Disubstituted cyclohexane

- [Voiceover] Here we have two compounds. So this one and this one that would both be called 1, 2-dimethylcyclohexane, but the top one here has two methyl groups going up in space or coming out at us. So those two methyl groups must be on the same side of the ring, and we call that cis. For this one we have one methyl group with a wedge, and one methyl group with a dash. So those two methyl groups are on opposite sides of the ring, and we call that trans. So first we're gonna look at the cis-1,2-dimethylcyclohexane compound, and we're gonna draw both chair conformations. And then we'll look at the trans. Here we have our chair conformation at carbon one, we have methyl group that is up axial. We also have a hydrogen that's down equatorial, which is a little bit hard to see here, and the hydrogen's green so we can see it better. At carbon two, we have a methyl group that is up equatorial, and then we have a hydrogen that's down axial. So again it's green to see it better. When this chair conformation undergoes a ring flip, I rotate this carbon up and I rotate this carbon down. And then we turn it a little bit so we can see our other chair conformation, and then we analyze what happened to our groups. Now at carbon one, we have a methyl group that's up equatorial and our hydrogen is now down axial. And at carbon two, our methyl group is up axial and our hydrogen is down equatorial. Now let's draw our chair conformations. So we'll start with the one on the left. So you've seen how to draw chair conformations in earlier videos, we start with our two parallel lines that are off set from each other. So there's one line and there's our other line. Next we draw a dotted line that just touches the top part of the top line. So there's our first dotted line, so it's supposed to come close to this point, and then our other dotted line is gonna go right here and touch the bottom point of the bottom line. Next we think about another set of parallel lines. So if we draw a line from the top one down to here, and then we draw one parallel to that over here, and then finally we put in our last set of parallel lines. So from this point to here and then from this point to here. If we call this carbon one, we start up axial at carbon one, as we've seen in earlier videos, and then carbon two would be down axial since we alternate. I'll stop there, I won't draw in the rest of the hydrogens just to save time. If we go back to carbon one we know that next we go down, down equatorial so I put that one in, and then at carbon two this would be up. So let's look at our picture here, and we can see that our methyl group is up axial at carbon one so we put in a CH3 up axial. Then we have a hydrogen down equatorial right here at carbon one. At carbon two, our methyl group is up equatorial. So we put that in, and then we have a hydrogen that's down axial. So this is the cis compound. Both these methyl groups are on the same side, they're both going up relative to a flat plane of the ring. We know that this chair conformation is in equilibrium with our other chair conformations, so let's go ahead and draw the one on the right now. So we start with our two parallel lines that are a little offset so here's one of the lines, and then here is the other one. Next we draw our dotted lines intersecting that top point, and intersecting the bottom point here. Finally we think about our next set of parallel lines, so this one and then this one, and finally our last set of parallel lines so from here to here and then from here to here. Now we can see that this is carbon one, so here is carbon one after we undergo a ring flip, and now we start down axial at carbon one. So I'll draw it down axial at carbon one. At carbon two now it's up axial, so up axial at carbon two. So let's put in our methyl groups, and to do that we need to put in the other bonds. So this would be up and then down. So at carbon one, we can see our methyl group is up equatorial so we put in our CH3 here, and our hydrogen is down axial. And then at carbon two, our methyl group is up axial, and then our hydrogen is down equatorial. So when this compound underwent a ring flip. Alright we know this is carbon one where our methyl group was up axial, and then this is carbon one. Our methyl group is still up relative to the plane of the ring, but now it is equatorial. So that's what happens when you do a ring flip. And then carbon two, let me change colors here. So carbon two, we had a methyl group that was up equatorial, and now our methyl group is up axial. So for both chair conformations the methyl groups are on the same side, and that's why we say cis. In terms of which one is the more stable conformation, for both of these we have one methyl group axial and one methyl group equatorial. So they are equivalent, so they're the same in terms of energy. Next let's look at trans-1,2-dimethylcyclohexane. Here we have trans-1,2-dimethylcyclohexane, and you can see at carbon one we have a methyl group that's up axial, and a hydrogen that's down equatorial. And at carbon two, we have a hydrogen that's up equatorial, and a methyl group that's down axial. If this undergoes a ring flip, so I lift this carbon up, and pull this carbon down and then turn it so we can see our other chair conformation. Now let's analyze what happened to our methyl groups. At carbon one, now our methyl group is up equatorial, and at carbon two our