Lecture 10. Polarizing Power and Covalent Character
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Brindley, Amanda
Chem 1A is the first quarter of General Chemistry and covers the following topics: atomic structure; general properties of the elements; covalent, ionic, and metallic bonding; intermolecular forces; mass relationships. 
 So today we have two quick things to finish up from chapter two. Just two quick topics that we need to know before we can really move on, sort of background info. And then we're going to go on to the sort of VSEPR workshop that we had planned. So hopefully you all brought your candy into your picks. So we have this thing called polarizing power and polarizability. So these are sort of two opposite concepts in a way. So the more electrons that you have, the further they are from the nucleus, right? So that kind of, that gave us an idea of some of our trends as we were going down the periodic table. And this also has to do with polarizability and polarizing power. So if you have very far electrons, then the nucleus isn't going to be able to really affect things that are going on far away from it. So if two things are bonded to each other or near each other, an atom that has very far off electrons is not going to be able to affect the other nucleus's electrons very much. And that comes into the idea of polarizing power, the ability of one atom to polarize another. Now conversely to that, if something has a lot of electrons, it's very polarizable. So something with a lot of electrons doesn't have complete control over its electrons, right? It's trying to sort of balance all of these electrons that are a long ways away from it and try to control them. So if some other atom comes around that can move it around, it can push that electron density around. The more electrons, the more it can be pushed around, the more polarizable it is. And if it can't really even control its own electrons, it's not going to be able to push around other nuclei's electrons. So it's not going to have very much polarizing power. Now the opposite to that then is if something is small, if something is very small, something like Al3+, very highly positively charged small nuclei or small atoms, that's going to be able to push around other atoms' electrons pretty easily because it has a lot of polarizing power. It doesn't have a very large electron cloud, its nuclei can be felt a lot, it has a high effective nuclear charge, and those have a lot of polarizing power. Something as big with a lot of electrons is very polarizable, something that's small without very many electrons has a lot of polarizing power. And then one more small topic that we need to sort of talk about so that you have in your background knowledge when we talk about all sorts of things from now on is the difference in correlations between bond strengths and bond lengths. So something like a single bond is going to be weaker and longer than something like a triple bond. So if we compare the different types of carbon bonds, single bond is going to be the longest and then a double bond and then a triple bond. And of course now that we've talked about resonance, you know that we can have things that are in between that too, right? We can have bond orders of like one and a third or one and a half because of the way that Lewis structures work. So because of that we can't have in between things. So that's one of the ways that we can sort of tell what kind of bonds we're looking at. We can measure the lengths of them and we can say, well is it a single bond or a double bond or a triple bond based on how long it is? Or triple bond is your shortest. A single bond is your longest. So this is sort of good to have in mind as we're talking about different bonds and how they're related to each other. So this finishes up chapter two. So now we need to go on to molecular shape and structure chapter three. So now we get to go ahead and we get to learn how bonds and lone pairs are going to affect the geometry. So so far we've just been drawing them up and a lot of them I kind of drew up in the shape that they look like, but Lewis structures don't accurately represent that. Lewis structures alone aren't going to tell you what shape they are. You don't have to draw those in the shape that they are. And in fact in your homework you probably saw that purposely they were drawn in ways that maybe didn't show you the shape so that you have to guess it on your own. We're going to look at how these geometries work with what we learned last class about the polarities of bonds to give us whether it is or isn't a polar molecule. So we went through and we looked at all of our Lewis structures and we said, OK, these have polar bonds. But it was very careful to make sure that you guys realize we weren't deciding if the molecule is polar or not, right? They said we couldn't do that yet. So after today we'll be able to go through and we'll be able to say, OK, this molecule is polar, this molecule isn't and why, rather than just talking about the bonds. And then we're going to go into this concept of two different main theories of bonding. Two different ways that chemists look at how molecules bond and how they work together. So we'll talk about valence bond theory or hybridization, which is used a lot in the organic chemistry section. And it's very quick and easy once you know it, the key word there being once you know it. It works really well too. But it does break down sometimes. It's not 100% predictive. Well, not anything's 100% predictive. But it's very good at explaining things, but there's some problems with it. And so molecular orbital theory fixes some of that. But it creates a whole new problem of being super complicated at requiring computers and adding a wave functions. All those wave functions you love so much are going to come back and things of that sort that we're going to want to talk about too. So let's start with our VSEPR theory. So before we start filling out your worksheet and going through the workshop, we need to do a couple of definitions. So the idea here and what we're going to be thinking as we're doing all of these geometries is that we have these electrons that are all negatively charged. They don't want to be near each other. They all have the same charge. They're all negative charge. So they're going to repel each other. They want to be far away from each other. So the idea is how can we get these as far apart from each other as possible? Now in addition to this, electron pairs are going to show more repulsion than a bond. So if you have electrons in a bond, they still don't want to be near each other. But they're a little bit more willing to be near each other than something that's just a lone pair. When we go to do this, we're treating double bonds and single bonds and triple bonds as exactly the same thing for the geometrical purposes. So this is sort of what we're going to be keeping in mind as we're trying to space these molecules out in 3D space. Now two definitions that we need to go through and we need to talk about. Steric number and coordination number. So steric number is if we take one atom. With all of these cases, we're looking at one atom. And we say how many bonds does it have? And in this case, I really should be saying how many bonded atoms are there. And that's an important distinction. You count the number of atoms that are bonded to it. Single and double bonds are, excuse me, double and triple bonds are treated the exact same way as single bonds. And then you count up the lone pairs. Then we have something called coordination number. And this is just the bonded atoms. So notice the difference here. This has the bonded atoms and the electron pairs. This just has the bonded atoms. And again, double and triple bonds are treated as one in this case. So if we look at NH3, and we want to figure out its coordination and steric number, we say, well, how many things are bonded to it? One, two, three, how many lone pairs does it have? One. So its coordination number is going to be one, two, three. Steric number is going to be one, two, three, four. If we go into this one, now we have five bonded atoms. And we have no lone pairs. So if you're saying, but wait, there's lone pairs on the fluorines, remember we're just talking about the phosphorous here. So typically when we talk about steric number and coordination number, we're only going to be talking about atoms that are bonded to more than one thing. So that's going to be true when we're talking about the geometries and when we start talking about hybridization. We're focused on atoms that are bonded to more than one thing. So we're just focused on the central atom, the phosphorous. So five bonds, no lone pairs. So its steric number is five, as is its coordination number. Now if we have this one, now we see that we have five bonded atoms and one lone pair. So now our steric number is six because we have five bonded atoms, one lone pair equals six. Our coordination number is just five. OK. So now two more sets of definitions before we move on. So we have electron geometry and we have molecular geometry. Now you're not really going to know how to figure this out. On this slide, that's fine. Just write it down after this class, you will. But they are going to be different. So if we go back and we look at the elements that we just talked about. When we look at this, one geometry, the electron geometry, is going to be acting as if we can kind of see these electrons. If these electrons are part of it. And so something like this would be tetrahedral because there's four things, including the electrons. But its molecular geometry would be different. And we'll know how to name them by the end of the class. But the molecular geometry just looks as if you can only see the hydrogens and that you can't see the electron pairs. Now the electron pairs are still going to be affecting the molecular geometry though. So I get asked a lot, well, OK, so the electron geometry has to do with the electrons. The molecular geometry only has to do with what's bonded to it. It's not necessarily true. Kind of. Sure, the molecular geometry isn't looking at this lone pair specifically. That lone pair affects where the molecules can be. And so it's still affected by it. You can't really separate them. So if we look at this, now there is no lone pairs on our central atom. So our molecular and our electron geometry turn out to be the same. So whenever you don't have lone pairs on your central atom, they're going to be the same because there are no lone pairs that are factored in. If we look at something like this, we're back to the same idea where now we have a geometry as if we were including these electrons, if we could see these electrons, and then one of which we can't. Where suddenly these electrons aren't really there anymore. But they're still going to be affected. The geometry is still going to be affected by the fact that the lone pair is there. OK. So now the easiest way to go about doing this, because it's impossible to see it in 2D, is to actually build them all. This is why I asked you to bring toothpicks and candy here if you had a model kit, but a lot of times first year here you don't. So we want to be building these along with me as I'm going about it. So we have our worksheet that you can get. And so if you go through and you do this, we're going to start with our lowest steric number, which is 2. Again, only really talking about things that are bonded to more than one atom. So