If E/Z is a type of stereoisomerism, then you should be able to use the formula $2^n,$ where $n$ is the number of stereogenic centres. How is it that there are 16 possible E/Z isomers according to the answer in my textbook, but there are no stereogenic centres in all-trans-retinol?
2 Answers
A molecule may include
- any natural number including zero of double bonds (and for each of them, individually, one can check if their configuration can be described as E, Z, or if this label is not applicable here [e.g., ethene])
- any natural number including zero of stereogenic centres (either R, or S)
- any natural number including zero of helical axes (either P, or M)
These three properties are independent of each other.
The molecule contains four conjugated double bonds $\ce{C=C}$, which are all drawn in the E (trans) disposition. And there is no chiral carbon atom, so no R or S atom. But one, two, three or all of the double bonds $\ce{C=C}$ may be in the Z (cis) disposition. This produces $2^4 = 16$ different molecules which are all isomers. They are EEEE, ZEEE, EZEE, EEZE, EEEZ, then EEZZ, EZEZ, EZZE, ZEEZ, ZEZE, ZZEE, then EZZZ, ZZZE, ZZEZ, ZEZZ, and ZZZZ.