Question

The compound shown below is allowed to react with \(\mathrm{H}_{2} \mathrm{O} .\) Predict the number of optically active isomers formed in the reaction. CC(Br)C(Br)CCO Optically active isomers

Short answer

Two optically active isomers are formed.

Step-by-step solution

Understand the Compound

The compound structure is 2-bromo-3-bromobutane, which has two bromine substituents on a four-carbon chain with an alcohol group at the end (C4H10Br2O). The focus here is on the carbon atoms bearing the bromine substituents (C2 and C3), which could be chiral centers.

Identify Possible Chiral Centers

Determine the chiral centers in the molecule. A chiral center is a carbon atom that has four different groups attached to it. In 2-bromo-3-bromobutane, both C2 and C3 are attached to a methyl group, a hydrogen, a bromine, and another carbon chain, making them potential chiral centers.

Substitution Reaction Analysis

When the compound reacts with water, the bromine atoms are replaced by hydroxyl groups (-OH), resulting in a change in configuration at the chiral centers. This forms an alcohol where both C2 and C3 may theoretically still act as chiral centers, replacing Br with OH at each site.

Calculate Optically Active Isomers

Each chiral center can exist in two configurations (R and S), leading to different stereoisomers. With two chiral centers, the number of total stereoisomers is calculated as: \[ 2^n \] where \( n \) is the number of chiral centers. Hence, for two centers, there are \( 2^2 = 4 \) stereoisomers. Out of these, half will be optically active (enantiomers), while the other half will be meso compounds (optically inactive).

Identify Optically Active Isomers

Optically active isomers are those that rotate plane-polarized light. In this reaction, half of the 4 potential stereoisomers will be optically active. Hence there are 2 optically active isomers.

Key concepts

Chiral Centers

A chiral center is a carbon atom that is bonded to four different groups, making it asymmetrical. This lack of symmetry is crucial because it means the chiral center can exist in two different configurations, often referred to as "R" (rectus, right) and "S" (sinister, left). These configurations are mirror images of each other, much like our left and right hands are. Chiral centers are fundamental to the concept of optical activity in molecules.

When a molecule has one or more chiral centers, it can exist as different stereoisomers, which may have distinct chemical and physical properties. In the case of 2-bromo-3-bromobutane, C2 and C3 are identified as chiral centers. They both have a bromine attached, a methyl group, a hydrogen, and a part of the carbon chain, fulfilling the requirement of four different groups.

2-bromo-3-bromobutane

2-bromo-3-bromobutane is an organic compound with the molecular formula C4H8Br2. This compound features two bromine atoms attached to a butane chain, specifically at the second and third carbon positions. The structure includes two potential chiral centers, making this molecule a key study subject for optical activity.

The presence of the bromine atoms and the carbon backbone contributes to its reactivity, especially in substitution reactions. 2-bromo-3-bromobutane can undergo chemical reactions where the bromine atoms are replaced by other groups, such as hydroxyl groups (OH) when reacting with water. This results in the formation of stereoisomers due to changes at the chiral centers.

Stereoisomers

Stereoisomers are molecules that have the same structural formula but differ in the three-dimensional arrangement of their atoms. This property is due to the presence of chiral centers. Each chiral center in a molecule can have two orientations, leading to multiple possible stereoisomers.

The number of possible stereoisomers is calculated using the formula: \[ 2^n \] where \( n \) is the number of chiral centers. For instance, in 2-bromo-3-bromobutane, there are two chiral centers (C2 and C3), potentially leading to \( 2^2 = 4 \) stereoisomers.

Among these three-dimensional configurations, half are typically enantiomers and optically active, rotating plane-polarized light, whereas the rest can be meso compounds, which are optically inactive despite having chiral centers.

Substitution Reaction

A substitution reaction involves replacing one atom or group in a molecule with another. For 2-bromo-3-bromobutane reacting with water, the bromine atoms attached to the chiral centers are replaced with hydroxyl groups (OH). This change alters the three-dimensional configuration at the chiral centers, leading to the creation of new stereoisomers.

During the substitution, each chiral center can potentially switch from one enantiomeric configuration to another (from R to S or vice versa). This replacement can result in four new stereoisomers: two being enantiomers and two being meso compounds.