Determining the number of stereoisomers of a compound [closed]

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:

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.

$$1)$$ 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.

• 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? Jan 25, 2023 at 6:50
• 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? Jan 25, 2023 at 6:52
• 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. Jan 25, 2023 at 7:54
• 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 $4$. Jan 25, 2023 at 8:05
• I see! Thank you very much! Jan 25, 2023 at 10:39