Enantiomers vs. Diastereomers: Study with Video Lessons, Practice Problems & Examples

Stereoisomers can be predicted based on the number of chiral centers in a compound. Compounds with no chiral centers are usually achiral, while those with one chiral center are always chiral and can form enantiomers. Compounds with two or more chiral centers are typically chiral, except for meso compounds, and can form diastereomers. The total number of stereoisomers can be calculated using the formula $2^n$, where n is the number of stereocenters.

Using chiral centers to predict types of stereoisomers.

Now let's talk about ways to use caramel centers to predict the types of stereoisomers that we're going to get. Alright, so it turns out that the types of stereoisomers can be roughly divided into how many different chiral centers you have. Okay? So let's go ahead and just talk about the most simple situation, which is that how about if you have a compound with no chiral centers. Okay. Well, earlier today, I told you guys, okay, if there's no chiral centers, assume that it's achiral and that's still going to hold. As you can see here, I said that compounds with no chiral centers are usually achiral, but now notice that I did put the word usually in there. It's because there is a subset of these weird molecules called atropisomers that we're going to pay special attention to later that happen to kind of break the rules and they happen to be chiral for other reasons. But other than that, most molecules can be really well predicted by the number of chiral centers they have. If they have no chiral centers, then they're not chiral. Okay. Except for the case of atropisomers and I'll teach you exactly which ones those are. There are exceptions. Okay. So let's go on to the next category. How about if a compound has exactly one chiral center? Then that compound is always going to be chiral. Always always. There's no way to avoid it. And since it has one chiral center, that means that it's going to be able to form enantiomers. Okay? And remember what enantiomers were? They were the mirror images that you would get that were different from the original. The reason is because if you have one chiral center, that means it's going to be able to arrange itself in 2 different ways, a right-handed way and a left-handed way. So what that means is if you put it up to a mirror, you are going to get the enantiomer because there's one chiral center. Okay. Now let's talk about the last situation. What if you have 2 or more chiral centers? Okay. Well, those are going to be usually chiral. As I've been telling you yesterday, as long as you have chiral centers, assume that it's chiral. It turns out that there's also going to be an exception to that. The exception to that comes in the form of molecules called I'm going to just point it right here. Exception is meso compounds. Okay? But we're going to pay special attention to those as well. So what I'm trying to say here is that except for atropisomers, which are weird, and meso compounds, which are also weird, these rules always hold, which is that compounds with 2 or more chiral centers are going to be chiral unless they're meso. Now, if they have 2 or more chiral centers, then they will not form enantiomers necessarily. They also have the ability to form what's called diastereomers. Now diastereomers are, it's a very weird word. What's the definition of that? Well, the definition of a diastereomer is simply a non-mirror-image stereoisomer. Isomer. So basically, it's a stereoisomer that doesn't fall neatly into the enantiomer category. Remember that enantiomers are always 100% the mirror image of the other one. Diastereomers are anything that doesn't look exactly like the mirror image, but it's still a stereoisomer. Cool? We're going to talk about the differences between enantiomers and diastereomers in a second. By the way, sometimes it's really fun to hear your professor say diastereomers because there are so many different pronunciations and a lot of them have to do with foreign accents and it's kind of funny.

How to predict the total number of stereoisomers.

Let's talk about one more thing, and that's following the 2 to the n rule. It turns out that you can predict the total number of stereoisomers possible by using the 2 to the n rule, where n is equal to the number of stereo centers. So what that means is that you count up your stereo centers, and, whatever your stereo centers are, you take 2 to the n, which will tell you how many stereoisomers you're going to get. For example, I'll just give you guys a really easy example. If I had 4 stereocenters, remember that a stereocenter could be a chiral center and or a trigonal center. Both of those count as stereocenters. So, if I have 4 of those, then the total number of stereoisomers that I could get would be 24, which is equal to 16 different isomers, which is crazy. You're never going to be asked to draw 16 different isomers, but you may be asked to draw 4.

