Principles of Chemical Science/nVideo Lectures - Lecture 29/nTopics covered: /nThe Shapes of Molecules: VSEPR Theory/nInstructor: /nProf. Catherine Drennan/nTranscript - Lecture 29/nMonday's class really picks up from the lecture we had this past Monday. We started crystal field theory and then talked about octahedral-shaped molecules and splitting of d-orbitals. And then on Monday, we are going to continue with that topic./nWe are going to move in and talk about tetrahedral molecules, square planar molecules and how they are going to split the d-orbitals. And then how that relates to something, why we need to know about any of that. And that is because it is able to predict some of the properties of molecules, like their colors and also their properties in terms of spin and using various different spectroscopies to learn something about particular molecules, coordination complexes./nBefore we get into that unit, we are going to kind of take a step back and talk today about shapes of molecules. We introduced octahedral, but now we are going to talk about all the other kinds of shapes of molecules in today's lecture. This is kind of jumping around in the book a little bit. We have been in Chapter 16. And now, the way the book is divided, this particular unit is back in Chapter 3, although it is referred to a lot in Chapter 16. This is kind of some of the things that you need to know to finish up Chapter 16. And then on Monday we will be back in Chapter 16 as well. Again, this is a little bit odd order because of the way the calendar fell this year. All right. VSEPR, shapes of molecules, why do we need to know about this?/nWell, as most of you know, I do protein crystallography, which is all about structure. So, of course, I am going to think that structure is important, that shape and geometry are important. And, in fact, they have an influence on the physical properties and chemical properties of molecules. Things like melting points, boiling points, reactivities, and, in particular, in biological systems it is important./nA biological system has particular shapes of chiral molecules, it is a chiral environment, which we have talked about before. And so molecules must fit precisely in that environment. Often, if you are talking about an inhibitor of an enzyme, the inhibitor or the pharmaceutical drug is designed so it specifically fits into a particular crevice in an active site and blocks activity. A lot of the world of pharmaceuticals is all about shape of molecules and how you design particular types of shapes of molecules./nWe have learned a lot about this sort of area already, and we found that the shapes of molecules can be predicted pretty well using simple methods based on Lewis structures and also in terms of thinking about sort of where orbitals are and how that may affect the particular shape of the molecules. Again, this is sort of a simplistic view that works pretty well. And it will be also, on the next problem set, a good opportunity for you to review Lewis structures before you take the final. Sometimes this unit is with Lewis structures, there is some rationale for that, but it is also kind of nice to come back to it later in the semester as a way to review things that you learned before and get you ready for the final exam. The particular theory we are going to talk about today is referred to as VSEPR. And this is the valence-shell electron-pair repulsion theory./nAnd so, like crystal field theory, you are talking about repulsive effects. Here this is based on a simple principle that valence electron pairs will repel each other and that the geometry around a central atom will be such to minimize that repulsion. This is a lot like crystal field theory, where we were talking about the splitting of the d-orbitals. And we are talking about ligands as negative point charges heading toward those d-orbitals. A lot of these theories that work pretty well are just really based on the idea that repulsion is unfavorable. It is a pretty simple concept which can explain a lot in terms of properties of molecules. Before we get into this, there is always nomenclature that we must deal with. And here is the nomenclature here. We have A as a central atom./nWhatever is in the middle, which when we are talking about transition metals, complexes would be your metal, but this works for organic chemistry as well, when you are all talking about carbon, oxygen, sulfur, nitrogen. And X is going to be your bound atom, and E will be a lone pair of electrons, hence the E. There are just a few rules. It is not too bad compared to some of the other things we have done. Just a handful of rules that you need to know. First, you need to know that the steric number, abbreviated S.N., is used to predict geometries, and what steric number refers to. It refers to the number of atoms bound to central atom, plus the number of lone pair electrons on the central atom./nHere we are not concerned about double or triple bonds. We are only concerned about how many things are around our central atom, both the bonded and the lone pairs. Whether it is a double or a triple bond doesn't matter at all for these cases. It is the number of atoms bonded, not the number of bonds, which is important to remember. And so steric number, here, should not be confused with coordination number, which we talked about in transition metals, --/n-- which is just the number of ligands around the central metal. So, there are a number of different things that you are going to learn about. All right. For resonance structures, you can imply a VSEPR to any one of them. And there are two cases that we need to consider today. One is the case when there are no lone pairs, and other is the case when there are lone pairs. Those are all the rules. It is really not too complicated for this. We are just going to go through today and look at all these different molecules and consider the nomenclature and the geometry around them. First, we will consider formula type./nAnd so AX two would mean that you have a central atom A, and we have two atoms bound to it, so two Xs. And now we are considering the cases without lone pairs of electrons, so there won't be any Es until later. Then the steric number is going to be two. And so here would be the shape of the molecule. And so we have a center atom and two atoms bound to it. It would have linear geometry and a bond angle of 180./nThat is pretty simple. Now, we go to the next category, where you have three things bound, so that would have an SN number of three. And this is going to be the shape of that molecule. And what is this called? Trigonal planar. And what are the angles? 