steric number 2. And we're going to work our way up to steric number 6. And then each time we go through, we're going to take away one of the atoms and put a lone pair there. Take away another atom, put a lone pair there. And see how we can build all of these up and how they look very similar. And for all of these sorts of little animations, you can come here so that you can see them all since those don't come through on my slides. So for steric number 2, we want to find a way to space out our two atoms as much as possible. So if we want to take two things and we want to space them as far apart as you can space them, the way to do that is 180 degrees. It's to spread them out exactly like this. And to keep them as far apart from each other as possible. So if we look at this, we can kind of look and see what we think the geometry would be, right? First of all, the electron geometry and the molecular geometry are going to need to be the same because there are no lone pairs. And it's in a straight line, straight line, right? So we call that linear. They're the same because there's no lone pairs to factor in there. And then what is our bond angle? Well, from here to here, it's going to be 180 degrees. And so this is a linear molecule. So if you have steric number 2, it's just going to be linear. And this is what it looks like. So then moving on, we move on to steric number 3. So now we have to think, OK, using our geometry minds, where can I go to space all three of these out completely equally? And remember, we have three-dimensional space to work with here. So we can space them out everywhere. Now, it turns out both for steric number 2 and steric number 3, they are just on a plane. So if you try to space this out as much as possible, you get this. And this is the sort of geometry you're working with. Now, if both our steric number, if our steric number is 3 and we have no lone pairs, our coordination number is also 3. And so in that case, our electron and our molecular geometry are going to be the same. So now we have to decide what to call this. Well, look at the shape of it. We have three points. So that's a triangle. And it's all going to be on one plane, right? If I hold it like this, it's all in the up and down plane. So it's trigonal planar. So we have a trigonal planar geometry. Now people will say, well, do I have to memorize all of this? Yes. And there's a level of memorization to it, but it does make sense if you can see it. If you can see this, you can think of how the names work, and it makes it a lot easier to memorize the names. If you're just taking this table once we have it filled out and sitting down and memorizing it, that's a little rough and kind of useless. So memorize what they look like and then kind of relate the names to that. Now for binding angles, though, a lot of times you don't have to. There's one that's a little tricky if you don't memorize it. And I'd suggest just memorizing it. But for the rest of them, if you know what they look like, it's not really memorization. For instance, this one, if you know that it's three all on a plane, you know what it is all the way around, right? It's 360. It's a full circle all the way around. And so because of that, you know that each one of these is a third of that. So it's 120. So you don't really have to memorize that. So that's if we have steric number three and no lone pairs. But what if we have a lone pair? What if I take this off and I say, well, this is now, there's still something here, but it's a lone pair now. It's not an atom. So if we do that, now I have some examples here down down there for you for each one. So you can kind of use real molecules for it too. So if I do this now, we still have this shape. It's not like this is going to come in space out here because that lone pair is still, still there in this lone pair. Now, remember on that very first slide when I talked about Vessler theory and I said, lone pairs take up more room. That means that these lone pairs are going to be pushing down. It's going to be taking these and it's not, and just pushing down a little bit more. Not so much that the atom falls off. Or both of them. Okay. So if we do this, we can now decide what the shape of this molecule is. So if you look at the shape of this molecule, you can kind of call it bent, right? It's not linear. It's bent. It's kind of squished over. So our electron geometry stays the same because the electron geometry is still seeing this bond here, or this lone pair here. Our molecular geometry on the other hand is going to be bent because it's this way. It's not linear anymore. It's bent. Now comes our bond angle. So with our bond angle, it used to be 120. But in this case, it's not going to be quite 120 anymore because the lone pair is taking up more room and is squishing it down. It's squishing this bond angle so that it's more like this. And so what you're going to end up having is less than 120. It's not going to be quite 120 anymore. So there are a few examples of that one. So now that takes care of steric number three. We take off another one. We're back to this concept of only being bonded to one thing, in which case we don't really talk about geometries. So now we move on to steric number four. So we're going to be building something that looks like this. So this is a little bit, this one's a little bit tougher, I think, to see because you really have to think three-dimensionally to see this one easily. So if we go to do this, the way to space these out completely, and I think the easiest way to think about it, is to think about putting an atom in the middle of a box. And then drawing from the center of the box out to all four corners. And so we have this shape. So we have an atom in the center of a box drawn out to all four corners. And so we have a tetrahedron, right? So the shape of this whole thing, the shape that it would be making if we made this into a three-dimensional thing, would be a tetrahedron. So the molecular geometry of this, then, is called tetrahedral. So that's the molecular geometry. Now, or the electron geometry, excuse me. Now because this is also no-alone pairs, its steric number and its molecular, or its steric number and coordination number are the same, that means its molecular geometry is also going to be tetrahedral. All right? Now comes a bond angle part. And this one is not really super obvious. And unless you happen to be really good at geometry, this is one that you may just want to have to memorize. So the bond angle here is 109.5. It's not 90, right? Because it's not that we're taking 360 and dividing by four. We're taking 360 in all the dimensions and dividing by four. So it's not quite as obvious as the other ones. So this one is one that you may just want to memorize on some level. OK. So now we can take, and we can take one of those away. And we can put a lone pair there. If we do that, we get this geometry. Now if you look right here, well first of all, let's do our electron geometry, right? Our electron geometry doesn't change. Our electron geometry is still seeing as the shape. So our electron geometry is still tetrahedral. But our molecular geometry changes now, right? Because now we're just looking at the shape of the molecules or the atoms. Excuse me. So if we look at this, down here we have a triangle, right? These three, they form a triangle. But now it's not all in one plane. Now it's in a pyramid shape. So it's going to be trigonal pyramidal. So we have a triangle, base, and a pyramid shape. Now if we look at our bond angles, we still have the 109.5 about. But now we have this lone pair here that's squishing everything down a little bit. So it's not quite 109.5. It's less than 109.5. And you don't really have to worry about exactly what those numbers are. Just know that it's less than 109.5. On an exam, if you put 109.5, you're not right for this. It's got to be less than. And we expect you to know how much less than. But definitely know that it's less than. OK. So there's some common examples for that one. Now let's keep going. Now we can actually take off another one, and we can put another lone pair there. And we can get this shape. So now we have this shape. We have two lone pairs on there that we can't see in this sort of drawing. I suppose you could staple some balloons on it or whatever to show the lone pairs. And if you do this, our electron geometry is still tetrahedral. But we're back to a sort of bent structure, right? And this bent is definitely still called bent. But notice it's not the same as the other bent that we talked about. It's not the same as the bent where we took the trigonal planar. We took the steric number three, and we just took away one. Because when you did that, you can look back in your notes, and you saw that we had a bond angle of 120. But here that's not the case, right? Because this comes from a tetrahedral original electron geometry. So our bond angle is 109.5. So it's still going to be about 109.5, but it's going to be less than that. Furthermore, it's not only going to be less than 109.5, but it's going to be less than this too. Because with here, we only had one set of lone pairs pushing down. Here we have two sets of lone pairs pushing down. So you don't need to worry about which number that is, but you do need to know that it's less than that. So I could give you, on an example, let's say I could give you one of each of these, and tell you to rank their bond angles. And you would know that this one's going to be the biggest, and then this one, and then this one. I could also be tricky and give you something like this, one of these. And you would know that that's going to be bigger than all of these, because this one is based on 120. So this one is based on 109.5, and then moving down. So that takes us through that section of your table. So that gives us through steric number four. So now we need to do steric number five. OK, so this one now. Now we start getting complicated. The easiest way to go about building this one is to think about first putting them directly across from each other. So the first thing you do is put two atoms directly across from each other. That sets up two of them. Now comes the next three. Those go all along the center, equally spaced intervals. Put this down for a minute so we have some room. So we get this shape. So we have these two directly across from each other in a linear fashion. And then we have these three along the middle. And basically the same setup that we had our trigonal planar setup. So we have both of these combined together. This is that in three dimensions since I can't move mine around too much. So if we look at this now, we look at the shape of it. So remember this I said we have a triangle. And if we just ignore this for a minute. We just take this away. And we look at the shape that that makes. We could say well that's a triangle in sort of a pyramid shape. Triangle in sort of a pyramid shape. Now let's put this one back on and see what this one looks like. Now it's like we just doubled it. So we have a triangle in a pyramid shape up here. And then we flipped it and we made a triangle in a pyramid shape up here. So there's two of them. So trigonal bipyramidal. But there's two of them. So trigonal bipyramidal is the name of this one. So we have trigonal bipyramidal. And then because there's no lone pairs yet, we haven't gotten there yet. We have trigonal bipyramidal molecular geometry too. Now we have to look at bond angles. And this isn't quite as simple as the other