 grams per cubic centimeter. Cubic centimeters like a little sugar cube. Okay. They didn't give that. Instead they gave like kilograms instead of grams, and they gave meters instead of cubic centimeters. Okay. It doesn't matter. Why? We've got two units here. Okay. We have two units. We've got volume and we got mass. All right. Well, volume, that's what they're asking for. What is the volume? So we know we've got to leave this, this, the meters cube has to show up somewhere in this equation. And our answer. Okay. But what do we know, what do we know folks about this? Okay. If I had been nice, I would have said the molecular weight of copper is something. 56, I don't know what it is. What is it? It's right there. I can't read that. 63.5. Okay. So if I had said that, you're going to have periodic tables on the exam. So all you got to do is say, oh, now I know I've got a mass. I get rid of the mass. I got a mass here. I got a mass there. I'm going to end up with size. Okay. So that's what it looks like. Okay. We've already done that. So we have four atoms per unit cell. We know that one mole is equal to that many atoms, right? Six times 10 to the 23 atoms. There is your molecular weight of copper. You divide this whole thing through. You're going to get our moles there and we've got grams here. We've got atoms there and look what happens. So we got, we know that we've got four atoms per unit cell. So we got that, how many grams? The mass of the unit cell is that. Very straightforward. So I would, maybe what I should do is just let you, let me ask you. If you want me to put this up and you guys do it and then I explain it, what do I just do it? Because you have this in your notes. I want to do what makes it easiest for you. Okay. What's not easiest. I don't want what's easy at all for you, folks. I want what's best for you. So what would work best? I mean, me just put the question up and you guys struggle with it for two or three minutes, five minutes, and then I go through how I would solve it. Okay. That's what we'll do on the next one. Okay. So, but you can see how we approach this. Okay. And you might be going, you got a periodic table, folks. You got mass. Now you're screwed if you don't know this. Okay. I'm sorry. If you don't know that a mole is 6.0 or 6.02 times 10 and 23rd, then you got a problem. But that is something that you need to know in this class. Okay. So now folks, we've got how many grams we've got. Okay. So now what do we do with it? Okay. Well, they gave us the density, right? Nothing here, folks. This doesn't do us any good because here's what they gave us. Okay. But we do have grams, right? We got grams right here and we got kilograms right there. So look at how simple it is. The density, the density as I said is, we saw earlier, in that case it was kilograms over meters cubed. Okay. So it's just a mass or mass over the volume. Okay. That is the definition of density. One gram per cubic centimeter for water. So what is the volume? You've got the density. Did I give you the density? Sure. 8,920 kilograms. So we've got the density right there and we've got the mass right there. That's going to tell us the volume. So you look at this thing right here. You divide that out like that and you get that. Okay. Now, what you need to, as I said, I'm not trying to rag on your generation, but I think you maybe aren't quite as good as my generation at estimating sizes of lengths and volumes. Okay. What they gave us was they said a meter cubed. That's a meter. Okay. So it's this by this by this. So it's about this high. That's one meter. And that thing weighed 8,900 kilograms. That's like nine tons. Nine tons for something that's this big. Okay. Because its density was in, they gave it to us in meters cubed. Okay. In meters cubed, what is the density of water? What is the density of water in meters cubed? I'm going to walk up here and point to somebody. Think of it. Meters cubed. Yes, you. 1,000. Yes. Thank you. 1,000 kilograms because I just said that it's one gram per cubic centimeter. One gram per cubic centimeter. Then you just take grams and make it in a kilograms and centimeters and make it into meters. Okay. Now how many, how many liters? Oops. Oh, I'm getting a phone call. Pretty cool. Haven't got one in days. How many liters, folks, in a cubic meter? Okay. Well, a liter, folks, is 10 centimeters by 10 centimeters by 10 centimeters. So if this is my meter, I'd have one here, two, three, four, five, six, seven, eight, nine, ten. Ten this way, ten this way, and ten that way. What is ten times ten times ten? A thousand. So there's a thousand liters in a cubic meter. So we've got this meter. Now look at what the question was in. It didn't say give it to us in meters cubed. Okay. You lose a point or two. If this is a ten point question, you lose a point or two if you leave it like that. Okay. Because you've gotten the real volume, but I'm asking for you now to reduce it down to mills. Okay. So how would you do that? Well, you would do liters because you divided that by a thousand and then there's a thousand cubic centimeters per liter. So that is the volume right there. Four point seven three times ten to the twenty-third. That's how big, that's how big the unit cell is. And aside from knowing that it was a face-tended cubic, so you had four atoms per unit cell, you didn't need to know anything other than chem 1A and some simple math. So folks, if you're given something like this where you're going, I don't have enough information. Try to trust me, you do. Okay. You do have enough information. You've got a periodic table. Anytime you've got a periodic table, I'm going to ask you if I, if I, if right now, okay, here's a question. Here's a question. All right. You've got twenty-six grams of lithium. Twenty-six grams of lithium. How many molecules do it? You've got periodic tables here, there, there, and hopefully you can, if you can't see that, oh, no, I'm not going to tell you what to do. And don't cheat, okay? You should always bring a calculator, folks, especially in the following weeks. You're going to do a lot of stuff in class. Bring a calculator. What's all your data, everybody? I thought you weren't going to see it. I know. That's what I thought too. What happened? Oh, my mic. We have an answer yet? 2.5 times 10 to the 24th. Does that sound right? 2.25. What did somebody else get? We have an answer? I can't repeat it because I can't remember. I don't know if I said 23. 26. Okay, so 26 grams of lithium. So if I had been a nice guy and said 26 grams of lithium, how many moles? Then you would have just divided 26 by the molecular weight of lithium. And you'd have gotten, lithium is right there. So it's probably like about 6. Is that what it is? You've got a periodic table. What is lithium? 6.9. 6.9, I'm going to say 7. Okay, so lithium has 7. So 26 divided by 7 is close to 4. So we have about 4 moles. Then in question B, then I said, okay, so how many molecules is that? Then you'd say, oh, I've got the number of moles. It's 4 times 6 times 10 to the 22nd, so it's about 2.5 times 10 to the 24th. But, folks, I'm not always going to ask you in a nice, give me A, give me B, give me C, give me D to kind of let you work your way through. This time all I said was, you got this many grams. I didn't ask you how many moles it was. I asked how many molecules it was. So sometimes, folks, you don't, it's not as easy to see what, how do you get from A to Z? Okay? And, folks, let me tell you something. For those of you who go on to organic chemistry, okay, my problem in organic chemistry was, was that it wasn't solving problems like this. It was that you had to memorize that if I add a laser pointer plus a bottle of diapepsy, that then you get this thing, okay? And then you add two other things together to get something else. And then if you add those two things together plus this, you get something else. So you had to memorize these 100 or 200 different reactions. And then it was like, make this, okay? Well, I wasn't smart enough to memorize them the first time, or I was smart enough, I just was too lazy. And so, you know, going from A, literally some of the reactions are 20 steps, 20 steps. Now, if they'd have asked me, make this into this, and I would have, I'd go A plus B goes to C. And then they'd say now, take C and make E. I'd go, oh, C plus D goes to E. They don't do that. They'd say, starting with A, make Z. So there's no hand-holding, folks, okay? It's not easy. And that's why you have to know, it's like trying to do a crossword puzzle with a small vocabulary, okay? It's tough, okay? So I'm not going to ask you, I'm not going to give you this stepwise questions all the time, all right? So you see how you solve this? Let's try the next one, okay? So, folks, this is a legitimate question for an exam or something like this. And you have to know hardly anything about solids, except for the fact that this said that it was a face-in-a-cubic. Okay, I drew this one. Okay. Okay. Okay. Okay. So how many of you really don't have a clue on how to do this? That's why I'm here, folks, okay? You don't have a clue? I'm here to try and clue you in, okay? And once again to show you that, I haven't said this in this class, I think, but that units are our friend, okay? I honestly can't remember how to do most of these problems, okay? But I look at this right here and I say, oh, I think I've got, I've got grams per mil and I've got mils, okay? So that already tells me what I'm going to be dividing or multiplying by at some point, okay? Because I need molecules, okay? I need molecules. That's what Avogadro's number is. And so, so you're going to take your information knowing how many atoms are in a unit cell, okay? How many are in a hexagonal unit cell? Two atoms, okay? So you've got two atoms. So now you've got atoms. You've got grams. You've got grams per mil and what else? Yeah, you got, you got sides. You've got mils here. Mils there, grams there and you got atoms. Perfect. That's all you needed. Does that help anybody? So once again, the mass is equal to, once again, density is equal to volume, mass over volume. So this is just a rearrangement of that. So you've got, you've got 8.5 grams per mil, okay? Times that many mils. Now why are we multiplying it by this? Because it's mils in the bottom. You just, you knew you had either divide one by the other, okay? And so you had a 50-50 chance of dividing the right one. So you've got mils here in the denominator. So you multiply this by mils and you're just going to end up with grams and a little tiny, tiny bit, okay? So the mass is going to be some tiny little number in grams. Look at that. Three times 10 to 23 grams, okay? That is how many grams in a unit cell, okay? Does that make sense? So you've got that many grams in a unit cell. You've got this many grams for beryllium. Times two for the unit cells. You end up with six times 10 to the 23rd. Now folks, I would not give you an example. I would not give you a question like this on the exam without having gone over something like this in the class. Because it's a little bit convoluted, okay? For those of you who took Chem 1A, loved Chem 1A, did well in Chem 1A, then this is a pretty straightforward, maybe a little rushed on you, but this all makes sense to you. Others are going, oh man. I hope you don't ask this on an exam, okay? But it's math folks. It's the kind of math that you should not be afraid of. It's rearranging things. So practice this kind of thing, okay? So here's the difference, as I said, between a diamond which is bonded to four things and graphite. You have these layers of graphite where they're bonded to three things, one, two, three, and then you have these layers that are intermolecularly forced attraction here. And these layers just fall right off of your pencil, right onto the paper. Huge difference from something like glass or diamonds which can cut glass, okay? Huge difference, intermolecular forces. Okay, so once again. Nothing here that's a surprise. We've already said this. In this case, we've got the, oops, these are pointers dead. Oops. So we have atoms here, atoms there, lattice points are occupied by atoms. This is a, think of a diamond. Hard, brittle, high melting point. Alright, so that we've already said. So metallic crystals, they're a little bit different folks, okay? Lattice points are occupied by metal. Think of copper. Copper's a metal. So let me show you. It'll show you right here, okay? So the majority, the nucleus is right here, okay? And that's everything except the valence electrons, okay? It's all the valence electrons that are in this gray area. This is the nucleus here, the intershell electrons. And then you've got, it's almost like just this commune, you know, back in the 60s, you know? You share everything, you know? And so these electrons are what we call a sea of electrons. And so if you apply a little bit of electricity on this side, it just flows without much resistance at all. I mean very, very little resistance, okay? So this is a metallic crystal and that would be copper. Think of copper, think of gold, okay? Really good conductors of heat and of electricity. And so that's why we use them for that. This is in your notes. Look at it. So this is an example. This is a class filled with people, okay? This is a class. Look at this. This right here looks a lot like this, okay? There are parts over here that do look like the actual very nicely organized crystal. But in this case, there are, when things kind of went together, they didn't quite go together as nicely. And so then you end with this non-crystalline quartz glass, okay? Which has different properties than this would, all right? This is what it looks like when you've got empty seats. Haven't you ever heard of like the grading of a diamond, okay? The grade diamonds, you know? You can have like good, better, gemstone quality. What do you think that means? Diamonds are made by taking like coal and putting them under high pressure for millions of years and temperature. And sometimes there's some stuff that gets in there, okay? A perfect diamond would be just carbon. Just carbon and packed, like that's kind of like that, okay? But a diamond that has flaws is one that has, you know, some imperfections in the structure. So the better the diamond, the more expensive it's worth, or the more expensive it is. And the fewer of these it has. Yes? What does it mean by the carats, like now? Carats is just a weight. It's actually the weight of a, and I don't know what one carat is, but it's a weight, I don't know. And it comes from long, long ago. Questions? Okay, so once again, this is the non-crystalline, this is the crystalline. Okay, now, this is actually from your book. It's the first time I've used anything from the book. Well, the second time. This is the kind of stuff they give you, okay? How many of you have read the book? How many of those people their hands up are lying? Okay. Well, I just skim the book. Okay. So I want to, in this next half hour, show you a little bit, and I