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Difficulty: HardStructural Isomerism and Stereoisomerism

A molecule possessing two identical chiral carbon atoms, such as 2,32,3-dichlorobutane, yields a total of four optically active stereoisomers.

Answer: Answer

Answer

The statement is false. A molecule with two identical chiral carbon atoms generates three stereoisomers in total: one pair of optically active enantiomers and one optically inactive meso compound.
The statement is false because 2,32,3-dichlorobutane contains two identical chiral carbon atoms. Its internal plane of symmetry in the meso configuration causes internal compensation of optical rotation, yielding only two optically active enantiomers and one optically inactive meso form (three stereoisomers in total).

Step-by-Step Solution

1
Identify the chiral carbon atoms and their bonded groups in 2,32,3-dichlorobutane.
Carbon-2 and Carbon-3 are both chiral centers, each attached to four groups: −H-H, −Cl-Cl, −CH3-CH_3, and −CH(Cl)CH3-CH(Cl)CH_3. Because both carbons have identical sets of substituents, the chiral centers are identical.
Recognizing identical chiral centers is essential for identifying internal planes of symmetry.
2
Evaluate theoretical stereoisomer combinations using the 2n2^n rule.
The theoretical maximum without symmetry considerations is 22=42^2 = 4 configurations: (2R,3R)(2R, 3R), (2S,3S)(2S, 3S), (2R,3S)(2R, 3S), and (2S,3R)(2S, 3R).
The formula 2n2^n determines the upper limit of stereoisomers for nn chiral centers.
3
Examine internal symmetry and optical activity of the configurations.
The (2R,3R)(2R, 3R) and (2S,3S)(2S, 3S) forms are non-superimposable mirror images (enantiomers) and are optically active. However, the (2R,3S)(2R, 3S) and (2S,3R)(2S, 3R) structures are identical to each other due to an internal plane of symmetry. This single achiral meso compound is optically inactive via internal compensation.
Internal symmetry cancels optical rotation, leaving only two optically active stereoisomers and one optically inactive meso stereoisomer (3 total).

Key Concept

Meso compounds and internal optical compensation in molecules with identical chiral centers.
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Topics

Structural Isomerism and Stereoisomerism

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