Question

The addition of \(\mathrm{Br}_{2}\) to \(\mathrm{Z}-2\) butene gives: (a) \((\mathrm{R}, \mathrm{R})-2,3\) -dibromobutane only (b) \((\mathrm{S}, \mathrm{S})-2,3\) -dibromobutane only (c) \((\mathrm{R}, \mathrm{S})-2,3\) -dibromobutane only (d) A mixture of \((\mathrm{R}, \mathrm{R})\) and \((\mathrm{S}, \mathrm{S})-2,3\) -dibromobutanes \((50 \%: 50 \%)\) (e) \((\mathrm{R}, \mathrm{S})-1,2\) -dibromobutane

Short answer

The correct answer is (d) A mixture of (R,R) and (S,S)-2,3-dibromobutanes (50%:50%).

Step-by-step solution

Analyzing the Structure of Z-2-Butene

Z-2-butene is an isomer of butene with the configuration where the substituents (methyl groups) on the double-bonded carbons are on the same side. This is a cis isomer.

Understanding Bromination of an Alkene

Bromination involves the addition of  ext{Br}_2 to the alkene, where the bromine molecule adds across the double bond, resulting in a vicinal dibromo compound. The double bond opens to form a bromonium ion, followed by nucleophilic attack by bromide ion.

Formation of the Bromonium Ion Intermediate

When  ext{Br}_2 attacks the double bond of Z-2-butene, it forms a cyclic bromonium ion intermediate. This addition typically occurs anti to avoid steric hindrance, leading to trans product formation across the original alkene.

Nucleophilic Attack by Bromide Ion

The bromide ion attacks the more substituted carbon of the bromonium ion from the side opposite to the bromine bridge. This attack results in the opening of the bromonium ion and formation of the vicinal dibromide.

Identifying the Final Product Configuration

From Z-2-butene, the trans addition results in the formation of 2,3-dibromobutane. Because of the mirror image equivalency and the anti mechanism, we get a mixture of (R,R) and (S,S) stereoisomers.

Determining the Correct Answer Based on the Product Mix

Since the bromination of Z-2-butene leads to a 50:50 racemic mixture of (R,R) and (S,S)-2,3-dibromobutane, the correct answer is option (d).

Key concepts

Stereochemistry

Stereochemistry is the branch of chemistry that focuses on the spatial arrangement of atoms in molecules and how it influences the physical and chemical properties of those molecules. In the context of the bromination of alkenes, stereochemistry plays a pivotal role in determining the final configuration of the product. This is particularly relevant when dealing with isomers, like Z-2-butene, where even small changes in atom arrangement can lead to significantly different properties.

When bromine (\( \mathrm{Br}_2 \)) adds to an alkene such as Z-2-butene, the process involves considering the stereochemical orientation of the substituents on the original double bond. The definition of "cis" and "trans" isomers is crucial here. In the case of Z-2-butene, the methyl groups are on the same side of the double bond, making it a cis isomer.

Understanding these spatial arrangements helps predict the final stereochemical outcome of reactions, such as the formation of either (R,R) or (S,S) configurations in the resulting vicinal dibromide products.

Vicinal Dibromide

Vicinal dibromides are a type of compound where two bromine atoms are added to adjacent carbon atoms across a previously existing double bond. In the case of Z-2-butene during bromination, this compound is formed as the result of the bromine molecule (\( \mathrm{Br}_2 \)) reacting with the double bond.

When the bromine adds across the double bond of Z-2-butene, it results in breaking the π bond and the formation of a vicinal dibromide. Each carbon involved in the former double bond gets one bromine atom attached to it. This process can yield stereoisomers depending on how the substitution takes place.

In general, the formation of vicinal dibromides through such a reaction ensures that the two bromine atoms are added in a stereoselective manner due to the intermediate formation of a cyclic bromonium ion.

Bromonium Ion

The bromonium ion is a crucial intermediate in the addition of bromine to an alkene. Formation of the bromonium ion occurs when the double bond in an alkene reacts with a \( \mathrm{Br}_2 \) molecule. This leads to a cyclic structure, where one bromine atom is bonded to both carbons involved in the former double bond.

This intermediate is unique because it forms a three-membered ring with a positive charge on the bromine. The formation of the bromonium ion is a key feature that determines the stereochemical course of the reaction.

In the case of Z-2-butene, the bromonium ion forms such that the other bromine atom can attack from the side opposite to the ring. This attack results in an "anti" addition, meaning the two bromine atoms end up on opposite sides of the molecule, leading to the creation of the vicinal dibromide product.

Racemic Mixture

When referring to a racemic mixture in the context of bromination of alkenes, it is a 50:50 mixture of two stereoisomers that are mirror images of each other. In the reaction involving Z-2-butene, the products formed are (R,R)-2,3-dibromobutane and (S,S)-2,3-dibromobutane.

A racemic mixture is crucial because it does not exhibit optical activity. Each isomer in the racemic mixture rotates plane-polarized light to an equal extent but in opposite directions, canceling each other out.

The formation of a racemic mixture in the bromination of Z-2-butene highlights the formation of two enantiomers due to the symmetrical addition of bromine across the original double bond. Understanding racemic mixtures helps in predicting the physical properties of the reaction products and has implications in fields like medicinal chemistry, where the activity of one isomer over another can be significant.