don't want you to panic. People asked me last night, why are you showing us this? Or why did you show us this? And it's, once again, it's to try and get you to think a little bit outside the box. That's what I was trying with the atmospheric stuff the other day, and it didn't work too well. So I'm going to try something that's rather media-blabbering, actually, to show you something. Okay. So this is a math thing using atoms or molecules as a guide. Okay. So will there be something like this on the exam? Probably not on the first or second exam, but it could be on the final. Okay. There could be something, because on the final you've got two hours. A little bit more time to think, and I want to challenge some of you. But I can't say for sure. Okay. But please pay attention. It's simple math. It's logical stuff. It's stuff where I think you folks, you get to a point, just like you did on the last two questions, like, geez, I don't know where to go with this. I don't have enough information. I don't know this. I'm going to show you that you actually do have information, that you can be asked a question that you've never seen before. You can actually solve it. Okay. So we're going to start with filling spaces. Okay. I told you that the nature of horror is a vacuum. So we're going to start with a simple cubic. I'm going to get it all the way down to right there. Okay. So the question is, in terms of filling spaces, if you have something like this, how much space is empty space? How many, how much space doesn't have the atom in it? Okay. So who can tell me what is the equation for the area of a circle? Pi r squared. Pi r squared. Okay. Now what is the equation for a square? It's going to be, you know, length times width. Okay. And since they're the same, it's going to be this times itself. We understand that. So we've got a box, or a square, and we've got a circle. So if I told you right now that this radius was, I'm going to tell you that right now, okay, that this is one centimeter. Okay. One centimeter. What is the packing efficiency? How much of this box is filled with that atom? Do it. Do it right now. One centimeter right there. Okay. I don't know. So I'm asking you what the efficiency is. I'm not asking you how much. I'm saying, okay, look, you've got to take into consideration two things. You've got this volume and you've got that volume. I want to know what is the percentage? How much of it's filled? Do it right now. You don't need anything from me. This is a challenge, folks. It's a simple, this could be on an exam where I just said that is one centimeter. So people, you need to bring your calculators. You need to be interactive. Maybe I talk too much and don't listen enough. Okay. So from now on, you will be docked 10 points if you don't bring a calculator. Yeah. Okay. I'm taking this noise as that you know the answer. Who wants to give me an answer? You. What's that? Two or three? 78.5 he says. Okay. Anybody else want to give me another number? So what is the equation? What are the two equations you need? What is the length? We said that for a square, you need this length times this length, right? What is this length right there? Two R, right? It's two R or two centimeters since I was nice enough to give you one centimeter there. So what is two times two? Four is the volume of the square. The volume of the circle is pi, like this guy said early on. So it's just going to be pi divided by four. So 3.14 divided by four. That's it. 78 percent of this is filled. Okay. Now does that seem awfully, yes. This was just, I said just a square, not a cube. Yeah, this is just that. Okay. So just two dimensions. So does everybody see how simple that was? Was that simpler or am I just out of touch? Can I have some response? Was that, yes. You're raising your hand. Oh, your guy thumbs up. Simply says. Was it simple before I did it? So folks got that. Good. You didn't need anything. Hey, somebody didn't get it. Thank you for acknowledging that. Okay. Now do you see how to do it? Okay. Do you see how, and did I have to teach you any chemistry for this? This was like my sophomore year geometry class. Okay. Now it was a little tougher. This guy was wanting to know whether we had to do it as a cube. Okay. That's tougher. Okay. But we could do that. Oh, do that. Do it. Good thinking, buddy. I want to know what is the packing efficiency of that sphere now in that cubic box? Fourth arch pi r cubed. It is. So fourth arch pi r cubed, folks. That's something you should probably know. Fourth arch pi r cubed is the volume of a sphere. Now it's got to be fast, folks, because I made r1. Okay. So you should be able to do this problem in about less than a minute. You got it done? All right. What's the answer? I don't know the answer. It sounds about right. Okay. Who's got an answer? You. 52%. Okay. Perfect. Okay. Let me ask you a question. And I want an honest answer. How many got that right? Okay. Now, of those people with their hands up, keep them up, how many think they might not have gotten it right if I hadn't done this one first? Quite a few, right? So once again, folks, I'm not always going to be there to tell you that this is the first step. This is the second. Organic chemistry, folks, is not like that. Okay. And even the problems that we just did, knowing how to get to the end, okay? You got to think about it. But if you're asked a question and you're given something like this, instead of a picture, if I had said a circle fits exactly into a box, a square, what is the volume that is not filled? Instead of showing you, I might have had a problem with that. Okay. So it's math. It's simple math. Do not be afraid of it. And then you're going to see that this is exactly. So there it is right there. There's your pi r squared to r squared. And if you get rid of, look at this, r squared right there, r squared right there, just pi over two. Oh, two squared, pi over four. That's simple. Now, ooh, I'm going to ask you this one. That one right there. Packing efficiency for that. Okay. Now, how many know what the equation is for a circle or a sphere? Okay. This is one. There's just two dimensions again. Not three dimensions. It's just two dimensions. So this is going to be pi r squared for that area. How many know what the equation for the area of hexagon is? You do? Geez. Okay. Well, I had to look it up. Why would I know that? Okay. The area is equal to three, write this down, folks. You don't need to know it, but for this problem you do. The area is equal to three times the square root of three over two times the length right there. Okay. So that was, the area is equal to three times the square root of three over two times the square of that area right there. So let's say L squared. So, do you understand that? So now I want you to figure out in this box right there, or that one, it doesn't matter, they're all filled, what is the efficiency in terms of packing for circles in a hexagon as opposed to circles in a square? Got an answer already? I thought that young lady was stretching, I guess. Okay. So don't forget, the area is three times the square root of three over two, and then the whole thing's times L squared, that length squared. I'm not going to give you what the radius is this time. Oh, you don't need it. Yes. Six what? Might be. We'll have to wait and see. Okay. Oh, yeah, yeah. So we want the, okay, we don't just want that. Yeah. We want, what is the efficiency? How much of that dark stuff is there in there, okay? Or actually how much of the light blue is there? So we want a percent just like we had here. What? For which one? Oh, I'm not giving that to you this time. Yes. Okay. How many of you got about, are you done? How many got about 90%? Ooh. How about 91%? Okay. So I didn't need folks to give you what the radius was. Why not? This is where you got it all right here. Okay. Look at right here. Is that in the center of that circle? In the center of that circle? Okay. So what is the length of this piece right here? Two R. Right? It's two R. So you don't need to know that the radius is one or two or five thousand. As long as you got R in it, you got, you got to have an R in your circle equation and you're going to have an R in your other one. Okay. So we got, this is the, this is the only part you got and it's a little bit tricky. It's not really tricky. You got how many circles inside that hexagon? Three. One. And then you got a third. You got one, two, three, four. You got six thirds. So six times a third is two plus one is three. So you got three circles. So you need to have three circles in one hexagon. So when you multiply this thing through, you end up with this. There's your three. That is just pi R squared. Don't need to have what the R is. Okay. And down here, okay, remember we had, we had a, let me have three, no, two. We had a two. What did we have? Can I start? I got too much traffic. Oh, no, I've lost it. Thank you. There it is right there. So this had been a three in the front and that's right, three, square root of three over two. But the length here folks is two R, right? L is two R. So you square that. So you get rid of your squares and you had a two and a two. There's been a two underneath this. Okay. So you get rid of that and it's going to be these two times the three so it's just a six. Okay. So then you just divide everything in there. You got your R's, you got this. And in the end you get 90.7. Okay. It's a simple math. It has nothing to do with chemistry. I mean, I could, you could get this on a, on a, on a SAT or something. Okay. As long as they gave you a whole bunch of equations in the back because I would not expect you to remember what hexagon is because I can't remember. But that, so folks, this is a question from your book. Okay. It's the kind of thing that they would like you to be able to do but it's simple math and geometry. And it's common sense. Okay. If I had not the first time told you that this was one, some of you would have freaked out. Because with one you had a number you could plug in. In the end it was really just pi R squared over two R squared. You didn't need to know that it was one. So folks, sometimes you need to look a little bit deeper. You got to say, oh my gosh, I don't have enough information. And in reality you do have the information. Or you don't need the information. You don't need to know what R is here. So once again, folks, it's math. It's a math exercise. It's the kind of thing though that I can ask you a question on packing efficiency and you do some math on an exam. Okay. This one I just am going to show you what it looks like there. Okay. Okay. Just assume that's correct. Why am I showing you this? I'm not sure. Hold on. Maybe I'm just going to keep pushing this button. Okay. Answer. Thank you. Ladder's holes. This goes back to what Josette was talking about. So you have this lattice structure thing that all of a sudden there's a little tiny hole right in there. Guess what can happen? See that? Look at that. They're going everywhere. So you can have these little holes and stuff that I'm sure are important. Do you think, Josette? I'm not sure how important they are. We're done. I can't handle it anymore, folks. I'm sorry.
 Okay. I hope I can promise you that this is going to be the worst lecture of the quarter.  I'm just saying I hope that I don't do any worse than today because solids are just,  I think you guys will do better with it than I because your generation, you know, you guys  have these phones that you can make do just about anything. This is my phone. Okay. Yes.  Not easy to text with, you know. I got to hit four things to get an S. Okay. Yeah. So  I just don't do it very often, okay. So I could literally go two or three days without  even opening this phone. Okay. That's how little I use it. You don't like that too,  but you probably use it more than I do. And so, but what your generation is good at is  this kind of little electronic stuff. Computers, you just have a, it's like a second nature  because you play little video games when you're kids and stuff. And so also I think spinning  things. I mean, I think you guys had these, these games that you've played that have sort  of allowed your brain to expand a bit. So I'm hoping that this solid stuff, packing of,  of atoms and molecules together is going to be something that you actually find that you  can do because I find I can't, I'm not much better. I'm only a two dimensional kind of  guy. So, so we're going to talk about solids no more. I scared a lot of people, I guess,  on, on Tuesday with the, all the gas stuff. You know, I had like 20 people come to office  hours. I've been getting emails, people worried about stuff. So we're going to go to solids  now. I don't want to show you that and I don't want that. Here. Okay. Now, while I do not  particularly like the subject of solids, there are certain things you must know. Now solids  folks, we're in the intermolecular forces chapter. Okay. So this is still intermolecular  forces. It's just that now instead of it being a liquid, like water added with ethanol and  it's hydrogen bonding and why they stay liquids and all, now we're going to wire things solids  and how do they pack? Okay. Now there's seven different kinds. Okay. Of, of, of crystalline  solids. You only need to know one kind. Okay. And it is the cubic. Okay. Because my brain  does not, you'll see what the others look like. So this folks is a simple cubic. It's  a lot like this table right here. Okay. With an atom, it could be an atom, it could be an  ion, it could be a molecule. Something right there. That's called a lattice point. One  here, one here, one down there, one there, one here, one here, one here. Eight corners.  There's eight corners of a cube. Okay. So you have this one, it is called a simple cubic.  Now on a simple cubic, the atom, well let's say it's an atom here, is, its center is right  here. Okay. Right on the corner. So how many, how, when we start stacking these things,  how many centers or, or corners are there going to be right here? Look at this and tell  me, if I start packing stuff all around this point right there, how many cubes can I fit  around that point right there? Eight. Okay. You go, wait a minute, it's only got six sides.  Got six sides, we've got eight corners. So you can actually pack it if you don't believe  me, get some blocks and do it. Okay. So how much of that atom do you think is inside that  box? One eighth. Okay. This is called a simple cubic. Okay. It's a simple cubic and it's,  it's as simple as it gets, it's as empty as it gets. So how many atoms are, we can add  all the eighths up, how many atoms are inside, are inside a simple cubic? It would be, there's  eight of them, times one eighth is one. There's one atom in the unit cell for a simple cubic.  