methyl group is down equatorial. Now let's draw the chair conformations for the trans compound. The cis and trans compounds are isomers of each other. They're different molecules. So let's draw this chair conformation on the left, and we start with our parallel lines that are offset from each other. So there's one line and then there's the other one. Next we put in our dotted lines, and our dash lines here. So that one hits the top part, this one hits the bottom part like that, and then we draw a line from here to here and then a parallel to that. And then we put in our last set of parallel lines. So that gives us our carbon skeleton, and we start at carbon one, we start axial up. And then at carbon two is axial down, and then we have down and then up. So now since this is carbon one, we see our methyl group is up axial so we put our methyl group up axial here, and then we have our hydrogen down equatorial. So we put that in, at carbon two the hydrogen is up equatorial and the methyl group is down axial, so let's put that in. Alright, you can see those two methyl groups are on opposite sides of the ring. So one is going up, right this one is going up, and then this one is going down. So they're trans to each other. This chair conformation is in equilibrium with our other one. Let's draw the one on the right. So we start with our parallel lines offset, and then we draw in our dash or dotted line here. So next we put in our next set of parallel lines, so here to here, here to here, and then connect these points. So that's just a really rough chair, and then now this is carbon one so we start axial down at carbon one. Carbon two would be axial up and then let's put in our other ones here like that. Alright, for this one this is carbon one, and we see our methyl group is now up equatorial. So now our methyl group of carbon one is here, and we have a hydrogen going down at carbon one. At carbon two our hydrogen is up axial, and our methyl group is down equatorial, so here's our CH3. It's hard sometimes to see these equatorial bonds. So a good hint is to look at the axial ones. For example, you look at this bond here, you think, "Is this up or down relative "to the plane of the ring?" It's pretty hard to see, but this one is clearly up. So that means that this one must be down, so there's a little trick. Alright, let's look at those two groups and what happened in our ring flip. So let's start with carbon one, so here's carbon one with our methyl group that's up axial. For the ring flip that methyl group stayed up relative to the plane of the ring, but now it is equatorial. So there's that same methyl group. For carbon two, this was carbon two, our methyl group was down axial and here it is down equatorial. So for both of our chair conformations, the methyl groups are on opposite sides of the ring. If we analyze these two chair conformations in terms of stability, well for this one on the left we have two axial substituents. That's not as stable as the one on the right. The one on the right has our two relatively bulky methyl groups equatorial, and we know that's the best place for them. That decreases the steric hindrance. So the one on the right is the more stable conformation. Finally let's do a problem. So our goal is to draw the most stable conformation of trans-1-tert-butyl-3-methylcyclohexane. We know the most stable conformation is going to be a chair conformation. So let's start by drawing a chair. So we have one parallel line, so here's one of them, and then here is the other one so they're a little offset. And next we put in our dotted lines just as guidelines to help us with the drawing here. And our next set of parallel lines goes in, so this point to this point we try to draw a line parallel to that over here, and finally our last set. So from here to here and from here to here. Alright, so trans, which means that our two groups are on opposite sides of our ring. What are the two groups? We have a tert-butyl group at carbon one, and we have a methyl group at carbon three. So we know this is carbon one, so let me go ahead and start up axials. So here's up axial and then we alternate, so at carbon two must be down axial. Carbon three must be up axial. Let's go back and put in equatorials. So at carbon one must be down, carbon two must be up, and carbon three must be down. So let's put in our tert-butyl group at carbon one. So now we have two choices, where do we put our tert-butyl group? Do we put it axial, or do we put it equatorial? Well we know this is a very bulky group, and we put bulky groups equatorial. So we have only one choice at carbon one. We must put the tert-butyl group right here. Alright so now we chose to put the tert-butyl group down at carbon one, so this is down. And since this says trans, that means we must put the methyl group up at carbon three. So we go to carbon three, and then here's carbon three. We have only one choice, we must put the methyl group axial. That's the only one that's going up, so here is our CH3 like that. So let's go ahead and erase these other bonds here just to make this look a little prettier. So I'll just erase this stuff, and I'll just erase this stuff. You could put in all of your hydrogens, you could leave this stuff out. I'll just clean this up a little bit, take care of our dotted lines, and then so we can see our conformation. So here is the most stable conformation of trans-1-tert-butyl-3-methylcyclohexane.