Subjective Type

How do you calculate how many stereoisomers a compound has ?

Solution

Answer
For every atom that can exist in more than one configuration, you have R or S $$(sp^{3}) $$ or E or Z $$(sp^{2}) $$ you have two configurations for each of those atoms.

If you had 2 of those atoms (chiral centers), then you have 4 configuration combinations: (R, R), (R, S), (S, R), (S, S).

For 3 of those atoms (3 chiral centers), you have: (R,R,R), (R,R,S), (R,S,R), (S,R,R), (R,S,S), (S,R,S), (S,S,R), (S,S,S), which is 8.

Let us call an atom or group of atoms that can exist in more than one configuration a stereo unit.

That means for n stereo units, you have $$2^{n}$$ stereoisomers possible.

However, note that if there are any meso compounds (i.e. if the molecule has a chance of having a plane of symmetry dividing two identical halves that each contains asymmetric centers), then we must account for them because the symmetry reduces the number of different compounds.

An example of a meso compound vs. a regular chiral compound. Thus, we revise the formula to give:
Total Stereoisomers $$ = 2^{n} - $$where n=number of stereounits.

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