Folks, that is as easy as it gets. Okay. The next one then is a body centered cubic. That  would be like if this was one more atom and I stuck it right here. Okay. Inside, completely  inside. See that one right there? There it is right there. It's completely inside this  cube. So now how many atoms are there per unit cell? Two. Okay. And then we get down  here where there is the same, it always has these eight corner points, but then we're  going to put one right here. So it's half in, half out. One here, half in, half out. One  here, half in, half out. One here, half in, half out. One here, half in, half out. And  one down here. It's got six faces. Okay. And it's half in, half out. So that's going to  be six times a half. Okay. So how many atoms are in a face centered cubic unit cell? Four.  One for these guys and then you've got one, two, three. You can't see the other three.  These are half and so you have four. So folks, on the exam, you're going to be expected to  know these numbers. There will be a multiple choice question. It would be something like  a body centered cubic has one, two, three or four atoms in the unit cell. That's simple.  Is there anybody here who could have missed that? If anybody misses that, I'm going to  put up a list of names after the exam and say these people were not in class obviously  because I'm too good of a teacher to not have you understand this. Okay. One, two, four.  Okay. Now you can only remember and memorize that but the real important thing folks is  that you are able to conceptually see this in three dimensions. Okay. So any questions  on these? And then what happens is the unit cell folks is the smallest part that allows  you to then duplicate that exact entity. What I mean by that is like an atom. If you break  an atom, a sodium atom is the smallest unit, you start pulling off a neutron or a proton  or electron, it's no longer sodium. So a whole atom is the smallest you can be. Then you  can have a whole bunch of atoms and make a mole of atoms if you want. The unit cell,  it's the same thing. That is the smallest thing that defines what it looks like. You  have one of these and you start stacking them together. One of these you start stacking  together. This is what it looks like when you've got eight unit cells together, eight  unit cells, eight unit cells. Okay. So once again it's the smallest piece that you can  have and still recognize it as one of these things here. Okay. Does that make sense? And  once again folks it's important for you to understand that we can have, they say this  is gold. Okay. So I guess gold, polonium and uranium. That's how they stack. All right.  Then it can be an atom, it can be an ion, it can be a molecule like water. You can have  water at each one of these points. Okay. So once again, simple cubic, body centered cubic,  face centered cubic. Same thing. Okay. This is what I'm talking about. The unit cell looks  like this. Now is this, would you call this a cubic? No. It's not a cubic. This is something  else. Some other shape. Maybe like a rhombus or a, yeah, probably a rhombus. What is this?  Who can tell me what is that? What is that shape, that geometric shape? Rhombus? Oh,  good. Parallelogram. Parallelogram. Okay. Well, I think a parallelogram is also a square  cube, I think. But anyway, okay. What is that? Parallelopiped? Oh, I see. Okay. Well, thank  you for that comment. That will not be on the exam. But this is how they pack, okay.  Once you have this shape, then you can put them together and make the big thing. It's  like blocks. If you cut a block in half, it doesn't do any good. You can't tell what  the block look like. You need the whole block and then you can build a bunch of stuff. So,  what does this thing say? Crystalline solids. Okay. So there are some general things. Unfortunately,  they're not that specific. Okay. So, possessed rigid, long range order. That is true. Crystalline  solid. Adams molecules or ions can occupy. That is absolutely true. And an amorphous  is not possessed well defined arrangements and long range molecular order. So what I'm  going to use, I'm going to use this classroom as an example. Okay. If every seat were filled  today, every seat, then we would say we are a crystalline solid. But there's a seat right  there, empty in one there, in one there, and there's a bunch of them. So these holes tend  to make it a little bit less perfect. And these holes can cause destruction or distortion  in how things look and all. So that would be more of an amorphous. This is still too  ordered for amorphous, but still. Amorphous can have some order to it, then it's got a  hole, or it's got some weird kind of bonding going on. So the amorphous, once again, does  not have this well defined lattice structure. And once again, the unit cell is the basic  repeating structure. Lattice point, lattice point I said it can be either atoms, molecules,  or ions. Okay. We already did this. It just looks a little bit different now. This is  what it would look like once again. It's harder to see. I will not ask you to draw these.  Okay. Because if we do, all the females, almost all the females will do a much better job  than the males. It's a stereotype that I probably shouldn't have, or it's a bias, but  I have two sons and a daughter. And I've had female students. Who's writing can you  not read downstairs, Josette, in the lab book? Brent. Yes, yes. Can you read Gloria? Yes,  perfect. Okay. So I can't draw these very well. You're not going to have to draw them  either, but I want you to understand the basic structure. Okay. That's the main point. Okay.  So simple cubic. You can see there's nothing stuck inside there. Okay. Body centered cubic.  There's one inside. It's easier to see right there for me. That one's a little confusing  down there. And then this one. Okay. This just sort of shows how on this side there's  four sides here, and then there's one that cuts it in half, and then there's four more.  Okay. So this is the one that's got the eight, and then this is, I think that's right. Corner  out of here. And this is one just cut in half. Okay. More of the same. This looks like the  exact same one I just showed. Okay. We're doing the math now. You don't have to do the math  on the exam. You just need to know. But you know, I don't want you to memorize it. I want  you to remember what does this thing look like? Okay. The cubic means you always have those  little ones out there on the corners. You've got an eighth times eight. Okay. Face centered.  Can't get any more obvious than that. That means it's on the face. There's six faces.  You can only, if you've got one, two sides, you mean you have to share half with each.  So you've got a half of an atom in the face centered. Body centered just one stuff in  the middle. Okay. So you don't need to do this math, but you very well may need to on  an exam say that, you know, a body centered cubic has two atoms. This is just an example  of different types of crystals. This is an atomic solid, an ionic solid. This is just  sodium chloride here. Molecular solid is with water at each point. Okay. So once again,  you can have any. You can have an atom. You can just have a bunch of copper. Okay. Copper  is something that we use. It's, those kinds of metals are very good at conducting electricity  in heat. That's why we have copper wires, all of your computers. And if you are, we  had an infinite amount of gold, we have gold instead or gold something because gold conducts  even better. Okay. But so again, three different, four different things here. Now what I want  you to, well, I think we'll come back to this, but this is a diamond. Diamonds are kind of  interesting because it's just carbon. It's just like you're, the lead in your pencil,  it is just carbon. It's like a chunk of coal. That's what a diamond is. Okay. And we will  learn maybe next chapter or the chapter after that in thermodynamics that there's just  a tiny energy difference between a, you know, one pound diamond and a one pound piece of  coal. But huge difference in price. Okay. Turns out that for a diamond, it has four bonds.  Okay. And you got a carbon and it's, it's the unit cell. I'm not sure what the unit  cell looks like there, but it's bonded to four things. For your lead in your pencil,  which is graphite, it's got these layers where they're bonded together, but there's only  three bonds and then their inner, their, their intermolecular forces are what keep these  layers together. That's why when you drag your pencil across a piece of paper, stuff  just slides right off and goes right on the paper. Okay. That bond is not nearly as strong  as diamond. Diamond is like one of the hardest things in the world. Okay. Seven types. So,  I would say, huh. Now, do you think this is a tri-clinic and a monoclinic? Okay. Well,  I'm not even going to, you guys, that would be on the exam. This entire page would be  on the exam. Like, I'm lying. Okay. You need to know there are seven though. You need to  know that there are seven different kinds of unit cells. This is the only one for which  you need to know how they pack in. Okay. Because it's the only one that my mind will allow  me to understand and, and, and remember. Okay. These other ones, obviously, you're going  to put points, you know, you're going to still have a, a, a, a last point right there. You  can have eight of them here, eight of them here, eight of them here. This one looks like  it's got a little bit more than eight. But they just get too complicated for me. Okay.  So feel free to learn all this. You do need to know that there are seven, seven types  of unit cells. You can get an exam question. Number of unit cells. One, three, five, seven,  eight. Okay. Okay. This is where I start having problems. Okay. So metals have high thermal  and electric conductivity. I said that about so, or about copper. If you, I, I actually,  I don't wear my wedding ring anymore because I got too fat and plus, plus, that's probably  the word I can't say. I put on some weight. But I have some arthritis in my finger joint  here. So my wedding ring doesn't quite fit. But I remember one day about 10 years ago,  I walked out of this room and the door didn't have the resistance that I was expecting. The  spring was broken or something like this. And when I opened the door, I pulled kind  of hard and the door just went open really fast like this. And it turns out that my,  the handle was like this and my hand sort of slammed into the wall. Not hard. I wasn't  hurt. But my ring was smashed. I mean, it literally just got like bent in and that's  because gold is very malleable. It says that's right there, right there. Okay. Very, I mean,  if you have really good gold, I mean like 24 karat kind of stuff, I mean, it's like soft.  Okay. So it is very much like, and that's why we can have wires, wires that are copper  wires that actually bend. Okay. So, but, but, but these properties folks, all of these properties  are related to their atomic interactions within the lattice. So this is a few things here.  So this is how they pack stuff. Okay. I can, I'm good to write there. Okay. You got yellow  ones and then you got blue ones. They're going to put some blue ones on top now. Okay. Top  view, side view. I'm not sure where they came up with the extra yellows there, but anyway,  this is the closest packing. Okay. Look at that. You guys understand that? It's like  making a sandwich. Okay. One layer on top, one layer on top, one layer. It's just that  they're balls and stuff and round things or whatever and they pack on top of each other.  And nature kind of folks doesn't like empty space. So what that means is that there's  not as many of the simple cubics as there are body centered cubics or face centered  cubics. I mean, it's just, I think there's something that says nature adores a vacuum.  Is that something you've ever heard? Okay. Has anybody ever heard that? Okay. Well, maybe  somebody made it up. Okay. So things tend to pack so that you cram as much stuff in as  possible. Be like this room. Be nice if there were much bigger lounge chairs, right? But  then you'd sleep. But then you'd be more comfortable, but right now they got you packed in like  on an airplane. Okay. So hexagonal close packed structure. Okay. But so this one on top of  this one, here's the unit cell. Top view like this unit cell looks like that. What does  that look like? Okay. The problem is when they draw these drawings is this thing, this  blue thing is actually, I guess there's three of them inside, isn't there? Okay. Hold on.  Let's see what it says. Oh, great. See, it just gets complicated. Josette, do you understand  this stuff at all? Okay. Good. Good. Office hours. Go to, I mean, this stuff to me. Anyway,  those cubic, or cubic close packed. Okay. That's what that's called. You're going to  have to know that in a minute. I'll show you why. Okay. Note, cubic close packed is face  centered cubic. That you need to know. Okay. Because there's different terminology. And  so if you get something that says you've got a cubic close packed structure, how many  atoms are in it in the unit cell? You say, oh, well, I know that it's a face centered  cubic, so there must be four. So, types. Okay. Look at this first one. Okay. What would  you say this is? Would you call that body centered? I'd call it body centered. Now,  the zinc one looks like it's face centered. Okay. Because I see a face right here. Anyway,  I think it's face centered and it's got these other, um, um, sulfurs in here. Eh. Who wants  to take a guess at this? Well, maybe it's going to tell us. I don't know. You know the  answer to that? Sulfur. Okay. The holes. We're going to get to the whole stuff later. Yes,  thank you. Okay. So before it was just a face centered, but that was too empty. Okay. So,  sulfurs end up going in there and jumping in those holes. Okay. That makes sense. Ion  and crystal. So what would a molecular crystal be? It's got a molecule. What would an atomic  crystal be? It's got an atom. Okay. So, ionic crystal. I want you people to sort of be able  to visualize something. Can somebody give me an example of an ionic crystal? It's something  I talked about in class. Salt. Thank you. Okay. So if I had a block of salt right here,  would you say that it's hard? Brittle. If I drop the salt, it would just shatter. Okay.  And you wouldn't know it had a high melting point, but trust me, you can take some heat  and put it to it and it just sits there and it's just salt. So those are general characteristics  of an ionic crystal. Okay. Think of salt. And you wouldn't know this, but if we had  this block of salt and we put an electric charge on one side and something on the other  side, it wouldn't conduct very well. Okay. You just don't have the electron flow that  you need. Okay. So we're going to do a problem. Okay. Why are we going to do a problem? We're  going to do a problem because you're worried about this and you don't know what kind of  questions I can ask on an exam. Okay. This question right here, folks, goes back to Chem1A.  For those of you who have not had Chem1A in a while, I know there are some of you who  took AP chemistry in high school and have passed out of Chem1A. So for those of you  who, that's the case, you're going to want to pay close attention. This is a very simple  question. Okay. But last night when I went over it in class, people were freaking out.  