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 (Nu') a to \(\mathrm{d}\) is \(\left[\mathrm{Nu}^{-}=\begin{array}{lll}\text { (a) } \mathrm{PhO}^{-} & \text {(b) } \mathrm{AcO}^{-} & \text {(c) } \mathrm{HO}^{-} & \text {(d) } \mathrm{CH}_{3} \mathrm{O}^{-}\end{array}\right]\) (a) \(\mathrm{d}>\mathrm{c}>a>\mathrm{b}\) (b) \(\mathrm{d}>\mathrm{c}>\mathrm{b}>\mathrm{a}\) (c) \(a>b>c>d\) (d) \(b>d>c>a\)

Short answer

The correct order is (a) \(\mathrm{d} > \mathrm{c} > a > \mathrm{b}\).

Step-by-step solution

Understand the Reaction Type

The given reaction is an example of a nucleophilic substitution reaction, specifically an S_N2 reaction. In S_N2 reactions, the nucleophile attacks a carbon atom, leading to the replacement of a leaving group, which in this case is bromine (Br⁻). The rate of S_N2 reactions is influenced by the basicity and steric hindrance of the nucleophile.

Analyze the Given Nucleophiles

The nucleophiles given are: (a) \(\mathrm{PhO}^{-}\) (phenoxide), (b) \(\mathrm{AcO}^{-}\) (acetate), (c) \(\mathrm{HO}^{-}\) (hydroxide), and (d) \(\mathrm{CH}_{3}\mathrm{O}^{-}\) (methoxide). We need to compare their nucleophilicity, which is affected by their basicity. Generally, stronger bases are better nucleophiles in S_N2 reactions.

Evaluate Basicity and Nucleophilicity

Structures that are less stabilized (weaker acids' conjugate bases) are stronger bases and better nucleophiles in polar aprotic solvents typical for S_N2 reactions. (a) Phenoxide \((\mathrm{PhO}^{-})\) is resonance-stabilized, lowering its basicity and nucleophilicity. (b) Acetate \((\mathrm{AcO}^{-})\) is also resonance-stabilized and weaker in nucleophilicity.(c) Hydroxide \((\mathrm{HO}^{-})\) is a strong base due to the lack of resonance stabilization.(d) Methoxide \((\mathrm{CH}_{3}\mathrm{O}^{-})\) is similar to hydroxide but more basic due to the electron-donating effect of the methyl group, making it the strongest nucleophile among these.

Rank the Nucleophiles by Nucleophilicity

Using the insights on basicity: (d) Methoxide is the strongest nucleophile because of its high basicity. (c) Hydroxide follows as it is less stabilized than phenoxide and acetate. (a) Phenoxide comes next due to resonance stabilization, which is less influential than acetate. (b) Acetate is the weakest because of its resonance stabilization and reduced negative charge concentration.

Determine the Correct Order

Based on the analysis, the decreasing order of the nucleophiles' strength in the given reaction context is:\[\text{(d) } \mathrm{CH}_{3}\mathrm{O}^{-} > \text{(c) } \mathrm{HO}^{-} > \text{(a) } \mathrm{PhO}^{-} > \text{(b) } \mathrm{AcO}^{-}\] This corresponds to option (a) \(\mathrm{d} > \mathrm{c} > a > \mathrm{b}\).

Key concepts

Nucleophilicity

Nucleophilicity refers to the ability of a molecule or ion to donate an electron pair to form a chemical bond. It's an essential concept in organic chemistry, especially when studying nucleophilic substitution reactions, like the S_N2 reaction. Nucleophiles are attracted to electron-deficient centers, such as positive charges or partial positive charges, typically on carbon atoms.

Factors influencing nucleophilicity include:

• **Charge:** Negatively charged species tend to be better nucleophiles than their neutral counterparts. For example, methoxide \((\text{CH}_3\text{O}^-)\) is more nucleophilic than methanol \((\text{CH}_3\text{OH})\).
• **Basicity:** In general, stronger bases are also stronger nucleophiles. This relation holds particularly well in aprotic solvents.
• **Solvent Effects:** Aprotic solvents enhance the reactivity of nucleophiles by leaving them less solvated, thus more "free" to attack the electrophile.
• **Steric Hindrance:** Bulkier nucleophiles face more steric hindrance, reducing their nucleophilicity compared to their smaller counterparts.

Understanding these factors is key to predicting reaction outcomes and designing efficient synthesis strategies.

Basicity

Basicity is a measure of an atom or molecule's tendency to accept protons \((\text{H}^+)\). It's a crucial aspect in determining nucleophilicity, as there's often a correlation - stronger bases are typically stronger nucleophiles. However, one must not confuse the two.

Considerations for basicity include:

• **Conjugate Acid Strength:** The stability of the conjugate acid derived from a base significantly impacts its basicity. Strong acids yield weak conjugate bases and vice versa.
• **Resonance Stabilization:** When a base is resonance-stabilized, it's less basic. For instance, phenoxide ion \((\text{PhO}^-)\) is less basic due to resonance delocalization.
• **Inductive Effects:** Electron-donating groups increase basicity, as seen in methoxide \((\text{CH}_3\text{O}^-)\), where the methyl group donates electron density.

By appreciating these distinctions, one can correctly predict which species will dominate as a base or nucleophile under specific conditions.

Nucleophilic Substitution

Nucleophilic substitution is a fundamental reaction in organic chemistry where a nucleophile replaces a leaving group from a substrate molecule. The canonical pathways include S_N1 and S_N2 mechanisms. In this context, we focus on SN2 mechanisms, which are concerted one-step processes.

Characteristics of the S_N2 mechanism include:

• **Bimolecular Reaction:** Both the nucleophile and substrate participate simultaneously in the rate-limiting step. Hence, the rate is dependent on the concentration of both.
• **Back-Side Attack:** The nucleophile approaches the carbon atom from the side opposite to the leaving group, resulting in inversion of stereochemistry at the carbon atom.
• **Solvent Effects:** Polar aprotic solvents, like acetone or DMSO, are ideal as they do not solvate the nucleophile strongly, maintaining its nucleophilicity.
• **Leaving Group:** A good leaving group is crucial for the reaction to proceed. Typically, these are stable anions or neutral molecules once they depart from the substrate.

Understanding nucleophilic substitution processes is essential for synthesizing new molecules and interpreting reaction mechanisms.

Leaving Group

A leaving group is a fragment of a molecule that departs with an electron pair after bond cleavage in nucleophilic substitution reactions. Its ability to stabilize negative charge post-departure is crucial to its effectiveness.

Key aspects of effective leaving groups include:

• **Stability Post-Departure:** Highly stable anions, like halides \(\text{Br}^-\) or tosylates, make excellent leaving groups.
• **Polarization and Bond Strength:** Weak bonds with polarized character make for better leaving groups, as they break more readily.
• **Electron-Withdrawing Nature:** Groups that stabilize negative charge through electron withdrawal improve leaving group ability.

Understanding the nature of leaving groups is pivotal in designing efficient reaction conditions and substrates for desired transformations.