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Comparing the stability of different kinds of carbocations using hyperconjugation. Mechanism of carbocation rearrangements including methyl and hydride shifts.  Created by Jay.
Video transcript
Let's take a look at these four carbocations. Carbocations have a positive 1 formal charge on that carbon. And you can check out the earlier video on formal charges to explain why. And because there's a positive charge on it, you can see you can see that those carbons have only three bonds to them and only six electrons around it. And we know carbon likes to have four bonds and be surrounded by an octet. That makes carbocations very reactive. Let's look at the carbocation all the way over here on the left. This is called a methyl cargocation. So let's go ahead and write that in here. And if you replace one of those hydrogens with an alkyl group, the carbon that has the positive charge on it is now directly bonded to one other carbon. We call this a primary carbocation. If I move over to the third example, the carbon with the positive charge on it is bonded to two other carbons. So we call that a secondary carbocation. And finally, the carbon with the positive charge is bonded to three alkyl groups, directly bonded to three other carbons. We call this a tertiary carbocation. In terms of stability, the tertiary carbocation turns out to be the most stable. So tertiary carbocation is more stable than secondary, secondary is more stable than primary, and primary is more stable than methyl. So you can see, as we increase the number of alkyl groups, we increase in carbocation stability. And, the reason why is this an effect called hyperconjugation. So let's go ahead and write that down here. So hyperconjugation explains why carbocation stability increases as the number of alkyl groups increase. And let's go ahead and draw pictures to see if we can better understand the effect of hyperconjugation. And we'll start with a methyl carbocation, simply because it's the easiest to draw. So a methyl carbocation is carbon directly bonded two three hydrogens. And we know, carbon bonded to three different atoms gives us a steric number of 3, which means we have SP2 hybridization. So they're SP2 hybridized orbitals from that carbon bonding with S orbitals of those hydrogens. And in SP2 hybridized carbon, we know that there's also an unhybridized P orbital. So let me go ahead and draw in that P orbital on that SP2 hybridized carbon. So let me go ahead and make this a positively charged, right? This is positively charged. And this carbon right here is SP2 hybridized, meaning the geometry is trigonal planer. So that's a methyl carbocation, the least stable kind. Let's take that carbocation and let's put a methyl group on it. So let's go ahead and redraw this part of the molecule. This is my carbocation over here, so this carbon is positively charged. And since this is my SP2 hybridized carbon, it's going to have a P orbital. So I'll go ahead and put a P orbital there. And instead of bonding this carbon directly to a hydrogen, as it on the left, let's go ahead and bond it to a carbon. And then let's make this carbon into a methyl group here. So I'll go ahead and say this is my methyl group with a hydrogen. And a hydrogen over here. And if this carbon to the left is a methyl group, this carbon on the left must be SP3 hybridized. So let's see if we get a different color in there. This is an SP3 hybridized carbon, meaning the geometry is much more tetrahedral. And let me go ahead and draw in one of the SP3 hybridized orbitals that this carbon has. That's going to represent an SP3 hybridized orbital, forming one bond with the S orbital of another hydrogen. So here's a hydrogen. And we'll show the overlap of the S orbital of that hydrogen, with that SP3 hybridized orbital like that. So this is our situation. We have bonded our carbocation to a methyl group. And this alkyl group is going to stabilize the carbocation through donating some of the electron density in this sigma bond. So this is a sigma bond here. So there are electrons in here. And some of that electron density can be shared into this empty P orbital. And since that carbon is positively charged, right, opposite charges attract that electron density. That negatively charged electron density is going to help stabilize the positive charge. And so this is the effect of hyperconjugation. And it makes sense, the more alkyl groups you have, the more electron density from sigma bonds that can be shared with the MTP orbital, therefore the more stable your carbocation. So it's all about opposite charges. Carbocations are important for one reason, because they can rearrange in mechanisms. So let's go ahead and write that down. So possible rearrangement. Sp the first type that we will do is something called a methyl shift. So let's go ahead and look at a methyl shift first. And, if you're doing a mechanism that involves a carbocation, let's say one of your intermediates turned out to look like this. Now let me go ahead and draw this molecule here. So we'll put a methyl group here. And, we're going to make of this carbon our carbocation. This carbon has a positive 1 charge on it. Sometimes students have a hard time identifying carbocations because the hydrogens aren't drawn in there. Right? But if someone tells you that carbon has a positive charge, right now it looks like that