one. Because we have two different sets. This one and this one aren't really the same geometrically. They are not actually identical. So if we look at this bond angle, hold it this way for you, we look at this bond angle here to here. That's a 90 degree angle, right? We know that this is 180. And so that's being split in half. So that's a 90 degree angle. But now if you look at this one from here to here, all the way around is 360. And it's being split in thirds. It's like our trigonal planar. So this angle is 120. This angle is 90. So actually you have to list both of them. Now continuing on with our pattern, let's take one of these away and turn it into a lone pair. Now though, there's some extra complications. When I took away one from the trigonal planar, or I took away one from the tetrahedral, it didn't really matter which one we took. Geometrically, they were all completely equal. All the bond angles were the same. It didn't matter where I put it. If I put it in one place, it was the same as just rotating it around and putting it in a different place. That's not true here anymore though. Now we have different bond angles. Now we have a 90 degree and we have a 120. So are we going to want to put it where it has 90 degrees to play with or 120 degrees to play with? So just decide on that. We have to decide which one takes up more room. Does a bond take up more room, or does a lone pair take up more room? Sure, a bond takes up, or excuse me, a lone pair takes up more room. So we need to give the lone pair as much room to maneuver as possible. So if we want to give the lone pair a lot of room, are we going to give it 90 degrees to play with, or are we going to give it 120 degrees to play with? Yeah, we want to give it 120 degrees to play with. So we take it off from here. Now we also have this case where because this is a situation where these atoms are not the same, we need to have a way to designate the difference between them. We need some nomenclature here. We need to know what we can call this as opposed to what we can call this. And so if you think of this as being a globe in exactly the fashion that I am holding it right now, what runs down the center of a globe? An axis. So these are axial. Oh, this one and this one are axial. Then what runs around the center of a globe? The equator. So these are equatorial. So we have axial and we have equatorial. So you always want to take away an atom and put a lone pair on an equatorial position. You want to give it 120 degrees on each side to play with, not just 90. So now we have this shape. These shapes are a little bit easier to see if you flip them sideways. So if we flip this sideways and we look at how it looks like, we can think of it as one of those teeter-totter things that we saw. But teeter-totter is not the proper terminology here. We want to use the other word for it, which is seesaw. So this molecular geometry is going to be seesaw. Now our bond angles, same as before, they're just going to be the 120 and 190, except that now this lone pair is pushing on everything a little bit. And so this angle is going to be a little bit less than 120. This angle is going to be a little bit less than 90. So we're talking about this angle here. This is going to be less than 120. And be careful to write it this way. A lot of times students will write 90, and then the less than sign, which doesn't work. You can't flip that like that, because that's saying that 90 is less than the angle. This angle is less than 90. So make sure you write it like this. So there's a couple of examples. All of these examples that I'm putting up here, that's just for your info, so you can actually have some practice drawing them. So you should really go home and take all of these different examples that I've put up, and use them as Lewis structure practice. Go through and draw the Lewis structures. Make sure you can draw them, and then make sure you can see the geometries. It's good like just putting in a blank pile practice, and then using them, figuring out what they are, and matching them up to the slide, and see if you got them right. OK, so now we get to take away another atom, and we get to put a lone pair there. So if we do that, we have to decide where to take from. And again, we get this choice of a little bit less than 120, or we get this choice of a little bit less than 90. And so we're going to want to take away which one. Yeah, the one that's greater than 120, or excuse me, less than 120. And that means that we're going to have this shape. And so again, to name this, let's flip it on its side, since that one does not want to stay on. So if we flip it on its side, that's a T, right? It's shaped like a T, and so it's T-shaped. So electron geometry is same as before. Molecular geometry T-shaped. And now what are our bond angles? So before this angle right here was 90, and then it got to be less than 90, and now it's going to be even less than 90, or even more less than 90, I should say. It's going to be even smaller. So now it's going to be a little bit more tilted in. So we get that kind of shape to it. So that's our T-shaped molecule. Now, just like before, I can ask you to rank these all the way across. And I can ask you to go through and say, well, if I gave you one from here, one from here, and one from here, rank those in order of bond angle. And you would be able to say, well, this is going to be the largest. And then this one, and then this one. So now we have our last one in this steric number to do. So we take away our T-shaped. We have our T-shaped. And now we have to decide, well, are we taking it away from here, where we have about a 120 between this and the next lone pair, or here, where we have 90, or less than 90. So we're going to take again from our equatorial position. So now we have this shape. So still trigonal bipyramidal. Now we have linear, though. We have a linear shape again. Now, again, notice that this isn't quite the exact same linear as the previous linear that we did. We had a linear before where we had the steric number 2. Well, this isn't that case, right? Now we have a steric number 5. We have three lone pairs around here. So even though it's called the same thing, and we'll look at our bond angles here in a second, it's not. You still want to think of them as slightly different things, right? Because our electron geometries are going to be different. This is the trigonal bipyramidal electron geometry, where the other electron geometry with a steric number 2 was just linear as well. So our bond angle here. So what do we think? What is our bond angle? Do we still have this 120, or excuse me, this 90? Well, that's not really a bond angle anymore, because there's no bond here. We can't really have this 120 here anymore either, because there's no bond here to compare to. So it's really just 180. Now the question is, is it less than 180? Because all of these were less than. It's not going to be less than 180, right? Because all of these are going to be pushing the same. So we have a lone pair here, a lone pair here, and a lone pair here. And they're all pushing equally on all of these atoms. And so because of that, it's just 180. So examples of this one would be like i3 minus or xcf2. OK, so now our last set of steric numbers. The most difficult to go through and do with these. Because I seem to be having problems keeping the styrofoam on, I'm going to just switch to doing it with the sticks. So if we move to our steric number 5 or 6, sorry, steric number 6, the way that these get spaced out are all equally like this. So they're all equally spaced. You can think of them basically as the three different axes in a Cartesian graph, right? x, y, z. So they're directly across from each other. So it looks like that. Now we're back to all of these being geometrically equal. What I mean by that is there's no real difference between this spot and this spot, right? Now if I just were to rotate it like this, this would be exactly the same. I didn't change anything. So that's what I mean by all being the same. So we don't have to worry about this equatorial or axial thing that we did with the trigonal bipyramidal. So this is going to be called octahedral. Now that is not super obvious. So count how many things we have bonded, first of all. Steric number 6. So we have six things bonded, and yet we call it octahedral. So why is that? Why is that name like it is? Why isn't it hexahedral? So keep in mind, we're looking at the shape, the three dimensional shape that this makes. So if you look at this three dimensional shape, what you actually have is an eight sided figure. You have a side here, side here, side here, side here. It's like a pyramid with a square base. It's like a square pyramid on both top and bottom. So there's eight sides. And so because there's eight faces to this shape, it's called octahedral, not like hexahedral or anything like that. It's talking about the shape of the molecule or the shape of this thing rather than how many things are bonded to it. It just happened with the way that the tetrahedral was set up that both formed the tetrahedron and it had four things. This is a little bit different. Our electron and molecular geometry are the same. So you don't have any lone pairs. And we have a bond angle of 90. So the 90, this is another one. Don't worry about memorizing this. You can look at it. If you know what the molecule looks like, there's no memorization here. You know that each of these are like your different x, y, z axis, right? You know that from here to here, it's 180 degrees. And it's split in half. From here to here, it's 180 degrees split in half, all the way around. So they're all going to be just 90 degrees. OK, so that's steric number 6, coordination number 6. Now what happens if we take one away and we put a lone pair there? Well, first of all, in this shape, does it matter which one I take away? And it doesn't, right? They're all the same, basically. You can treat them all the same. They all have the same bond angles. So I'm just going to take this one away at random. So now we have this sort of shape. Now our electron geometry, of course, is still going to be what? It's going to be octahedral. Now we have to think about our molecular geometry, though. So this one goes back to thinking about what the shape looks like. So if you look at the base, what I have sitting on this plane for you guys, it's a square, right? Now you add this one in, and now you have a pyramid shape. So it's square pyramidal. So again, there's a little bit of memorization there. But if you remember what it looks like, it's not too bad to memorize. It makes sense. There's a logic to it. And our bond angles, they're going to be less than 90, right? Because we have all these lone pairs, or this lone pair, and it's pushing everything down or up, in this case. And so it's squishing everything a little bit, making everything a little bit less than 90. OK, so now we get to take away another one. And we get to take one of these away. Now the question is, does it matter which one I take? So we know that lone pairs show the most repulsion. We know that lone pairs don't want to be around each other. So are we going to take one away here and put it right next to the lone pair? So we have a lone pair here and a lone pair right here. And then same thing with this one, this one, or this one. Or would we want to put it directly across from it, where now you have a lone pair here and a lone pair here, completely on opposite sides of the molecule? And