They're going, how am I supposed to know this? How am I supposed to know that? So while I'm  trying not to draw too heavily on what you learned in Chem1A, I do expect you to know  what a mole is. Okay. I expect you to know how many molecules or particles or atoms there  are in a mole. And I expect you to know what the molecular weight of something means. If  something has a molecular weight of 18, okay, then that means that there's 18 grams per  mole. That's what the molecular weight means. If something's got a molecular weight of 165,  you need 165 grams to come up with 6 times 10 to the 23rd pieces. Okay. So you have to,  you know, I don't want to have those of you who either didn't do well in Chem1A or haven't  had it in a while be at a disadvantage. But this is a class that builds on the previous  quarter. So looking at this, okay, the element copper, okay, copper has a CCP packing, okay,  with a face centered, now they didn't have to tell you that, they could have just told  you this. So I told you, I had to know this CCP was face centered cubic. Okay. How many  atoms in a face centered cubic? Four. Okay. So if I were giving this on an exam, and I  were taking this exam, I would just write down four atoms per unicell. I would just  write that down. Okay. It says the density of copper is 8,920 kilograms per meter cubed.  Calculate the volume of the unit cell. Now, you might look at that and go, what the heck?  Okay. It's actually quite simple. Okay. It's quite simple. Density is usually given in  grams per CC. I tell you that the density of water, we did the water the other day,  water was at four degrees was 1.0 grams per cubic centimeter. Cubic centimeters like a  little sugar cube. Okay. They didn't give that. Instead they gave like kilograms instead  of grams, and they gave meters instead of cubic centimeters. Okay. It doesn't matter.  Why? We've got two units here. Okay. We have two units. We've got volume and we got mass.  All right. Well, volume, that's what they're asking for. What is the volume? So we know  we've got to leave this, this, the meters cube has to show up somewhere in this equation.  And our answer. Okay. But what do we know, what do we know folks about this? Okay. If  I had been nice, I would have said the molecular weight of copper is something. 56, I don't  know what it is. What is it? It's right there. I can't read that. 63.5. Okay. So if I had  said that, you're going to have periodic tables on the exam. So all you got to do is say, oh,  now I know I've got a mass. I get rid of the mass. I got a mass here. I got a mass there.  I'm going to end up with size. Okay. So that's what it looks like. Okay. We've already done  that. So we have four atoms per unit cell. We know that one mole is equal to that many  atoms, right? Six times 10 to the 23 atoms. There is your molecular weight of copper.  You divide this whole thing through. You're going to get our moles there and we've got  grams here. We've got atoms there and look what happens. So we got, we know that we've  got four atoms per unit cell. So we got that, how many grams? The mass of the unit cell  is that. Very straightforward. So I would, maybe what I should do is just let you, let  me ask you. If you want me to put this up and you guys do it and then I explain it,  what do I just do it? Because you have this in your notes. I want to do what makes it  easiest for you. Okay. What's not easiest. I don't want what's easy at all for you,  folks. I want what's best for you. So what would work best? I mean, me just put the  question up and you guys struggle with it for two or three minutes, five minutes, and  then I go through how I would solve it. Okay. That's what we'll do on the next one. Okay.  So, but you can see how we approach this. Okay. And you might be going, you got a periodic  table, folks. You got mass. Now you're screwed if you don't know this. Okay. I'm sorry. If  you don't know that a mole is 6.0 or 6.02 times 10 and 23rd, then you got a problem.  But that is something that you need to know in this class. Okay. So now folks, we've got  how many grams we've got. Okay. So now what do we do with it? Okay. Well, they gave us  the density, right? Nothing here, folks. This doesn't do us any good because here's what  they gave us. Okay. But we do have grams, right? We got grams right here and we got  kilograms right there. So look at how simple it is. The density, the density as I said  is, we saw earlier, in that case it was kilograms over meters cubed. Okay. So it's just a mass  or mass over the volume. Okay. That is the definition of density. One gram per cubic  centimeter for water. So what is the volume? You've got the density. Did I give you the  density? Sure. 8,920 kilograms. So we've got the density right there and we've got the  mass right there. That's going to tell us the volume. So you look at this thing right  here. You divide that out like that and you get that. Okay. Now, what you need to, as  I said, I'm not trying to rag on your generation, but I think you maybe aren't quite as good  as my generation at estimating sizes of lengths and volumes. Okay. What they gave us was they  said a meter cubed. That's a meter. Okay. So it's this by this by this. So it's about  this high. That's one meter. And that thing weighed 8,900 kilograms. That's like nine  tons. Nine tons for something that's this big. Okay. Because its density was in, they  gave it to us in meters cubed. Okay. In meters cubed, what is the density of water? What  is the density of water in meters cubed? I'm going to walk up here and point to somebody.  Think of it. Meters cubed. Yes, you. 1,000. Yes. Thank you. 1,000 kilograms because I  just said that it's one gram per cubic centimeter. One gram per cubic centimeter. Then you just  take grams and make it in a kilograms and centimeters and make it into meters. Okay.  Now how many, how many liters? Oops. Oh, I'm getting a phone call. Pretty cool. Haven't  got one in days. How many liters, folks, in a cubic meter? Okay. Well, a liter, folks,  is 10 centimeters by 10 centimeters by 10 centimeters. So if this is my meter, I'd have  one here, two, three, four, five, six, seven, eight, nine, ten. Ten this way, ten this way,  and ten that way. What is ten times ten times ten? A thousand. So there's a thousand liters  in a cubic meter. So we've got this meter. Now look at what the question was in. It didn't  say give it to us in meters cubed. Okay. You lose a point or two. If this is a ten point  question, you lose a point or two if you leave it like that. Okay. Because you've gotten  the real volume, but I'm asking for you now to reduce it down to mills. Okay. So how would  you do that? Well, you would do liters because you divided that by a thousand and then there's  a thousand cubic centimeters per liter. So that is the volume right there. Four point  seven three times ten to the twenty-third. That's how big, that's how big the unit cell  is. And aside from knowing that it was a face-tended cubic, so you had four atoms per unit cell,  you didn't need to know anything other than chem 1A and some simple math. So folks, if  you're given something like this where you're going, I don't have enough information. Try  to trust me, you do. Okay. You do have enough information. You've got a periodic table. Anytime  you've got a periodic table, I'm going to ask you if I, if I, if right now, okay, here's  a question. Here's a question. All right. You've got twenty-six grams of lithium. Twenty-six  grams of lithium. How many molecules do it? You've got periodic tables here, there, there,  and hopefully you can, if you can't see that, oh, no, I'm not going to tell you what to  do. And don't cheat, okay? You should always bring a calculator, folks, especially in the  following weeks. You're going to do a lot of stuff in class. Bring a calculator.  What's all your data, everybody? I thought you weren't going to see it. I know. That's  what I thought too. What happened? Oh, my mic.  We have an answer yet? 2.5 times 10 to the 24th. Does that sound right? 2.25. What did  somebody else get? We have an answer? I can't repeat it because I can't remember. I don't  know if I said 23. 26. Okay, so 26 grams of lithium. So if I had been a nice guy and  said 26 grams of lithium, how many moles? Then you would have just divided 26 by the  molecular weight of lithium. And you'd have gotten, lithium is right there. So it's probably  like about 6. Is that what it is? You've got a periodic table. What is lithium? 6.9.  6.9, I'm going to say 7. Okay, so lithium has 7. So 26 divided by 7 is close to 4. So  we have about 4 moles. Then in question B, then I said, okay, so how many molecules is  that? Then you'd say, oh, I've got the number of moles. It's 4 times 6 times 10 to the 22nd,  so it's about 2.5 times 10 to the 24th. But, folks, I'm not always going to ask you in  a nice, give me A, give me B, give me C, give me D to kind of let you work your way through.  This time all I said was, you got this many grams. I didn't ask you how many moles it  was. I asked how many molecules it was. So sometimes, folks, you don't, it's not as easy  to see what, how do you get from A to Z? Okay? And, folks, let me tell you something. For  those of you who go on to organic chemistry, okay, my problem in organic chemistry was,  was that it wasn't solving problems like this. It was that you had to memorize that if I  add a laser pointer plus a bottle of diapepsy, that then you get this thing, okay? And then  you add two other things together to get something else. And then if you add those two things  together plus this, you get something else. So you had to memorize these 100 or 200 different  reactions. And then it was like, make this, okay? Well, I wasn't smart enough to memorize  them the first time, or I was smart enough, I just was too lazy. And so, you know, going  from A, literally some of the reactions are 20 steps, 20 steps. Now, if they'd have asked  me, make this into this, and I would have, I'd go A plus B goes to C. And then they'd  say now, take C and make E. I'd go, oh, C plus D goes to E. They don't do that. They'd  say, starting with A, make Z. So there's no hand-holding, folks, okay? It's not easy.  And that's why you have to know, it's like trying to do a crossword puzzle with a small  vocabulary, okay? It's tough, okay? So I'm not going to ask you, I'm not going to give  you this stepwise questions all the time, all right? So you see how you solve this? Let's  try the next one, okay? So, folks, this is a legitimate question for an exam or something  like this. And you have to know hardly anything about solids, except for the fact that this  said that it was a face-in-a-cubic. Okay, I drew this one.  Okay.  Okay.  Okay.  Okay.  So how many of you really don't have a clue on how to do this? That's why I'm here, folks,  okay? You don't have a clue? I'm here to try and clue you in, okay? And once again to show  you that, I haven't said this in this class, I think, but that units are our friend, okay?  I honestly can't remember how to do most of these problems, okay? But I look at this right  here and I say, oh, I think I've got, I've got grams per mil and I've got mils, okay?  So that already tells me what I'm going to be dividing or multiplying by at some point,  okay? Because I need molecules, okay? I need molecules. That's what Avogadro's number is.  And so, so you're going to take your information knowing how many atoms are in a unit cell,  okay? How many are in a hexagonal unit cell? Two atoms, okay? So you've got two atoms.  So now you've got atoms. You've got grams. You've got grams per mil and what else? Yeah,  you got, you got sides. You've got mils here. Mils there, grams there and you got atoms.  Perfect. That's all you needed. Does that help anybody? So once again, the mass is equal  to, once again, density is equal to volume, mass over volume. So this is just a rearrangement  of that. So you've got, you've got 8.5 grams per mil, okay? Times that many mils. Now why  are we multiplying it by this? Because it's mils in the bottom. You just, you knew you  had either divide one by the other, okay? And so you had a 50-50 chance of dividing the  right one. So you've got mils here in the denominator. So you multiply this by mils  and you're just going to end up with grams and a little tiny, tiny bit, okay? So the  mass is going to be some tiny little number in grams. Look at that. Three times 10 to  23 grams, okay? That is how many grams in a unit cell, okay? Does that make sense? So  you've got that many grams in a unit cell. You've got this many grams for beryllium.  Times two for the unit cells. You end up with six times 10 to the 23rd. Now folks, I would  not give you an example. I would not give you a question like this on the exam without  having gone over something like this in the class. Because it's a little bit convoluted,  okay? For those of you who took Chem 1A, loved Chem 1A, did well in Chem 1A, then this is  a pretty straightforward, maybe a little rushed on you, but this all makes sense to you. Others  are going, oh man. I hope you don't ask this on an exam, okay? But it's math folks. It's  the kind of math that you should not be afraid of. It's rearranging things. So practice this  kind of thing, okay? So here's the difference, as I said, between a diamond which is bonded  to four things and graphite. You have these layers of graphite where they're bonded to  three things, one, two, three, and then you have these layers that are intermolecularly  forced attraction here. And these layers just fall right off of your pencil, right onto  the paper. Huge difference from something like glass or diamonds which can cut glass,  okay? Huge difference, intermolecular forces. Okay, so once again. Nothing here that's a  surprise. We've already said this. In this case, we've got the, oops, these are pointers  dead. Oops. So we have atoms here, atoms there, lattice points are occupied by atoms. This  is a, think of a diamond. Hard, brittle, high melting point. Alright, so that we've already  said. So metallic crystals, they're a little bit different folks, okay? Lattice points  are occupied by metal. Think of copper. Copper's a metal. So let me show you. It'll show you  right here, okay? So the majority, the nucleus is right here, okay? And that's everything  except the valence electrons, okay? It's all the valence electrons that are in this gray  area. This is the nucleus here, the intershell electrons. And then you've got, it's almost  like just this commune, you know, back in the 60s, you know? You share everything, you  know? And so these electrons are what we call a sea of electrons. And so if you apply a little  bit of electricity on this side, it just flows without much resistance at all. I mean very,  very little resistance, okay? So this is a metallic crystal and that would be copper.  Think of copper, think of gold, okay? Really good conductors of heat and of electricity.  