Question

How many diastereomers can be in any given molecule?

Answer 1

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.