Out of the following which will not undergo ${S_N}^1$ reaction pathway:

1-Bromo-3,3-dimethylbutane

The correct answer is Option 3. 1-Bromo-3,3-dimethylbutane.

The \(S_N1\) (nucleophilic substitution unimolecular) reaction involves two main steps:

Formation of a Carbocation: The leaving group departs, creating a carbocation intermediate.

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

Factors Influencing \(S_N1\) Reactions

Carbocation Stability: The stability of the carbocation is crucial. More stable carbocations (tertiary > secondary > primary) favor the \(S_N1\) mechanism.

Steric Hindrance: Bulky groups around the reaction site can hinder nucleophiles, making SN2 less favorable, while also influencing the likelihood of carbocation formation.

Analyzing Each Compound

1. 1-Chloro-1,1,1-triphenylmethane:

Forms a very stable tertiary carbocation due to resonance from three phenyl groups. Can easily undergo SN1 due to high carbocation stability.

2. 2-Iodo-2-methylpropane:

Forms a tertiary carbocation upon iodide leaving. Also likely to proceed via \(S_N1\) due to the stability of the carbocation.

3. 1-Bromo-3,3-dimethylbutane:

Upon losing the bromide ion, it forms a secondary carbocation. However, the presence of two bulky tert-butyl groups on either side of the reaction site creates significant steric hindrance. Secondary carbocations are less stable than tertiary ones, and the steric hindrance makes it less favorable for the carbocation to form, thus favoring \(S_N2\) over \(S_N1\).

4. 3-Bromoprop-1-ene:

This would form a primary carbocation when the bromide leaves, which is very unstable. Thus, while it may be less likely to proceed via \(S_N1\), it is more unstable than 1-bromo-3,3-dimethylbutane, but the steric effects of the two bulky groups in 1-bromo-3,3-dimethylbutane make it even less favorable for \(S_N1\).

Conclusion

1-Bromo-3,3-dimethylbutane, due to its secondary carbocation and significant steric hindrance, does not favor the \(S_N1\) pathway. Instead, it would more likely undergo an \(S_N2\) mechanism, where the nucleophile attacks the substrate directly without the formation of a stable carbocation.