Chirality and number of isomers

mohad · Jun 18, 2011

I encountered a question a few days ago that asked how many stereoisomers could be formed based on the number of chiral centers a molecule had. One molecule was a asymmetric epoxide on a ring and the answer to the number of stereoisomers was 4. I thought the answer was 2 because the epoxide group could come out of the page or into the page. I understand the 2^n power rule, but that doesn't make sense in this case because to have the 3rd and 4th isomer, one bond would have to go into the page and the other bond would have to go out of the page. I can't find the exact compound right now, but if I find it again, I'll post the name.

I came across another question asking for the number of stereoisomers on camphor and I picked 4 using the same logic that the epoxide question followed. Apparently the answer to this question was 2 and they used the same train of thought I did for the epoxide question. Can someone help me understand what the hell the book means?

whiteshadodw · Jun 18, 2011

mohad said:
I encountered a question a few days ago that asked how many stereoisomers could be formed based on the number of chiral centers a molecule had. One molecule was a asymmetric epoxide on a ring and the answer to the number of stereoisomers was 4. I thought the answer was 2 because the epoxide group could come out of the page or into the page. I understand the 2^n power rule, but that doesn't make sense in this case because to have the 3rd and 4th isomer, one bond would have to go into the page and the other bond would have to go out of the page. I can't find the exact compound right now, but if I find it again, I'll post the name.

I came across another question asking for the number of stereoisomers on camphor and I picked 4 using the same logic that the epoxide question followed. Apparently the answer to this question was 2 and they used the same train of thought I did for the epoxide question. Can someone help me understand what the hell the book means?

you're probably assigning chiral centers wrong. if a carbon has 2 Hs or two of any identical atom its automatically achiral. if a carbon has 3 different substituents then its chiral, and two identical atoms can count as different substituents if they have different priorities (ie one carbon is attach to more carbons than another carbon, or one carbon is attached to more oxygens or something).

MT Headed · Jun 18, 2011

mohad, we would have to see your first molecule to be sure. It sounds like you do have a very good grasp on what's going on. I agree that an epoxide on a ring would eliminate some stereoisomers. Either the book has a mistake (like every other book I've read) or you missed some other part of the molecule. It sounds like a cool molecule.

Figuring out the number of stereoisomers on a bicyclic molecule like camphor, now that's bad @ss! Most ochem students would just start to cry.

mohad · Jun 18, 2011

Ok, I had the molecule wrong. It looks like a type of steroid-thing lol. I found it while rereading material in my review book.

Another question. I found this one to be annoying too. I thought the answer to the number of isomers was 4, but it is 16.

salim271 · Jun 18, 2011

Yes, it can go into the page or out of the page at each stereocenter. So its 2 for each stereocenter, therefore 4 total. Organic chem on the MCAT most of the time is basic stuff, you just have to have it down perfectly otherwise little things like that trip you up because you dont really have time to think everything through, you have to know it cold.

Stereochemistry is a weakness of mine too :/ lol. I'm bad with direction, I form an L with my left hand index finger and thumb to remind myself that its my left hand. fml...

mohad · Jun 18, 2011

Well is there any sort of rule or trend for the exceptions? It kind of frustrates me not knowing cause there is always a chance some sketchy question like this could show up in the future. I have this urge to know everything lol.

MShopes · Jun 19, 2011

mohad said:
Well is there any sort of rule or trend for the exceptions? It kind of frustrates me not knowing cause there is always a chance some sketchy question like this could show up in the future. I have this urge to know everything lol.

What I don't get is that I'm not sure if the carbon going into the board at the right is really connected to that right ring or not. If it is connected by any way, then we have another two chiral carbons in addition to the two forming the epoxide to give 4 chiral carbons and hence 2^4=16 stereoisomers. I noticed that this molecule is one type of enediyne. Can you give the correct name of this molecule so that I can search it up and see what is exactly with these two carbons in the right and understand why is it 16 stereoisomers?

If I was you, I would have chosen 4 as well due to the fact that I see only 2 chiral carbons but then I'm still very skeptical.

BHaus9 · Jun 19, 2011

Just remember that that 6-membered carbon ring is not locked into a single conformation and simply "flipped over" to allow for, e.g., an epoxide inversion. The bond angles can be distorted/twisted, and while the steric hindrance created by inversion of only one epoxide carbon may prevent the actual formation of a given stereoisomer, there are still a theoretical 2^n possibilities (where n = number of chiral centers).

As a rough analogy (look at the half-chair and twist conformers):

http://en.wikipedia.org/wiki/Cyclohexane_conformation

So, to summarize, I guess there's a subtle distinction between questions that ask "how many isomers are there" and "how many isomers could there be"

orgohacks · Jun 19, 2011

mohad said:
Ok, I had the molecule wrong. It looks like a type of steroid-thing lol. I found it while rereading material in my review book.

Your concerns are valid on both of these questions. These are examples where they are trying to get you to apply the concepts of 1) recognizing stereocenters and 2) realizing that the number of stereoisomers is potentially 2 to the power of n.

In the first epoxide example there are 9 stereocenters, but the actual number of stereoisomers is 2 to the power of 8, since two configurations are disallowed (as you said, epoxides must both be connected to the same face).

The second example is even worse because in addition to the epoxide, if the configuration is changed at the position where the epoxide is, then the 10 membered ring can no longer form.

Classic example of how a little knowledge can be a dangerous thing.

MShopes · Jun 19, 2011

orgohacks said:
Your concerns are valid on both of these questions. These are examples where they are trying to get you to apply the concepts of 1) recognizing stereocenters and 2) realizing that the number of stereoisomers is potentially 2 to the power of n.

