How many stereoisomers can exist for cortisone?

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How many stereoisomers can exist for cortisone?

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Answer 1 · 2015-12-03T00:57:49

Cortisone can be found on wikipedia. I've redrawn the structure below, with standard steroid numbering. Noting that $s p^{3}$ $sp^3$ 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 $2^{n} - meso structures$ $2^n - "meso structures"$ , but since there is no plane of symmetry, it is just $2^{n}$ $2^n$ , where $n$ $n$ is the number of stereounits.

Thus, $2^{6} = 64$ $2^6 = color(blue)(64)$ stereoisomers.

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How many stereoisomers can exist for cortisone?

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