Molecular Geometry and Bonding Theory Molecular Geometry and the VSEPR Theory Molecular Shapes for Steric Number 5 & 6 Page [1 of 3] Okay, let’s keep going and look at steric number 5, which it turns out is the most complicated of all of the possibilities. The reason is that steric number 5 is dictated by something called the “trigonal bi-pyramid,” and the trigonal bi- pyramid is characterized as having three that are at the corners of an equilateral triangle, and I’m going to hold that flat, and then there’s one at the north pole and one at the south pole, and you can see that the three that are in the plane, and then the one at the north pole are at the vertices of a pyramid. And then if we take the three in the plane and consider the one at the south pole, we have another pyramid, and so these are sort of back-to-back pyramids, hence the name, trigonal bi-pyramids.
Now, one thing that makes that trigonal bi-pyramid really complicated is the fact that in the trigonal bi-pyramid all of the positions are not equivalent, whereas in the idealized tetrahedral geometry, for instance, all of the positions are exactly equivalent. That is to say that the trigonal bi-pyramid has something more in common with something like a lemon, which is not perfectly spherical or not as highly symmetric compared to a bocce ball, which you can see is very highly symmetric. The trigonal bi-pyramid is of lower symmetry. When we look at steric number 6, steric number 6 is build on the octahedron and once again will have that very high symmetry where very atom position is equivalent to every other atom position.
So we have a distinction, and that distinction we’re going to label axial, for the two that are at the north pole at the south pole, and I’ve put these in yellow to remind you that there is this distinction, and then the three that are in the triangular plane, we’re going to call these equatorial. So we have axial and we have equatorial.
Now, the bond angles in the trigonal bi-pyramid, there are three different bond angles. There is the 90-degree bond angle between the north pole and any of the balls on the equatorial plane, or for that matter, the south pole and any of the balls on the equatorial plane—that’s 90 degrees. And then from the north pole to the south pole, of course, that’s 180 degrees. And then the third bond angle is from one equatorial atom to another equatorial atom. That’s going to be 120 degrees. So there are three different bond angles in the trigonal bi-pyramid.
Now, the molecule that has the idealized trigonal bi-pyramidal geometry, or an example would be something like phosphorous pentachloride, . And if you look at this picture here, I’ve labeled the chlorines that are equatorial, of which there are three. The way we draw this, a solid wedge is drawn to indicate that this one is coming out towards you. So it’s not in the plane, but it’s coming out towards you. And then the dashed line, that chlorine atom is going into the plane away from you, whereas these three chlorines, where we draw with just a single line, these are done to indicate that these three are in the plane. And so it’s possible, for instance, if we set it up like this, you can see that the north pole and the south pole, and one of the atoms in the equatorial plane are all in the same plane with the phosphorus atom, and then there’s one atom going towards you and one atom going away from you. So that’s the way we indicate it when we have a model for which we need to express three-dimensional geometry.
So that’s the idealized trigonal bi-pyramid, but what happens if we have a lone pair? Why is this a problem? The problem is we have to decide should the lone pair live in an equatorial position or should the lone pair live in an axial position, because that’s going to give rise to two different predictions about geometry.
Now, the rules—and I’m just going to list them off now and then show you how they work—are that rule 1—eliminate any structure that has lone pair/lone pair interaction at 90 degrees. Now, that rule is not going to be important for steric number 5, but it’s going to be very important for steric number 6. And then the second rule is of the remaining structures, choose the one with the fewest lone pair/bond pair interactions at 90 degrees. So again, the magic angle is 90 degrees. That’s what we need to focus on.
So let’s consider a model of sulfur tetrafluoride, , and if we think about what the Lewis Dot structure for looks like it’s going to have single bonds between sulfur and each of the four fluorines, and then there’s going to be a lone pair. And that lone pair on sulfur we’re just going to indicate with this cloud where there’s the lone pair there. Now, you don’t see the lone pair, so when we’re describing the shape of the molecule, we’re just going to focus on the relative positions of the nuclei, just like before.