In the first epoxide example there are 9 stereocenters, but the actual number of stereoisomers is 2 to the power of 8, since two configurations are disallowed (as you said, epoxides must both be connected to the same face).

The second example is even worse because in addition to the epoxide, if the configuration is changed at the position where the epoxide is, then the 10 membered ring can no longer form.

Classic example of how a little knowledge can be a dangerous thing.

What does that sentence in bold mean then? The answer clearly says 2^9 stereoisomers not 2 to the power of 8.

BerkReviewTeach · Jun 19, 2011

MShopes said:
What does that sentence in bold mean then? The answer clearly says 2^9 stereoisomers not 2 to the power of 8.

The answer shown in the picture is wrong. Orgohacks is comepletely correct. The epoxide ring must be on the same face, meaning the bonds must be cis to one another. If the bonds were trans, there is no way for the 3-membered ring to form. This is exactly as mohad pointed out in the op.

So instead of being able to get four stereoisomers out of the epoxide ring, you can only get two. Organohacks recommends using 2^8 to get the answer, which is correct. Perhaps it might be more specific to say it's (2^9)/2, because half of those supposed 512 stereoisomers would not be allowed. But (2^9)/2 is 2^8.

MShopes · Jun 19, 2011

BerkReviewTeach said:
The answer shown in the picture is wrong. Orgohacks is comepletely correct. The epoxide ring must be on the same face, meaning the bonds must be cis to one another. If the bonds were trans, there is no way for the 3-membered ring to form. This is exactly as mohad pointed out in the op.

So instead of being able to get four stereoisomers out of the epoxide ring, you can only get two. Organohacks recommends using 2^8 to get the answer, which is correct. Perhaps it might be more specific to say it's (2^9)/2, because half of those supposed 512 stereoisomers would not be allowed. But (2^9)/2 is 2^8.

Sorry if I sound stupid but aren't those bonds in the epoxide cis to each other? how are they trans?

BerkReviewTeach · Jun 19, 2011

MShopes said:
Sorry if I sound stupid but aren't those bonds in the epoxide cis to each other? how are they trans?

Exactly, they are cis! They can only be cis. They physically cannot be trans in that molecule because of the cyclohexene ring. The half of 512 that we are eliminating are the ones that would require the epoxide ring to be trans, which cannot be.

MShopes · Jun 19, 2011

BerkReviewTeach said:
Exactly, they are cis! They can only be cis. They physically cannot be trans in that molecule because of the cyclohexene ring. The half of 512 that we are eliminating are the ones that would require the epoxide ring to be trans, which cannot be.

I see! So whenever we see an epoxide ring with two chiral carbons, we really take into account only one chiral carbon and add it in the 2^n rule? Or by other way take into account two chiral carbons from epoxide and divide by 2 at the end like you said? is that the rule of any epoxide ring or it has to be attached to some ring like cyclohexene?

BerkReviewTeach · Jun 19, 2011

MShopes said:
I see! So whenever we see an epoxide ring with two chiral carbons, we really take into account only one chiral carbon and add it in the 2^n rule? Or by other way take into account two chiral carbons from epoxide and divide by 2 at the end like you said? is that the rule of any epoxide ring or it has to be attached to some ring like cyclohexene?

It's more of a general rule for polycyclic compounds with fused rings. Personally, while it seems like this concept is fair game, I have to believe the test writers would ask it in a way with more hints. Something along the lines of having you explain why an epoxide-steroid ring system only has 256 possible stereoisomers instead of 512 despite having 9 stereocarbons.

MShopes · Jun 19, 2011

BerkReviewTeach said:
It's more of a general rule for polycyclic compounds with fused rings. Personally, while it seems like this concept is fair game, I have to believe the test writers would ask it in a way with more hints. Something along the lines of having you explain why an epoxide-steroid ring system only has 256 possible stereoisomers instead of 512 despite having 9 stereocarbons.

I thought I mastered organic chem completely but that question woke me up. Thank you so much!

mohad · Jun 20, 2011

Ok, thanks for clearing this up. These questions have really been grinding my gears just because of how they contradict each other.

BHaus9 · Jun 20, 2011

Um, but can't the bonds remain -cis with an inversion of configuration at just one of the stereocenters? just imagine a methyl or a hydrogen on one of the epoxide carbons being reoriented to face inward, toward the ring. obviously, this is energetically prohibitive, but i think such a structure can still be drawn without violating any laws of space and time.

Entadus · Feb 7, 2013

BHaus9 said:
Um, but can't the bonds remain -cis with an inversion of configuration at just one of the stereocenters? just imagine a methyl or a hydrogen on one of the epoxide carbons being reoriented to face inward, toward the ring. obviously, this is energetically prohibitive, but i think such a structure can still be drawn without violating any laws of space and time.

No.

"cis" means both bonds are going "up" or both are going "down". If we draw the molecule with one "wedgie" and one "dashie", this is defining the relationship as "trans". The two bonds are not going in the same direction. (They're not going in exactly opposite directions either, but they don't need to be).

mcloaf · Feb 7, 2013

Entadus said:
No.

"cis" means both bonds are going "up" or both are going "down". If we draw the molecule with one "wedgie" and one "dashie", this is defining the relationship as "trans". The two bonds are not going in the same direction. (They're not going in exactly opposite directions either, but they don't need to be).

Why the bump?

Entadus · Feb 8, 2013

mcloaf said:
Why the bump?

Because the thread was still viewable via google search (that's how I found it), and I had something to add.

Chirality and number of isomers

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