Problem 177 - A Complete Resource Book in Chemistry for JEE Main

Question

\(\mathrm{CH}_{3} \mathrm{Br}+\mathrm{Nu} \longrightarrow \mathrm{CH}_{3}-\mathrm{Nu}+\mathrm{Br}^{-}\) The decreasing order of the rate of the above reaction with nucleophiles \(\left(\mathrm{Nu}^{-}\right)\)(a) to \((\mathrm{d})\) is [2006] \(\left[\mathrm{Nu}^{-}=\left(\right.\right.\)a) \(\mathrm{Ph} \mathrm{O}^{-}\)(b) \(\mathrm{AcO}^{-}\)(c) \(\mathrm{HO}^{-}\)(d) \(\left.\mathrm{CH}_{3} \mathrm{O}^{-}\right]\) (a) \(4>3>1>2\) (b) \(4>3>2>1\) (c) \(1>2>3>4\) (d) \(2>4>3>1\)

Step-by-Step Solution

Answer

(a) The correct order is 4 > 3 > 1 > 2.

Step 1: Understand the Reaction Type

The reaction given is a nucleophilic substitution reaction where the nucleophile (Nu\(^-\)) attacks the carbon atom bonded to the bromine atom in \( \mathrm{CH}_3\mathrm{Br} \), replacing the bromine.

Step 2: Recognize Nucleophile Strength

In nucleophilic substitution reactions, the rate generally increases with the strength of the nucleophile. The nucleophiles in order are: a) \( \mathrm{PhO}^- \), b) \( \mathrm{AcO}^- \), c) \( \mathrm{HO}^- \), d) \( \mathrm{CH}_3\mathrm{O}^- \). Among these, \( \mathrm{CH}_3\mathrm{O}^- \) is the strongest due to the electron-donating effect of the methyl group.

Step 3: Analyze Electron Donating/Withdrawing Effects

\( \mathrm{CH}_3\mathrm{O}^- \) is a stronger nucleophile than \( \mathrm{HO}^- \) because the methyl group donates electrons. \( \mathrm{PhO}^- \) has resonance stabilization which decreases its nucleophilicity compared to \( \mathrm{CH}_3\mathrm{O}^- \) and \( \mathrm{HO}^- \). \( \mathrm{AcO}^- \) (acetate) is even weaker due to resonance between the two oxygen atoms.

Step 4: Arrange Reaction Rates

Based on nucleophile strengths: \( \mathrm{CH}_3\mathrm{O}^- \) > \( \mathrm{HO}^- \) > \( \mathrm{PhO}^- \) > \( \mathrm{AcO}^- \). Assign numbers: \( 4 > 3 > 1 > 2 \).

Step 5: Match with Given Options

The rearrangement in descending order of rate is \( 4, 3, 1, 2 \). Compare with provided options and select the matching one.

Key Concepts

Nucleophile Strength

The strength of a nucleophile is a crucial factor in determining the rate of a nucleophilic substitution reaction. A nucleophile donates a pair of electrons to form a chemical bond with an electrophile. Nucleophiles are typically negatively charged or neutral molecules with lone pairs. The stronger the nucleophile, the more readily it can attack and bond with the electrophile.

Several factors influence nucleophile strength, including charge, electronegativity, and the steric factors of the nucleophile. Generally,

• An increase in negative charge enhances nucleophilicity because there is a greater electron density to participate in bonding.
• Less electronegative atoms make better nucleophiles since they hold onto electrons less tightly and can donate them more easily.
• Smaller, less hindered nucleophiles are typically stronger because they can approach and attack the electrophile more effectively.

In our given example, the \(\text{CH}_3\text{O}^-\) ion is the strongest nucleophile because the electron-donating methyl group pushes electron density towards the oxygen, making it more ready to attack the electrophile.

Reaction Mechanism

Nucleophilic substitution reactions typically follow two main types of mechanisms:

• \( S_N1 \) (unimolecular nucleophilic substitution)
• \( S_N2 \) (bimolecular nucleophilic substitution).

The mechanism depends on the structure of the substrate and the conditions of the reaction. In an \( S_N2 \) reaction, the nucleophile attacks from the opposite side of the leaving group, leading to an inversion of configuration at the carbon center. Whether the reaction follows an \( S_N1 \) or \( S_N2 \) pathway affects the rate and outcome of the reaction.

For the example provided, \( \text{CH}_3\text{Br} \), the reaction typically follows an \( S_N2 \) mechanism. Methyl bromide is a primary haloalkane, making it more suitable for \( S_N2 \) reactions because there is less steric hindrance around the carbon atom. The nucleophile attacks directly, resulting in the displacement of the bromide ion. This type of mechanism is favored by strong nucleophiles like \( \text{CH}_3\text{O}^- \).

Electron Donating and Withdrawing Effects

Understanding how electron donating and withdrawing groups affect nucleophilicity is key in predicting reaction outcomes. Electron-donating groups (EDGs) increase the electron density on a nucleophile, enhancing its ability to donate electrons. Conversely, electron-withdrawing groups (EWGs) decrease electron density, reducing nucleophile strength.

For example, \( \text{CH}_3\text{O}^- \) is stronger than \( \text{HO}^- \) because the methyl group acts as an electron-donating group, providing increased electron density at the oxygen atom. On the other hand, \( \text{AcO}^- \) is weakened due to the resonance interaction which distributes and decreases the effective lone pair electron density on the oxygens, making it a weaker nucleophile. In this scenario, \( \text{PhO}^- \) is less nucleophilic than \( \text{CH}_3\text{O}^- \) due to resonance which stabilizes the charge.

Resonance Stabilization

Resonance stabilization plays a significant role in determining the reactivity of nucleophiles. Resonance refers to the delocalization of electrons across a molecule, stabilizing it by spreading out charge over multiple atoms or bonds. However, this stabilization can also negatively impact nucleophilicity.

In resonance-stabilized nucleophiles, the lone pair electrons that would typically be available for bonding are instead delocalized. This delocalization lowers the electron density, reducing the nucleophile's reactivity.

Taking \( \text{PhO}^- \) as an example, the negative charge on the oxygen is delocalized into the aromatic ring of the phenoxide ion, stabilizing it through resonance structures. While this stabilization lowers the reactivity of the ion as a nucleophile, it tends to make the ion more stable overall. Similarly, in \( \text{AcO}^- \), resonance between the two oxygen atoms reduces its effectiveness as a nucleophile.