May 25, 2019, 03:51:24 PM
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### Topic: How many pairs of diastereomers are there in a compound with 3 chiral centers?  (Read 596 times)

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#### zuriel

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##### How many pairs of diastereomers are there in a compound with 3 chiral centers?
« on: February 22, 2019, 08:40:24 AM »
Say for example I have the ring structure shown below (chiral centers shown in red).
I know there are the following FOUR pairs of enantiomers (which I can draw):

[R, R, R] - [S, S, S]

[S, R, R] - [R, S, S]

[R, S, R] - [S, R, S]

[R, R, S] - [S, S, R]

However, how many pairs of diastereomers are there? For a system with two chiral centers there are four pairs of diastereomers and two pairs of enantiomers.
Here, am I correct in saying that if [R, R, R] can form part of six diastereomeric pairs then so can [S, R, R], [R, S, R] and [R, R, S] giving 24 possible PAIRS of compounds related as diastereomers?
I've had someone else suggest different numbers to me and I'm just wondering if anyone else has more input into this, thanks!

#### Bakterien

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##### Re: How many pairs of diastereomers are there in a compound with 3 chiral centers?
« Reply #1 on: February 22, 2019, 11:39:33 AM »
I think it's 4. You have 8 diffrent enantiomers so half of them are not mirror images off eachother . So

R,R,R
R,S,R
R,S,S
R,R,S

Or the inverse

#### zuriel

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##### Re: How many pairs of diastereomers are there in a compound with 3 chiral centers?
« Reply #2 on: February 22, 2019, 12:46:30 PM »
*edited*

#### zuriel

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##### Re: How many pairs of diastereomers are there in a compound with 3 chiral centers?
« Reply #3 on: February 22, 2019, 12:53:22 PM »
EDIT on closer inspection, I left out some pairs of compounds NOT related as mirror images. This brings the number to 18.

#### Weiman

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##### Re: How many pairs of diastereomers are there in a compound with 3 chiral centers?
« Reply #4 on: February 22, 2019, 01:01:05 PM »
EDIT on closer inspection, I left out some pairs of compounds NOT related as mirror images. This brings the number to 18.

You're on the right track. Pair the right column of stereoisomers of each quadrant in your image and you'll get 24 pairs total.

#### zuriel

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##### Re: How many pairs of diastereomers are there in a compound with 3 chiral centers?
« Reply #5 on: February 22, 2019, 01:07:05 PM »
EDIT on closer inspection, I left out some pairs of compounds NOT related as mirror images. This brings the number to 18.

You're on the right track. Pair the right column of stereoisomers of each quadrant in your image and you'll get 24 pairs total.

But if I paired everything on the left hand side some of the pairings are repeated which is why I left those out, I was at 24 initially and then I came back to 18 when I deleted the double entries.

#### Weiman

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##### Re: How many pairs of diastereomers are there in a compound with 3 chiral centers?
« Reply #6 on: February 22, 2019, 01:17:53 PM »
EDIT on closer inspection, I left out some pairs of compounds NOT related as mirror images. This brings the number to 18.

You're on the right track. Pair the right column of stereoisomers of each quadrant in your image and you'll get 24 pairs total.

But if I paired everything on the left hand side some of the pairings are repeated which is why I left those out, I was at 24 initially and then I came back to 18 when I deleted the double entries.

I apologize, my phrasing was ambiguous. I've shown the missing pairs are in blue.

#### zuriel

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##### Re: How many pairs of diastereomers are there in a compound with 3 chiral centers?
« Reply #7 on: February 22, 2019, 01:20:36 PM »
Ah, sorry, now I understand.

So it is correct to say that, for this compound:

- there are 8 possible stereoisomers
- there are four pairs of enantiomers
- there are 24 pairs of diastereomers

?

#### Weiman

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##### Re: How many pairs of diastereomers are there in a compound with 3 chiral centers?
« Reply #8 on: February 22, 2019, 01:23:17 PM »
Ah, sorry, now I understand.

So it is correct to say that, for this compound:

- there are 8 possible stereoisomers
- there are four pairs of enantiomers
- there are 24 pairs of diastereomers

?

You got it

#### zuriel

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##### Re: How many pairs of diastereomers are there in a compound with 3 chiral centers?
« Reply #9 on: February 22, 2019, 01:28:37 PM »
Thank you very much Weiman!!