yeah, you're going to want to give it room. So you want to put them on opposite sides. So you take it from the opposite side. We took this one from the bottom in this case. So we take this one from the top. And so we get that shape. So now our electron geometry is still going to be octahedral, because we still have an electron pair here and an electron pair here that didn't change. Now our molecular geometry. So we have a square, but it's all on one plane. It's not an A sort of pyramid or something like that. So it's square planar. Now comes our bond angles. So before we had said originally it was 90, then we put a lone pair and we said, OK, now it's less than 90. Well, what happens when we put another lone pair and we put it here? Is it going to be even less than 90? Well, if you think about it, we have this pushing up. We have this pushing down. And they're both a lone pair, so they're going to be pushing with the exact same force. And so they balance each other out. And so you're back to just 90. It's not less than 90 anymore. It's exactly 90. This is pushing up with the same amount that this is pushing down. And so there's a couple of examples of those, one of which we already have drawn. And this ends up being like this. So that kind of completes your worksheet in your workshop. So now what we're going to do is we're going to keeping all of this in mind and stopping to sort of build these as you need to. We're going to go back through all of those Lewis structures that we drew. We're going to decide what are the electron trees and the molecular geometries of all of them. OK. So again, keeping in mind, there are some times that I skip just because it doesn't really fit. So great example of that in this one. The N2, there's not really a geometry to talk about here. There's only two molecules, or there's only two atoms. So we're only talking about geometries when they're bonded to more than one thing. So this one we're not really going to talk about. So now if we look at this one. So things to ask yourself when you're going through this is what is the steric number? What is the coordination number? And then out of that, what are each of your geometries? So to shorten this up, I'm going to use SN and CN for steric number and coordination number. I'm going to use EG and NG for electron geometry and molecular geometry. So if we look at our steric number, we have one, two, three things bonded to it in no lone pairs. We're just looking at our carbon, right? We're not saying, well, there's lone pairs on the oxygen. We don't care about the oxygen. We're just looking at the central atom. So one, two, three things bonded to it. Sure, there's four bonds, but we treat double and triple bonds the exact same as we do single bonds. So our coordination number and our steric number are both three. So for the sake of time, I'm just going to switch to using these. So if we have this, we have three things bonded. So we want to use the geometry that spaces them out the most. And so we're left with trigonal planar. And that, because our steric number and our coordination number are the same, that's going to be both, both electron and molecular geometry. So that's how we do that one. And again, we don't care that there's a double bond there. We just treat that as one. We're not counting bonds. We're counting numbers of things that are bonded to the atom. OK, now let's do this one. Now this one's interesting in the fact that we have two central atoms. So what do we do? Well, we look at both of them completely separately. So we look at the boron, and then we look at the nitrogen. Now in this case, they happen to be the same, but that's OK. So if we look at boron, its steric number is the same as this coordination number, right? Because there's no lone pairs on it. And both of those are equal to 3. And so we're left with the exact same situation we had in the last one. And we'll use them all to get so you can see. Something weird going on with the projector at the moment, I think. OK, well, we'll just keep it zoomed like that. All right, so with the boron and nitrogen, we're going to end up with the same thing that we did in the last one, where we have these three, and they're all evenly spaced. And so we have trigonal planar for all of them. Oh, wait. No, our steric number's 4. Sorry about that. Steric number's definitely 4, so it's not trigonal planar, right? So now we have four of these things. Space like this. We have this spacing. So if we look at this, we have tetrahedral. And that's going to be both. Because our steric number and our coordination number are the same. So now our nitrogen. Our nitrogen winds up having the exact same thing. Let's try to fix this a little bit here. OK, so for our nitrogen, we have a steric number and a coordination number both equal to 4. So we have 1, 2, 3, 4. And so we're left with the same thing, where we have four things bonded to it, no lone pairs. And so our electron is going to be the same as the other two. And so we have a star. We have two things bonded to it, no lone pairs. And so our electron geometry and our molecular geometry are both tetrahedral. OK, next one. So now we have our xef4, 4 plus. So same as before, we count our steric number and we count our coordination number. And in this case, they're the same. So 1, 2, 3, 4. So that means that our molecular geometry and our electron geometry are the same. And that's going to be tetrahedral. For the same reason as before, we space them all out in the most even way possible. And that gives us tetrahedral. OK, now we get to move on to our N2O. And keeping in mind just our most stable one. And again, we're just looking at our central atom here. And if we have two central atoms, we'll look at both of them individually. So in this case, we're just looking at nitrogen. And so there are two things spaced evenly across from each other because it's linear, right? Or it's 180 degrees across. That's the way to spread two atoms out in the most even way possible. So we're left with a linear geometry. So steric number 2, coordination number equals 2. And our geometries are the same, and they're linear. Yeah, it's a good idea to sort of have toothpicks with you while you're doing these sorts of homework problems and practice doing them with things in your hands that you can play with and you can see the geometries. If you just happen to be really good at seeing in three dimensions, OK, maybe that's not so important to you. But a lot of people, myself included, are not. So now we have S, F6. So when you look at this one and we decide what our coordination number and our steric number is, we say, well, how many things are bonded to it? One, two, three, four, five, six. No lone pairs, so they're both the same. Now we have to decide what geometry is it. So if you want to space these out all equally, this is how you end up needing to do it. And so you end up with six equally spaced of things. It's shaped like an octahedron, then. And so it's octahedral. And the more you do them, the better you'll get at naming them quickly. It may take you a while at first to figure out the shapes in your head. Now it's time for a tricky one. XEF4. So if we have XEF4, originally we'll have a steric number of one, two, three, four, five, six. Because we count the number of bonded atoms and we count the lone pairs. But now our coordination number is going to change, because our coordination number just counts the bonded atoms. So we have four. And when we try to draw this out, we end up with a shape that looks like this. And for our electron geometry. So if we have our electron geometry, that's going to be equal to whatever this looks like, which is octahedral. Now we have to put two lone pairs on. So we have to take two of these atoms and replace them with lone pairs. So again, we have to think about, well, are we going to put them here and here, or do we want to space them out? Of course, we want to space them out. So we're putting a lone pair here and a lone pair here, which leaves this as a square planar shape. So and of course, our bond angles here, which you don't want to forget, our bond angles here, are they 90, 180, what are they? Well, that originally started as 90. And it's still going to be 90, because we have a lone pair here and a lone pair here. They're pushing on each other equally. And so because of that, our bond angles here are still 90. OK. Next one. So our HSO4. So remember, this is how all of our oxoacids are kind of set up. So it's always good to kind of keep this structure in mind so that you remember them. We have our oxygens all bonded to our central atom and our hydrogens off our oxygens. So if we look at this and we go through and we say, well, we don't care that these are double bonds. We don't care that sulfur is breaking the octet rule. None of that matters to us for the sake of the geometry. We've already talked about why those are all OK. So for the geometry for the sulfur, we're going to look at it and we're going to say, well, there's four things bonded to it, no lone pairs, one, two, three, four. So both its steric number and its coordination number is equal to four. Now that means that both its electron geometry and its molecular geometry are going to be tetrahedral. Now remember we talked about having, we can have two central atoms, right? As long as something's bonded to more than one atom, we can talk about it in the same way. So we can do the exact same thing for the oxygen. Now what's the steric number on the oxygen? One, two, three, four. So what's the coordination number on the oxygen? It's just one, two. It's the same thing for both oxygens. Remember we're just talking about these, not these, because these are only bonded to one thing. OK, so now this is still going to be tetrahedral, right? Because there's four things. Now with this one, we had a tetrahedral electron geometry. Now we have taken two of those and we've replaced two of those with lone pairs. And so that leaves us with a bent geometry. But be careful not to see that, oh, we're going to have two things bonded to it. It must be linear, right? Well, no, because we still have the electrons that we have to worry about. So even though there's only two things bonded to it, there's these electrons that are taking up room. And so it's keeping it in its bent form. Now we're about out of time for the day. So go home and practice doing all of these that we just did. And we kind of skipped bond angles on purpose so we can go back through them and talk about them again. And the geometries again is a little bit of review at the very beginning of next class. So we'll finish up bond angles in next class. And we'll finish up the rest of the Lewis structures next time. In the meantime, go home, practice doing those, see if you can fill in all the bond angles, and then we'll check and see if you're right as of next time. And then we'll take what we've learned and we'll combine it with last class's lecture where we talked about polarity. And we'll actually be able to go through now and say, well, based on the geometries and the polar bonds, which one of these molecules are actually polar and which ones aren't going to be polar?