Draw stereoisomers and determine relationship

So let's go on to this example and I want to use this more as a teaching moment than anything else. Just sit back and watch me do what I am doing. Okay? So what I want you guys to do with us together is we're going to draw all the stereo isomers that are possible for this compound, 2-bromocyclohexan-1-ol. Alright. Then we're going to determine their relationships to each other. Okay. So first of all, how could we predict how many stereo isomers we are going to have? It says here draw all of them. Does it say how many? No. So we're going to have to use some kind of method to figure out like how many stereoisomers there are. What are you guys thinking of? 2n. Let me use 2n because I can just count up the number of stereocenters I have and that will tell me. So how many stereo centers do I have? That means chiral centers and trigonal centers combined. Well, I don't have any trigonal centers, but I do have 2 chiral centers. This is a chiral center and this is a chiral center. Both of these carbons have 4 different groups on them. So I am going to go ahead and plug this in, 22 and that gives me 4 different isomers. Okay. So this is a situation where I am going to be drawing 4. Okay, let's go ahead and start off with the easiest combination possible, which would just be let's have them both facing towards me because remember that these stereo isomers, the way they are going to change is that some will face towards the front, some will face towards the back. So let's go ahead and draw our first one. And this one will be the easiest example. Let’s make both the OH and the Br let’s make them both face towards me. That would definitely be one of the stereoisomers. Now can you guys think of another stereoisomer that could possibly exist? Remember, we need 4 total. Another one could be that both of them face the back. Would that be the same exact molecule? No, it would actually be a completely different molecule in terms of stereo isomer. Because there’s no way I know some of you guys are thinking, but can't I just rotate that and it will become the blue one? No. If I rotate that over, the OH and the Br will switch positions. So that means that if I rotate it like this, I like to call that sometimes like a pancake flip, you flip it over like a pancake. The Br would now be on the top. The OH would be on the bottom. They'd be different compounds. So those are different compounds. So then are there any other combinations we can think of? Well, how about if we keep the OH in front, but we put the Br in the back? Would that be the same thing? No, that would be its own unique combination too. That one is unlike the other 2. Okay? And then finally, our last combination could be that I have my OH in the back and my Br upfront. So that's my 4th isomer. Alright? So notice that what I just did was I just went ahead and drew out all the possible stereo isomers that were possible according to my 2n rule. 2n, all it does is it tells you all the different combinations of front and back that are possible. Okay? Now we've drawn all the isomers. Now I want to know what their relationships are. So what I am looking for is molecules that have perfectly opposite configurations, meaning that if the OH is facing towards the front on 1, I want it to face towards the back on the other in order for it to be an enantiomer. Remember that enantiomer means that it’s the mirror image, so that means every single configuration should be different. So if I’m looking for an enantiomer, in this case, I'm trying to figure out which of these are related to each other as enantiomers. What I'm going to look at is which of them have perfectly opposite configurations or perfectly opposite chiral centers. The obvious choice to me is this top one right here. K? This relationship here has to be enantiomers. K, why is that? Well, because if you’ll notice here for the OH, it's facing towards the front, the Br is facing towards the front. When I look at the green one, they're both facing towards the back. So this is the mirror image of the other one. And in fact, if I were to rotate it and put them up against the mirror, they would be mirror images of each other if I were to rotate them both facing up. Okay. Both facing so that the OH and the Br are up. Okay. So those are enantiomers from each other. Remember that basically enantiomers have to be completely opposite. Okay? So are there any other pairs of enantiomers here? For example, are red and blue related to each other as enantiomers? What do you guys think? Actually, no. Because they're not perfectly opposite. The Br is opposite. 1 is facing towards the front, 1 is facing towards the back. But the OH is the same so that relationship can't be enantiomers. K. Is there anything else here that's enantiomers? I think you guys might have found it, red and black. So these 2 guys are also going to be enantiomers, meaning mirror images. Why? Because red and black, you can see that the OH is opposite and the Br is opposite. Okay. So those are also related to each other as enantiomers. Okay. How about something like red and green? How are those related to each other? Well, that's not enantiomers. Okay? So then what's the name that we give to all these other relationships that aren't really enantiomers, but they’re different stereoisomers? For example, red and blue, they're not mirror images, but they're still different. They're not the same. Well, the answer is these are all going to be diastereomers of each other. So this is going to be diastereomers. K. Those are diastereomers. This is diastereomers. Okay. And all of these are diastereomers. K? Why is that? Okay? So that applies to these in relation to each other and these in relation to each other. Okay. Why are they all related as diastereomers? The reason is because diastereomers is the word that we use for molecules that are stereoisomers but not perfect mirror images. Every single relationship I just showed you either had basically one of the chiral centers the same and the other one different. Okay? So we're going to say here is that diastereomers are basically not completely opposite. This is going to help you later once you start trying to figure out the relationships between isomers. Okay? So but they're also not completely the same either. So they're kind of in the middle. They're not completely opposite but they’re also not completely the same because if they were the same, they’d just be identical. So they're just like in between. Does that make sense? Cool.

