How many stereoisomers can exist for cortisone?

1 Answer
Dec 3, 2015

Cortisone can be found on wikipedia. I've redrawn the structure below, with standard steroid numbering. Noting that #sp^3# carbons are potential chiral centers, I've marked them.

Carbon-8: S
Carbon-9: S
Carbon-10: R
Carbon-13: S
Carbon-14: S
Carbon-17: R

So, we see six stereocenters. We also don't see any carbons that can allow any cis-trans geometric isomers. Finally, there is no plane of symmetry anywhere here. So, with that in mind, the number of stereounits (stereocenters + cis-trans centers) is still six.

The number of stereoisomers is known to be #2^n - "meso structures"#, but since there is no plane of symmetry, it is just #2^n#, where #n# is the number of stereounits.

Thus, #2^6 = color(blue)(64)# stereoisomers.