Determining the number of stereoisomers of a compound [closed]








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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:


[![enter image description here](https://i.stack.imgur.com/Bjkpt.png)](https://i.stack.imgur.com/Bjkpt.png)




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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