And so that's why we use them for that. This is in your notes. Look at it. So this is an  example. This is a class filled with people, okay? This is a class. Look at this. This  right here looks a lot like this, okay? There are parts over here that do look like the  actual very nicely organized crystal. But in this case, there are, when things kind of  went together, they didn't quite go together as nicely. And so then you end with this non-crystalline  quartz glass, okay? Which has different properties than this would, all right? This is what it  looks like when you've got empty seats. Haven't you ever heard of like the grading of a diamond,  okay? The grade diamonds, you know? You can have like good, better, gemstone quality.  What do you think that means? Diamonds are made by taking like coal and putting them  under high pressure for millions of years and temperature. And sometimes there's some  stuff that gets in there, okay? A perfect diamond would be just carbon. Just carbon and packed,  like that's kind of like that, okay? But a diamond that has flaws is one that has, you  know, some imperfections in the structure. So the better the diamond, the more expensive  it's worth, or the more expensive it is. And the fewer of these it has. Yes?  What does it mean by the carats, like now? Carats is just a weight. It's actually the  weight of a, and I don't know what one carat is, but it's a weight, I don't know. And it  comes from long, long ago. Questions? Okay, so once again, this is the non-crystalline,  this is the crystalline. Okay, now, this is actually from your book. It's the first time  I've used anything from the book. Well, the second time. This is the kind of stuff they  give you, okay? How many of you have read the book? How many of those people their hands  up are lying? Okay. Well, I just skim the book. Okay. So I want to, in this next half  hour, show you a little bit, and I don't want you to panic. People asked me last night,  why are you showing us this? Or why did you show us this? And it's, once again, it's  to try and get you to think a little bit outside the box. That's what I was trying with the  atmospheric stuff the other day, and it didn't work too well. So I'm going to try something  that's rather media-blabbering, actually, to show you something. Okay. So this is a math  thing using atoms or molecules as a guide. Okay. So will there be something like this  on the exam? Probably not on the first or second exam, but it could be on the final.  Okay. There could be something, because on the final you've got two hours. A little bit  more time to think, and I want to challenge some of you. But I can't say for sure. Okay.  But please pay attention. It's simple math. It's logical stuff. It's stuff where I think  you folks, you get to a point, just like you did on the last two questions, like, geez,  I don't know where to go with this. I don't have enough information. I don't know this.  I'm going to show you that you actually do have information, that you can be asked a  question that you've never seen before. You can actually solve it. Okay. So we're going  to start with filling spaces. Okay. I told you that the nature of horror is a vacuum.  So we're going to start with a simple cubic. I'm going to get it all the way down to right  there. Okay. So the question is, in terms of filling spaces, if you have something like  this, how much space is empty space? How many, how much space doesn't have the atom in it?  Okay. So who can tell me what is the equation for the area of a circle? Pi r squared. Pi  r squared. Okay. Now what is the equation for a square? It's going to be, you know,  length times width. Okay. And since they're the same, it's going to be this times itself.  We understand that. So we've got a box, or a square, and we've got a circle. So if I  told you right now that this radius was, I'm going to tell you that right now, okay,  that this is one centimeter. Okay. One centimeter. What is the packing efficiency? How much  of this box is filled with that atom? Do it. Do it right now. One centimeter right there.  Okay. I don't know. So I'm asking you what the efficiency is. I'm not asking you how  much. I'm saying, okay, look, you've got to take into consideration two things. You've  got this volume and you've got that volume. I want to know what is the percentage? How  much of it's filled? Do it right now. You don't need anything from me. This is a challenge,  folks. It's a simple, this could be on an exam where I just said that is one centimeter.  So people, you need to bring your calculators. You need to be interactive. Maybe I talk too  much and don't listen enough. Okay. So from now on, you will be docked 10 points if you  don't bring a calculator. Yeah. Okay. I'm taking this noise as that you know the answer.  Who wants to give me an answer? You. What's that? Two or three? 78.5 he says. Okay. Anybody  else want to give me another number? So what is the equation? What are the two equations  you need? What is the length? We said that for a square, you need this length times this  length, right? What is this length right there? Two R, right? It's two R or two centimeters  since I was nice enough to give you one centimeter there. So what is two times two? Four is the  volume of the square. The volume of the circle is pi, like this guy said early on. So it's  just going to be pi divided by four. So 3.14 divided by four. That's it. 78 percent of  this is filled. Okay. Now does that seem awfully, yes. This was just, I said just a square,  not a cube. Yeah, this is just that. Okay. So just two dimensions. So does everybody  see how simple that was? Was that simpler or am I just out of touch? Can I have some response?  Was that, yes. You're raising your hand. Oh, your guy thumbs up. Simply says. Was it simple  before I did it? So folks got that. Good. You didn't need anything. Hey, somebody didn't  get it. Thank you for acknowledging that. Okay. Now do you see how to do it? Okay. Do  you see how, and did I have to teach you any chemistry for this? This was like my sophomore  year geometry class. Okay. Now it was a little tougher. This guy was wanting to know whether  we had to do it as a cube. Okay. That's tougher. Okay. But we could do that. Oh, do that. Do  it. Good thinking, buddy. I want to know what is the packing efficiency of that sphere now  in that cubic box? Fourth arch pi r cubed. It is. So fourth arch pi r cubed, folks. That's  something you should probably know. Fourth arch pi r cubed is the volume of a sphere.  Now it's got to be fast, folks, because I made r1. Okay. So you should be able to do  this problem in about less than a minute. You got it done? All right. What's the answer?  I don't know the answer. It sounds about right. Okay. Who's got an answer? You. 52%. Okay.  Perfect. Okay. Let me ask you a question. And I want an honest answer. How many got  that right? Okay. Now, of those people with their hands up, keep them up, how many think  they might not have gotten it right if I hadn't done this one first? Quite a few, right?  So once again, folks, I'm not always going to be there to tell you that this is the first  step. This is the second. Organic chemistry, folks, is not like that. Okay. And even the  problems that we just did, knowing how to get to the end, okay? You got to think about  it. But if you're asked a question and you're given something like this, instead of a picture,  if I had said a circle fits exactly into a box, a square, what is the volume that is  not filled? Instead of showing you, I might have had a problem with that. Okay. So it's  math. It's simple math. Do not be afraid of it. And then you're going to see that this  is exactly. So there it is right there. There's your pi r squared to r squared. And if you  get rid of, look at this, r squared right there, r squared right there, just pi over  two. Oh, two squared, pi over four. That's simple. Now, ooh, I'm going to ask you this  one. That one right there. Packing efficiency for that. Okay. Now, how many know what the  equation is for a circle or a sphere? Okay. This is one. There's just two dimensions again.  Not three dimensions. It's just two dimensions. So this is going to be pi r squared for that  area. How many know what the equation for the area of hexagon is? You do? Geez. Okay.  Well, I had to look it up. Why would I know that? Okay. The area is equal to three, write  this down, folks. You don't need to know it, but for this problem you do. The area is equal  to three times the square root of three over two times the length right there. Okay. So  that was, the area is equal to three times the square root of three over two times the  square of that area right there. So let's say L squared. So, do you understand that?  So now I want you to figure out in this box right there, or that one, it doesn't matter,  they're all filled, what is the efficiency in terms of packing for circles in a hexagon  as opposed to circles in a square? Got an answer already? I thought that young lady was stretching,  I guess. Okay. So don't forget, the area is three times the square root of three over  two, and then the whole thing's times L squared, that length squared. I'm not going to give  you what the radius is this time. Oh, you don't need it. Yes. Six what? Might be. We'll  have to wait and see. Okay. Oh, yeah, yeah. So we want the, okay, we don't just want  that. Yeah. We want, what is the efficiency? How much of that dark stuff is there in there,  okay? Or actually how much of the light blue is there? So we want a percent just like we  had here. What? For which one? Oh, I'm not giving that to you this time. Yes.  Okay. How many of you got about, are you done? How many got about 90%? Ooh. How about 91%?  Okay. So I didn't need folks to give you what the radius was. Why not? This is where you  got it all right here. Okay. Look at right here. Is that in the center of that circle?  In the center of that circle? Okay. So what is the length of this piece right here? Two  R. Right? It's two R. So you don't need to know that the radius is one or two or five  thousand. As long as you got R in it, you got, you got to have an R in your circle equation  and you're going to have an R in your other one. Okay. So we got, this is the, this is  the only part you got and it's a little bit tricky. It's not really tricky. You got how  many circles inside that hexagon? Three. One. And then you got a third. You got one,  two, three, four. You got six thirds. So six times a third is two plus one is three. So  you got three circles. So you need to have three circles in one hexagon. So when you  multiply this thing through, you end up with this. There's your three. That is just pi  R squared. Don't need to have what the R is. Okay. And down here, okay, remember we had,  we had a, let me have three, no, two. We had a two. What did we have? Can I start? I got  too much traffic. Oh, no, I've lost it. Thank you. There it is right there. So this had  been a three in the front and that's right, three, square root of three over two. But  the length here folks is two R, right? L is two R. So you square that. So you get rid  of your squares and you had a two and a two. There's been a two underneath this. Okay.  So you get rid of that and it's going to be these two times the three so it's just a  six. Okay. So then you just divide everything in there. You got your R's, you got this. And  in the end you get 90.7. Okay. It's a simple math. It has nothing to do with chemistry.  I mean, I could, you could get this on a, on a, on a SAT or something. Okay. As long as  they gave you a whole bunch of equations in the back because I would not expect you to  remember what hexagon is because I can't remember. But that, so folks, this is a question  from your book. Okay. It's the kind of thing that they would like you to be able to do  but it's simple math and geometry. And it's common sense. Okay. If I had not the first  time told you that this was one, some of you would have freaked out. Because with one you  had a number you could plug in. In the end it was really just pi R squared over two R  squared. You didn't need to know that it was one. So folks, sometimes you need to look  a little bit deeper. You got to say, oh my gosh, I don't have enough information. And  in reality you do have the information. Or you don't need the information. You don't  need to know what R is here. So once again, folks, it's math. It's a math exercise. It's  the kind of thing though that I can ask you a question on packing efficiency and you do  some math on an exam. Okay. This one I just am going to show you what it looks like there.  Okay. Okay. Just assume that's correct. Why am I showing you this? I'm not sure. Hold  on. Maybe I'm just going to keep pushing this button. Okay. Answer. Thank you. Ladder's  holes. This goes back to what Josette was talking about. So you have this lattice structure  thing that all of a sudden there's a little tiny hole right in there. Guess what can happen?  See that? Look at that. They're going everywhere. So you can have these little holes and stuff  that I'm sure are important. Do you think, Josette? I'm not sure how important they are.  We're done. I can't handle it anymore, folks. I'm sorry.
