Problem 123 - A Complete Resource Book in Chemistry for JEE Main

Question

Arrange the following halides in the decreasing order of \(\mathrm{S}_{\mathrm{N}}^{1}\) reactivity. I. \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Cl}\) II. \(\mathrm{CH}_{2}=\mathrm{CHCH}(\mathrm{Cl}) \mathrm{CH}_{3}\) III. \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}(\mathrm{Cl}) \mathrm{CH}_{3}\) (a) \(\mathrm{I}>\mathrm{II}>\mathrm{III}\) (b) \(\mathrm{II}>\mathrm{III}>\mathrm{I}\) (c) \(\mathrm{II}>\mathrm{I}>\mathrm{III}\) (d) III > II >I

Step-by-Step Solution

Answer

The order of reactivity is II > III > I, option (b).

Step 1: Understand the SN1 Reaction

The SN1 reaction mechanism involves two steps: formation of a carbocation intermediate and the subsequent nucleophilic attack. The stability of the carbocation is crucial in determining the rate of the reaction; more stable carbocations react faster. This means tertiary carbocations are more stable (and thus react faster) than secondary, and secondary are more stable than primary.

Step 2: Analyze Molecular Structures

Review each compound's structure to determine the type of carbocation that would form if the leaving group (Cl-) were to leave, thus initiating an SN1 reaction. - Compound I: The leaving group will form a primary carbocation. - Compound II: The leaving group will form a secondary carbocation with resonance stabilization due to the double bond. - Compound III: The leaving group will form a secondary carbocation.

Step 3: Determine Carbocation Stability

Assess the stability of the carbocations: - A primary carbocation (compound I) is least stable. - A secondary carbocation with resonance (compound II) is the most stable. - A secondary carbocation without resonance (compound III) is less stable than a resonance-stabilized tertiary or secondary carbocation.

Step 4: Rank Reactivity Based on Stability

Given that the SN1 reactivity is directly related to carbocation stability: - Compound II, with the resonance-stabilized secondary carbocation, is the most reactive. - Compound III, with a secondary carbocation, is less reactive than II but more so than I. - Compound I, with a primary carbocation, is the least reactive.

Key Concepts

Carbocation Stability

In the context of SN1 reactions, carbocation stability plays a pivotal role in determining the reaction rate. Carbocations are positively charged carbon atoms, and their stability is critical because they form as intermediates during SN1 reactions. The most stable carbocations are those that can distribute charge efficiently. This stability often follows the order: tertiary > secondary > primary.
Carbocations can gain extra stability through mechanisms like resonance. In resonance, the charge is delocalized over multiple atoms rather than being concentrated in one spot, which helps stabilize the intermediate. For example, in compound II from the exercise, a secondary carbocation benefits from resonance due to its attachment to a double bond. Thus, it is more stable than the secondary carbocation in compound III, which does not have resonance support.
In summary:

• A tertiary carbocation has more neighboring carbon groups providing stabilization.
• A secondary carbocation can be stabilized further through resonance.
• Primary carbocations are usually very unstable and less favorable in reactions like SN1.

Understanding carbocation stability is the cornerstone of predicting SN1 reaction outcomes.

Nucleophilic Substitution

Nucleophilic substitution is a fundamental reaction in organic chemistry where a nucleophile replaces a leaving group on a carbon atom. There are two main types of these reactions: SN1 and SN2. In the context of the exercise, we focus on SN1 reactions:
**SN1 Reaction Characteristics**

• Unimolecular: The rate-determining step involves only the substrate.
• Occurs in two steps: Formation of a carbocation, followed by nucleophilic attack.
• The reactivity largely depends on the stability of the intermediate carbocation.

An SN1 reaction starts when the leaving group (such as chloride in the given compounds) departs, forming a carbocation. Then, the nucleophile attacks this positively charged intermediate, resulting in the substitution. The rate of SN1 reactions is directly proportional to the formation rate of the carbocation.
Key factors influencing SN1 reactions:

• Leaving Group Ability: Better leaving groups facilitate faster reactions.
• Carbocation Stability: More stable carbocations form more readily.
• Solvent Effects: Polar protic solvents help stabilize carbocations and facilitate the reaction.

In conclusion, understanding nucleophilic substitution, especially the SN1 type, is vital for predicting reaction behavior.

Halides Reactivity

Halides, such as chlorides in the provided compounds, serve as leaving groups in SN1 reactions. The ability of a halide to leave efficiently greatly influences the reaction rate. In general, the reactivity of halides as leaving groups follows the trend: Iodide > Bromide > Chloride > Fluoride. However, in this exercise, since we're only dealing with chlorides, it's more relevant to focus on the structure of the compound and the resulting carbocation.
**Factors Affecting Halide Reactivity in SN1**

• Carbocation Stability: More stable carbocations encourage a faster reaction, regardless of the specific halide involved.
• Nature of the Halide: While not varied in this exercise, generally, larger halides like iodides leave more readily.
• Compound Structure: The arrangement that results in the most stable carbocation will be the most reactive in SN1.

In the case of the exercise examples, the resonance-stabilized carbocation of compound II elevates its reactivity, despite all compounds having a chloride leaving group. Thus, within SN1 reactions featuring the same type of halide, it's the potential to stabilize a carbocation that drives reactivity.