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I am confused about:

  1. Does stereoisomers include both cis-trans isomers and enantiomers (those with chiral carbons)

  2. If a cyclic compound exhibits cis trans isomerism, is it able to exhibit optical isomerism on the same carbons

  3. How to determine the total number of stereoisomers if a compound has both cis-trans and optical isomerism

The question is as follows:

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2 Answers 2

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The prostaglandin molecule you have given has four stereogenic centers: Three on ring substitutions and one in a one of long side chains $(\ce{-CH(OH)(CH2)4CH3})$. Since none have other symmetric factors such as plain of symmetry, usual numbers of stereo isomers of the molecule are $2^4 = 16$. However, both long chain substitutions contain disubstituted double bonds, each of which can exist as $E$- and $Z$-isomers ($cis/trans$). Thus, each of the original 16 isomers can exist as four other srereoisomers: $EE$-, $EZ$-, $ZE$-, and $ZZ$-isomers. For example: $(2S,3S,4S,3''R)$- isomer can exist as $(2S,3S,4S,3''R)$-$(2'E,1''E)$-, $(2S,3S,4S,3''R)$-$(2'E,1''Z)$-, $(2S,3S,4S,3''R)$-$(2'Z,1''E)$- and $(2S,3S,4S,3''R)$-$(2'Z,1''Z)$-isomers, all four of which are stereoisomers with optical activity. Thus, you may find total of 64 optical active isomers in given prostaglandins.

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$1)$ Cis-trans isomers are also stereoisomers. They are called as diastereomers.

$2)$ Consider, 1-bromo-3-methylcyclohexane. It shows cis-trans isomerism and each of the isomers(that is cis and trans) have enantiomers.

$3)$ Again, consider the above example. 1-bromo-3-methylcyclohexane has $4$ stereoisomers, each of them is chiral.

The compound you have given have 16 stereoisomers excluding cis-trans isomers.

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  • $\begingroup$ Hi for point 3), if 1-bromo-3-methylcyclohexane has one site for cis-trans isomerism and two chiral carbons (on carbon 1 and 3) does that mean that the total number of stereoisomers is 2^(1+2) = 8? $\endgroup$
    – zolotl
    Jan 25, 2023 at 6:50
  • $\begingroup$ Also, for the compound in my question, how many sites for cis-trans isomerism are there and what would be the total number of stereoisomers possible? $\endgroup$
    – zolotl
    Jan 25, 2023 at 6:52
  • $\begingroup$ Yes. In general the maximum numbers of stereoisomers a molecule can have is $2^{m+n}$, where $m=$ number of chiral centres and $n=$ number of double bonds that can give cis-trans isomerism . For the compound you gave , there are $2$ sites of double bond that give cis-trans isomerism. $\endgroup$
    – Natasha J
    Jan 25, 2023 at 7:54
  • $\begingroup$ Remember that cyclohexane exists in chair conformation , so cis corresponds to both functional group facing upwards and trans corresponds to one group facing upwards and the other downwards. So your first comment, there are no sites for cis-trans due to double bonds, so total number of stereoisomers is $4$. $\endgroup$
    – Natasha J
    Jan 25, 2023 at 8:05
  • $\begingroup$ I see! Thank you very much! $\endgroup$
    – zolotl
    Jan 25, 2023 at 10:39

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