Determine total number of stereoisomers

And the answer was 8. Okay. Why? Because I've got 3 stereo centers. I've got this one. I've got this one. Then that actually counts as a stereo center, my double bond because it can form cis and trans. Okay? So that means that I've got 8 different combinations or basically 2 to the 3 combinations of ways that I could orient these; front, back, cis, trans. I could combine all of them and I would get 8 total. Do you have to draw all of these? Please don't. That would be a really, really long task. But you can just visualize that it would have to do with moving front back, moving front and back, and then the double bond moving cis and trans. Okay? And those would all be stereo isomers of each other. Cool guys. So let's go ahead and move on to the next topic.

Here’s what students ask on this topic:

What is the difference between enantiomers and diastereomers?

Enantiomers are stereoisomers that are non-superimposable mirror images of each other. They have identical physical properties except for their interaction with plane-polarized light and reactions in a chiral environment. Diastereomers, on the other hand, are stereoisomers that are not mirror images of each other. They have different physical and chemical properties. Enantiomers occur when a molecule has one chiral center, while diastereomers occur in molecules with two or more chiral centers.

How do you calculate the number of stereoisomers for a compound?

The number of stereoisomers for a compound can be calculated using the formula 2ⁿ, where n is the number of stereocenters (chiral centers and/or trigonal centers) in the molecule. For example, if a molecule has 3 stereocenters, the total number of stereoisomers would be 2³ = 8. This formula helps predict the possible stereoisomers a compound can have.

What are meso compounds and how do they affect stereoisomer count?

Meso compounds are molecules with multiple chiral centers that are achiral due to an internal plane of symmetry. This symmetry causes the molecule to be superimposable on its mirror image, making it achiral. Meso compounds reduce the total number of stereoisomers because they do not form enantiomers. For example, a molecule with two chiral centers would typically have 2² = 4 stereoisomers, but if one of them is a meso compound, the actual number of stereoisomers would be 3.

Can a compound with no chiral centers be chiral?

Compounds with no chiral centers are usually achiral. However, there are exceptions such as atropisomers, which are chiral due to restricted rotation around a bond, leading to non-superimposable mirror images. These exceptions are rare and specific, but they demonstrate that chirality can arise from structural features other than chiral centers.

What is the 2ⁿ rule in stereochemistry?

The 2ⁿ rule in stereochemistry is used to predict the total number of stereoisomers a compound can have. Here, n represents the number of stereocenters (chiral centers and/or trigonal centers) in the molecule. For instance, if a molecule has 4 stereocenters, the total number of stereoisomers would be 2⁴ = 16. This rule helps in understanding the complexity and diversity of stereoisomers in organic compounds.