Question

The number of enantiomers of the compound \(\mathrm{CH}_{3} \mathrm{CHBrCHBrCOOH}\) is (a) 1 (b) 2 (c) 3 (d) 4

Short answer

The number of enantiomers is 2.

Step-by-step solution

Identify the Chiral Centers

A chiral center is a carbon atom that is attached to four different groups. The compound given is \( \mathrm{CH}_{3} \mathrm{CHBrCHBrCOOH} \). Examine each carbon atom in the compound to find the chiral centers. Both of the central carbon atoms bonded to a bromine (\( \ce{Br} \)) are chiral, making them the chiral centers in this compound.

Analyze the Stereochemistry

Each chiral center can have two stereochemical configurations: R or S. Therefore, for each chiral center, two possible configurations exist. Since there are two chiral centers in this compound, you should consider the possible combinations of R, S configurations present.

Calculate the Total Number of Stereoisomers

The total number of stereoisomers for a compound with \( n \) chiral centers is given by \( 2^n \). Here, \( n = 2 \), so substituting \( n = 2 \) gives us \( 2^2 = 4 \) stereoisomers. These include both enantiomers and diastereomers.

Determine the Number of Enantiomers

Enantiomers are stereoisomers that are non-superimposable mirror images of each other. Every pair of stereoisomers in this case would have exactly one enantiomer. Since there are 4 stereoisomers (R,R; R,S; S,R; S,S), there are 2 pairs of enantiomers.

Key concepts

Chiral Centers

A chiral center is crucial for understanding molecular symmetry and enantiomer formation. In an organic molecule, a carbon atom that is bonded to four different groups becomes a chiral center. This asymmetry allows the molecule to exist in more than one form, which often includes enantiomers.
In the compound \(\mathrm{CH}_{3}\mathrm{CHBrCHBrCOOH}\), both of the central carbons are bonded to a bromine atom and different groups, making them chiral centers. Identifying these chiral centers is essential because they dictate the stereochemical possibilities of the molecule, ultimately affecting the number of stereoisomers. Recognizing chiral centers helps students predict the potential diversity in molecular structures and is the first step in analyzing a compound's stereochemistry.

Stereochemistry

Stereochemistry is the branch of chemistry that studies the spatial arrangement of atoms in molecules. It is vital for understanding how molecules interact, as well as their function and reactivity. In stereochemistry, each chiral center can be arranged in different spatial configurations, commonly known as 'R' (rectus) and 'S' (sinister) configurations. Each configuration of a chiral center creates an opportunity for a new 3D molecular arrangement.
Stereochemistry can significantly influence the biological activity of a compound, as different stereoforms often have different effects in biological systems. Understanding stereochemistry enables students to predict how these different forms might interact with biological systems, which is crucial in fields like drug development and biochemistry. As you examine the compound \(\mathrm{CH}_{3}\mathrm{CHBrCHBrCOOH}\), knowing its stereochemical possibilities helps anticipate its various biological activities.

Stereoisomers

Stereoisomers are molecules that have the same molecular formula and sequence of bonded atoms, but differ in the 3-dimensional orientations of their atoms in space. This difference can lead to variations in physical and chemical properties. For a compound with chiral centers, the number of possible stereoisomers can be calculated using the formula \(2^n\), where \(n\) is the number of chiral centers.
In our example, the compound \(\mathrm{CH}_{3}\mathrm{CHBrCHBrCOOH}\) has 2 chiral centers, leading to \(2^2 = 4\) possible stereoisomers. These include enantiomers, which are non-superimposable mirror images, and other types of stereoisomers such as diastereomers. Each stereoisomer has unique properties and reactivities, which can be important to consider in practical applications like synthesis and pharmacology.

R and S Configurations

R and S configurations are the nomenclature used to describe the 3D orientation of chiral centers in a molecule. By following a set of rules, known as the Cahn-Ingold-Prelog priority rules, chemists can assign an 'R' or 'S' designation to each chiral center.

• Assign priorities to the groups attached to the chiral center based on atomic number. Highest atomic number gets highest priority.
• Look at the molecule from a perspective where the group with the lowest priority is facing away from you.
• If the order of 1, 2, 3 is clockwise, the configuration is 'R'. If counterclockwise, it is 'S'.

In the compound \(\mathrm{CH}_{3}\mathrm{CHBrCHBrCOOH}\), analyzing the configurations of its chiral centers helps determine the correct stereoisomer forms (R,R; R,S; S,R; S,S). Understanding these configurations not only helps in identifying the specific stereoisomers present but also guides how the molecule might interact with other molecules, especially in biological systems.