But we can ask does that lone pair live or prefer to live in an equatorial position or does it prefer to live in an axial position. And so now we have to think about our rules. Since we only have one lone pair in each of these two structures, we don’t have to worry about the lone pair/lone pair interactions right now. We only have to worry about
Molecular Geometry and Bonding Theory Molecular Geometry and the VSEPR Theory Molecular Shapes for Steric Number 5 & 6 Page [2 of 3] lone pair/bond pair interactions. I just realized I misspoke before. We are going to have to worry about rule 1 later on, but we don’t have to worry about rule 1 here.
So let’s count the lone pair/bond pair interactions at 90 degrees. For this possible structure we have one to that fluorine, and we have one to that fluorine for a total of two. Whereas, for this structure we have one to that fluorine, and one to that fluorine, and one to the fluorine in the back, so we have a total of three. And recall that rule 2 says that we want to minimize the number of lone pair/bond pair interactions. Why do we want to do this? Well, it turns out, again, that lone pairs sort of seem to take up more space. And you’ll recall that electrons, being negatively charged, repel each other. And so what we’re basically saying is that we’re trying to minimize the coulomb repulsions, or the repulsions of electrons for each other by minimizing these lone pair/bond pair interactions, where again, lone pairs seem to be bigger. They have a greater physical extent, and so they’re the thing that we need to focus on most.
So given that, this structure has fewer lone pair/bond pair interactions, this is going to be the preferred geometry for sulfur tetrafluoride, and if we go back to our trigonal bi-pyramidal structure, remember, lone pairs just represent the absence of an atom, and so what we’ve got is we’ve got something that looks like this. It’s still built on the same model, but there’s a lone pair out here that affects the geometry. So this is most definitely—so sulfur tetrafluoride is most definitely not a tetrahedral molecule. Right? What is it? Well, we describe this geometry as being a see-saw. Why is it a see-saw? Well, you can see that if we put it on its side it looks a little like a see-saw.
Now, what are the bond angles? Just as before, since the lone pair appears to take up a little more space, you might imagine that the north pole to sulfur, the south pole angle is going to be a little bit less than 180 degrees, but not much, and similarly the equatorial fluorine to sulfur to fluorine, that bond angle might be a little bit less than 120, but pretty close to the idealized bond angles for the trigonal bi-pyramid.
Okay. What happens if we have steric number 5 and two lone pairs? If we have steric number 5 and two lone pairs, then what we have to do is we have to consider rule number 1, and I’ll remind you that rule number 1 says avoid lone pair/lone pair interactions at 90 degrees. So chlorine trifluoride is an example of a molecule that has steric number 5 and two lone pairs. And you can convince yourself from a Lewis dot structure that that should be true. First of all, rule 1 says throw out any structures that have lone pair/lone pair interactions at 90 degrees. So let’s look at our possibilities. Why do we have three possibilities? Well, if you think about it, the three possibilities where two lone pairs are having both lone pairs equatorial, that’s this one, having both lone pairs axial, that’s the middle one, and then the third one is having one lone pair equatorial and one lone pair axial, and you can convince yourself that there really are only three possibilities. Well, of these, the only one that gets thrown out because of rule 1 is the third one here, which has one lone pair equatorial and one lone pair axial. Why is that? Because the relative orientation of these two is 90 degrees. So this one is out. And now we have to consider of the remaining two—and again, this one is out because of rule 1. And now, of the remaining two, which of these is preferred based on rule 2?
So let’s count lone pair/bond pair interactions. We have, for this one, from the cloud that’s sort of coming towards you, we have a lone pair/bond pair interaction of 90 degrees to the fluorine at the south pole, and then another one to the fluorine at the north pole, and then similarly for the back one, we have one to the north pole and one to the south pole. So there are a total of four lone pair/bond pair interactions with this geometry of the chlorine trifluoride molecule. And if we go to this middle possibility, we’re going to see that there are six because there are one, two, three, from the lone pair that’s living at the south pole, and then there are going to be three more from the lone pair that’s living at the north pole, and so there are going to be a total of 6 lone pair/bond pair interactions for this shape.
