1,3-Butadiene reacts with one equivalent \(Br_2\) to form 1,2 and 1,4 addition products simultaneously due to

resonance stabilization of carbocation

The correct answer is option 1. resonance stabilization of carbocation.

The reason 1,3-butadiene reacts with one equivalent of \(Br_2\) to form both 1,2 and 1,4 addition products is due to: (1) Resonance stabilization of the bromonium ion intermediate

Here is why the other options are not the most fitting explanation:

(2) Resonance stabilization of carbanion: Carbanions are not involved in this reaction. Bromine addition is electrophilic, and carbanions are nucleophilic species.

(3) Conjugate effect of the diene: The conjugate effect can influence the stability of intermediates and products, but it doesn't directly explain the formation of both 1,2 and 1,4 addition products in this case.

(4) Hyperconjugative effect in the diene: While hyperconjugation can contribute to the stability of a molecule, it's not the primary factor driving the formation of both addition products here.

Explanation:

The reaction involves the initial addition of \(Br_2\) to the pi bond of 1,3-butadiene, forming a bromonium ion intermediate. This intermediate can be attacked by \(Br^-\) at two different positions:

1,2-addition: \(Br^-\) attacks the carbon adjacent to the positively charged carbon in the bromonium ion, leading to a 1,2-dibromobutene product.

1,4-addition: \(Br^-\) attacks the terminal carbon of the conjugated double bond in the bromonium ion, leading to a 1,4-dibromobutene product.

Resonance stabilization plays a key role because the bromonium ion can be represented by two equivalent Lewis structures. This delocalization of the positive charge makes the intermediate more stable, allowing for both reaction pathways (1,2 and 1,4 addition) to occur competitively.

Therefore, the ability of the bromonium ion to adopt different resonance structures, each allowing for a different attack by \(Br^-\), is the primary reason for the formation of both 1,2 and 1,4 addition products.