120. Okay. Now, if we move up to four, and this one should be pretty familiar to you, if we have four things bound, SN number of four, this is the molecular shape that we have. And you all know this as tetrahedral. And the angles of tetrahedral are 109.5. These are all things you have to memorize./nThis is written in your notes, but if you don't look at your notes and just try to think about it, it will be a good review for the next exam on this topic. All right. If we go into the next category, when we have five things bound, that would be AX five, five atoms bound, SN number of five. We have this trigonal bipyramidal geometry. And what are the angles around the equator here connecting the red atoms? 120. And what about red to black? 90. All right. Then, if we go to the next category, when we have six things, we talked a lot about this in the last two classes, what kind of geometry is this? It is octahedral geometry, with angles of 90./nRight. These are all the basic shapes when you just have two through six atoms bound. Let's take a look at a couple of examples of molecules when we have actual atoms listed. If we look at CO two, what is our SN number? Two, right. We are only considering the number of atoms bound. We don't care that they are double bonds. We are only concerned with the atoms that are linked to the central atom here. Then the geometry is what? Linear. And angles? 180, right. We will look at another example here. Is this one going to be the same or different from the one above? The same, right, because we don't care about the double or triple bonds. We can go through. SN number is still two./nIt is still linear. And the angle is still 180. We move into another example here. And I will just say that these lecture handouts have this information in here. This is the most requested lecture handout that I have from people who have been in the classes who get up to other level classes and need to know this stuff. And, for some reason, some of them have not kept their 5.111 notes sort of next to their pillow in later years./nI am not really sure why, but sometimes it gets lost and they request this handout, because it is a really nice summary of all of these things. You might want to keep it in a nice special place for future reference. All right. Some day I should bring in what my freshman chemistry textbook looked like with like everything highlighted and stuff just for entertainment value. All right. This molecule here would have a SN number of three. And its shape again? Trigonal planar. And angles? 180. By the time you get through with lecture today, you should have all of this memorized, because we are going to see these a couple more times. All right. This one, what molecule is this? Does someone know its name? Methane, right. Again, what is this geometry?/nTetrahedral. SN number of four. And angles of? 109.5, right. Okay. Now we get into a few more complicated molecules that you do not see quite as often, although I think we have seen this one quite often in different kinds of problems, including chemical equilibrium and other things. SN number here? Five. Geometry? It is hard to say that one in unison. We can work on this for the end of lecture. Then we can all say it in harmony. All right. And our angles again? Yeah. Okay. And one last one. This should be very familiar to you. This is SN number six. Geometry? Octahedral. Angles? 90. Okay. People are doing well./nHere is some stuff that you may not have heard before, or maybe have in another chemistry course, but now we are going to introduce lone pairs and see what effect this has. It gets a little bit more complicated at this point. For lone pairs, we think of them as being sort of centrally located. And I brought in some props to talk about the spatial distribution of electrons. One can imagine that the electrons are spread out as far as they can go. They like to have a lot of space. And so the lone pair electrons are going to take up more space and experience more repulsion then when you have the electrons as part of bonds to atoms. The lone pairs are not sort of held in as much, they are not sort of forced to be in one location, so they will spread out more./nAnd so because of this, their spreading out more, they are taking up room, they are kind of pushing everything away, because they want to have as much room as they possibly can. That means that lone pairs are going to be more repulsive than the atoms that are bound. Even though electrons are involved in those bonds, they are not quite as bad. The worst thing you can have is two sets of lone pairs near each other. They want all the room./nAnd so they are going to be sort of bumping into each other and trying to force the other set farther away. See, this is much more bulky than if you just have the two atoms bound with bonds to a central atom. The next would be a lone pair versus a bonding pair. And then the least repulsive will be two bonding pairs because those electrons are sort of fixed into locations for the bonds. They are not requiring as much space./nThey are not sort of spreading out and taking over all the space that is available. Worst is lone pair-lone pair, then lone pair bonding, and then bonding-bonding. And, if you think about this sort of simple rule, you can predict a lot about the shapes of molecules. Let's look at what shape something will have if it has this sort of set molecule. Again, A, the central atom. X is four atoms that are bonded to the central atom, and E is one set of lone pair. And so this is going to have what is known as a seesaw shape. And let's think about why that would be the case. If we have this sort of central framework, but one of these bonded atoms is now going to be replaced with a lone pair. There are five things around this framework./nOne is a lone pair. Where are you going to put it? If we put it on top, what are the angles between these lone pairs on top and the three red bonded atoms? 