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Okay. I hope I can promise you that this is going to be the worst lecture of the quarter. I'm just saying I hope that I don't do any worse than today because solids are just, I think you guys will do better with it than I because your generation, you know, you guys have these phones that you can make do just about anything. This is my phone. Okay. Yes. Not easy to text with, you know. I got to hit four things to get an S. Okay. Yeah. So I just don't do it very often, okay. So I could literally go two or three days without even opening this phone. Okay. That's how little I use it. You don't like that too, but you probably use it more than I do. And so, but what your generation is good at is this kind of little electronic stuff. Computers, you just have a, it's like a second nature because you play little video games when you're kids and stuff. And so also I think spinning things. I mean, I think you guys had these, these games that you've played that have sort of allowed your brain to expand a bit. So I'm hoping that this solid stuff, packing of, of atoms and molecules together is going to be something that you actually find that you can do because I find I can't, I'm not much better. I'm only a two dimensional kind of guy. So, so we're going to talk about solids no more. I scared a lot of people, I guess, on, on Tuesday with the, all the gas stuff. You know, I had like 20 people come to office hours. I've been getting emails, people worried about stuff. So we're going to go to solids now. I don't want to show you that and I don't want that. Here. Okay. Now, while I do not particularly like the subject of solids, there are certain things you must know. Now solids folks, we're in the intermolecular forces chapter. Okay. So this is still intermolecular forces. It's just that now instead of it being a liquid, like water added with ethanol and it's hydrogen bonding and why they stay liquids and all, now we're going to wire things solids and how do they pack? Okay. Now there's seven different kinds. Okay. Of, of, of crystalline solids. You only need to know one kind. Okay. And it is the cubic. Okay. Because my brain does not, you'll see what the others look like. So this folks is a simple cubic. It's a lot like this table right here. Okay. With an atom, it could be an atom, it could be an ion, it could be a molecule. Something right there. That's called a lattice point. One here, one here, one down there, one there, one here, one here, one here. Eight corners. There's eight corners of a cube. Okay. So you have this one, it is called a simple cubic. Now on a simple cubic, the atom, well let's say it's an atom here, is, its center is right here. Okay. Right on the corner. So how many, how, when we start stacking these things, how many centers or, or corners are there going to be right here? Look at this and tell me, if I start packing stuff all around this point right there, how many cubes can I fit around that point right there? Eight. Okay. You go, wait a minute, it's only got six sides. Got six sides, we've got eight corners. So you can actually pack it if you don't believe me, get some blocks and do it. Okay. So how much of that atom do you think is inside that box? One eighth. Okay. This is called a simple cubic. Okay. It's a simple cubic and it's, it's as simple as it gets, it's as empty as it gets. So how many atoms are, we can add all the eighths up, how many atoms are inside, are inside a simple cubic? It would be, there's eight of them, times one eighth is one. There's one atom in the unit cell for a simple cubic. Folks, that is as easy as it gets. Okay. The next one then is a body centered cubic. That would be like if this was one more atom and I stuck it right here. Okay. Inside, completely inside. See that one right there? There it is right there. It's completely inside this cube. So now how many atoms are there per unit cell? Two. Okay. And then we get down here where there is the same, it always has these eight corner points, but then we're going to put one right here. So it's half in, half out. One here, half in, half out. One here, half in, half out. One here, half in, half out. One here, half in, half out. And one down here. It's got six faces. Okay. And it's half in, half out. So that's going to be six times a half. Okay. So how many atoms are in a face centered cubic unit cell? Four. One for these guys and then you've got one, two, three. You can't see the other three. These are half and so you have four. So folks, on the exam, you're going to be expected to know these numbers. There will be a multiple choice question. It would be something like a body centered cubic has one, two, three or four atoms in the unit cell. That's simple. Is there anybody here who could have missed that? If anybody misses that, I'm going to put up a list of names after the exam and say these people were not in class obviously because I'm too good of a teacher to not have you understand this. Okay. One, two, four. Okay. Now you can only remember and memorize that but the real important thing folks is that you are able to conceptually see this in three dimensions. Okay. So any questions on these? And then what happens is the unit cell folks is the smallest part that allows you to then duplicate that exact entity. What I mean by that is like an atom. If you break an atom, a sodium atom is the smallest unit, you start pulling off a neutron or a proton or electron, it's no longer sodium. So a whole atom is the smallest you can be. Then you can have a whole bunch of atoms and make a mole of atoms if you want. The unit cell, it's the same thing. That is the smallest thing that defines what it looks like. You have one of these and you start stacking them together. One of these you start stacking together. This is what it looks like when you've got eight unit cells together, eight unit cells, eight unit cells. Okay. So once again it's the smallest piece that you can have and still recognize it as one of these things here. Okay. Does that make sense? And once again folks it's important for you to understand that we can have, they say this is gold. Okay. So I guess gold, polonium and uranium. That's how they stack. All right. Then it can be an atom, it can be an ion, it can be a molecule like water. You can have water at each one of these points. Okay. So once again, simple cubic, body centered cubic, face centered cubic. Same thing. Okay. This is what I'm talking about. The unit cell looks like this. Now is this, would you call this a cubic? No. It's not a cubic. This is something else. Some other shape. Maybe like a rhombus or a, yeah, probably a rhombus. What is this? Who can tell me what is that? What is that shape, that geometric shape? Rhombus? Oh, good. Parallelogram. Parallelogram. Okay. Well, I think a parallelogram is also a square cube, I think. But anyway, okay. What is that? Parallelopiped? Oh, I see. Okay. Well, thank you for that comment. That will not be on the exam. But this is how they pack, okay. Once you have this shape, then you can put them together and make the big thing. It's like blocks. If you cut a block in half, it doesn't do any good. You can't tell what the block look like. You need the whole block and then you can build a bunch of stuff. So, what does this thing say? Crystalline solids. Okay. So there are some general things. Unfortunately, they're not that specific. Okay. So, possessed rigid, long range order. That is true. Crystalline solid. Adams molecules or ions can occupy. That is absolutely true. And an amorphous is not possessed well defined arrangements and long range molecular order. So what I'm going to use, I'm going to use this classroom as an example. Okay. If every seat were filled today, every seat, then we would say we are a crystalline solid. But there's a seat right there, empty in one there, in one there, and there's a bunch of them. So these holes tend to make it a little bit less perfect. And these holes can cause destruction or distortion in how things look and all. So that would be more of an amorphous. This is still too ordered for amorphous, but still. Amorphous can have some order to it, then it's got a hole, or it's got some weird kind of bonding going on. So the amorphous, once again, does not have this well defined lattice structure. And once again, the unit cell is the basic repeating structure. Lattice point, lattice point I said it can be either atoms, molecules, or ions. Okay. We already did this. It just looks a little bit different now. This is what it would look like once again. It's harder to see. I will not ask you to draw these. Okay. Because if we do, all the females, almost all the females will do a much better job than the males. It's a stereotype that I probably shouldn't have, or it's a bias, but I have two sons and a daughter. And I've had female students. Who's writing can you not read downstairs, Josette, in the lab book? Brent. Yes, yes. Can you read Gloria? Yes, perfect. Okay. So I can't draw these very well. You're not going to have to draw them either, but I want you to understand the basic structure. Okay. That's the main point. Okay. So simple cubic. You can see there's nothing stuck inside there. Okay. Body centered cubic. There's one inside. It's easier to see right there for me. That one's a little confusing down there. And then this one. Okay. This just sort of shows how on this side there's four sides here, and then there's one that cuts it in half, and then there's four more. Okay. So this is the one that's got the eight, and then this is, I think that's right. Corner out of here. And this is one just cut in half. Okay. More of the same. This looks like the exact same one I just showed. Okay. We're doing the math now. You don't have to do the math on the exam. You just need to know. But you know, I don't want you to memorize it. I want you to remember what does this thing look like? Okay. The cubic means you always have those little ones out there on the corners. You've got an eighth times eight. Okay. Face centered. Can't get any more obvious than that. That means it's on the face. There's six faces. You can only, if you've got one, two sides, you mean you have to share half with each. So you've got a half of an atom in the face centered. Body centered just one stuff in the middle. Okay. So you don't need to do this math, but you very well may need to on an exam say that, you know, a body centered cubic has two atoms. This is just an example of different types of crystals. This is an atomic solid, an ionic solid. This is just sodium chloride here. Molecular solid is with water at each point. Okay. So once again, you can have any. You can have an atom. You can just have a bunch of copper. Okay. Copper is something that we use. It's, those kinds of metals are very good at conducting electricity in heat. That's why we have copper wires, all of your computers. And if you are, we had an infinite amount of gold, we have gold instead or gold something because gold conducts even better. Okay. But so again, three different, four different things here. Now what I want you to, well, I think we'll come back to this, but this is a diamond. Diamonds are kind of interesting because it's just carbon. It's just like you're, the lead in your pencil, it is just carbon. It's like a chunk of coal. That's what a diamond is. Okay. And we will learn maybe next chapter or the chapter after that in thermodynamics that there's just a tiny energy difference between a, you know, one pound diamond and a one pound piece of coal. But huge difference in price. Okay. Turns out that for a diamond, it has four bonds. Okay. And you got a carbon and it's, it's the unit cell. I'm not sure what the unit cell looks like there, but it's bonded to four things. For your lead in your pencil, which is graphite, it's got these layers where they're bonded together, but there's only three bonds and then their inner, their, their intermolecular forces are what keep these layers together. That's why when you drag your pencil across a piece of paper, stuff just slides right off and goes right on the paper. Okay. That bond is not nearly as strong as diamond. Diamond is like one of the hardest things in the world. Okay. Seven types. So, I would say, huh. Now, do you think this is a tri-clinic and a monoclinic? Okay. Well, I'm not even going to, you guys, that would be on the exam. This entire page would be on the exam. Like, I'm lying. Okay. You need to know there are seven though. You need to know that there are seven different kinds of unit cells. This is the only one for which you need to know how they pack in. Okay. Because it's the only one that my mind will allow me to understand and, and, and remember. Okay. These other ones, obviously, you're going to put points, you know, you're going to still have a, a, a, a last point right there. You can have eight of them here, eight of them here, eight of them here. This one looks like it's got a little bit more than eight. But they just get too complicated for me. Okay. So feel free to learn all this. You do need to know that there are seven, seven types of unit cells. You can get an exam question. Number of unit cells. One, three, five, seven, eight. Okay. Okay. This is where I start having problems. Okay. So metals have high thermal and electric conductivity. I said that about so, or about copper. If you, I, I actually, I don't wear my wedding ring anymore because I got too fat and plus, plus, that's probably the word I can't say. I put on some weight. But I have some arthritis in my finger joint here. So my wedding ring doesn't quite fit. But I remember one day about 10 years ago, I walked out of this room and the door didn't have the resistance that I was expecting. The spring was broken or something like this. And when I opened the door, I pulled kind of hard and the door just went open really fast like this. And it turns out that my, the handle was like this and my hand sort of slammed into the wall. Not hard. I wasn't hurt. But my ring was smashed. I mean, it literally just got like bent in and that's because gold is very malleable. It says that's right there, right there. Okay. Very, I mean, if you have really good gold, I mean like 24 karat kind of stuff, I mean, it's like soft. Okay. So it is very much like, and that's why we can have wires, wires that are copper wires that actually bend. Okay. So, but, but, but these properties folks, all of these properties are related to their atomic interactions within the lattice. So this is a few things here. So this is how they pack stuff. Okay. I can, I'm good to write there. Okay. You got yellow ones and then you got blue ones. They're going to put some blue ones on top now. Okay. Top view, side view. I'm not sure where they came up with the extra yellows there, but anyway, this is the closest packing. Okay. Look at that. You guys understand that? It's like making a sandwich. Okay. One layer on top, one layer on top, one layer. It's just that they're balls and stuff and round things or whatever and they pack on top of each other. And nature kind of folks doesn't like empty space. So what that means is that there's not as many of the simple cubics as there are body centered cubics or face centered cubics. I mean, it's just, I think there's something that says nature adores a vacuum. Is that something you've ever heard? Okay. Has anybody ever heard that? Okay. Well, maybe somebody made it up. Okay. So things tend to pack so that you cram as much stuff in as possible. Be like this room. Be nice if there were much bigger lounge chairs, right? But then you'd sleep. But then you'd be more comfortable, but right now they got you packed in like on an airplane. Okay. So hexagonal close packed structure. Okay. But so this one on top of this one, here's the unit cell. Top view like this unit cell looks like that. What does that look like? Okay. The problem is when they draw these drawings is this thing, this blue thing is actually, I guess there's three of them inside, isn't there? Okay. Hold on. Let's see what it says. Oh, great. See, it just gets complicated. Josette, do you understand this stuff at all? Okay. Good. Good. Office hours. Go to, I mean, this stuff to me. Anyway, those cubic, or cubic close packed. Okay. That's what that's called. You're going to have to know that in a minute. I'll show you why. Okay. Note, cubic close packed is face centered cubic. That you need to know. Okay. Because there's different terminology. And so if you get something that says you've got a cubic close packed structure, how many atoms are in it in the unit cell? You say, oh, well, I know that it's a face centered cubic, so there must be four. So, types. Okay. Look at this first one. Okay. What would you say this is? Would you call that body centered? I'd call it body