 So today we have two quick things to finish up from chapter two.  Just two quick topics that we need to know before we can really move on, sort of background  info.  And then we're going to go on to the sort of VSEPR workshop that we had planned.  So hopefully you all brought your candy into your picks.  So we have this thing called polarizing power and polarizability.  So these are sort of two opposite concepts in a way.  So the more electrons that you have, the further they are from the nucleus, right?  So that kind of, that gave us an idea of some of our trends as we were going down the periodic  table.  And this also has to do with polarizability and polarizing power.  So if you have very far electrons, then the nucleus isn't going to be able to really affect  things that are going on far away from it.  So if two things are bonded to each other or near each other, an atom that has very far  off electrons is not going to be able to affect the other nucleus's electrons very much.  And that comes into the idea of polarizing power, the ability of one atom to polarize  another.  Now conversely to that, if something has a lot of electrons, it's very polarizable.  So something with a lot of electrons doesn't have complete control over its electrons,  right?  It's trying to sort of balance all of these electrons that are a long ways away from  it and try to control them.  So if some other atom comes around that can move it around, it can push that electron  density around.  The more electrons, the more it can be pushed around, the more polarizable it is.  And if it can't really even control its own electrons, it's not going to be able to push  around other nuclei's electrons.  So it's not going to have very much polarizing power.  Now the opposite to that then is if something is small, if something is very small, something  like Al3+, very highly positively charged small nuclei or small atoms, that's going to be  able to push around other atoms' electrons pretty easily because it has a lot of polarizing  power.  It doesn't have a very large electron cloud, its nuclei can be felt a lot, it has a high  effective nuclear charge, and those have a lot of polarizing power.  Something as big with a lot of electrons is very polarizable, something that's small  without very many electrons has a lot of polarizing power.  And then one more small topic that we need to sort of talk about so that you have in  your background knowledge when we talk about all sorts of things from now on is the difference  in correlations between bond strengths and bond lengths.  So something like a single bond is going to be weaker and longer than something like  a triple bond.  So if we compare the different types of carbon bonds, single bond is going to be the longest  and then a double bond and then a triple bond.  And of course now that we've talked about resonance, you know that we can have things  that are in between that too, right?  We can have bond orders of like one and a third or one and a half because of the way  that Lewis structures work.  So because of that we can't have in between things.  So that's one of the ways that we can sort of tell what kind of bonds we're looking at.  We can measure the lengths of them and we can say, well is it a single bond or a double  bond or a triple bond based on how long it is?  Or triple bond is your shortest.  A single bond is your longest.  So this is sort of good to have in mind as we're talking about different bonds and how  they're related to each other.  So this finishes up chapter two.  So now we need to go on to molecular shape and structure chapter three.  So now we get to go ahead and we get to learn how bonds and lone pairs are going to affect  the geometry.  So so far we've just been drawing them up and a lot of them I kind of drew up in the  shape that they look like, but Lewis structures don't accurately represent that.  Lewis structures alone aren't going to tell you what shape they are.  You don't have to draw those in the shape that they are.  And in fact in your homework you probably saw that purposely they were drawn in ways  that maybe didn't show you the shape so that you have to guess it on your own.  We're going to look at how these geometries work with what we learned last class about  the polarities of bonds to give us whether it is or isn't a polar molecule.  So we went through and we looked at all of our Lewis structures and we said, OK, these  have polar bonds.  But it was very careful to make sure that you guys realize we weren't deciding if the  molecule is polar or not, right?  They said we couldn't do that yet.  So after today we'll be able to go through and we'll be able to say, OK, this molecule  is polar, this molecule isn't and why, rather than just talking about the bonds.  And then we're going to go into this concept of two different main theories of bonding.  Two different ways that chemists look at how molecules bond and how they work together.  So we'll talk about valence bond theory or hybridization, which is used a lot in the  organic chemistry section.  And it's very quick and easy once you know it, the key word there being once you know  it.  It works really well too.  But it does break down sometimes.  It's not 100% predictive.  Well, not anything's 100% predictive.  But it's very good at explaining things, but there's some problems with it.  And so molecular orbital theory fixes some of that.  But it creates a whole new problem of being super complicated at requiring computers and  adding a wave functions.  All those wave functions you love so much are going to come back and things of that  sort that we're going to want to talk about too.  So let's start with our VSEPR theory.  So before we start filling out your worksheet and going through the workshop, we need to  do a couple of definitions.  So the idea here and what we're going to be thinking as we're doing all of these geometries  is that we have these electrons that are all negatively charged.  They don't want to be near each other.  They all have the same charge.  They're all negative charge.  So they're going to repel each other.  They want to be far away from each other.  So the idea is how can we get these as far apart from each other as possible?  Now in addition to this, electron pairs are going to show more repulsion than a bond.  So if you have electrons in a bond, they still don't want to be near each other.  But they're a little bit more willing to be near each other than something that's just  a lone pair.  When we go to do this, we're treating double bonds and single bonds and triple bonds as  exactly the same thing for the geometrical purposes.  So this is sort of what we're going to be keeping in mind as we're trying to space these molecules  out in 3D space.  Now two definitions that we need to go through and we need to talk about.  Steric number and coordination number.  So steric number is if we take one atom.  With all of these cases, we're looking at one atom.  And we say how many bonds does it have?  And in this case, I really should be saying how many bonded atoms are there.  And that's an important distinction.  You count the number of atoms that are bonded to it.  Single and double bonds are, excuse me, double and triple bonds are treated the exact same  way as single bonds.  And then you count up the lone pairs.  Then we have something called coordination number.  And this is just the bonded atoms.  So notice the difference here.  This has the bonded atoms and the electron pairs.  This just has the bonded atoms.  And again, double and triple bonds are treated as one in this case.  So if we look at NH3, and we want to figure out its coordination and steric number, we  say, well, how many things are bonded to it?  One, two, three, how many lone pairs does it have?  One.  So its coordination number is going to be one, two, three.  Steric number is going to be one, two, three, four.  If we go into this one, now we have five bonded atoms.  And we have no lone pairs.  So if you're saying, but wait, there's lone pairs on the fluorines, remember we're just  talking about the phosphorous here.  So typically when we talk about steric number and coordination number, we're only going  to be talking about atoms that are bonded to more than one thing.  So that's going to be true when we're talking about the geometries and when we start talking  about hybridization.  We're focused on atoms that are bonded to more than one thing.  So we're just focused on the central atom, the phosphorous.  So five bonds, no lone pairs.  So its steric number is five, as is its coordination number.  Now if we have this one, now we see that we have five bonded atoms and one lone pair.  So now our steric number is six because we have five bonded atoms, one lone pair equals  six.  Our coordination number is just five.  OK.  So now two more sets of definitions before we move on.  So we have electron geometry and we have molecular geometry.  Now you're not really going to know how to figure this out.  On this slide, that's fine.  Just write it down after this class, you will.  But they are going to be different.  So if we go back and we look at the elements that we just talked about.  When we look at this, one geometry, the electron geometry, is going to be acting as if we can  kind of see these electrons.  If these electrons are part of it.  And so something like this would be tetrahedral because there's four things, including the  electrons.  But its molecular geometry would be different.  And we'll know how to name them by the end of the class.  But the molecular geometry just looks as if you can only see the hydrogens and that you  can't see the electron pairs.  Now the electron pairs are still going to be affecting the molecular geometry though.  So I get asked a lot, well, OK, so the electron geometry has to do with the electrons.  The molecular geometry only has to do with what's bonded to it.  It's not necessarily true.  Kind of.  Sure, the molecular geometry isn't looking at this lone pair specifically.  That lone pair affects where the molecules can be.  And so it's still affected by it.  You can't really separate them.  So if we look at this, now there is no lone pairs on our central atom.  So our molecular and our electron geometry turn out to be the same.  So whenever you don't have lone pairs on your central atom, they're going to be the  same because there are no lone pairs that are factored in.  If we look at something like this, we're back to the same idea where now we have a geometry  as if we were including these electrons, if we could see these electrons, and then one  of which we can't.  Where suddenly these electrons aren't really there anymore.  But they're still going to be affected.  The geometry is still going to be affected by the fact that the lone pair is there.  OK.  So now the easiest way to go about doing this, because it's impossible to see it in 2D, is  to actually build them all.  This is why I asked you to bring toothpicks and candy here if you had a model kit, but  a lot of times first year here you don't.  So we want to be building these along with me as I'm going about it.  So we have our worksheet that you can get.  And so if you go through and you do this, we're going to start with our lowest steric  number, which is 2.  Again, only really talking about things that are bonded to more than one atom.  So steric number 2.  And we're going to work our way up to steric number 6.  And then each time we go through, we're going to take away one of the atoms and put a lone  pair there.  Take away another atom, put a lone pair there.  And see how we can build all of these up and how they look very similar.  And for all of these sorts of little animations, you can come here so that you can see them  all since those don't come through on my slides.  So for steric number 2, we want to find a way to space out our two atoms as much as  possible.  