Question

\((2 R, 3 S)-2,3-\) dihydroxybutanedioic acid and \((2 S, 3 R)-2,3-\) dihydroxybutanedioic acid are: meso compounds. the same molecule. enantiomers. (A) \(\quad\) I only (B) \(\quad \$ II only (C) \)\quad\( I and II only (D) \)\quad$ I and III only

Short answer

Only option III is correct (D).

Step-by-step solution

- Identify the molecules

Identify the given compounds: - \( (2 R, 3 S)-2,3- \) dihydroxybutanedioic acid \ - \( (2 S, 3 R)-2,3- \) dihydroxybutanedioic acid

- Determine relationship between configurations

Recognize that the configurations \( (2 R, 3 S) \) and \( (2 S, 3 R) \) are mirror images of each other. Therefore, the compounds are enantiomers.

- Check for meso compound

A meso compound is a molecule with multiple chiral centers that is superimposable on its mirror image due to an internal plane of symmetry. Since these compounds are enantiomers, they cannot be meso compounds.

- Evaluate molecular identity

Since one compound is the mirror image of the other and cannot be superimposed on it, they are not the same molecule.

- Determine the correct options

Based on the analysis, the compounds are only enantiomers. Hence, only option III is correct.

Key concepts

meso compounds

In organic chemistry, a meso compound is a molecule with multiple chiral centers that is superimposable on its mirror image. This means that, despite having chiral centers, the molecule itself is achiral due to an internal plane of symmetry. Consider a molecule with two chiral centers, arranged such that one center has an 'R' configuration, and the other an 'S' configuration. If you can draw a plane through the molecule, dividing it into two symmetrical halves, then the molecule is a meso compound. Noteworthy characteristics of meso compounds:

• They are achiral.
• They are optically inactive.
• They have identical halves mirrored on either side of an internal symmetry plane.

For instance, (2R, 3S)-2,3-dihydroxybutanedioic acid appears to be a candidate for a meso compound. However, the mirrored image is not superimposable due to the difference in configurations at the chiral centers. As such, it is not a meso compound.

chiral centers

Chiral centers, also known as stereocenters or asymmetric carbons, are key in organic chemistry for understanding molecular diversity and behavior. A chiral center typically involves a carbon atom bonded to four distinct groups. This unique arrangement means that the carbon can exist in two non-superimposable forms, which are mirror images of each other. These two configurations are known as enantiomers. Properties of chiral centers:

• They contribute to the optical activity of a molecule.
• A molecule with one chiral center will always be chiral.
• More than one chiral center can lead to multiple stereoisomers.

In our exercise, (2R, 3S)-2,3-dihydroxybutanedioic acid and (2S, 3R)-2,3-dihydroxybutanedioic acid both contain chiral centers at positions 2 and 3. Because the configurations of these chiral centers are different, the compounds are enantiomers, not identical molecules.

mirror images

In the context of molecular chemistry, mirror images refer to two structures that are non-superimposable reflections of each other, akin to how your left and right hands are reflections but not identical. These structures, known as enantiomers, display interesting properties in chiral molecules. Characteristics of mirror images (enantiomers):

• They have identical physical properties, such as melting points and densities.
• They rotate plane-polarized light in opposite directions.
• They often have significantly different interactions with other chiral substances, including biological molecules.

Our exercise highlights the fact that (2R, 3S)-2,3-dihydroxybutanedioic acid and (2S, 3R)-2,3-dihydroxybutanedioic acid are mirror images of each other. They are enantiomers because they cannot be superimposed, meaning they are true non-identical mirror images, not the same molecule or meso compounds. Understanding this concept is crucial for recognizing molecular behavior in biological systems and synthetic chemistry.