90. That is kind of close and not so favorable. If we instead put one over here, then we have still the sort of negative interaction with the 90 here and the 90 here. But we only have two of them instead of three. And these guys are 120 apart, so it is not so bad. There is a little bit more space in the equatorial position. And so that is why you get this seesaw shape, because you would want to put it in the equatorial position, where there is only sort of these two rather than three./nThere is just a little bit more space, because these guys are farther away. That gives rise to seesaw geometry. You can sort of again, these rules are more to explain in retrospect what is observed about those molecules, and then you rationalize. But the rationalization works pretty well. If we do that, if we put a lone pair, then, here, instead of one of these top positions, we get this seesaw geometry./nAnd so let me help you remember this. See? Get the seesaw geometry. How many of you actually grew up with seesaws in the neighborhood playground? Still most people, okay. They are actually one of the most dangerous toys. And I think a lot of playgrounds have removed them because of the one kid who sort of sits on it and keeps you, like, stuck up in the air because they are a little heavier than you are./nAnd you are stuck there for a really long time, and then eventually they get up and you go falling and flying. We may have to give this a new name at some point when all seesaws are removed from playgrounds, but it sounds like it is still usable. Now, if we wanted to put another lone pair on that same structure, we still have essential atom, three atoms bound. Now we have two lone pairs. Those two lone pairs, then, will go into the equatorial positions as well. And so you kind of have this sort of arrangement. And they were so repulsive they actually made the atom unbonded from it. Okay./nThat leaves you with this shape, which is a T-shape molecule. Again, this is a rationalization. Someone figured out that a molecule like this had this T-shape ad it could be rationalized by the fact that the lone pairs wanted to sort of fill out in that equatorial plane. And they could move away slightly from each other, and that would minimize the amounts of repulsion. All right. If we keep going here and look, now, at a molecule with this geometry, AX four E two molecule. That is based on kind of what structural framework? What is the sort of parent structure when you have six things bound? Yeah, based on an octahedral geometry./nIf you take your octahedral molecule and if you want to figure out where you are going to put your lone pairs, you could stick one down here in the equatorial, but that doesn't do you as much good this time because now your other equatorial things are at 90. This one would have a lot of crashes down here. What ends up happening is the two lone pairs would go one above and one below, so they would be as far away from each other as possible. You have one below and another one on top. And remember, the worst thing to have is a lone pair-lone pair. Even though you have four atoms at 90 that it is interacting with, at least it is far away from the other lone pair./nEach kind of gets half the molecule, one up top and one on the bottom, so they have the most room, those electrons, to spread out. And so that gives you what kind of geometry? Square planar, right. All right. You can also predict something about what might happen to the angles that you have all now pretty much memorized on the previous slides. That if you do have a lone pair, and out here we have an AX three E, SN number of four, so four things bound, one lone pair and three atoms, and this is based then on what kind of structure? With SN number of four, what is the kind of the parent geometry there? Yeah, tetrahedral is the parent geometry./nAnd now we have replaced one of the bonded atoms with a lone pair. And so what that is going to do is that lone pair is really not in that bad of shape. You put it on top. You have 109.5 now between those angles pointing down in the parent geometry. And that was better than the others which were at 90, but it is still not good enough for it. And so it actually presses down even more. Those lone pairs, they are going to spread out as much as they possibly can and repel those bonded atoms away to the extent possible. In this molecule, what is observed is that the angles in between here, in between the hydrogens, instead of being 109.5, which is what you would expect for the true tetrahedral geometry, they are 106.7. This lone pair is pressing down, compressing the bonded atoms even closer to each other than what is sort of the normal framework./nThis really takes up a lot of room here and is repulsive toward these bonded angles. Again, the VSEPR theory can predict these kinds of, or really explain these kinds of changes. If you observe the smaller angle you can say, oh, there was a lone pair. That makes sense that it would be a smaller angle because there would be repulsion down. Again, you can think about it. You can make one of these lone pairs yourself, low tech and think about the shapes here. All right. We can also rationalize the difference between a PH3 and NH3 molecule. They have pretty much the same framework here, based on tetrahedral