Question

Addition of \(\mathrm{Br}_{2}\) to trans-butene-2 gives (1) a racemic mixture of 2,3 -dibromo butane. (2) meso form of 2,3 -dibromo butane. (3) dextro form of 2,3 -dibromo butane. (4) laevo form of 2,3 -dibromo butane.

Short answer

A racemic mixture of 2,3-dibromo butane is formed.

Step-by-step solution

Understand the Reaction

Addition of \(\text{Br}_2\) to trans-butene-2 will proceed through a halogenation reaction, where bromine will add across the double bond in an anti addition manner.

Identify the Product Formed

The product formed will be 2,3-dibromo butane. Since trans-butene-2 is symmetrical, the bromine atoms will add to opposite sides of the double bond.

Determine the Stereochemistry

For trans-butene-2, the bromine atoms add in such a way that the resulting product has two chiral centers. The anti addition will lead to the formation of both R, S and S, R enantiomers.

Identify the Type of Mixture Formed

Since we have a pair of enantiomers (R, S and S, R) in equal amounts, the resulting mixture is a racemic mixture.

Key concepts

Halogenation Reaction

Halogenation refers to the addition of halogen atoms (like bromine or chlorine) to a compound. In the case of alkenes, this reaction typically occurs across the double bond. This process is quite straightforward:

• An alkene, such as trans-butene-2, reacts with a halogen like \(\text{Br}_2\) in a solvent (commonly dichloromethane or chloroform).
• The double bond in the alkene breaks, and each carbon from the double bond forms a bond with an atom from the halogen molecule.

This forms a dihalogenated alkane, turning the double bond into a single bond while attaching halogen atoms to the carbon atoms that were part of the original double bond. Understanding halogenation provides a strong foundation for further reactions involving alkenes.

Anti Addition

In organic chemistry, anti addition refers to the addition of two substituents to opposite sides (or faces) of a double or triple bond. This is crucial for understanding the product formation in halogenation reactions involving alkenes. Let’s break this down:

• When \(\text{Br}_2\) adds to trans-butene-2, one bromine atom attaches to one carbon and the second bromine atom attaches to the opposite carbon of the double bond.
• Because they add to opposite faces, this addition is termed as anti addition.

This anti addition leads to a specific spatial arrangement of atoms in the resultant dihaloalkane. It significantly affects the stereochemistry of the molecule, which is key for understanding properties and reactions of the product formed.

Racemic Mixture

A racemic mixture is a 50:50 mixture of two enantiomers of a chiral compound. Here are the defining features:

• Enantiomers are mirror-image isomers (non-superimposable) of the same molecule, often referred to as 'left-handed' (laevo) and 'right-handed' (dextro) forms.
• Racemic mixtures have no net optical activity because the effects of the two enantiomers cancel each other out.

For the reaction between \(\text{Br}_2\) and trans-butene-2, the product is a racemic mixture of 2,3-dibromo butane. This is because the anti addition mechanism leads to equal amounts of the R,S and S,R enantiomers. Hence, understanding racemic mixtures is crucial in stereochemistry and chiral centers.

Chiral Centers

Chiral centers are atoms in a molecule that have four different substituents, leading to the possibility of non-superimposable mirror images called enantiomers. Here's how they come into play:

• For a carbon to be a chiral center, it must be attached to four different groups.
• In the product of \(\text{Br}_2\) addition to trans-butene-2, both carbon atoms involved in the original double bond become chiral centers in 2,3-dibromo butane.

This becomes evident as each of these carbons is attached to four distinct groups once the bromine atoms are added. Recognizing chiral centers helps in predicting the stereochemistry and understanding the isomerism in organic compounds.