Problem 133 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following order represents the increasing order of reactivity towards \(\mathrm{Br}^{-}\)under \(\mathrm{S}_{\mathrm{N}}{\underline{\phantom{xx}}}^{1}\) conditions? 1\. vinyl chloride 2\. methyl chloride 3\. ethyl chloride 4\. allyl chloride (a) \(4<3<2<1\) (b) \(1<2<3<4\) (c) \(2<1<3<4\) (d) \(2<1<4<3\)

Step-by-Step Solution

Answer

The increasing order of reactivity toward \(\mathrm{Br}^-\) under \(\mathrm{S}_{\mathrm{N}}{\underline{\phantom{xx}}}^{1}\) is (b) \(1<2<3<4\).

Step 1: Understand the Reaction Type

The question involves substitution reactions under \(\mathrm{S}_{\mathrm{N}}{\underline{\phantom{xx}}}^{1}\) conditions, where a halide ion, \(\mathrm{Br}^-\), replaces the chlorine atom in chlorides.

Step 2: Recall Factors Affecting \(\mathrm{S}_{\mathrm{N}}{ }^{1}\) Reactivity

For \(\mathrm{S}_{\mathrm{N}}{\underline{\phantom{xx}}}^{1}\) reactions, the stability of the carbocation intermediate is important. More substituted carbocations (including resonance-stabilized ones) increase the reactivity.

Step 3: Compare Carbocation Stability

1. Vinyl chloride forms a \(\mathrm{vinyl}\) carbocation, which is unstable with no resonance stabilization. 2. Methyl chloride forms a \(\text{methyl}\) carbocation, which is primary and very unstable.3. Ethyl chloride forms a \(\text{ethyl}\) carbocation, which is a bit more stable (secondary).4. Allyl chloride forms an \(\mathrm{allylic}\) carbocation, which is resonance-stabilized and the most stable of the four.

Step 4: Determine Reactivity Order

Since \(\mathrm{S}_{\mathrm{N}}{\underline{\phantom{xx}}}^{1}\) reactivity increases with carbocation stability, the increasing order of reactivity would be: Vinyl chloride < Methyl chloride < Ethyl chloride < Allyl chloride.

Step 5: Match with Given Options

Checking the options provided, the correct order matches option (b): \(1<2<3<4\). So, in increasing order of reactivity, it is Vinyl < Methyl < Ethyl < Allyl chloride.

Key Concepts

Carbocation Stability

Understanding carbocation stability is essential for predicting reactivity in \( \mathrm{S}_{\mathrm{N}}^{1} \) reactions. These reactions proceed via the formation of a carbocation intermediate after the leaving group departs.

The stability of this carbocation determines the rate of reaction. Stable carbocations are formed quickly, altering the reaction landscape.

• **Primary Carbocations**: Least stable, as seen with methyl chlorides, due to no substituents to disperse positive charges.
• **Secondary Carbocations**: More stable, formed with ethyl chlorides, offering mild stability through electron donating groups.
• **Tertiary Carbocations**: Very stable due to extensive charge distribution by multiple adjacent substituents.
• **Resonance-Stabilized Carbocations**: Exceptionally stable, e.g., allyl chloride, where delocalization across the molecule provides outstanding stability.

In essence, reactivity increases as carbocations become more stable, enhancing substitution rates.

Vinyl Chloride

Vinyl chloride, a compound integral in the production of PVC, exhibits unique reactivity patterns.

When it forms a carbocation, it's termed a vinyl carbocation. This type of carbocation is particularly unstable because it lacks resonance stabilization.

The double bond associated with vinyl chloride does not participate in stabilizing the positive charge, leading to a high-energy, less reactive system.

Generally, vinyl chlorides are poor candidates for \( \mathrm{S}_{\mathrm{N}}^{1} \) reactions due to their instability when forming a carbocation.

• **Non-resonating double bond**: Offers no stabilization to the positive charge.
• **Unstable carbocation**: Results in sluggish reaction rates under \( \mathrm{S}_{\mathrm{N}}^{1} \) conditions.

Consequently, in the context of reactivity, vinyl chloride ranks lower than other chlorides.

Methyl Chloride

Methyl chloride is another simple organic molecule involved in \( \mathrm{S}_{\mathrm{N}}^{1} \) reactions.

Forming a methyl carbocation upon losing chlorine, it is characterized as primary and highly unstable.Since there are no additional carbon atoms or substituents to distribute the positive charge, the methyl carbocation exists in a high-energy, reactive state.

Key points to note include:

• **Absence of charge stabilizing groups**: The single carbon structure imparts minimal stability.
• **Fast to react**: Despite its instability, when it does react, the process happens swiftly.

Primarily, methyl chloride reacts more readily than vinyl chloride but less so compared to more stable carbocations like those formed by allyl chloride.

Allyl Chloride

Allyl chloride stands out in \( \mathrm{S}_{\mathrm{N}}^{1} \) reactions due to its ability to form a highly stable allylic carbocation.

This stability arises from resonance, allowing the positive charge to be delocalized across adjacent pi bonds, thereby lowering the energy state.

Notably, allyl chlorides under \( \mathrm{S}_{\mathrm{N}}^{1} \) conditions react swiftly due to this stability.Key characteristics include:

• **Resonance**: Provides superior stability by spreading the charge over multiple atoms.
• **Enhanced reactivity**: Due to the lower energy state of the carbocation.

What sets allyl chloride apart is its predisposition for fast reactions, outpacing both vinyl and methyl chlorides due to its inherent stabilizing features.