So if we want to take two things and we want to space them as far apart as you can space  them, the way to do that is 180 degrees.  It's to spread them out exactly like this.  And to keep them as far apart from each other as possible.  So if we look at this, we can kind of look and see what we think the geometry would be,  right?  First of all, the electron geometry and the molecular geometry are going to need to be  the same because there are no lone pairs.  And it's in a straight line, straight line, right?  So we call that linear.  They're the same because there's no lone pairs to factor in there.  And then what is our bond angle?  Well, from here to here, it's going to be 180 degrees.  And so this is a linear molecule.  So if you have steric number 2, it's just going to be linear.  And this is what it looks like.  So then moving on, we move on to steric number 3.  So now we have to think, OK, using our geometry minds, where can I go to space all three of  these out completely equally?  And remember, we have three-dimensional space to work with here.  So we can space them out everywhere.  Now, it turns out both for steric number 2 and steric number 3, they are just on a plane.  So if you try to space this out as much as possible, you get this.  And this is the sort of geometry you're working with.  Now, if both our steric number, if our steric number is 3 and we have no lone pairs, our  coordination number is also 3.  And so in that case, our electron and our molecular geometry are going to be the same.  So now we have to decide what to call this.  Well, look at the shape of it.  We have three points.  So that's a triangle.  And it's all going to be on one plane, right?  If I hold it like this, it's all in the up and down plane.  So it's trigonal planar.  So we have a trigonal planar geometry.  Now people will say, well, do I have to memorize all of this?  Yes.  And there's a level of memorization to it, but it does make sense if you can see it.  If you can see this, you can think of how the names work, and it makes it a lot easier  to memorize the names.  If you're just taking this table once we have it filled out and sitting down and memorizing  it, that's a little rough and kind of useless.  So memorize what they look like and then kind of relate the names to that.  Now for binding angles, though, a lot of times you don't have to.  There's one that's a little tricky if you don't memorize it.  And I'd suggest just memorizing it.  But for the rest of them, if you know what they look like, it's not really memorization.  For instance, this one, if you know that it's three all on a plane, you know what it is  all the way around, right?  It's 360.  It's a full circle all the way around.  And so because of that, you know that each one of these is a third of that.  So it's 120.  So you don't really have to memorize that.  So that's if we have steric number three and no lone pairs.  But what if we have a lone pair?  What if I take this off and I say, well, this is now, there's still something here, but  it's a lone pair now.  It's not an atom.  So if we do that, now I have some examples here down down there for you for each one.  So you can kind of use real molecules for it too.  So if I do this now, we still have this shape.  It's not like this is going to come in space out here because that lone pair is still,  still there in this lone pair.  Now, remember on that very first slide when I talked about Vessler theory and I said,  lone pairs take up more room.  That means that these lone pairs are going to be pushing down.  It's going to be taking these and it's not, and just pushing down a little bit more.  Not so much that the atom falls off.  Or both of them.  Okay.  So if we do this, we can now decide what the shape of this molecule is.  So if you look at the shape of this molecule, you can kind of call it bent, right?  It's not linear.  It's bent.  It's kind of squished over.  So our electron geometry stays the same because the electron geometry is still seeing this  bond here, or this lone pair here.  Our molecular geometry on the other hand is going to be bent because it's this way.  It's not linear anymore.  It's bent.  Now comes our bond angle.  So with our bond angle, it used to be 120.  But in this case, it's not going to be quite 120 anymore because the lone pair is taking  up more room and is squishing it down.  It's squishing this bond angle so that it's more like this.  And so what you're going to end up having is less than 120.  It's not going to be quite 120 anymore.  So there are a few examples of that one.  So now that takes care of steric number three.  We take off another one.  We're back to this concept of only being bonded to one thing, in which case we don't  really talk about geometries.  So now we move on to steric number four.  So we're going to be building something that looks like this.  So this is a little bit, this one's a little bit tougher, I think, to see because you really  have to think three-dimensionally to see this one easily.  So if we go to do this, the way to space these out completely, and I think the easiest way  to think about it, is to think about putting an atom in the middle of a box.  And then drawing from the center of the box out to all four corners.  And so we have this shape.  So we have an atom in the center of a box drawn out to all four corners.  And so we have a tetrahedron, right?  So the shape of this whole thing, the shape that it would be making if we made this into  a three-dimensional thing, would be a tetrahedron.  So the molecular geometry of this, then, is called tetrahedral.  So that's the molecular geometry.  Now, or the electron geometry, excuse me.  Now because this is also no-alone pairs, its steric number and its molecular, or its steric  number and coordination number are the same, that means its molecular geometry is also  going to be tetrahedral.  All right?  Now comes a bond angle part.  And this one is not really super obvious.  And unless you happen to be really good at geometry, this is one that you may just want  to have to memorize.  So the bond angle here is 109.5.  It's not 90, right?  Because it's not that we're taking 360 and dividing by four.  We're taking 360 in all the dimensions and dividing by four.  So it's not quite as obvious as the other ones.  So this one is one that you may just want to memorize on some level.  OK.  So now we can take, and we can take one of those away.  And we can put a lone pair there.  If we do that, we get this geometry.  Now if you look right here, well first of all, let's do our electron geometry, right?  Our electron geometry doesn't change.  Our electron geometry is still seeing as the shape.  So our electron geometry is still tetrahedral.  But our molecular geometry changes now, right?  Because now we're just looking at the shape of the molecules or the atoms.  Excuse me.  So if we look at this, down here we have a triangle, right?  These three, they form a triangle.  But now it's not all in one plane.  Now it's in a pyramid shape.  So it's going to be trigonal pyramidal.  So we have a triangle, base, and a pyramid shape.  Now if we look at our bond angles, we still have the 109.5 about.  But now we have this lone pair here that's squishing everything down a little bit.  So it's not quite 109.5.  It's less than 109.5.  And you don't really have to worry about exactly what those numbers are.  Just know that it's less than 109.5.  On an exam, if you put 109.5, you're not right for this.  It's got to be less than.  And we expect you to know how much less than.  But definitely know that it's less than.  OK.  So there's some common examples for that one.  Now let's keep going.  Now we can actually take off another one, and we can put another lone pair there.  And we can get this shape.  So now we have this shape.  We have two lone pairs on there that we can't see in this sort of drawing.  I suppose you could staple some balloons on it or whatever to show the lone pairs.  And if you do this, our electron geometry is still tetrahedral.  But we're back to a sort of bent structure, right?  And this bent is definitely still called bent.  But notice it's not the same as the other bent that we talked about.  It's not the same as the bent where we took the trigonal planar.  We took the steric number three, and we just took away one.  Because when you did that, you can look back in your notes, and you saw that we had a bond  angle of 120.  But here that's not the case, right?  Because this comes from a tetrahedral original electron geometry.  So our bond angle is 109.5.  So it's still going to be about 109.5, but it's going to be less than that.  Furthermore, it's not only going to be less than 109.5, but it's going to be less than  this too.  Because with here, we only had one set of lone pairs pushing down.  Here we have two sets of lone pairs pushing down.  So you don't need to worry about which number that is, but you do need to know that it's  less than that.  So I could give you, on an example, let's say I could give you one of each of these,  and tell you to rank their bond angles.  And you would know that this one's going to be the biggest, and then this one, and then  this one.  I could also be tricky and give you something like this, one of these.  And you would know that that's going to be bigger than all of these, because this one  is based on 120.  So this one is based on 109.5, and then moving down.  So that takes us through that section of your table.  So that gives us through steric number four.  So now we need to do steric number five.  OK, so this one now.  Now we start getting complicated.  The easiest way to go about building this one is to think about first putting them directly  across from each other.  So the first thing you do is put two atoms directly across from each other.  That sets up two of them.  Now comes the next three.  Those go all along the center, equally spaced intervals.  Put this down for a minute so we have some room.  So we get this shape.  So we have these two directly across from each other in a linear fashion.  And then we have these three along the middle.  And basically the same setup that we had our trigonal planar setup.  So we have both of these combined together.  This is that in three dimensions since I can't move mine around too much.  So if we look at this now, we look at the shape of it.  So remember this I said we have a triangle.  And if we just ignore this for a minute.  We just take this away.  And we look at the shape that that makes.  We could say well that's a triangle in sort of a pyramid shape.  Triangle in sort of a pyramid shape.  Now let's put this one back on and see what this one looks like.  Now it's like we just doubled it.  So we have a triangle in a pyramid shape up here.  And then we flipped it and we made a triangle in a pyramid shape up here.  So there's two of them.  So trigonal bipyramidal.  But there's two of them.  So trigonal bipyramidal is the name of this one.  So we have trigonal bipyramidal.  And then because there's no lone pairs yet, we haven't gotten there yet.  We have trigonal bipyramidal molecular geometry too.  Now we have to look at bond angles.  And this isn't quite as simple as the other one.  Because we have two different sets.  This one and this one aren't really the same geometrically.  They are not actually identical.  So if we look at this bond angle, hold it this way for you,  we look at this bond angle here to here.  That's a 90 degree angle, right?  