Molecular geometry (VSEPR theory) | Chemistry | Khan Academy

A molecule of carbon dioxide is pretty much straight, whereas a molecule of water is bent. Why the difference? More importantly, is there a way to predict what the shape looks like in three dimensions of any molecule? The answer is yes, by using a theory called valence shell electron pair repulsion theory, or VSEPR for short.

So, in this video, VSEPR is going to help us predict the shapes of different molecules by using their Lewis structures. Let's begin. Let's directly start with an example. Say we have methane; its Lewis structure is given this way. Remember, Lewis structures do not give us the shape of the molecule—that's what we want to figure out.

Now, how does VSEPR help us predict the shape of methane, for example? VSEPR says look at the central atom, which in this case is carbon, and count the number of electron groups around it. For example, the electrons that are participating in the bond: well, there's a group over here, and there are a couple of electrons, so that's one group. Here’s a second group, here’s a third group, and here’s a fourth group. So, in this particular case, there are four electron groups around the central atom.

A quick question could be, why do we say electron groups and not just bonds? Well, as we will see, that it not just applies to bonds; it applies to other things as well. So think of it as electron groups and not just bonds. Okay, and VSEPR says that these four groups of electrons are going to repel each other, which makes sense, and then arrange themselves in such a way that they’re as far away from each other as possible, as big an angle that they can make as possible.

Now, in two dimensions, if you had to do that, if you had to spread them out evenly and as far away as possible, this is what it would look like at 90 degrees apart. But remember, our molecules are in three dimensions. In three dimensions, they’re going to spread out like this, with the angle between them more than 90 degrees. Actually, the angle turns out to be 109.5 degrees. The angle between any two bonds over here would be 109.5 degrees.

It's hard to see it in the picture, but I have in front of me a model over here. Look at that; the angle between all the bonds is exactly the same. They are the farthest apart in all three dimensions. We give a name to this shape: we call it a tetrahedral geometry. We call it so because the vertices over here lie at the vertices of a tetrahedron. A tetrahedron is basically a pyramid with a triangular base.

Anyways, we have found the shape of methane: it's tetrahedral, with carbon at the center and the four hydrogen atoms over here. The bond angle is going to be 109.5 degrees. Now, let's go to the next one. Next up, we have ammonia, whose Lewis structure looks like this. Remember that nitrogen has a lone pair over here.

Anyways, we have one, two, three bonds surrounding the central atom, right? But VSEPR says, "I don't care about the number of bonds; I care about the number of electron groups." Okay, so if we count, we have one, two, three, and the lone pair of electrons is also an electron group, right? Because VSEPR says I don't care whether the electron group is bonded or not bonded or whether it’s a lone pair; what matters is the number of groups.

Then, there are four groups. So even in this case, there are four electron groups around the central atom. This is the reason we say electron groups and not bonds. Okay, by the way, the technical name is electron domains, so there are four electron domains, but you can think of this as electron groups.

Anyways, the good news is since this is basically four electron groups, we already know what the shape is going to look like. Anytime we have four electron groups, the shape will always be tetrahedral—boom! Got it. But there's a tiny difference; it’s just that here, because there are only three actual bonds, only three of these will be actually hydrogen atoms.

So, for example, only three of these will be hydrogen atoms; the fourth one is occupied by the lone pair. This is something how we show it, and a small detail over here is because the lone pair electrons are not bonded, they are very close to the nucleus of the nitrogen. Unlike the electrons over here, which are shared between the nuclei of nitrogen and hydrogen, the lone pairs will have much stronger repulsion compared to normal single bonds.

Therefore, they're going to push on these bonds slightly more than usual single bonds do, and as a result, the angle between the bonds over here is going to be less than 109.5 degrees. It happens to be somewhere close to 107.5 degrees. The actual number is not really important, but it makes sense why it is less than that actual tetrahedral bond angle of 109.5 degrees, right?

But anyways, now what is the shape of ammonia? We might say it's tetrahedral, but that will not be accurate because there's nothing—there's no atom occupying this space, right? The actual shape would be just this. This is how we show it, and we give a different name to it: we call this shape trigonal pyramidal. You can just basically think of this as a tetrahedral shape with one of the corners removed.

Whatever we get is now like a tripod-shaped trigonal pyramidal, okay? And so we distinguish between these two things. We call this the electron geometry because this is the shape that represents how the electron groups are oriented. But then when we get rid of the lone pair and we talk about only the atoms—only the bonds that are actually present—we call this the molecular geometry. When people are talking about the shape of a molecule, they're actually talking about the molecular geometry.

The shape of ammonia is not tetrahedral but trigonal pyramidal. In the back of my head, it’s kind of the same thing; it's basically a tetrahedral shape where there's nothing over here, so you get rid of it, and now you get this new shape that looks like a tripod, so trigonal pyramidal makes sense, right?

Anyways, in the previous case, note that the electron geometry and the molecular geometry were the same because we only had bonds over here; there were no lone pairs. On to the next one—water molecule, whose Lewis structure looks like this. Why don't you pause the video and think about what the shape is going to be? Think about the number of electron groups around it; try to figure out the electron geometry and then the molecular geometry. Pause and try.

All right, here we go! This time we see there are two bonds, but you probably know by now what VSEPR says: "I don't care about the number of bonds; count the number of electron groups." So I have one, two, three, four, because there are two lone pairs. There are still four groups. So, I immediately know because there are four electron groups around the central atom, and the central atom over here is oxygen, I already know what that shape is going to look like.