geometry AX3E, SN number of four./nBut now, instead of the number for methane that we saw of 109.5, and instead of the 106.7 for NH3, we now get a really small angle between here, between the angle between hydrogen and phosphorus. And hydrogen is now 93.3, so it is even more compressed. And the reason why is because we are moving down in the Periodic Table. And so as we move down the column in the Periodic Table, we are going to have lone pairs that have even larger spatial volumes. And so they are going to compress even more. Now it is an even bigger sort of situation here. The lone pairs are trying to fill up even more volume./nAnd so they are sort of trying to compress as much as possible these atoms away. They are filling up all available space and making the angle here even smaller. And so if asked about this, if asked to predict, you could sort of look at where things are in the Periodic Table. Here is nitrogen, here is phosphorus. And so if we had a compound based on nitrogen or phosphorus that was based on tetrahedral geometry, one might expect that the angle becomes even smaller as you move down the Periodic Table, as that lone pair that is on there is filling up even more and more spatial volume. This kind of combines ideas of trends in the Periodic Table with shapes of molecules. All right. Another thing that you can sometimes predict is about bond lengths./nIf you experimentally observed different bond lengths in a molecule, you could use VSEPR to go back and think about where that may have come from. What is this geometry here, the one that is shown and also the parent geometry? The one that is shown is what? Seesaw. And the parent geometry? Right, trigonal bipyramidal. All right. Here we have AX four E. We have an SN number of five. We have four atoms bound. We have one lone pair. And now it is observed that there are two sets of SF bonds. One set is 1.545, and one is 1.646. What do you think those different bond sets --/nThere are two types of bonds. We have one lone pair. Likely one set would involve the gray atoms, and the other would be the black atoms. Which do you think would be longer? Do you think the gray or the black would be longer, the bond lengths from the central atom to the gray or to the black would be longer? Gray. And why is that? Right, because these are at 90 going down. Whereas, this is at 120. The 90 is more repulsive, so it basically kind of pushes that up farther and down farther, moves them farther away. The black atoms are already farther and won't feel the repulsion as much./nAnother way to sort of, if you have a lone pair here, for the lone pair to feel like it really has the space that it requires, is to sort of repel the atoms that are closer in terms of distance, repel them just a little bit farther away. And then it can kind of fill out and feel like it has enough space. Again, if you had an experimentally observed set of bond lengths, you could rationalize using VSEPR, why you would have this./nOkay. As we said, more repulsion between the lone pair electrons and the axial ones because those are at 90, so those would move farther away. That is a lot of the theory. Now we are just going to run through these sheets and talk about the different types of geometries, the names of the different types of geometries when you have the lone pairs on there. And then look at some examples. Again, if you call out the answers, and if we go through this quickly, this is all that we need to go over for today, and it will be a good review. You will sort of have the opportunity, today, to memorize this. You might want to go back over it a couple times, but pretty much this is the whole unit. It is not too challenging. If we have AX two E, we are going to have a SN number of three./nAnd a molecular shape. I will draw that. And what is the name of that geometry? It is bent. And that is because you are only considering the bonded atoms. You are not talking about the lone pair. We don't really see the lone pair, two bends, and so it would just look bent to us. That is where that comes from. And what angles would this have for this particular case, SN number of three? Okay. We have this one here. The SN three would have a trigonal planar parent geometry./nBut if we take a lone pair and put that on instead of an atom, then it will also be somewhat compressing of those two atoms down there. We won't really know, without knowing what the central atom is, we cannot really predict how bad the compression is going to be. What you would put is less than 120 here, because it would be 120 if this was an atom and not a lone pair. If this is a lone pair, then it is less than 120./nAll right. Here is another case. Now we have three atoms bound, one lone pair, SN number of four. And our parent geometry here would be tetrahedral. And now we have a lone pair. We saw this a little bit before. And what is that geometry called? Here, we have this picture. What is this called? Trigonal pyramidal. We have this. And what would the angles be here? Less than 109.5. All of you should know the answers because they are actually in your handout, so feel free and confident to yell them out. All right. Again, this is going to be less than 109.5 because we have a lone pair pressing down./nYou have to in all these cases consider what the parent geometry is. And then the angles are going to be a little less than that if you have one lone pair sitting on top. All right. AX two E two has a SN number of four. All right. What geometry is this based on? Yeah, tetrahedral again. We have two lone pairs on that. And what does that look like it should be called? Bent as well. And now the angles are going to be less than 109.5. So, you see, we have two bent molecules, but the angle isn't the same. It depends on whether it is based on a trigonal planar or it is based on tetrahedral. You need to sort of know what the whole molecule was to figure out what degree of bend you have in these two./nAll right. AX