JEE Challenger
More from Organic Chemistry - Basic Principles
ChemHardAdv 2009 • Paper 1

Stereoisomerism and Enantiomers of Unsaturated Diol Compound X

The correct statement(s) about the compound H3C(HO)HC−CH=CH−CH(OH)CH3\text{H}_3\text{C}(\text{HO})\text{HC}-\text{CH}=\text{CH}-\text{CH}(\text{OH})\text{CH}_3 (X\mathbf{X}) is(are)

Options

A

The total number of stereoisomers possible for X\mathbf{X} is 6

Correct
B

The total number of diastereomers possible for X\mathbf{X} is 3

C

If the stereochemistry about the double bond in X\mathbf{X} is trans\textit{trans}, the number of enantiomers possible for X\mathbf{X} is 4

D

If the stereochemistry about the double bond in X\mathbf{X} is cis\textit{cis}, the number of enantiomers possible for X\mathbf{X} is 2

Correct

Topics & Concepts

Organic Chemistry - Basic PrinciplesIsomerism

Step-by-Step Solution

To determine the correct statement(s) regarding the compound X\mathbf{X}, CH3−CH(OH)−CH=CH−CH(OH)−CH3\text{CH}_3-\text{CH(OH)}-\text{CH}=\text{CH}-\text{CH(OH)}-\text{CH}_3 (hex-3-ene-2,5-diol\text{hex-3-ene-2,5-diol}), we analyze its stereocenters and symmetry.

1. Analysis of Stereogenic Units:

The compound has:

  • Two similar chiral centers at C2\text{C}_2 and C5\text{C}_5, each attached to −H-\text{H}, −OH-\text{OH}, −CH3-\text{CH}_3, and the central alkenyl group.
  • One stereogenic double bond at C3=C4\text{C}_3=\text{C}_4, which can exhibit geometrical isomerism (cis\textit{cis} or trans\textit{trans}).

The molecule is symmetrical, with identical groups on both sides of the double bond.

2. Enumeration of Stereoisomers:

Case I: The double bond is trans\textit{trans} (EE)

The possible configurations for (C2,C3=C4,C5)(\text{C}_2, \text{C}_3=\text{C}_4, \text{C}_5) are:

  1. (2R,3E,5R)(2R, 3E, 5R)
  2. (2S,3E,5S)(2S, 3E, 5S)
    • These two forms are non-superimposable mirror images of each other, forming a single pair of enantiomers (total of 22 enantiomers).
  3. (2R,3E,5S)(2R, 3E, 5S)
    • Due to the internal symmetry (a center of inversion CiC_i in its appropriate conformation), this form is identical to (2S,3E,5R)(2S, 3E, 5R) and is an optically inactive meso compound.

Thus, for the trans\textit{trans} configuration, there are 33 stereoisomers (one pair of enantiomers, i.e., 22 enantiomers, and 11 meso compound).

  • Therefore, Option C is incorrect.

Case II: The double bond is cis\textit{cis} (ZZ)

The possible configurations for (C2,C3=C4,C5)(\text{C}_2, \text{C}_3=\text{C}_4, \text{C}_5) are:

  1. (2R,3Z,5R)(2R, 3Z, 5R)
  2. (2S,3Z,5S)(2S, 3Z, 5S)
    • These two forms are non-superimposable mirror images of each other, forming a pair of enantiomers (total of 22 enantiomers).
  3. (2R,3Z,5S)(2R, 3Z, 5S)
    • Due to the plane of symmetry (σ\sigma), this form is identical to (2S,3Z,5R)(2S, 3Z, 5R) and is an optically inactive meso compound.

Thus, if the stereochemistry about the double bond is cis\textit{cis}, the number of enantiomers (chiral stereoisomers that exist as enantiomeric pairs) is 22.

  • Therefore, Option D is correct.

3. Total Number of Stereoisomers:

Summing the stereoisomers from both cases:
Total number of stereoisomers=3 (trans)+3 (cis)=6\text{Total number of stereoisomers} = 3 \, (\textit{trans}) + 3 \, (\textit{cis}) = 6

  • Therefore, Option A is correct.

4. Diastereomers:

Diastereomers are non-superimposable, non-mirror image stereoisomers. Any given stereoisomer of X\mathbf{X} has several diastereomers among the other 5 stereoisomers; hence the total number of diastereomers is not 3.

  • Therefore, Option B is incorrect.

Conclusion:

The correct statements are A and D.

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