How many diastereomers can be in any given molecule?

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Jan 11, 2017

The maximum number of diastereomers is #2^n - 2#.

You have probably learned that the maximum number of optical isomers is #2^n#, where #n# is the number of chiral centres.

The number decreases if some of the optical isomers are meso compounds.

The number of diastereomers is less than #2^n# because two of the isomers must be a pair of enantiomers.

However, every other optical isomer is a diastereomer of each enantiomer.

Thus, the maximum number of diastereomers is #2^n-2#.

If #n = 1#,
#2^n-2 = 2^1-2 = "2 - 2" =0# (no diastereomers).

If #n = 2#,
#2^n-2 = 2^2-2 = "4 - 2" =2# (2 diastereomers).

If #n = 3#,
#2^n-2 = 2^3-2 = "8 - 2" =6# (6 diastereomers).

If #n = 4#,
#2^n-2 = 2^4-2 = "16 - 2" =14# (14 diastereomers).

For example, D-glucose has 4 chiral carbons, so there are 16 aldohexoses (8 D and 8 L).

L-Glucose is an enantiomer of D-glucose, and the other 14 aldohexoses are diastereomers of them.

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