centered. Now, the zinc one looks like it's face centered. Okay. Because I see a face right here. Anyway, I think it's face centered and it's got these other, um, um, sulfurs in here. Eh. Who wants to take a guess at this? Well, maybe it's going to tell us. I don't know. You know the answer to that? Sulfur. Okay. The holes. We're going to get to the whole stuff later. Yes, thank you. Okay. So before it was just a face centered, but that was too empty. Okay. So, sulfurs end up going in there and jumping in those holes. Okay. That makes sense. Ion and crystal. So what would a molecular crystal be? It's got a molecule. What would an atomic crystal be? It's got an atom. Okay. So, ionic crystal. I want you people to sort of be able to visualize something. Can somebody give me an example of an ionic crystal? It's something I talked about in class. Salt. Thank you. Okay. So if I had a block of salt right here, would you say that it's hard? Brittle. If I drop the salt, it would just shatter. Okay. And you wouldn't know it had a high melting point, but trust me, you can take some heat and put it to it and it just sits there and it's just salt. So those are general characteristics of an ionic crystal. Okay. Think of salt. And you wouldn't know this, but if we had this block of salt and we put an electric charge on one side and something on the other side, it wouldn't conduct very well. Okay. You just don't have the electron flow that you need. Okay. So we're going to do a problem. Okay. Why are we going to do a problem? We're going to do a problem because you're worried about this and you don't know what kind of questions I can ask on an exam. Okay. This question right here, folks, goes back to Chem1A. For those of you who have not had Chem1A in a while, I know there are some of you who took AP chemistry in high school and have passed out of Chem1A. So for those of you who, that's the case, you're going to want to pay close attention. This is a very simple question. Okay. But last night when I went over it in class, people were freaking out. They're going, how am I supposed to know this? How am I supposed to know that? So while I'm trying not to draw too heavily on what you learned in Chem1A, I do expect you to know what a mole is. Okay. I expect you to know how many molecules or particles or atoms there are in a mole. And I expect you to know what the molecular weight of something means. If something has a molecular weight of 18, okay, then that means that there's 18 grams per mole. That's what the molecular weight means. If something's got a molecular weight of 165, you need 165 grams to come up with 6 times 10 to the 23rd pieces. Okay. So you have to, you know, I don't want to have those of you who either didn't do well in Chem1A or haven't had it in a while be at a disadvantage. But this is a class that builds on the previous quarter. So looking at this, okay, the element copper, okay, copper has a CCP packing, okay, with a face centered, now they didn't have to tell you that, they could have just told you this. So I told you, I had to know this CCP was face centered cubic. Okay. How many atoms in a face centered cubic? Four. Okay. So if I were giving this on an exam, and I were taking this exam, I would just write down four atoms per unicell. I would just write that down. Okay. It says the density of copper is 8,920 kilograms per meter cubed. Calculate the volume of the unit cell. Now, you might look at that and go, what the heck? Okay. It's actually quite simple. Okay. It's quite simple. Density is usually given in grams per CC. I tell you that the density of water, we did the water the other day, water was at four degrees was 1.0 grams per cubic centimeter. Cubic centimeters like a little sugar cube. Okay. They didn't give that. Instead they gave like kilograms instead of grams, and they gave meters instead of cubic centimeters. Okay. It doesn't matter. Why? We've got two units here. Okay. We have two units. We've got volume and we got mass. All right. Well, volume, that's what they're asking for. What is the volume? So we know we've got to leave this, this, the meters cube has to show up somewhere in this equation. And our answer. Okay. But what do we know, what do we know folks about this? Okay. If I had been nice, I would have said the molecular weight of copper is something. 56, I don't know what it is. What is it? It's right there. I can't read that. 63.5. Okay. So if I had said that, you're going to have periodic tables on the exam. So all you got to do is say, oh, now I know I've got a mass. I get rid of the mass. I got a mass here. I got a mass there. I'm going to end up with size. Okay. So that's what it looks like. Okay. We've already done that. So we have four atoms per unit cell. We know that one mole is equal to that many atoms, right? Six times 10 to the 23 atoms. There is your molecular weight of copper. You divide this whole thing through. You're going to get our moles there and we've got grams here. We've got atoms there and look what happens. So we got, we know that we've got four atoms per unit cell. So we got that, how many grams? The mass of the unit cell is that. Very straightforward. So I would, maybe what I should do is just let you, let me ask you. If you want me to put this up and you guys do it and then I explain it, what do I just do it? Because you have this in your notes. I want to do what makes it easiest for you. Okay. What's not easiest. I don't want what's easy at all for you, folks. I want what's best for you. So what would work best? I mean, me just put the question up and you guys struggle with it for two or three minutes, five minutes, and then I go through how I would solve it. Okay. That's what we'll do on the next one. Okay. So, but you can see how we approach this. Okay. And you might be going, you got a periodic table, folks. You got mass. Now you're screwed if you don't know this. Okay. I'm sorry. If you don't know that a mole is 6.0 or 6.02 times 10 and 23rd, then you got a problem. But that is something that you need to know in this class. Okay. So now folks, we've got how many grams we've got. Okay. So now what do we do with it? Okay. Well, they gave us the density, right? Nothing here, folks. This doesn't do us any good because here's what they gave us. Okay. But we do have grams, right? We got grams right here and we got kilograms right there. So look at how simple it is. The density, the density as I said is, we saw earlier, in that case it was kilograms over meters cubed. Okay. So it's just a mass or mass over the volume. Okay. That is the definition of density. One gram per cubic centimeter for water. So what is the volume? You've got the density. Did I give you the density? Sure. 8,920 kilograms. So we've got the density right there and we've got the mass right there. That's going to tell us the volume. So you look at this thing right here. You divide that out like that and you get that. Okay. Now, what you need to, as I said, I'm not trying to rag on your generation, but I think you maybe aren't quite as good as my generation at estimating sizes of lengths and volumes. Okay. What they gave us was they said a meter cubed. That's a meter. Okay. So it's this by this by this. So it's about this high. That's one meter. And that thing weighed 8,900 kilograms. That's like nine tons. Nine tons for something that's this big. Okay. Because its density was in, they gave it to us in meters cubed. Okay. In meters cubed, what is the density of water? What is the density of water in meters cubed? I'm going to walk up here and point to somebody. Think of it. Meters cubed. Yes, you. 1,000. Yes. Thank you. 1,000 kilograms because I just said that it's one gram per cubic centimeter. One gram per cubic centimeter. Then you just take grams and make it in a kilograms and centimeters and make it into meters. Okay. Now how many, how many liters? Oops. Oh, I'm getting a phone call. Pretty cool. Haven't got one in days. How many liters, folks, in a cubic meter? Okay. Well, a liter, folks, is 10 centimeters by 10 centimeters by 10 centimeters. So if this is my meter, I'd have one here, two, three, four, five, six, seven, eight, nine, ten. Ten this way, ten this way, and ten that way. What is ten times ten times ten? A thousand. So there's a thousand liters in a cubic meter. So we've got this meter. Now look at what the question was in. It didn't say give it to us in meters cubed. Okay. You lose a point or two. If this is a ten point question, you lose a point or two if you leave it like that. Okay. Because you've gotten the real volume, but I'm asking for you now to reduce it down to mills. Okay. So how would you do that? Well, you would do liters because you divided that by a thousand and then there's a thousand cubic centimeters per liter. So that is the volume right there. Four point seven three times ten to the twenty-third. That's how big, that's how big the unit cell is. And aside from knowing that it was a face-tended cubic, so you had four atoms per unit cell, you didn't need to know anything other than chem 1A and some simple math. So folks, if you're given something like this where you're going, I don't have enough information. Try to trust me, you do. Okay. You do have enough information. You've got a periodic table. Anytime you've got a periodic table, I'm going to ask you if I, if I, if right now, okay, here's a question. Here's a question. All right. You've got twenty-six grams of lithium. Twenty-six grams of lithium. How many molecules do it? You've got periodic tables here, there, there, and hopefully you can, if you can't see that, oh, no, I'm not going to tell you what to do. And don't cheat, okay? You should always bring a calculator, folks, especially in the following weeks. You're going to do a lot of stuff in class. Bring a calculator. What's all your data, everybody? I thought you weren't going to see it. I know. That's what I thought too. What happened? Oh, my mic. We have an answer yet? 2.5 times 10 to the 24th. Does that sound right? 2.25. What did somebody else get? We have an answer? I can't repeat it because I can't remember. I don't know if I said 23. 26. Okay, so 26 grams of lithium. So if I had been a nice guy and said 26 grams of lithium, how many moles? Then you would have just divided 26 by the molecular weight of lithium. And you'd have gotten, lithium is right there. So it's probably like about 6. Is that what it is? You've got a periodic table. What is lithium? 6.9. 6.9, I'm going to say 7. Okay, so lithium has 7. So 26 divided by 7 is close to 4. So we have about 4 moles. Then in question B, then I said, okay, so how many molecules is that? Then you'd say, oh, I've got the number of moles. It's 4 times 6 times 10 to the 22nd, so it's about 2.5 times 10 to the 24th. But, folks, I'm not always going to ask you in a nice, give me A, give me B, give me C, give me D to kind of let you work your way through. This time all I said was, you got this many grams. I didn't ask you how many moles it was. I asked how many molecules it was. So sometimes, folks, you don't, it's not as easy to see what, how do you get from A to Z? Okay? And, folks, let me tell you something. For those of you who go on to organic chemistry, okay, my problem in organic chemistry was, was that it wasn't solving problems like this. It was that you had to memorize that if I add a laser pointer plus a bottle of diapepsy, that then you get this thing, okay? And then you add two other things together to get something else. And then if you add those two things together plus this, you get something else. So you had to memorize these 100 or 200 different reactions. And then it was like, make this, okay? Well, I wasn't smart enough to memorize them the first time, or I was smart enough, I just was too lazy. And so, you know, going from A, literally some of the reactions are 20 steps, 20 steps. Now, if they'd have asked me, make this into this, and I would have, I'd go A plus B goes to C. And then they'd say now, take C and make E. I'd go, oh, C plus D goes to E. They don't do that. They'd say, starting with A, make Z. So there's no hand-holding, folks, okay? It's not easy. And that's why you have to know, it's like trying to do a crossword puzzle with a small vocabulary, okay? It's tough, okay? So I'm not going to ask you, I'm not going to give you this stepwise questions all the time, all right? So you see how you solve this? Let's try the next one, okay? So, folks, this is a legitimate question for an exam or something like this. And you have to know hardly anything about solids, except for the fact that this said that it was a face-in-a-cubic. Okay, I drew this one. Okay. Okay. Okay. Okay. So how many of you really don't have a clue on how to do this? That's why I'm here, folks, okay? You don't have a clue? I'm here to try and clue you in, okay? And once again to show you that, I haven't said this in this class, I think, but that units are our friend, okay? I honestly can't remember how to do most of these problems, okay? But I look at this right here and I say, oh, I think I've got, I've got grams per mil and I've got mils, okay? So that already tells me what I'm going to be dividing or multiplying by at some point, okay? Because I need molecules, okay? I need molecules. That's what Avogadro's number is. And so, so you're going to take your information knowing how many atoms are in a unit cell, okay? How many are in a hexagonal unit cell? Two atoms, okay? So you've got two atoms. So now you've got atoms. You've got grams. You've got grams per mil and what else? Yeah, you got, you got sides. You've got mils here. Mils there, grams there and you got atoms. Perfect. That's all you needed. Does that help anybody? So once again, the mass is equal to, once again, density is equal to volume, mass over volume. So this is just a rearrangement of that. So you've got, you've got 8.5 grams per mil, okay? Times that many mils. Now why are we multiplying it by this? Because it's mils in the bottom. You just, you knew you had either divide one by the other, okay? And so you had a 50-50 chance of dividing the right one. So you've got mils here in the denominator. So you multiply this by mils and you're just going to end up with grams and a little tiny, tiny bit, okay? So the mass is going to be some tiny little number in grams. Look at that. Three times 10 to 23 grams, okay? That is how many grams in a unit cell, okay? Does that make sense? So you've got that many grams in a unit cell. You've got this many grams for beryllium. Times two for the unit cells. You end up with six times 10 to the 23rd. Now folks, I would not give you an example. I would not give you a question like this on the exam without having gone over something like this in the class. Because it's a little bit convoluted, okay? For those of you who took Chem 1A, loved Chem 1A, did well in Chem 1A, then this is a pretty straightforward, maybe a little rushed on you, but this all makes sense to you. Others are going, oh man. I hope you don't ask this on an exam, okay? But it's math folks. It's the kind