We know that this is 180.  And so that's being split in half.  So that's a 90 degree angle.  But now if you look at this one from here to here,  all the way around is 360.  And it's being split in thirds.  It's like our trigonal planar.  So this angle is 120.  This angle is 90.  So actually you have to list both of them.  Now continuing on with our pattern,  let's take one of these away and turn it into a lone pair.  Now though, there's some extra complications.  When I took away one from the trigonal planar,  or I took away one from the tetrahedral,  it didn't really matter which one we took.  Geometrically, they were all completely equal.  All the bond angles were the same.  It didn't matter where I put it.  If I put it in one place, it was the same as just rotating  it around and putting it in a different place.  That's not true here anymore though.  Now we have different bond angles.  Now we have a 90 degree and we have a 120.  So are we going to want to put it where it has 90 degrees  to play with or 120 degrees to play with?  So just decide on that.  We have to decide which one takes up more room.  Does a bond take up more room, or does a lone pair  take up more room?  Sure, a bond takes up, or excuse me,  a lone pair takes up more room.  So we need to give the lone pair as much room to maneuver  as possible.  So if we want to give the lone pair a lot of room,  are we going to give it 90 degrees to play with,  or are we going to give it 120 degrees to play with?  Yeah, we want to give it 120 degrees to play with.  So we take it off from here.  Now we also have this case where because this  is a situation where these atoms are not the same,  we need to have a way to designate the difference between them.  We need some nomenclature here.  We need to know what we can call this as opposed  to what we can call this.  And so if you think of this as being a globe in exactly the fashion  that I am holding it right now, what  runs down the center of a globe?  An axis.  So these are axial.  Oh, this one and this one are axial.  Then what runs around the center of a globe?  The equator.  So these are equatorial.  So we have axial and we have equatorial.  So you always want to take away an atom  and put a lone pair on an equatorial position.  You want to give it 120 degrees on each side to play with,  not just 90.  So now we have this shape.  These shapes are a little bit easier  to see if you flip them sideways.  So if we flip this sideways and we look at how it looks like,  we can think of it as one of those teeter-totter things  that we saw.  But teeter-totter is not the proper terminology here.  We want to use the other word for it, which is seesaw.  So this molecular geometry is going to be seesaw.  Now our bond angles, same as before,  they're just going to be the 120 and 190,  except that now this lone pair is pushing on everything  a little bit.  And so this angle is going to be a little bit less than 120.  This angle is going to be a little bit less than 90.  So we're talking about this angle here.  This is going to be less than 120.  And be careful to write it this way.  A lot of times students will write 90,  and then the less than sign, which doesn't work.  You can't flip that like that, because that's  saying that 90 is less than the angle.  This angle is less than 90.  So make sure you write it like this.  So there's a couple of examples.  All of these examples that I'm putting up here,  that's just for your info, so you can actually  have some practice drawing them.  So you should really go home and take  all of these different examples that I've put up,  and use them as Lewis structure practice.  Go through and draw the Lewis structures.  Make sure you can draw them, and then make  sure you can see the geometries.  It's good like just putting in a blank pile practice,  and then using them, figuring out what they are,  and matching them up to the slide,  and see if you got them right.  OK, so now we get to take away another atom,  and we get to put a lone pair there.  So if we do that, we have to decide where to take from.  And again, we get this choice of a little bit less than 120,  or we get this choice of a little bit less than 90.  And so we're going to want to take away which one.  Yeah, the one that's greater than 120, or excuse me, less than 120.  And that means that we're going to have this shape.  And so again, to name this, let's flip it on its side,  since that one does not want to stay on.  So if we flip it on its side, that's a T, right?  It's shaped like a T, and so it's T-shaped.  So electron geometry is same as before.  Molecular geometry T-shaped.  And now what are our bond angles?  So before this angle right here was 90,  and then it got to be less than 90,  and now it's going to be even less than 90,  or even more less than 90, I should say.  It's going to be even smaller.  So now it's going to be a little bit more tilted in.  So we get that kind of shape to it.  So that's our T-shaped molecule.  Now, just like before, I can ask you  to rank these all the way across.  And I can ask you to go through and say, well,  if I gave you one from here, one from here, and one from here,  rank those in order of bond angle.  And you would be able to say, well,  this is going to be the largest.  And then this one, and then this one.  So now we have our last one in this steric number to do.  So we take away our T-shaped.  We have our T-shaped.  And now we have to decide, well, are we taking it away from here,  where we have about a 120 between this and the next lone pair,  or here, where we have 90, or less than 90.  So we're going to take again from our equatorial position.  So now we have this shape.  So still trigonal bipyramidal.  Now we have linear, though.  We have a linear shape again.  Now, again, notice that this isn't quite the exact same linear  as the previous linear that we did.  We had a linear before where we had the steric number 2.  Well, this isn't that case, right?  Now we have a steric number 5.  We have three lone pairs around here.  So even though it's called the same thing,  and we'll look at our bond angles here in a second,  it's not.  You still want to think of them as slightly different things,  right?  Because our electron geometries are going to be different.  This is the trigonal bipyramidal electron geometry,  where the other electron geometry with a steric number 2  was just linear as well.  So our bond angle here.  So what do we think?  What is our bond angle?  Do we still have this 120, or excuse me, this 90?  Well, that's not really a bond angle anymore,  because there's no bond here.  We can't really have this 120 here anymore either,  because there's no bond here to compare to.  So it's really just 180.  Now the question is, is it less than 180?  Because all of these were less than.  It's not going to be less than 180, right?  Because all of these are going to be pushing the same.  So we have a lone pair here, a lone pair here,  and a lone pair here.  And they're all pushing equally on all of these atoms.  And so because of that, it's just 180.  So examples of this one would be like i3 minus or xcf2.  OK, so now our last set of steric numbers.  The most difficult to go through and do with these.  Because I seem to be having problems keeping the styrofoam  on, I'm going to just switch to doing it with the sticks.  So if we move to our steric number 5 or 6, sorry,  steric number 6, the way that these get spaced out  are all equally like this.  So they're all equally spaced.  You can think of them basically as the three different axes  in a Cartesian graph, right?  x, y, z.  So they're directly across from each other.  So it looks like that.  Now we're back to all of these being geometrically equal.  What I mean by that is there's no real difference  between this spot and this spot, right?  Now if I just were to rotate it like this,  this would be exactly the same.  I didn't change anything.  So that's what I mean by all being the same.  So we don't have to worry about this equatorial or axial thing  that we did with the trigonal bipyramidal.  So this is going to be called octahedral.  Now that is not super obvious.  So count how many things we have bonded, first of all.  Steric number 6.  So we have six things bonded, and yet we call it octahedral.  So why is that?  Why is that name like it is?  Why isn't it hexahedral?  So keep in mind, we're looking at the shape, the three  dimensional shape that this makes.  So if you look at this three dimensional shape,  what you actually have is an eight sided figure.  You have a side here, side here, side here, side here.  It's like a pyramid with a square base.  It's like a square pyramid on both top and bottom.  So there's eight sides.  And so because there's eight faces to this shape,  it's called octahedral, not like hexahedral or anything  like that.  It's talking about the shape of the molecule  or the shape of this thing rather than how many things  are bonded to it.  It just happened with the way that the tetrahedral was  set up that both formed the tetrahedron  and it had four things.  This is a little bit different.  Our electron and molecular geometry are the same.  So you don't have any lone pairs.  And we have a bond angle of 90.  So the 90, this is another one.  Don't worry about memorizing this.  You can look at it.  If you know what the molecule looks like,  there's no memorization here.  You know that each of these are like your different x, y, z  axis, right?  You know that from here to here, it's 180 degrees.  And it's split in half.  From here to here, it's 180 degrees split in half,  all the way around.  So they're all going to be just 90 degrees.  OK, so that's steric number 6, coordination number 6.  Now what happens if we take one away  and we put a lone pair there?  Well, first of all, in this shape,  does it matter which one I take away?  And it doesn't, right?  They're all the same, basically.  You can treat them all the same.  They all have the same bond angles.  So I'm just going to take this one away at random.  So now we have this sort of shape.  Now our electron geometry, of course, is still going to be what?  It's going to be octahedral.  Now we have to think about our molecular geometry, though.  So this one goes back to thinking about what  the shape looks like.  So if you look at the base, what I have sitting on this plane  for you guys, it's a square, right?  Now you add this one in, and now you have a pyramid shape.  So it's square pyramidal.  So again, there's a little bit of memorization there.  But if you remember what it looks like,  it's not too bad to memorize.  It makes sense.  There's a logic to it.  And our bond angles, they're going to be less than 90, right?  Because we have all these lone pairs, or this lone pair,  and it's pushing everything down or up, in this case.  And so it's squishing everything a little bit, making  everything a little bit less than 90.  OK, so now we get to take away another one.  And we get to take one of these away.  Now the question is, does it matter which one I take?  So we know that lone pairs show the most repulsion.  We know that lone pairs don't want to be around each other.  So are we going to take one away here and put it right next  to the lone pair?  So we have a lone pair here and a lone pair right here.  And then same thing with this one, this one, or this one.  Or would we want to put it directly across from it,  where now you have a lone pair here and a lone pair here,  completely on opposite sides of the molecule?  