Again, it's going to be a tetrahedral shape, and just like before, this time there are only two of these occupied by hydrogen, and the rest two would be your lone pairs. So let’s say these two are hydrogen; we'll replace these two with lone pairs. Just like before, the lone pairs are going to cause more repulsion. So what will happen to this bond angle? It's going to be smaller than 109.5 degrees.

But here's a question for you: in the previous case, in ammonia, the bond angle was about 107.5 degrees. What do you think the bond angle over here is going to be? Is it going to be less than this number or more than that? What do you think? Well, I'm thinking that there are two lone pairs over here, so probably the push is going to be stronger, and probably as a result, the bond angle is going to be much smaller, right?

Guess what? That's exactly what happens. The bond angle actually becomes even smaller. Again, the exact number is not important, but look at where we've reached: not only are we predicting the shape of the molecules, but we are even comparing and intuitively thinking about which bond angles must be bigger and smaller. That’s pretty awesome if you ask me.

But anyways, just like before, this represents the electron geometry. If you now want the molecular geometry, we’ll just get rid of these two. Whatever now remains is the molecular shape of water, and look, that shape is just the bent shape. So this is the molecular geometry. Again, in the back of my head, it’s basically tetrahedral because there are four groups, but because there's nothing occupying over here, I just get rid of it, and look what remains: that bent shape.

There you have it—that's why the water molecule has this bent shape. Okay, so we got three done so far; let's do a couple more. Next up, we'll look at formaldehyde, whose Lewis structure looks like this. Again, it's a great idea to pause the video and see if you can predict what the geometric is going to look like. It's fun to do that.

Anyways, now I’m looking at this and I say, "Hmmm, there's one, two, three, and four bonds around the central atom." Again, VSEPR is going to tell me, "I don’t care about the number of bonds; I only care about the number of groups." Count the number of groups around the central atom. I’m like, "Okay, okay, okay, okay."

So there’s group number one, the second group, and what about this? This is one entire group. Again, VSEPR doesn’t care whether that group is single bonded electrons, a group of four electrons in a double bond, or a lone pair—none of that matters. This is one group. So there’s one, two, and three. There are three electron groups around the central atom this time.

But wait a second, what about the lone pair? Shouldn’t we also consider the lone pair? Remember, VSEPR says, "Around the central atom." The central atom is carbon; the lone pair is not on the carbon, not on the central atom. Okay, so let's not get confused by that. I don’t care about any other atoms. VSEPR only cares about the central atom.

All right, so we have three electron groups, and now we have a geometry in which three groups are going to try and be as far away from each other as possible. What does that geometry look like? That geometry is going to look like this—it’s like a fidget spinner, you can think of it.

Basically, all of them would be in the same plane, and they will be 120 degrees apart. So we call this the trigonal planar because they're all going to stay in the same plane. Notice how it's different than what we got in ammonia—that was trigonal pyramidal. Again, remember for ammonia, we had tetrahedral electron geometry, so we got rid of one of them and we got trigonal pyramidal.

Notice that these four are not in the same plane. If I keep it on the table, the blue central atom is protruding up. But look at your formaldehyde structure—these atoms are in the same plane. Can you see that? They’re all in the same plane. That’s why it is trigonal planar. So if you have three electron groups surrounding a central atom, you'll always get a trigonal planar.

By the way, if you’re wondering, "Shouldn’t this be a double bond?" Yes, I’m not really showing the molecule; I’m just showing the shape of the molecule. So yes, there will be a double bond over here. There’ll be an oxygen here, hydrogen over here, and another hydrogen over here.

On to the next one. The last one we'll consider is carbon dioxide. The Lewis structure looks like this. Okay, the central atom over here is carbon. How many groups of electron groups are around the carbon? I have one group of electrons—again, notice I don't care that it's a double bond and there are four electrons over here; it becomes one single group. And there's a second group. So there are two electron groups around the central atom.

Again, do I care about these lone pairs? No, because that's not on the central atom. Only compare—only look at the central atom. Alright, so what does the shape look like? If I have two electron groups around the central atom, they will be as far away from each other as possible, and if you have just two groups, and they want to be far away from each other, they’ll just be opposite to each other, giving you a linear structure with a bond angle of 180 degrees.

And this now answers our original question as to why carbon dioxide is linear: because there are only two groups repelling each other versus, when it comes to water, notice there were four groups—even though there were two atoms, oxygen was bonded to there four groups because of the lone pair. That's why we had the tetrahedral electron geometry, giving us the bent molecular geometry.

So, it answers our original question, isn't it? Here’s a summary on one page. I know it sounds—it looks daunting, but think about it logically, okay? So if you have four electron groups surrounding a central atom, then you'll get tetrahedral electron geometry.

Now if all of them happen to be four bonds and there are no lone pairs, that is the molecular geometry. But out of it, if there's one lone pair, get rid of that lone pair; what remains is trigonal pyramidal. Out of that tetrahedral, if there are two lone pairs, get rid of them, and what remains is the bent geometry.

If you have three electron groups surrounding the central atom, then you'll get a trigonal planar electron geometry. If all three are bonds, then that itself becomes the molecular geometry as well. If you have two of them, well, it just ends up becoming linear.

I personally don't like to memorize these things over here or even refer to a table because all of this can be done logically. That was the whole point of VSEPR, right? So, I will always like to figure out the central atom, count the number of electron groups, figure out what the electron geometry is going to be, and then get rid of all the lone pairs and then finally arrive at the molecular geometry.