Question

In the following reaction sequence, if P can show stereoisomerism. Relation between \(\mathrm{R}\) and \(\mathrm{S}\) is (A) Identical (B) Enantiomer (C) Diastereomers (D) Structural Isomer

Short answer

Based on the given information, we cannot definitively determine the relationship between R and S without more details about the molecule's structure or the reaction sequence. Both Enantiomers (B) and Diastereomers (C) are plausible options, but without further information, we cannot specify which one is correct.

Step-by-step solution

Understand stereoisomerism

Stereoisomers are molecules with the same molecular formula and sequence of bonded atoms (constitution), but which have different three-dimensional orientations of their atoms in space. There are two types of stereoisomers: enantiomers and diastereomers. Enantiomers are mirror images of each other, while diastereomers are not. Structural isomers, on the other hand, have different bonding patterns or sequences of atoms.

Analyze the structure of R and S

Since we know that the product can show stereoisomerism, it must have chiral centers. A chiral center is an atom that has four different substituents bonded to it. In this case, R and S represent two different configurations at the chiral center(s). To determine the relationship between R and S, we need more information about the chiral centers and their substituents in both isomers.

Determine the relationship between R and S

Without further information about the specific structure and configuration of R and S, we must analyze each option and determine if any relationship can be firmly established based on the given information. (A) Identical - If R and S are identical, it means that they have the same configuration at each chiral center. However, this would not lead to stereoisomerism, as the product would not show any difference between the isomers. (B) Enantiomers - Enantiomers have opposite configurations at each chiral center. If R and S are enantiomers, it means that each chiral center of one stereoisomer will have opposite configuration as the same chiral center in the other stereoisomer. This option is plausible, as enantiomers are a type of stereoisomers and the product P can show stereoisomerism. (C) Diastereomers - Diastereomers have opposite configuration at one or more, but not all chiral centers. If R and S are diastereomers, it means that only some of the chiral centers have opposite configuration, while others have the same as in the other stereoisomer. This option is also plausible, as diastereomers are also a type of stereoisomers and the product P can show stereoisomerism. (D) Structural Isomers - Structural isomers have different bonding patterns or sequences of atoms. In this case, R and S are not stereoisomers but rather have different molecular structures. Since the product P can show stereoisomerism, and structural isomers are not a type of stereoisomers, this option is not plausible. Based on the given information, we cannot definitively determine the relationship between R and S without more details about the molecule's structure or the reaction sequence. Both Enantiomers (B) and Diastereomers (C) are plausible options, but without further information, we cannot specify which one is correct.

Key concepts

Enantiomers

Enantiomers are one type of stereoisomers that are non-superimposable mirror images of each other, just like one's left and right hand are mirror images but cannot be aligned perfectly upon each other. They have the same molecular formula, the same atom connectivity, but they differ in the way they are oriented in space. Each molecule in an enantiomeric pair has a chiral center with substituents arranged in a configuration that is the mirror image of the other molecule's chiral center.

Enantiomers display identical physical and chemical properties in a non-chiral environment, but they can exhibit markedly different behavior in a chiral setting, such as interactions with biological systems, where they could produce entirely different effects. They also differ in the way they rotate plane-polarized light; one enantiomer will rotate it in one direction (dextrorotatory) and the other in the opposite direction (levorotatory). An equal mixture of these enantiomers, known as a racemic mixture, has no net optical activity, as the rotations cancel each other out.

Diastereomers

Diastereomers are the other major class of stereoisomers, different from enantiomers in that they are not mirror images of each other. Molecules can be diastereomers if they have two or more chiral centers and differ in the configuration of one or more, but not all, of these centers. Because they are not mirror images, diastereomers can display very different physical and chemical properties.

An easy way to understand diastereomers is to think of them as 'cousins.' While enantiomers are identical twins differing only in handedness, diastereomers can have noticeably different features. For instance, they often have different melting points, boiling points, solubilities, and reactivity. In a complex molecule with numerous chiral centers, there can be many diastereomeric pairs, leading to a rich tapestry of molecular diversity.

Chiral Centers

A chiral center, often referred to as a stereocenter, is typically a carbon atom that is bonded to four different groups. Its chirality results from the lack of symmetry within the molecule, preventing it from being superimposable on its mirror image, akin to the asymmetry between left and right hands.

The presence of a chiral center in a molecule is a prerequisite for the molecule to exhibit chirality. A molecule with a single chiral center is guaranteed to be chiral, and therefore exist as a pair of enantiomers. However, when a molecule has multiple chiral centers, it's possible for it to be achiral if the centers are arranged in a symmetrical way or if configurations of chiral centers cancel each other's chirality. Understanding and identifying chiral centers are essential steps in characterizing the stereochemistry of complex organic molecules and predicting their behaviors in different chemical environments.