Question

Which of the following alkyl halides will undergo the fastest rate of nucleophilic substitution via an \(\text{S}_{\text{N}}1\) mechanism when treated with an aqueous nucleophile?

• A. \(\text{CH}_3\text{Cl} \)
• B. \((\text{CH}_3)_3\text{CCl} \)
• C. \(\text{CH}_3\text{CH}_2\text{Cl} \)
• D. \((\text{CH}_3)_2\text{CHCl} \)

Hint:

Carbocation stability and \(\text{S}_{\text{N}}1\) reaction rates follow the exact same structural trend: \(\text{Tertiary } (3^\circ) > \text{Secondary } (2^\circ) > \text{Primary } (1^\circ) > \text{Methyl}\).

Answer 1

The Correct Option is B

Concept: The rate-determining step of an \(\text{S}_{\text{N}}1\) substitution mechanism is the unimolecular dissociation of the leaving group to form a carbocation intermediate: \[ \text{R--X} \xrightarrow{\text{Slow}} \text{R}^+ + \text{X}^- \] The overall reaction rate depends directly on the stability of this intermediate carbocation.

Step 1: Evaluate intermediate carbocation stability trends.
Comparing the carbocations formed when the leaving groups dissociate:
• \(\text{CH}_3\text{Cl} \rightarrow \text{CH}_3^+\) (Methyl carbocation, highly unstable)
• \(\text{CH}_3\text{CH}_2\text{Cl} \rightarrow \text{CH}_3\text{CH}_2^+\) (\(1^\circ\) Primary carbocation)
• \((\text{CH}_3)_2\text{CHCl} \rightarrow (\text{CH}_3)_2\text{CH}^+\) (\(2^\circ\) Secondary carbocation)
• \((\text{CH}_3)_3\text{CCl} \rightarrow ({CH}_3)_3\text{C}^+\) (\(3^\circ\) Tertiary carbocation, stabilized by 9 hyperconjugative \(\alpha\)-hydrogens) The tertiary halide dissociates fastest because it forms the most stable intermediate carbocation.