of math that you should not be afraid of. It's rearranging things. So practice this kind of thing, okay? So here's the difference, as I said, between a diamond which is bonded to four things and graphite. You have these layers of graphite where they're bonded to three things, one, two, three, and then you have these layers that are intermolecularly forced attraction here. And these layers just fall right off of your pencil, right onto the paper. Huge difference from something like glass or diamonds which can cut glass, okay? Huge difference, intermolecular forces. Okay, so once again. Nothing here that's a surprise. We've already said this. In this case, we've got the, oops, these are pointers dead. Oops. So we have atoms here, atoms there, lattice points are occupied by atoms. This is a, think of a diamond. Hard, brittle, high melting point. Alright, so that we've already said. So metallic crystals, they're a little bit different folks, okay? Lattice points are occupied by metal. Think of copper. Copper's a metal. So let me show you. It'll show you right here, okay? So the majority, the nucleus is right here, okay? And that's everything except the valence electrons, okay? It's all the valence electrons that are in this gray area. This is the nucleus here, the intershell electrons. And then you've got, it's almost like just this commune, you know, back in the 60s, you know? You share everything, you know? And so these electrons are what we call a sea of electrons. And so if you apply a little bit of electricity on this side, it just flows without much resistance at all. I mean very, very little resistance, okay? So this is a metallic crystal and that would be copper. Think of copper, think of gold, okay? Really good conductors of heat and of electricity. And so that's why we use them for that. This is in your notes. Look at it. So this is an example. This is a class filled with people, okay? This is a class. Look at this. This right here looks a lot like this, okay? There are parts over here that do look like the actual very nicely organized crystal. But in this case, there are, when things kind of went together, they didn't quite go together as nicely. And so then you end with this non-crystalline quartz glass, okay? Which has different properties than this would, all right? This is what it looks like when you've got empty seats. Haven't you ever heard of like the grading of a diamond, okay? The grade diamonds, you know? You can have like good, better, gemstone quality. What do you think that means? Diamonds are made by taking like coal and putting them under high pressure for millions of years and temperature. And sometimes there's some stuff that gets in there, okay? A perfect diamond would be just carbon. Just carbon and packed, like that's kind of like that, okay? But a diamond that has flaws is one that has, you know, some imperfections in the structure. So the better the diamond, the more expensive it's worth, or the more expensive it is. And the fewer of these it has. Yes? What does it mean by the carats, like now? Carats is just a weight. It's actually the weight of a, and I don't know what one carat is, but it's a weight, I don't know. And it comes from long, long ago. Questions? Okay, so once again, this is the non-crystalline, this is the crystalline. Okay, now, this is actually from your book. It's the first time I've used anything from the book. Well, the second time. This is the kind of stuff they give you, okay? How many of you have read the book? How many of those people their hands up are lying? Okay. Well, I just skim the book. Okay. So I want to, in this next half hour, show you a little bit, and I don't want you to panic. People asked me last night, why are you showing us this? Or why did you show us this? And it's, once again, it's to try and get you to think a little bit outside the box. That's what I was trying with the atmospheric stuff the other day, and it didn't work too well. So I'm going to try something that's rather media-blabbering, actually, to show you something. Okay. So this is a math thing using atoms or molecules as a guide. Okay. So will there be something like this on the exam? Probably not on the first or second exam, but it could be on the final. Okay. There could be something, because on the final you've got two hours. A little bit more time to think, and I want to challenge some of you. But I can't say for sure. Okay. But please pay attention. It's simple math. It's logical stuff. It's stuff where I think you folks, you get to a point, just like you did on the last two questions, like, geez, I don't know where to go with this. I don't have enough information. I don't know this. I'm going to show you that you actually do have information, that you can be asked a question that you've never seen before. You can actually solve it. Okay. So we're going to start with filling spaces. Okay. I told you that the nature of horror is a vacuum. So we're going to start with a simple cubic. I'm going to get it all the way down to right there. Okay. So the question is, in terms of filling spaces, if you have something like this, how much space is empty space? How many, how much space doesn't have the atom in it? Okay. So who can tell me what is the equation for the area of a circle? Pi r squared. Pi r squared. Okay. Now what is the equation for a square? It's going to be, you know, length times width. Okay. And since they're the same, it's going to be this times itself. We understand that. So we've got a box, or a square, and we've got a circle. So if I told you right now that this radius was, I'm going to tell you that right now, okay, that this is one centimeter. Okay. One centimeter. What is the packing efficiency? How much of this box is filled with that atom? Do it. Do it right now. One centimeter right there. Okay. I don't know. So I'm asking you what the efficiency is. I'm not asking you how much. I'm saying, okay, look, you've got to take into consideration two things. You've got this volume and you've got that volume. I want to know what is the percentage? How much of it's filled? Do it right now. You don't need anything from me. This is a challenge, folks. It's a simple, this could be on an exam where I just said that is one centimeter. So people, you need to bring your calculators. You need to be interactive. Maybe I talk too much and don't listen enough. Okay. So from now on, you will be docked 10 points if you don't bring a calculator. Yeah. Okay. I'm taking this noise as that you know the answer. Who wants to give me an answer? You. What's that? Two or three? 78.5 he says. Okay. Anybody else want to give me another number? So what is the equation? What are the two equations you need? What is the length? We said that for a square, you need this length times this length, right? What is this length right there? Two R, right? It's two R or two centimeters since I was nice enough to give you one centimeter there. So what is two times two? Four is the volume of the square. The volume of the circle is pi, like this guy said early on. So it's just going to be pi divided by four. So 3.14 divided by four. That's it. 78 percent of this is filled. Okay. Now does that seem awfully, yes. This was just, I said just a square, not a cube. Yeah, this is just that. Okay. So just two dimensions. So does everybody see how simple that was? Was that simpler or am I just out of touch? Can I have some response? Was that, yes. You're raising your hand. Oh, your guy thumbs up. Simply says. Was it simple before I did it? So folks got that. Good. You didn't need anything. Hey, somebody didn't get it. Thank you for acknowledging that. Okay. Now do you see how to do it? Okay. Do you see how, and did I have to teach you any chemistry for this? This was like my sophomore year geometry class. Okay. Now it was a little tougher. This guy was wanting to know whether we had to do it as a cube. Okay. That's tougher. Okay. But we could do that. Oh, do that. Do it. Good thinking, buddy. I want to know what is the packing efficiency of that sphere now in that cubic box? Fourth arch pi r cubed. It is. So fourth arch pi r cubed, folks. That's something you should probably know. Fourth arch pi r cubed is the volume of a sphere. Now it's got to be fast, folks, because I made r1. Okay. So you should be able to do this problem in about less than a minute. You got it done? All right. What's the answer? I don't know the answer. It sounds about right. Okay. Who's got an answer? You. 52%. Okay. Perfect. Okay. Let me ask you a question. And I want an honest answer. How many got that right? Okay. Now, of those people with their hands up, keep them up, how many think they might not have gotten it right if I hadn't done this one first? Quite a few, right? So once again, folks, I'm not always going to be there to tell you that this is the first step. This is the second. Organic chemistry, folks, is not like that. Okay. And even the problems that we just did, knowing how to get to the end, okay? You got to think about it. But if you're asked a question and you're given something like this, instead of a picture, if I had said a circle fits exactly into a box, a square, what is the volume that is not filled? Instead of showing you, I might have had a problem with that. Okay. So it's math. It's simple math. Do not be afraid of it. And then you're going to see that this is exactly. So there it is right there. There's your pi r squared to r squared. And if you get rid of, look at this, r squared right there, r squared right there, just pi over two. Oh, two squared, pi over four. That's simple. Now, ooh, I'm going to ask you this one. That one right there. Packing efficiency for that. Okay. Now, how many know what the equation is for a circle or a sphere? Okay. This is one. There's just two dimensions again. Not three dimensions. It's just two dimensions. So this is going to be pi r squared for that area. How many know what the equation for the area of hexagon is? You do? Geez. Okay. Well, I had to look it up. Why would I know that? Okay. The area is equal to three, write this down, folks. You don't need to know it, but for this problem you do. The area is equal to three times the square root of three over two times the length right there. Okay. So that was, the area is equal to three times the square root of three over two times the square of that area right there. So let's say L squared. So, do you understand that? So now I want you to figure out in this box right there, or that one, it doesn't matter, they're all filled, what is the efficiency in terms of packing for circles in a hexagon as opposed to circles in a square? Got an answer already? I thought that young lady was stretching, I guess. Okay. So don't forget, the area is three times the square root of three over two, and then the whole thing's times L squared, that length squared. I'm not going to give you what the radius is this time. Oh, you don't need it. Yes. Six what? Might be. We'll have to wait and see. Okay. Oh, yeah, yeah. So we want the, okay, we don't just want that. Yeah. We want, what is the efficiency? How much of that dark stuff is there in there, okay? Or actually how much of the light blue is there? So we want a percent just like we had here. What? For which one? Oh, I'm not giving that to you this time. Yes. Okay. How many of you got about, are you done? How many got about 90%? Ooh. How about 91%? Okay. So I didn't need folks to give you what the radius was. Why not? This is where you got it all right here. Okay. Look at right here. Is that in the center of that circle? In the center of that circle? Okay. So what is the length of this piece right here? Two R. Right? It's two R. So you don't need to know that the radius is one or two or five thousand. As long as you got R in it, you got, you got to have an R in your circle equation and you're going to have an R in your other one. Okay. So we got, this is the, this is the only part you got and it's a little bit tricky. It's not really tricky. You got how many circles inside that hexagon? Three. One. And then you got a third. You got one, two, three, four. You got six thirds. So six times a third is two plus one is three. So you got three circles. So you need to have three circles in one hexagon. So when you multiply this thing through, you end up with this. There's your three. That is just pi R squared. Don't need to have what the R is. Okay. And down here, okay, remember we had, we had a, let me have three, no, two. We had a two. What did we have? Can I start? I got too much traffic. Oh, no, I've lost it. Thank you. There it is right there. So this had been a three in the front and that's right, three, square root of three over two. But the length here folks is two R, right? L is two R. So you square that. So you get rid of your squares and you had a two and a two. There's been a two underneath this. Okay. So you get rid of that and it's going to be these two times the three so it's just a six. Okay. So then you just divide everything in there. You got your R's, you got this. And in the end you get 90.7. Okay. It's a simple math. It has nothing to do with chemistry. I mean, I could, you could get this on a, on a, on a SAT or something. Okay. As long as they gave you a whole bunch of equations in the back because I would not expect you to remember what hexagon is because I can't remember. But that, so folks, this is a question from your book. Okay. It's the kind of thing that they would like you to be able to do but it's simple math and geometry. And it's common sense. Okay. If I had not the first time told you that this was one, some of you would have freaked out. Because with one you had a number you could plug in. In the end it was really just pi R squared over two R squared. You didn't need to know that it was one. So folks, sometimes you need to look a little bit deeper. You got to say, oh my gosh, I don't have enough information. And in reality you do have the information. Or you don't need the information. You don't need to know what R is here. So once again, folks, it's math. It's a math exercise. It's the kind of thing though that I can ask you a question on packing efficiency and you do some math on an exam. Okay. This one I just am going to show you what it looks like there. Okay. Okay. Just assume that's correct. Why am I showing you this? I'm not sure. Hold on. Maybe I'm just going to keep pushing this button. Okay. Answer. Thank you. Ladder's holes. This goes back to what Josette was talking about. So you have this lattice structure thing that all of a sudden there's a little tiny hole right in there. Guess what can happen? See that? Look at that. They're going everywhere. So you can have these little holes and stuff that I'm sure are important. Do you think, Josette? I'm not sure how important they are. We're done. I can't handle it anymore, folks. I'm sorry.
Now solids folks, we're in the intermolecular stay liquids and all, now we're going to wire So, but, but, but these properties folks, all of Well, the second time. This is the kind of stuff