Question

Identify total number of stereoisomer's if double bond is present in cis configuration in given compound (X)

Answer 1

3

Answer 2

The given compound is 2,5-dihydroxyhex-3-ene. The structure is $\text{CH}_3-\text{CH(OH)}-\text{CH=CH}-\text{CH(OH)}-\text{CH}_3$.

There are two chiral centers at C2 and C5. The double bond is between C3 and C4.

The question specifies that the double bond is in cis configuration.

Let's analyze the symmetry of the molecule. The molecule is of the form A-CH(X)-CH=CH-CH(X)-A, where A = $\text{CH}_3$ and X = $\text{OH}$.

The chiral centers are at C2 and C5.

Let's consider the possible stereoisomers due to the chiral centers. Each chiral center can have R or S configuration. So, there are $2^2 = 4$ possible configurations: (R,R), (S,S), (R,S), (S,R).

Since the molecule has two identical chiral centers and a cis double bond, we need to check for meso compounds.

A meso compound is a stereoisomer that is achiral despite having chiral centers. This is usually due to the presence of a plane of symmetry or a center of inversion.

Consider the (R,R) isomer with cis double bond. This is a chiral molecule. Its enantiomer is the (S,S) isomer with cis double bond. These are two distinct stereoisomers.

Consider the (R,S) isomer with cis double bond. Let's check for a plane of symmetry. The molecule has a plane of symmetry passing through the midpoint of the C3-C4 double bond and perpendicular to the plane of the double bond, bisecting the C2-C5 bond. This plane reflects one half of the molecule into the other half, with the configuration of the chiral centers being opposite. Therefore, the (R,S)-cis isomer is a meso compound.

Consider the (S,R) isomer with cis double bond. This is the mirror image of the (R,S)-cis isomer. Since the (R,S)-cis isomer is meso and thus achiral, its mirror image is identical to itself. So, the (S,R)-cis isomer is the same as the (R,S)-cis isomer, and it is also a meso compound.

Thus, for the cis configuration of the double bond, we have the following stereoisomers:

1. (2R,5R)-cis (chiral)
2. (2S,5S)-cis (enantiomer of (2R,5R)-cis, chiral)
3. (2R,5S)-cis (meso, achiral)

The (2S,5R)-cis isomer is the mirror image of (2R,5S)-cis, and since (2R,5S)-cis is meso, (2S,5R)-cis is identical to (2R,5S)-cis.

Therefore, there are a total of 3 stereoisomers when the double bond is in cis configuration: one pair of enantiomers ((2R,5R)-cis and (2S,5S)-cis) and one meso compound ((2R,5S)-cis).