Arrange the following compounds in increasing order of \(S_N1\) reactivity

A. Primary alkyl halide

B. Tertiary alkyl halide 

C. Vinylic halide

D. Secondary alkyl halide 

E. Allylic halide

Choose the correct answer from the options given below:

C, A, D, B, E

The correct answer is option 4. C, A, D, B, E.

The reactivity of alkyl halides towards the \(S_N1\) mechanism primarily depends on the stability of the carbocation intermediate formed during the reaction. The more stable the carbocation, the faster the reaction will proceed. Here's a detailed breakdown of each compound's reactivity and why they follow the order C < A < D < B < E:

C. Vinylic halide

A vinylic halide has a halogen atom attached directly to a double-bonded carbon (sp² hybridized carbon). In an \(S_N1\) reaction, the halide would need to leave, forming a carbocation. However, a carbocation on an sp² hybridized carbon is extremely unstable due to the high s-character, which pulls electrons closer to the nucleus, making it less able to stabilize a positive charge.

Result: Vinylic halides are extremely unreactive in \(S_N1\) reactions because they do not easily form stable carbocations. Thus, C is the least reactive.

A. Primary alkyl halide

A primary alkyl halide has the halogen attached to a carbon bonded to only one other carbon (or no other carbons if it's methyl). When the halide leaves, a primary carbocation is formed. This carbocation is relatively unstable because it lacks sufficient alkyl groups to donate electron density through hyperconjugation or inductive effects to stabilize the positive charge.

Result: Primary alkyl halides are more reactive than vinylic halides but still very slow in \(S_N1\) reactions because the primary carbocation is unstable.

D. Secondary alkyl halide

A secondary alkyl halide has the halogen attached to a carbon bonded to two other carbons. When the halide leaves, a secondary carbocation is formed. This carbocation is more stable than a primary carbocation due to increased hyperconjugation and inductive effects from the additional alkyl group. These effects help distribute the positive charge more effectively, stabilizing the intermediate.

Result: Secondary alkyl halides are moderately reactive in \(S_N1\) reactions because they form reasonably stable carbocations

B. Tertiary alkyl halide

A tertiary alkyl halide has the halogen attached to a carbon bonded to three other carbons. When the halide leaves, a tertiary carbocation is formed, which is highly stable. The three surrounding alkyl groups provide maximum hyperconjugation and inductive effects, distributing the positive charge over a larger area.

Result: Tertiary alkyl halides are very reactive in \(S_N1\) reactions because they form the most stable carbocation among alkyl halides (after allylic halides).

E. Allylic halide

An allylic halide has the halogen attached to a carbon adjacent to a double bond. When the halide leaves, an allylic carbocation is formed. This carbocation is exceptionally stable because of resonance stabilization. The positive charge can delocalize over the adjacent double bond, spreading the charge across multiple atoms.

Result: Allylic halides are the most reactive in \(S_N1\) reactions due to the resonance stabilization of the carbocation.

Thus, the correct order of increasing reactivity for \(S_N1\) reactions is: C (Vinylic) < A (Primary) < D (Secondary) < B (Tertiary) < E (Allylic)