Which of the following S_N2 and E2 reactions, respectively, is faster? Justify your choice.
(a)

Verified step by step guidance

1. Step 1: Analyze the reaction conditions for each case. In the first reaction, NaOH is used as the nucleophile in an aqueous solution, which promotes an SN2 mechanism due to the strong nucleophilicity of OH⁻. In the second reaction, H₂O acts as the nucleophile, which is weaker and favors an SN1 mechanism rather than SN2.
2. Step 2: Consider the substrate structure. Both reactions involve a primary alkyl bromide (CH₃CH₂Br), which is highly favorable for SN2 reactions due to minimal steric hindrance around the electrophilic carbon.
3. Step 3: Compare the nucleophiles. OH⁻ is a stronger nucleophile than H₂O because it is negatively charged and more reactive. This makes the first reaction faster under SN2 conditions.
4. Step 4: Evaluate the solvent effects. The first reaction occurs in a polar aprotic environment (NaOH in H₂O), which enhances the nucleophilicity of OH⁻ and accelerates the SN2 reaction. The second reaction occurs in a polar protic solvent (H₂O), which stabilizes the nucleophile and slows down the SN2 reaction.
5. Step 5: Conclude that the first reaction (NaOH in H₂O) is faster for the SN2 mechanism due to the stronger nucleophile and favorable reaction conditions. For E2 reactions, the analysis would depend on the presence of a strong base and the substrate's ability to undergo elimination, which is not explicitly shown in the given problem.

Key Concepts

SN2 Reactions

SN2 (Substitution Nucleophilic Bimolecular) reactions involve a nucleophile attacking an electrophile in a single concerted step, resulting in the displacement of a leaving group. The reaction rate depends on the concentration of both the nucleophile and the substrate, making it second-order. Steric hindrance significantly affects the rate, with primary substrates reacting faster than secondary or tertiary ones.

E2 Reactions

E2 (Elimination Bimolecular) reactions are characterized by the simultaneous removal of a leaving group and a hydrogen atom from adjacent carbon atoms, leading to the formation of a double bond. This reaction also occurs in a single step and is second-order, depending on the concentrations of both the substrate and the base. The reaction rate is influenced by the strength of the base and the structure of the substrate, with bulky bases favoring more sterically accessible sites.

Reaction Conditions

The rate of SN2 and E2 reactions can be influenced by various factors, including solvent type, temperature, and substrate structure. Polar aprotic solvents favor SN2 reactions by stabilizing the nucleophile without solvation, while strong bases and high temperatures enhance E2 reactions. Understanding these conditions is crucial for predicting which reaction will proceed faster under specific circumstances.