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Double Newman diagram for methylcyclohexane. Created by Sal Khan.
Video transcript
In the last video we saw that the two chair shapes, or the two chair configurations of just plain vanilla cyclohexane, were equally stable. There was nothing that would imply that this is more stable than that or vice versa. What we want to do in this video is address what happens if, instead of just a pure cyclohexane, what if we added a methyl group to it? And so instead of just a cyclohexane, let's think about a methylcyclohexane, so we know what to do when we're naming things. So methylcyclohexane will look like that. We'll have a hexagon here. This is the way we've been drawing it historically. We've been drawing it just like that. And then we'll have a methyl group. And you could literally just draw a methyl group like this or maybe like this. And by implication, you have a carbon here, essentially a CH3 group here, and, of course, you have another hydrogen bonded here. Now, if you were to draw this methyl group in three dimensions like this, it would look just like our different chair positions before, but instead of this H being just an H, we could make this entire methyl group, so we could turn this CH3 right here, so this-- let me draw it out in a different color. We could make this carbon that implicitly has three hydrogens on it, so this is a CH3 group that is a methyl group that's right there. We could substitute one of these hydrogens with it, and then this would be one of the shapes of this methylcyclohexane, CH3. Let me write it down, just to practice our naming. So this is methylcyclohexane. Now, this is one of their chair positions, and then if this were to flip down and the other side were to flip up, the other chair position would take this methyl group from being in an axial position, and it would put it in an equatorial position. So this is the same group right here. Let me put a circle around it. It's a whole group. That's the CH3. Now, the question we want to answer in this video, is one of these two configurations going to be more stable? Now, you might just be able to eyeball it looking at this diagram, and say, hey, when we're in the position where the methyl group is in the axial position, it's going to be closer to all of these other carbons over here, closer to their electron clouds. Maybe it has higher potential energy. Maybe it'll want to spring away. And if that was what you're guessing or what you're kind of eyeballing, you'd be right, because in this position, this methyl is much further away from all of the stuff out here, so there'll be less, I guess you can consider it, electron cloud crowding, if you will. Now, to see that a little bit more clear, I want to do what we call a double Newman diagram. And really, that's the whole motivation of this video is to kind of expose you to that. A Newman diagram isn't just useful for simple things like a butane or an ethane. You can actually do it with cyclical rings. And to do the Newman diagram, let me number these carbons. So we could number them like this. So this is carbon one, two, three, four, five, six. And you don't have to call this one methylcyclohexane, because whenever you have only one group attached to the ring, you implicitly start numbering at the carbon that the group is attached. So that is the one carbon over here. This is the one carbon, two, three, four, five, six. And over here, once again, is the one carbon, two, three, four, five, six. Now, what I want to do is draw two Newman projections, and both of them will involve-- well, actually, I'll draw four, but you'll see what I'm talking about in a second. So the first Newman projection, I'm going to start at that carbon right over there. So let's think about what that would look like. So we're at the front. We're staring straight on to that carbon. So this carbon's in the front, this carbon over here. This carbon, carbon number two, is in the back. So let me label this. This is carbon number one that we're looking head on. Now, right in the axial position you have that methyl group. So let me draw that. So in the axial position you have that methyl group right over there. And then in the equatorial position right here, you have this hydrogen. Let me draw that. So you have this hydrogen. And then over here, this bond right over here, this gets us to another CH2 group. Let me draw that like this. So that gets us to another CH2. That's a CH2 right there, right? Or maybe I should circle it like this. This whole thing is a CH2. So it's bonded to the carbon, but the carbon has two hydrogens on it. And this is actually carbon number six. So this is the front. Now, if we're staring straight and carbon number two is right behind it-- let me draw carbon number two. I'll do it in this blue color. So carbon number two, that bigger circle. Now carbon number two, what's going on over there? It has a hydrogen in the axial position going straight down. This hydrogen right over there. And it has another hydrogen going equatorial. So this green hydrogen right here is going equatorial. It looks like that. And then it connects to carbon number three, which is another CH2. It has two hydrogens branching off of it. In front, we have carbon number one. In the back, we have carbon number two. Let me color code it a little better. Carbon number two. And then carbon number two branches off to-- so if you think of this branch right here, that's carbon number two branching off to carbon number three, or CH3 right there. Let me do that in a new color. So this is actually a CH2 group. That's a CH2. This is a carbon, and it has two hydrogens, right? So this is a CH2. This is carbon number three right there. And then that goes-- and actually, I'll pause there. What I'll do now is I'll draw another Newman projection, but for this Newman projection, we'll be looking straight on our carbon number five. We're going to see we're going to form a ring because the first Newman projection we just did essentially covers this bond. This bond is sitting straight into the screen the way I did it right now. Carbon number two is directly behind carbon number one. So I guess the opposite side of the ring is five to four. If you look at, here, one to two is there, and then five to four is just like that. So you can imagine when we're doing the Newman projections, we're looking straight on here on the left Newman projection. We're going to look straight in that direction on the right Newman projection. So if we have carbon number five in front, what are its bonds going to look like? Well, it's going to bond to carbon number