four E has SN number of five. And so our shape here, what is this one going to be? Yeah, this is going to be a seesaw. And so what are our angles going to be? Right, less than 120, less than 90. It could be that really the 120 are not going to be that affected, but that will be what you will put down because you don't really know. This is just a rough predictor of what those are going to be, so it is less than what the parent molecule was. All right. SN number of five. And so what are we going to be doing here? We are going to add another lone, take off an atom, add another lone pair./nAnd what are we going to get here? Right, T-shaped. And the angles will be... At this point is our T-shape, and so we will have less than 90. You will have the two lone pairs in the equatorial position, as we talked about before, trying to spread out as much as they possibly can. Now we are replacing another one with a lone pair. Another bonded atom. Our SN number is still five. And what shape are we going to get in that case? Linear, right. They all go in these equatorial positions to spread out as much as they possibly can. And so we are going to end up with a linear molecule, so we would replace here. And what are our angles here? They are exactly 180. Yeah?/nIt could be that there would, but they probably will just be really spreading out around to fill out as much room as possible around the whole equatorial place. You can just sort of think about it as if there was space, they would move into it, so they have really filled up this space. And pretty much you might as well keep them there, because whichever way they move, they are just going to get repelled in another direction./nThat's kind of the one exception, are these ones that turn out to be linear. There is one other exception where the angles are not going to change as well, where you have orbitals on kind of either side that counteract. That is a good question. All right. One more. We have AX five E, SN number of six. This is based on what parent molecule? Octahedral. We are going to take off one ligand, and so this would be, if we removed one of the ligands here, we get this parent shape, which is called square pyramidal. And what are the angles going to be, here? Less than 90. Okay./nEvery year, when I do this unit, I like to reward people who are in class. And so I give a little hint about the final. And the hint will be that this will be on the final, [LAUGHTER] so you might want to put that down. The last couple of years I did seesaw, which really is my personal favorite, but at some point I have to switch. This time it will be this one. And it is always so sad to me when people get that one wrong, so please get that one right. Okay. Let's keep going. SN number is six. And so we are going to put on another lone pair. And where are we going to put it? We are going to try to move it so that there is the least amount of repulsion between the lone pairs, so it is going to be up on top./nThis geometry keeps the lone pairs as far away from each other as possible. And what is the remaining thing called when you have those lone pairs on there? That is going to be square planar. And what about the angles in this case? In this case they are just 90, because you have a lone pair on top pushing down and a lone pair on the bottom pushing up. This is another example where it is not less than. All right. Next one. We add another lone pair. And at this point does it matter where you put the lone pair? No. They are all equivalent positions, so it doesn't make any difference. It is going to be one of these guys gets replaced, and so that is going to leave you with the what geometry?/nT-shaped. And angle here is going to be this time less than 90, right, because it will repel this one and this one if you have a big lone pair in this position. All right. One more. Again, the same geometry. We take another bonded atom off and put another lone pair. And what are we left with in this case? Linear. Again, this is going to be 180. All right. Now we have looked at all of those, and we can very quickly go down. And in this handout, I have most of it written. I don't have the angles, so that you can write the angles in and have your complete set for this as well. Now let's look at water. The Lewis structure for water, you would end up with two lone pairs on the oxygen./nAnd so what formula type would this be? AX two E two. SN number of four. Geometry? Bent angle. Less than 109.5, because this is based on the tetrahedral geometry. Remember, bent could either be less than 120 or less than 109.5, but if you have a SN number of four then it is based on tetrahedral geometry. It would be less than 109.5, which is the tetrahedral angles. Okay. SF four, here is our structure. Formula type for this would be? AX four E. And that is a SN number of five. And the shape? Seesaw./nAnd angles? Yeah, less than 90 and less than 120. Here is another one, BrF three. These are all probably ones that you did Lewis structure for. If not, I am sure you will before the final. Here is another one. The formula type for this would be AX three E two. And SN number? Five. And geometry? T-shaped. Angles? Less than 90. Okay. If we keep going, here is another example, selenium and fluoride. And we have three sets of lone pairs. What is the formula type? AX two E three. SN number of five. Geometry? Linear. Angle?/n180. Okay. BrF five. Formula type? AX five E. SN number? Six. Geometry? Square pyramidal. Angles? Less than 90. You want to remember that one. Okay. Here is another one with an addition lone pair. Formula type? AX four E two. SN number? Six. Geometry? Square planar. Angle? 90, exactly. That completes that list. Again, the theory of VSEPR, you are taking experimental results and then trying to apply a theory to it. It is not good at really making exact predictions about things./nBut it is really good at rationalizing what they have. All right. Have a wonderful Thanksgiving, everybody.