Enantiomers and diastereomers

- [Narrator] We've already spent a lot of time talking about enantiomers. These are stereoisomers that are nonsuperimposable mirror images of each other, and they have opposite configurations at all chirality centers. Diastereomers are also stereoisomers, but these are stereoisomers that are nonsumperimposable, non-mirror images of each other. So these are stereoisomers that are not enantiomers. And diastereomers have opposite configurations at some chirality centers. If we look at this compound up here, we have a cyclopropane ring with a bromine coming off, and a chlorine coming off. We know from earlier videos that there are two chirality centers. So this carbon is a chiral center, and so is this one. The total number of stereoisomers is two to the n, where n is equal to the number of chiral centers. And since n is equal to two for this drawing, we would expect to be able to draw two to the second power, or four stereoisomers. So there should be a total of four stereoisomers. Actually, two to the n is just a maximum, and we'll talk about that in later videos. So let's draw all four stereoisomers, and let's look at the relationship between them. Let's think about how to draw our four stereoisomers. For the first one, we could have both halogens coming out at us in space, so I put the bromine on a wedge, and I put the chlorine on a wedge. Next, we could have both halogens going away from us in space. So I put the bromine on a dash, and same with the chlorine. Next, for our third stereoisomer, we could have one halogen coming out at us, so I'll make that the bromine, and one going away from us. And for the last one, we could just reverse it. We could have the bromine going away from us, and the chlorine coming out at us. Next, let's look at the relationships between our stereoisomers. And let's start with the relationship between stereoisomer one and stereoisomer two. Model sets really help in stereo chemistry, so we're gonna look at videos for a lot of these. Let's go look at the video comparing stereoisomers one and stereoisomer two. On the left we have stereoisomer one. Both halogens are coming out at us in space. On the right is stereoisomer two, where both halogens are going away from us in space. If I hold these two stereoisomers next to each other, and I rotate the one on the right, we can see that they're actually mirror images of each other, and they're nonsuperimposable mirror images. If I line up the chlorines, then the bromines are not in the right position. And if I try to line up the bromines, now the chlorines are not in the right position. So these are nonsuperimposable mirror images of each other. These are enantiomers. So we saw in the video that one and two are enantiomers of each other. They are nonsuperimposable mirror images, and they have opposite configurations at all chirality centers. And that's easy to see if you look at the drawings, here. So at this carbon, we have bromine on a wedge, and if we change it to a dash, right, we see we have this one on the right. We look at this chiral center, we have chlorine on a wedge, and here it's changed to a dash. So that's an opposite configuration at both chiral centers, and so that's how we know, that's one way of knowing that this one on the right is the mirror image of the one on the left. They are enantiomers. Let's look at the relationship between stereoisomers three and four. On the left is stereoisomer three, with bromine up and chlorine down. On the right is four, with bromine down and chlorine up. If we hold them together and I rotate the one on the right, it's easy to see that these are mirror images of each other, and they are nonsuperimposable. If I put the chlorines on top of each other, now the bromines don't line up, and if I try to line up the bromines, then the chlorines don't. So these are nonsuperimposable mirror images of each other. These are enantiomers. So three and four are enantiomers of each other. They are nonsuperimposable mirror images, and they have opposite configurations at all chirality centers. So at this chiral center, we have bromine on a wedge, and over here, we have bromine on a dash. At this chiral center, we have chlorine on a dash, and over here, we have it on wedge. So we have opposite configurations at both chirality centers. Next, let's compare stereoisomers two and three. So what's the relationship between two and three? On the left is stereoisomer two, with the bromine and the chlorine going away from us in space. On the right is three, with bromine up and chlorine down. If I hold the two stereoisomers next to each other, and I rotate the one on the right, we can see that these are not mirror images of each other. The bromines look right, but the chlorines don't. One chlorine is up, and one chlorine is down. If I try to superimpose these, I can get the bromines to match, but not the chlorines. And if I try to make the chlorines line up, then the bromines won't. So these are nonsuperimposable, non-mirror images. These are diastereomers. We saw in the video that two and three are nonsuperimposable, and they're also non-mirror images. Therefore they are diastereomers. So let me write that down, here. So two and three represent a pair of diastereomers, and diastereomers have opposite configurations at some chirality centers. So if we look at this carbon, we have bromine on a dash, and over here, we have bromine on a wedge. So that's opposite. But if we look at this one, we have chlorine on a dash, and over here, we have chlorine on a dash. So that's the same. So we only have an opposite configuration at one chiral center. And so these are diastereomers. What about comparing two, stereoisomer two, with stereoisomer four? So let's look at the video for that. On the left is stereoisomer two, with the bromine and chlorine going away from us. On the right is four, with bromine down and chlorine up. So we hold the two stereoisomers next to each other, and we rotate the one on the right. And we can see that these are not mirror images. The chlorines look right, but the bromines don't. One bromine's down, and one bromine is up. If we try to superimpose one on top of the other, the chlorines line up, but not the bromines, and if I try matching the bromines, now the chlorines don't. So these are nonsuperimposable, non-mirror images. These are diastereomers. So two and four are diastereomers. They are nonsuperimposable, non-mirror images of each other. And they only have opposite configurations at some chirality centers, in this case, one. So if we look at this chiral center, the bromine's on a dash, and we look at this one, the bromine's also on a dash. So that's the same. If we look at this one, the chlorine is on a dash, and over here, the chlorine is on a wedge. So that's an opposite configuration at only one chiral center. So two and four are diastereomers. What about comparing one and three? So, thinking about one and three. So we don't need a video for this, anymore. I think we've got the hang of it. And if we look at this carbon, we have bromine on a wedge, and at this carbon, we have bromine on a wedge. So that's the same. At this carbon, we have chlorine on a wedge, and at this one, we have chlorine on a dash. So that's different. So we only have an opposite configuration at one chirality center. So one and three are diastereomers of each other. And the same thing if you're thinking about one and four. Those would also be diastereomers of each other.