The most reactive halide towards \(S_N1\) reaction is

tert-butyl chloride

The correct answer is option 2. tert-butyl chloride.

Let us delve into why tert-butyl chloride is the most reactive halide towards \(S_N1\) (unimolecular nucleophilic substitution) reactions compared to the other options provided.

\(S_N1\) reactions proceed in two main steps:

Formation of Carbocation: The leaving group (halide ion) leaves the substrate, forming a carbocation intermediate

\(\text{R-X} \rightarrow \text{R}^+ + \text{X}^-\)

Nucleophilic Attack: A nucleophile attacks the carbocation to form the substitution product.

\(\text{R}^+ + \text{Nu}^- \rightarrow \text{R-Nu}\)

Factors Affecting Reactivity in \(S_N1\) Reactions

The rate-determining step in \(S_N1\) reactions is the formation of the carbocation intermediate. Therefore, the stability of the carbocation significantly influences the reactivity of the alkyl halide:

Carbocation Stability: Carbocations stabilize through hyperconjugation (alkyl groups donate electron density through sigma bonds) and inductive effects (electron-donating alkyl groups). The stability of carbocations follows the order: tertiary > secondary > primary > methyl.

Comparison of Options

1. sec-Butyl chloride: Forms a secondary carbocation intermediate. Secondary carbocations are less stable than tertiary but more stable than primary carbocations.

2. tert-Butyl chloride: Forms a tertiary carbocation intermediate. Tertiary carbocations are highly stable due to hyperconjugation and steric hindrance around the positively charged carbon atom.

3. n-Butyl chloride: Forms a primary carbocation intermediate. Primary carbocations are the least stable among alkyl halides due to lack of hyperconjugation and increased exposure of the positive charge.

4. Allyl chloride: Forms an allylic carbocation intermediate, which can be stabilized by resonance. Resonance stabilization provides additional stability to the carbocation, making allyl halides reactive in \(S_N1\) reactions.

Conclusion

Among the options provided, tert-butyl chloride is the most reactive halide towards \(S_N1\) reaction because it forms a tertiary carbocation intermediate. Tertiary carbocations are highly stable due to the electron-donating effects of three methyl groups (hyperconjugation) and steric hindrance, which disfavor backside attack by the nucleophile.

Therefore, in \(S_N1\) reactions, the reactivity order of alkyl halides based on carbocation stability is: tert-butyl chloride > allyl chloride > sec-butyl chloride > n-butyl chloride

This stability trend correlates directly with the reactivity towards SN1 reactions, with more stable carbocations leading to faster reaction rates.