six over here. So we can make this right-- let me do that in a different color. This right here, this bond right here is this bond right here to that same CH2 that our first Newman projection bonded to. And then he's going to have two hydrogens. I haven't drawn them here. Let me draw them, just so you can see them. It's going to have two hydrogens, one in an axial position and one in an equatorial position. It's hard to see now, but he's going to have one hydrogen in an axial and one in an equatorial position. And then in the back we're going to draw carbon number four. And carbon number four, I will do in this green color. So carbon number four-- actually, , well, yeah I'll do carbon number four in that green color. This is really just an exercise in visualization. That's why I wanted to do it with you. So carbon number four has an axial hydrogen, so it has a hydrogen pointing straight down. That hydrogen is that hydrogen. It has an equatorial hydrogen going out like that. And then it bonds to carbon number three. So this bond right here is this bond just like that. So what do we see immediately when we draw this chair position? When our methyl group is in the axial position, what do we see? Methyl in axial position. We see that it's gauche, or gowche. I don't know the best way to pronounce it. It's only 60 degrees away from carbon number three. This is only 60 degrees, or a dihedral angle. When you use the Newman projection, this is only a 60-degree angle. It is gauche to carbon number three. So maybe they're crowding each other a little bit. Let's compare it to the situation where our methyl group is equatorial, where the carbon that it's attached to is on the down part of the chair. Let's see what that Newman projection looks like. So same thing. Let me scroll over to the right a little bit. So this is this configuration and it's in equilibrium with this configuration right here. We'll do the exact same exercise. Carbon number one. But now carbon number one, in carbon number one right here, the hydrogen is now axial and it's pointing straight down. Let me draw that. So we have a hydrogen pointing straight down now. Hydrogen's pointing down and now the CH3 is in an equatorial position, which you can see more clearly on this than over here. So you have a CH3. The methyl group is right there. And now this bond to carbon number six will look like this. So you have a CH2. This is number six right over there. And now if we were to go to the back, if we were go to carbon number two in the back, which we had done in the blue color before, so I'll do it in the blue color again. Carbon number two in black, it has a hydrogen in the axial position going straight up. That's that hydrogen right there. It has a hydrogen going straight up. It has another hydrogen over here, and then it bonds to carbon number three in the back, so CH2 over here. So this guy's the same thing as this guy, but now we've flipped configurations, so he bonds to that guy in the back. And now we do the Newman diagram looking straight on to carbon number five, or looking, actually, straight on to-- right, carbon number five. So we're looking straight in this direction for this Newman projection. Now we're going to look straight in this direction for our other Newman projection. So carbon number five, if we draw it in the front-- I haven't drawn it here, but it has a hydrogen at the axial position, and it has a hydrogen in the equatorial position. So carbon number five, if we look at this, and this is really-- if you're getting a little stressed out about this because it's a little hard to understand, you might want to rewatch. This is really just an example of visualizations. I really hope this isn't confusing you. If you find this really daunting, this isn't going to really trip you up in the rest of organic chemistry, but if you can get it, it's even better. You'll be that much better at visualizing some of these molecules. So if we look straight on at carbon number five, we have a hydrogen in the axial position coming straight down. It is bonded. Carbon number five is bonded to carbon number six, which is right over there. So let me make it very clear. So this bond right here, I want to do it in a different color. This bond it right here is the same thing as this one. This is a really good way to-- if you can do this, then your brain is pretty good at translating between Newman projections and these kind of seat diagrams that we have up here. So this is this bond. This axial hydrogen is this axial hydrogen. And then we have another hydrogen. We have this hydrogen right here, which would be that like that. And then behind it, you have carbon number four. Carbon number four is like that, so carbon number four, draw a circle. It has a hydrogen in its axial position, another hydrogen like that, and then it bonds to carbon number three. So this was number three right here. So just like that. So what do we see about this methyl group here? In this situation, this methyl group is anti-. There's two ways to think about it. It's dihedral angle versus carbon number three is now 180 degrees. Over here it was gauche. Its dihedral angle to carbon number three was 60 degrees. Now, it's 180 degrees. So it's much further. And now its dihedral angle to carbon number six is also 120 degrees. So in this situation, where our methyl group is equatorial, it's axial here. It's equatorial here when we jumped back down because notice, it's parallel. The bond is parallel to parts of the ring. In this situation, we are farther away from the other methyl groups. There's less crowding, and so this is a more stable situation. So you could say it is anti-configuration relative to carbon number three, while over here, it was gauche to carbon number three. I don't know if I'm saying it. Is it gowche, gauche? I don't know the best way to pronounce it. So in this case, there's less crowding. This is more stable, lower potential energy. So hopefully you found that interesting. This was really a way, just an exercise in being able to go from this visualization to kind of this double Newman diagram. And if it makes it any easier, the way you could think about it is we're kind of viewing in this Newman diagram right here, where this carbon number six is this carbon number six. This CH2 is this one back there. So when we're looking at it from this, we're kind of looking at this hexane ring from this direction. We see this in front. This is this, and we see that in back. That is that. Over here, same thing. We're looking at it directly from this direction. We see this guy on top is over here, and this guy on the bottom is over here.