Question

For the given compound X, the total number of optically active stereoisomers is

• A. 2
• B. 4
• C. 6
• D. 8

Answer 1

Answer: (D)

8

Answer 2

The molecule has four stereogenic centers: two on the cyclopentane ring and one on each of the two side chains. The double bond in the first side chain is trans. The double bond in the second side chain can be cis or trans (2 possibilities). The two hydroxyl groups on the cyclopentane ring are cis to each other.

The two chiral centers on the ring with cis relative stereochemistry can exist as (R,R) and (S,S) configurations, which are enantiomers and optically active (2 possibilities). The first side chain has a fixed trans double bond and a fixed chiral center, contributing 1 stereoisomer. The second side chain has a double bond that can be cis or trans (2 possibilities) and a chiral center that can be R or S (2 possibilities), leading to $2 \times 2 = 4$ possibilities.

The total number of stereoisomers is the product of the possibilities for each part: $2 (\text{ring}) \times 1 (\text{side chain 1}) \times 4 (\text{side chain 2}) = 8$.

Since the two side chains are different, none of the stereoisomers are expected to be meso (achiral). Therefore, all 8 stereoisomers are optically active.