And so maybe your intuition said that the chlorine trifluoride molecule should adopt its most symmetrical structure, and that turns out not to fit with reality. Remember, this is all about making a prediction from the model and checking to see what the reality is. And the reality is that the chlorine trifluoride molecule has a t-shape. Why is it called t-shaped? Well, here’s our trigonal bi-pyramidal structure again. If we take out another atom then you can see that this is the former equatorial plane—this is the north pole and this is the south pole, and so now we have a molecule that is t- shaped. And again, there will be slight distortions because the lone pairs seem to take up more space. This bond angle from here to here, going this way is probably going to be a little bit smaller than 180 degrees, so these will be bent downwards just a little bit.
Molecular Geometry and Bonding Theory Molecular Geometry and the VSEPR Theory Molecular Shapes for Steric Number 5 & 6 Page [3 of 3] Last one—let’s think about steric number 5 with three lone pairs, and we’re going to use rule 1 a couple of times here. Rule 1, again, get rid of any structures that have lone pair/lone pair interactions of 90 degrees, so that means this guy. There’s a lone pair sitting in the equatorial site, that’s an axial site, so that’s a 90 degrees, so this guy is out. And similarly, that’s equatorial, that’s axial, that’s 90 degrees, so this guy is out, and so all we’re left with is we’re left with putting all of the lone pairs into the equatorial sites, and that gives that the triiodide anion is a linear molecule, and so again, trigonal bi-pyramid, but now we’ve totally removed the atoms from the equatorial plane, and so we have what’s left. Triiodide in a linear molecule.
Let’s summarize for steric number 5. It’s built on the model of the trigonal bi-pyramid, but once you start introducing lone pairs you can have a see-saw shape, a t-shape, and a linear shape. Try to remember that your intuition of making things as symmetrical as possible is not going to hold, necessarily, for steric number 5.
Now, when we go to steric number 6, steric number 6 is built on something called the octahedron, and the octahedron, if you think about this, these atoms are at the face centers of a cube. So in other words, if you put a cube over this whole thing, and then you put a point in the middle of each face of a cube and drew a line from the center of the cube to the face center, you’d get an octahedron. In the octahedron all the atoms positions are equivalent again, so we don’t have to worry about axial and equatorial the way we did with steric number 5. So the molecule with the idealized octahedral structure is sulfur hexafluoride, , and you can convince yourself from the Lewis dot structure that the steric number at the sulfur is 6 and it has no lone pairs, so sulfur hexafluoride would look exactly like this with 90 degree fluorine, sulfur, fluorine bond angles.
Now, if we consider bromine pentafluoride, which has the same steric number as sulfur hexafluoride, but it’s got a lone pair, and so the lone pair we represent by pulling out an atom, but remember, it still has an influence, so that’s why we’re building it on the octahedron. And this is what bromine pentafluoride looks like. It looks like a square pyramid. So the square is the base of the pyramid and then this would be the top of the pyramid. Now, because the lone pair seems to be a little bit bigger, it’s going to push these guys up a little bit, and so this bond angle from here to here is probably going to be a little bit less than 90 degrees, but for the most part it still looks like a square pyramid, and this is the geometry for bromine pentafluoride.
And finally, if we go to xenon tetrafluoride, which has steric number 6 with two lone pairs, the two lone pairs have to be opposite each other. We use the word “trans” to indicate that they have to be opposite each other on the molecule, and the reason is if they were perpendicular to each other, for instance, if we put the lone pairs here so now one is out here and one is over here, then you could see that’s a 90 degree interaction and that’s no good by rule 1. So we’re going to put the lone pairs opposite each other, trans—I mean, you could think of it as they’re both axial, and the geometry that results for the xenon tetrafluoride molecule is square planar, where now because the lone pairs are sort of both working exactly equivalently, these turn out to be exactly 90 degree bond angles again.
Okay, so let’s summarize. Steric number 5 is built on the trigonal bi-pyramid and you have to use the rules of considering lone pair/bond pair interactions to decide exactly what the geometry of the molecule will be. For steric number 6 it’s built on the octahedron and you once again have to use the rules, but you only have to use the rules for xenon tetrafluoride, and I think it’s reasonably clear why xenon tetrafluoride should be a square plane.