Will the following S_N2 reaction proceed more rapidly in DMSO or H₂O?

Verified step by step guidance

1. Step 1: Understand the reaction mechanism. The given reaction is an SN2 reaction, where the nucleophile (CN⁻) attacks the electrophilic carbon attached to the leaving group (Br⁻) in a single concerted step. SN2 reactions are bimolecular and proceed via a backside attack, leading to inversion of configuration at the carbon center.
2. Step 2: Analyze the role of the solvent in SN2 reactions. Polar aprotic solvents, such as DMSO (dimethyl sulfoxide), are ideal for SN2 reactions because they do not solvate the nucleophile strongly. This allows the nucleophile to remain reactive and attack the electrophilic carbon more efficiently. In contrast, polar protic solvents, such as H₂O, can hydrogen bond with the nucleophile, reducing its reactivity and slowing down the reaction.
3. Step 3: Evaluate the nucleophile and leaving group. In this reaction, CN⁻ is a strong nucleophile, and Br⁻ is a good leaving group. The efficiency of the nucleophile is enhanced in a polar aprotic solvent like DMSO, making the reaction proceed more rapidly.
4. Step 4: Consider steric factors. The substrate (2-bromopropane) is a secondary alkyl halide, which is moderately hindered. SN2 reactions are sensitive to steric hindrance, but the choice of solvent can significantly impact the reaction rate. DMSO will help minimize steric effects by enhancing nucleophilic attack.
5. Step 5: Conclude the solvent choice. Based on the principles of SN2 reaction mechanisms and solvent effects, the reaction will proceed more rapidly in DMSO compared to H₂O due to the increased nucleophilicity of CN⁻ in a polar aprotic environment.

Key Concepts

S_N2 Mechanism

The S_N2 mechanism is a type of nucleophilic substitution reaction where a nucleophile attacks an electrophile, resulting in the simultaneous displacement of a leaving group. This reaction is characterized by a single concerted step, leading to an inversion of configuration at the carbon center. The rate of the reaction depends on the concentration of both the nucleophile and the substrate.

Solvent Effects

The choice of solvent can significantly influence the rate of S_N2 reactions. Polar aprotic solvents, like DMSO, stabilize the nucleophile without solvation, enhancing its reactivity. In contrast, polar protic solvents, such as H₂O, can solvate the nucleophile, reducing its availability to attack the substrate, thus slowing the reaction.

Nucleophilicity

Nucleophilicity refers to the strength of a nucleophile in a chemical reaction, which is influenced by factors such as charge, electronegativity, and solvent effects. Stronger nucleophiles are more reactive and can more effectively attack electrophiles. In the context of the given reaction, the nucleophile CN^- from NaCN is crucial for determining the reaction rate in different solvents.