Problem 196 - A Complete Resource Book in Chemistry for JEE Main

Question

\(\mathrm{CH}_{3} \mathrm{Br}+\mathrm{Nu}^{-} \longrightarrow \mathrm{CH}_{3}-\mathrm{Nu}+\mathrm{Br} \quad\) [2006] The decreasing order of the rate of the above reaction with nucleophiles \(\left(\mathrm{Nu}^{-}\right) \mathrm{a}\) to \(\mathrm{d}\) is \(\left[\mathrm{Nu}^{-}=\begin{array}{lll}\text { (a) } \mathrm{PhO} & \text { (b) } \mathrm{AcO}^{-} \text {(c) } \mathrm{HO}^{-} & \left.\text {(d) } \mathrm{CH}_{3} \mathrm{O}^{-}\right]\end{array}\right.\) (a) \(\mathrm{d}>\mathrm{c}>\mathrm{a}>\mathrm{b}\) (b) \(\mathrm{d}>\mathrm{c}>\mathrm{b}>\mathrm{a}\) (c) \(a>b>c>d\) (d) \(\mathrm{b}>\mathrm{d}>\mathrm{c}>\mathrm{a}\)

Step-by-Step Solution

Answer

The decreasing order of nucleophile strength is d > c > a > b, so option (a) is correct.

Step 1: Identify the Reaction Type

The given reaction is a nucleophilic substitution where a methyl group is being attacked by a nucleophile Nu\(^{-}\). This is a bimolecular nucleophilic substitution reaction \(S_{N}2\).

Step 2: Understand Nucleophile Strength

In an \(S_{N}2\) reaction mechanism, a stronger nucleophile will result in a faster reaction. The strength of the nucleophile is often associated with its basicity. Methoxide (\(\mathrm{CH}_{3} \mathrm{O}^{-}\)) is the strongest base followed by hydroxide (\(\mathrm{HO}^{-}\)).

Step 3: Analyze Nucleophile Basicity

Ordering by basicity or strength of the nucleophile, we have: \(\mathrm{CH}_{3} \mathrm{O}^{-}\) (strongest base), \(\mathrm{HO}^{-}\), followed by \(\mathrm{PhO}^{-}\) and finally \(\mathrm{AcO}^{-}\) (weakest base). This order generally suggests the relative strength of these nucleophiles in an \(S_{N}2\) reaction.

Step 4: Determine the Rate with Respect to Nucleophiles

Given that the order of nucleophilicity from strongest to weakest is \(\mathrm{CH}_{3} \mathrm{O}^{-} > \mathrm{HO}^{-} > \mathrm{PhO}^{-} > \mathrm{AcO}^{-}\), the rate of reaction will follow this order since stronger nucleophiles react faster in \(S_{N}2\) mechanisms.

Step 5: Match with Given Options

Compare the determined order \(\mathrm{d} > \mathrm{c} > \mathrm{a} > \mathrm{b}\) with the provided options. Option (a) matches our order correctly.

Key Concepts

Nucleophilic Substitution

Nucleophilic substitution is a fundamental type of reaction in organic chemistry. It involves a nucleophile, a species with a lone pair of electrons, displacing a leaving group from a molecule. This particular reaction involving \( \mathrm{CH}_{3} \mathrm{Br} \) is a bimolecular nucleophilic substitution reaction (\(S_{N}2\)). In an \(S_{N}2\) mechanism, the nucleophile attacks the electrophilic carbon atom, resulting in the formation of a new bond and the departure of the leaving group. One key aspect of this reaction is its concerted nature, which means that the bond formation and bond breaking happen simultaneously.

• The nucleophile approaches the substrate from the side opposite to the leaving group.
• This leads to the inversion of configuration at the carbon atom if it is chiral.
• The rate of these reactions is highly dependent on the concentration and strength of the nucleophile.

Nucleophile Strength

In an \(S_{N}2\) reaction, the strength of the nucleophile significantly influences the reaction rate. A stronger nucleophile can more efficiently donate its pair of electrons to form a new chemical bond. This is critical in driving the reaction forward.

• Strong nucleophiles are generally negatively charged ions since they have a high affinity to donate electron pairs.
• In our reaction context, \(\mathrm{CH}_{3} \mathrm{O}^{-}\) (methoxide) is the strongest nucleophile due to its high electron density and ability to readily donate electrons.
• The next strongest is \(\mathrm{HO}^{-}\) (hydroxide), followed by \(\mathrm{PhO}^{-}\) (phenoxide) and \(\mathrm{AcO}^{-}\) (acetate).

Ultimately, a stronger nucleophile will lead to a quicker reaction rate in \(S_{N}2\) mechanisms.

Nucleophile Basicity

Basicity of a nucleophile is closely related to its ability to participate in nucleophilic substitution reactions. Basicity refers to the nucleophile's ability to accept protons or donate electron pairs. This property affects its strength significantly and thus the reaction rate in \(S_{N}2\) processes.

• Highly basic nucleophiles generally exhibit stronger nucleophilicity.
• Methoxide \(\mathrm{CH}_{3} \mathrm{O}^{-}\) is a stronger base than hydroxide, which is stronger than phenoxide. Lastly, acetate is the weakest base among these.

Hence, the order of basicity from strongest to weakest in the context of our reaction is precisely the order that would dictate the nucleophile strength.

Reaction Rate

The reaction rate of an \(S_{N}2\) reaction is influenced by several factors, with nucleophile strength being one significant aspect. A stronger nucleophile facilitates a faster reaction due to its increased ability to attack the electrophilic center of the substrate.

• The reaction rate is directly proportional to the concentration and strength of the nucleophile.
• In the provided nucleophiles—methoxide, hydroxide, phenoxide, and acetate—the reaction rate decreases as \(\mathrm{CH}_{3} \mathrm{O}^{-} > \mathrm{HO}^{-} > \mathrm{PhO}^{-} > \mathrm{AcO}^{-}\).
• This indicates the role of both the nucleophile's charge and steric accessibility, which can facilitate or hinder the approach to the reactive center.

Thus, the reaction rate hierarchy reflects these considerations, ensuring that the fastest reactions occur with the strongest nucleophiles.