And yeah, you're going to want to give it room.  So you want to put them on opposite sides.  So you take it from the opposite side.  We took this one from the bottom in this case.  So we take this one from the top.  And so we get that shape.  So now our electron geometry is still  going to be octahedral, because we still  have an electron pair here and an electron pair here  that didn't change.  Now our molecular geometry.  So we have a square, but it's all on one plane.  It's not an A sort of pyramid or something like that.  So it's square planar.  Now comes our bond angles.  So before we had said originally it was 90,  then we put a lone pair and we said, OK, now it's less than 90.  Well, what happens when we put another lone pair  and we put it here?  Is it going to be even less than 90?  Well, if you think about it, we have this pushing up.  We have this pushing down.  And they're both a lone pair, so they're  going to be pushing with the exact same force.  And so they balance each other out.  And so you're back to just 90.  It's not less than 90 anymore.  It's exactly 90.  This is pushing up with the same amount  that this is pushing down.  And so there's a couple of examples of those,  one of which we already have drawn.  And this ends up being like this.  So that kind of completes your worksheet in your workshop.  So now what we're going to do is we're  going to keeping all of this in mind  and stopping to sort of build these as you need to.  We're going to go back through all of those Lewis structures  that we drew.  We're going to decide what are the electron trees  and the molecular geometries of all of them.  OK.  So again, keeping in mind, there are some times  that I skip just because it doesn't really fit.  So great example of that in this one.  The N2, there's not really a geometry  to talk about here.  There's only two molecules, or there's only two atoms.  So we're only talking about geometries when they're bonded  to more than one thing.  So this one we're not really going to talk about.  So now if we look at this one.  So things to ask yourself when you're going through this  is what is the steric number?  What is the coordination number?  And then out of that, what are each of your geometries?  So to shorten this up, I'm going to use SN and CN  for steric number and coordination number.  I'm going to use EG and NG for electron geometry  and molecular geometry.  So if we look at our steric number,  we have one, two, three things bonded to it in no lone pairs.  We're just looking at our carbon, right?  We're not saying, well, there's lone pairs on the oxygen.  We don't care about the oxygen.  We're just looking at the central atom.  So one, two, three things bonded to it.  Sure, there's four bonds, but we treat double and triple bonds  the exact same as we do single bonds.  So our coordination number and our steric number are both three.  So for the sake of time, I'm just going to switch to using these.  So if we have this, we have three things bonded.  So we want to use the geometry that spaces them out the most.  And so we're left with trigonal planar.  And that, because our steric number and our coordination  number are the same, that's going to be both,  both electron and molecular geometry.  So that's how we do that one.  And again, we don't care that there's a double bond there.  We just treat that as one.  We're not counting bonds.  We're counting numbers of things that are bonded to the atom.  OK, now let's do this one.  Now this one's interesting in the fact  that we have two central atoms.  So what do we do?  Well, we look at both of them completely separately.  So we look at the boron, and then we look at the nitrogen.  Now in this case, they happen to be the same, but that's OK.  So if we look at boron, its steric number  is the same as this coordination number, right?  Because there's no lone pairs on it.  And both of those are equal to 3.  And so we're left with the exact same situation  we had in the last one.  And we'll use them all to get so you can see.  Something weird going on with the projector at the moment,  I think.  OK, well, we'll just keep it zoomed like that.  All right, so with the boron and nitrogen,  we're going to end up with the same thing that we did  in the last one, where we have these three,  and they're all evenly spaced.  And so we have trigonal planar for all of them.  Oh, wait.  No, our steric number's 4.  Sorry about that.  Steric number's definitely 4, so it's not trigonal planar,  right?  So now we have four of these things.  Space like this.  We have this spacing.  So if we look at this, we have tetrahedral.  And that's going to be both.  Because our steric number and our coordination number  are the same.  So now our nitrogen.  Our nitrogen winds up having the exact same thing.  Let's try to fix this a little bit here.  OK, so for our nitrogen, we have a steric number  and a coordination number both equal to 4.  So we have 1, 2, 3, 4.  And so we're left with the same thing,  where we have four things bonded to it, no lone pairs.  And so our electron is going to be  the same as the other two.  And so we have a star.  We have two things bonded to it, no lone pairs.  And so our electron geometry and our molecular geometry  are both tetrahedral.  OK, next one.  So now we have our xef4, 4 plus.  So same as before, we count our steric number  and we count our coordination number.  And in this case, they're the same.  So 1, 2, 3, 4.  So that means that our molecular geometry  and our electron geometry are the same.  And that's going to be tetrahedral.  For the same reason as before, we space them all out  in the most even way possible.  And that gives us tetrahedral.  OK, now we get to move on to our N2O.  And keeping in mind just our most stable one.  And again, we're just looking at our central atom here.  And if we have two central atoms, we'll  look at both of them individually.  So in this case, we're just looking at nitrogen.  And so there are two things spaced evenly across from each  other because it's linear, right?  Or it's 180 degrees across.  That's the way to spread two atoms out in the most even  way possible.  So we're left with a linear geometry.  So steric number 2, coordination number equals 2.  And our geometries are the same, and they're linear.  Yeah, it's a good idea to sort of have toothpicks with you  while you're doing these sorts of homework problems  and practice doing them with things in your hands  that you can play with and you can see the geometries.  If you just happen to be really good at seeing in three  dimensions, OK, maybe that's not so important to you.  But a lot of people, myself included, are not.  So now we have S, F6.  So when you look at this one and we decide what our  coordination number and our steric number is, we say,  well, how many things are bonded to it?  One, two, three, four, five, six.  No lone pairs, so they're both the same.  Now we have to decide what geometry is it.  So if you want to space these out all equally,  this is how you end up needing to do it.  And so you end up with six equally spaced of things.  It's shaped like an octahedron, then.  And so it's octahedral.  And the more you do them, the better you'll get at naming  them quickly.  It may take you a while at first to figure out the shapes  in your head.  Now it's time for a tricky one.  XEF4.  So if we have XEF4, originally we'll have a steric  number of one, two, three, four, five, six.  Because we count the number of bonded atoms and we count the  lone pairs.  But now our coordination number is going to change,  because our coordination number just  counts the bonded atoms.  So we have four.  And when we try to draw this out, we end up with a shape  that looks like this.  And for our electron geometry.  So if we have our electron geometry,  that's going to be equal to whatever this looks like,  which is octahedral.  Now we have to put two lone pairs on.  So we have to take two of these atoms and replace them  with lone pairs.  So again, we have to think about, well, are we going to put  them here and here, or do we want to space them out?  Of course, we want to space them out.  So we're putting a lone pair here and a lone pair here,  which leaves this as a square planar shape.  So and of course, our bond angles here,  which you don't want to forget, our bond angles here,  are they 90, 180, what are they?  Well, that originally started as 90.  And it's still going to be 90, because we have a lone pair  here and a lone pair here.  They're pushing on each other equally.  And so because of that, our bond angles here are still 90.  OK.  Next one.  So our HSO4.  So remember, this is how all of our oxoacids are kind of set up.  So it's always good to kind of keep this structure in mind  so that you remember them.  We have our oxygens all bonded to our central atom  and our hydrogens off our oxygens.  So if we look at this and we go through and we say, well,  we don't care that these are double bonds.  We don't care that sulfur is breaking the octet rule.  None of that matters to us for the sake of the geometry.  We've already talked about why those are all OK.  So for the geometry for the sulfur,  we're going to look at it and we're  going to say, well, there's four things bonded to it,  no lone pairs, one, two, three, four.  So both its steric number and its coordination number  is equal to four.  Now that means that both its electron geometry  and its molecular geometry are going to be tetrahedral.  Now remember we talked about having,  we can have two central atoms, right?  As long as something's bonded to more than one atom,  we can talk about it in the same way.  So we can do the exact same thing for the oxygen.  Now what's the steric number on the oxygen?  One, two, three, four.  So what's the coordination number on the oxygen?  It's just one, two.  It's the same thing for both oxygens.  Remember we're just talking about these, not these,  because these are only bonded to one thing.  OK, so now this is still going to be tetrahedral, right?  Because there's four things.  Now with this one, we had a tetrahedral electron geometry.  Now we have taken two of those and we've replaced two of those  with lone pairs.  And so that leaves us with a bent geometry.  But be careful not to see that, oh, we're going to have  two things bonded to it.  It must be linear, right?  Well, no, because we still have the electrons  that we have to worry about.  So even though there's only two things bonded to it,  there's these electrons that are taking up room.  And so it's keeping it in its bent form.  Now we're about out of time for the day.  So go home and practice doing all of these that we just did.  And we kind of skipped bond angles on purpose  so we can go back through them and talk about them again.  And the geometries again is a little bit of review  at the very beginning of next class.  So we'll finish up bond angles in next class.  And we'll finish up the rest of the Lewis structures next time.  In the meantime, go home, practice doing those,  see if you can fill in all the bond angles,  and then we'll check and see if you're right as of next time.  And then we'll take what we've learned  and we'll combine it with last class's lecture  where we talked about polarity.  And we'll actually be able to go through now and say,  well, based on the geometries and the polar bonds,  which one of these molecules are actually polar  and which ones aren't going to be polar?
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