carbon only has two bonds. But we know that there's another hydrogen there. We know that there is a hydrogen bonded to this carbon. Now, that carbon is bonded to three other atoms and it's easier to see that it is SP2 hybridized. And it's easier to see it has a positive charge on it right now. So what kind of a carbocation do we have for this dot structure. Well, the carbon that has the positive charge on it is directly bonded two other carbons. Right, so when the carbon that has a positive charge on is bonded to two other carbons, we call that a secondary carbocation. So this is a secondary carbocation. This carbocation can actually undergo a rearrangement to form a more stable carbocation. And we're going to call this methyl shift. So we're actually going to get this methyl group. This methyl group is actually going to migrate one carbon over, and form a bond with that carbocation. So let's see if we can draw a picture of what's happening here. The electrons in this bond, for this methyl group, are actually going to move over here and bond directly with that carbon. So let's go ahead and draw what we would get if that happens. Right, so if that methyl group group shifts over there to that carbon-- right, let me go ahead and make sure I use the same color for my electrons. Right, these are the electrons from the methyl group that just shifted. So this is my methyl group after it shifted. Right, there was still a hydrogen attached to this carbon. And then there was a CH3 right here as well. So that's our methyl shift. And the question is why? Why did that methyl group shift over there? Well, the answer is, it formed a more stable carbocation. Let's look at this now. OK. So this carbon over here on the left used to have four bonds to it. But we took away one of those bonds. The bond in that methyl group. So it used to have four bonds and now only has three. So it has to have a positive charge on it now, a positive 1 formal charge on this carbon. So your carbocation moved from the carbon on the right to the carbon on the left. Since the carbon on the left lost a bond, and the carbon on the right gained a bond. Therefore, the carbon on the right no longer has a formal charge, it has a formal charge of 0. So what kind of a carbocation do we have now? Well the carbon that has the positive charge on it is directly bonded to one, two, three other carbons. So we actually formed a tertiary carbocation because of our methyl shift. And we know that tertiary carbocations are more stable than secondary carbocations because of hyperconjugation. So this is the kind of rearrangement that you can expect to happen in organic chemistry mechanisms. All right, let's look at one other type of shift. We're going to call this hydride shift. So the other type of rearrangement, you could have a hydride shift. So what is a hydride? Let's look at that first of all. Well, a hydride is a hydrogen with two electrons, right? Two electrons. Hydrogen usually has one electron around it. Or bringing one electron to the dot structure. So two electrons would give it a negative 1 formal charge. So again, watch the videos on formal charge here. So two electrons gives hydrogen a negative overall charge. And we call this a hydride anion. All right, let's look at a hydride shift. It's going to look very similar to the example we just did. Right. If we have this set up. And let's make this once again, this is our carbocation. And we think to ourselves, what kind of a carbocation is that? Right, so this is the carbon that bears the positive charge. Once again, that carbon is bonded to one, two other carbons. Right? So it must be a secondary carbocation. And once again, even though we didn't draw the hydrogen in there, we know that there is a hydrogen here. Right? There's a hydrogen on that carbon. We know that because they gave us a positive charge on that carbon. So what do I mean by a hydride shift? Well, if I know that this carbon over here in the left in blue has three bonds to it, it must have another bond to a hydrogen like that. And this hydrogen can actually be the one that undergoes the shift. So completely analogous to the previous example. If these two electrons in here, right, shift with that hydrogen nucleus. It's the same idea as before. We're going to take those electrons. They're going to form a new bond with that carbon. So let's draw the product of that shift here. So what would we get? Well let's see, there are still some CH3's there. And let me go ahead and put this in right there. Those electrons, right, those are the electrons from the hydride shift. There was one the hydrogen already attached to that carbon. And then there was already a CH3 group attached that carbon like that. So the carbon on the right, this carbon right here, gained a bond. Right, that takes away its formal charge. It has a formal charge of 0. The carbon over here on the left, right? This carbon over here on the left, lost a bond. So it used to have four bonds. Now it only has three bonds, which gives it the positive 1 formal charge. And once again, if you were to categorize that carbocation right? It's attached to one, two, three other carbons. So it is tertiary. So once again, a tertiary carbocation is more stable than a secondary carbocatoin. So a hydride shift is possible as well. So look out for possible methyl shifts and hydride shifts whenever you get a carbocation in your mechanism.