Problem 126 - A Complete Resource Book in Chemistry for JEE Main

Question

The correct increasing order of the reactivity of halides for \(\mathrm{SN}_{1}\) reaction is (a) \(\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{X}<\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}-\mathrm{X}<\mathrm{CH}_{2}=\mathrm{CH}-\mathrm{CH}_{2}\) \(-\mathrm{X}<\mathrm{Ph} \mathrm{CH}_{2}-\mathrm{X}\) (b) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}-\mathrm{X}<\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{X}<\mathrm{CH}_{2}=\mathrm{CH}-\) \(\mathrm{CH}_{2}-\mathrm{X}<\mathrm{PhCH}_{2}-\mathrm{X}\) (c) \(\mathrm{PhCH}_{2}-\mathrm{X}<\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}-\mathrm{X}<\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{X}<\) \(\mathrm{CH}_{2}=\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{X}\) (d) \(\mathrm{CH}_{2}=\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{X}<\mathrm{PhCH}_{2}-\mathrm{X}<\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}\) \(-\mathrm{X}^{2}<\mathrm{CH}-\mathrm{CH}-\mathrm{X}\)

Step-by-Step Solution

Answer

The correct order is option (b): secondary < primary < allyl < benzyl.

Step 1: Understand SN1 Mechanism

In an SN1 (substitution nucleophilic unimolecular) reaction, the rate depends primarily on the stability of the carbocation intermediate formed. More stable carbocations lead to faster reaction rates in SN1 reactions.

Step 2: Identify Carbocation Stability Order

The stability of carbocations generally follows the order: allyl (resonance-stabilized) > benzyl (resonance-stabilized) > tertiary > secondary > primary.

Step 3: Analyze Each Option for Reactivity Order

Consider each option: - Option (a) proposes increasing reactivity from primary to benzyl halide. - Option (b) suggests a secondary < primary < allyl < benzyl order. - Option (c) suggests a benzyl < secondary < primary < allyl order. - Option (d) suggests allyl < benzyl < secondary < primary order. Carbocations with resonance (allylic and benzylic) are more stable than non-resonance (alkyl) ones.

Step 4: Determine the Correct Answer

Given the order of stability from Step 2, we expect the order to be primary < secondary < allylic < benzylic. Based on this reasoning, option (b) is correct as it follows the expected order for SN1 reactivity.

Key Concepts

Carbocation Stability

In the context of \(\text{SN}_1\) reactions, understanding carbocation stability is crucial. A carbocation is a positively charged carbon molecule, and its stability directly influences the rate of the reaction. More stable carbocations will lower the activation energy required, thus, accelerating the reaction.
It's essential to recognize that not all carbocations are created equal:

• **Allylic and Benzylic Carbocations**: These are generally the most stable due to resonance effects. They can delocalize the positive charge over a larger structure, providing added stabilization.
• **Tertiary Carbocations**: With three alkyl groups attached, these are more stable than secondary or primary carbocations because alkyl groups can donate electron density through inductive effects.
• **Secondary and Primary Carbocations**: Are relatively less stable due to fewer alkyl groups aiding in stabilization.
• **Methyl Carbocations**: These are rarely stable and are generally not seen in \(\text{SN}_1\) reactions owing to their high instability.

Stabilizing factors such as resonance and the inductive effect from surrounding atoms or groups significantly impact the rate of reaction. Thus, recognizing these factors ensures a deeper understanding of reaction mechanisms and outcomes.

Halide Reactivity

Halide reactivity in \(\text{SN}_1\) reactions varies significantly based on the ability of the halide to form a stable carbocation intermediate. The leaving group, typically a halide, affects the reaction rate. Ideally, the leaving group should be able to depart easily, allowing for carbocation formation.
Here's how different halides behave:

• **Iodides (I−)**: These generally make excellent leaving groups due to their large size and ability to stabilize the negative charge effectively after leaving.
• **Bromides (Br−) and Chlorides (Cl−)**: These are moderately good leaving groups. Bromides work well in many conditions, while chlorides may require more energy under some circumstances.
• **Fluorides (F−)**: These are poor leaving groups in SN1 reactions due to their strong bonds and tendency to hold on tightly to the carbon.

The reactivity order of halides is not just about leaving group ability. In \(\text{SN}_1\) reactions, halides that lead to more stable carbocations will react quicker. Therefore, understanding the interplay between carbocation stability and halide properties is key.

Substitution Nucleophilic Unimolecular Reaction

The \(\text{SN}_1\) reaction, also known as a substitution nucleophilic unimolecular reaction, is a multi-step process characterized by the formation of a carbocation intermediate. The mechanism unfolds as follows:

• **Step 1: Leaving Group Departure**: This is the slowest step, known as the rate-determining step. The leaving group departs, forming a carbocation.
• **Step 2: Carbocation Formation**: Once the carbocation is formed, its stability is crucial. More stable carbocations lead to faster reactions.
• **Step 3: Nucleophile Attack**: A nucleophile, which is rich in electrons, attacks the electropositive carbocation, forming a new bond.

Because of the rate-determining step, \(\text{SN}_1\) reactions are sensitive to both the leaving group's ability to depart and the resulting carbocation's stability. The reactions are unimolecular in the rate-determining step, meaning that only the substrate concentration affects the reaction rate.
Therefore, when predicting the behavior of different halides in such a reaction, always consider both the leaving group's efficacy and how stable the resulting carbocation will be. This understanding helps explain why certain substrates react faster than others in \(\text{SN}_1\) reactions.