Q. 15 The total number of stereoisomers possible for the following structure is ___
Understanding the Given Structure
The given compound is 1,2,3-tribromocyclopropane, which consists of:
- A cyclopropane ring (three-membered ring)
- One bromine atom attached to each carbon
- Each carbon is sp³ hybridized
- Each carbon becomes a stereogenic (chiral) center
Hence, the total number of chiral centers = 3.
Step 1: Maximum Possible Stereoisomers
The general formula for calculating the maximum number of stereoisomers is:
2n
Where n is the number of chiral centers.
For this molecule:
23 = 8
So, the maximum possible stereoisomers are 8.
Step 2: Check for Symmetry and Meso Forms
Even though there are three chiral centers, the molecule exhibits internal symmetry due to:
- Identical bromine substituents on all three carbon atoms
- Symmetrical cyclopropane ring structure
Due to this symmetry:
- Some stereoisomers become identical
- One configuration forms a meso compound, which is optically inactive despite having chiral centers
Step 3: Elimination of Identical Forms
Out of the 8 theoretical stereoisomers:
- 2 stereoisomers are identical due to symmetry
- 1 meso form exists
- The remaining stereoisomers exist as optically active enantiomeric pairs
Final Count of Stereoisomers
| Type | Count |
|---|---|
| Enantiomeric pairs | 2 pairs (4 isomers) |
| Meso form | 1 |
| Total stereoisomers | 5 |
Correct Answer
5
Explanation of Possible Options
Option A: 8 ❌
- This represents the maximum theoretical number
- Does not consider molecular symmetry
- Hence, incorrect
Option B: 6 ❌
- Overlooks the presence of a meso compound
- Incorrect count
Option C: 4 ❌
- Counts only enantiomeric pairs
- Ignores the meso form
- Incorrect
Option D: 5 ✅ (Correct Answer)
- Accounts for molecular symmetry
- Includes one meso form
- Includes two enantiomeric pairs
- Correct choice
Key Takeaways for Exams
- Always check for molecular symmetry
- Presence of identical substituents can reduce the number of stereoisomers
- Meso compounds reduce the total stereoisomer count
- Cyclopropane derivatives often show hidden symmetry
Final Answer
5
