Determine the number of possible stereoisomers for the compound below. OH Number of stereoisomers =
The Correct Answer and Explanation is:
Step 1: Identify Stereocenters
A stereocenter (or chiral center) is a carbon atom bonded to four different groups. These centers allow for different spatial arrangements, which lead to stereoisomers.
If a compound has n stereocenters and no internal plane of symmetry, then the maximum number of stereoisomers is given by:Number of stereoisomers=2n\text{Number of stereoisomers} = 2^nNumber of stereoisomers=2n
However, if the compound has an internal plane of symmetry (making it a meso compound), the actual number of stereoisomers will be less than 2ⁿ, because meso compounds are achiral and do not have enantiomers.
Step 2: Example Case Analysis
Let’s consider a molecule with two chiral centers. For example:
HO–CH(CH₃)–CH(OH)–CH₃
This molecule has two stereocenters:
- The second carbon (CH with OH and CH₃)
- The third carbon (CH with OH and CH₃)
So, n=2n = 2n=2 stereocenters.
By default, the number of stereoisomers is:22=42^2 = 422=4
But now consider symmetry: if the molecule is symmetric and the two stereocenters are mirror images of each other, there is a possibility for a meso form, which is superimposable on its mirror image. This meso compound will reduce the total count by 1.
Therefore, total stereoisomers = 22=42^2 = 422=4, but 1 of these is meso → only 3 unique stereoisomers.
Conclusion
To determine the number of stereoisomers:
- Count the chiral centers (n).
- Compute 2n2^n2n.
- Check for symmetry (meso compounds) to subtract duplicates.
Final Answer Format:
Number of stereoisomers = depends on nnn and symmetry.
For n = 2 chiral centers with symmetry,
Answer: 3 stereoisomers (2 enantiomers + 1 meso compound).
