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

Verified step by step guidance

1. Step 1: Analyze the reaction conditions for the SN2 reaction. In the first reaction, bromocyclohexane reacts with ethylamine (EtNH₂). SN2 reactions are favored by strong nucleophiles and polar aprotic solvents. Ethylamine is a strong nucleophile, and the reaction likely occurs in a polar aprotic solvent, which facilitates the SN2 mechanism.
2. Step 2: Consider steric hindrance in the SN2 reaction. Bromocyclohexane is a secondary alkyl halide, which is less favorable for SN2 reactions compared to primary alkyl halides due to increased steric hindrance. However, the reaction can still proceed if the nucleophile is strong enough.
3. Step 3: Analyze the reaction conditions for the E2 reaction. In the second reaction, bromocyclohexane reacts with lithium diethylamide (Et₂NLi), a strong base, followed by ethylamine. E2 reactions are favored by strong bases and anti-periplanar geometry between the leaving group and the β-hydrogen. Lithium diethylamide is a very strong base, which promotes the E2 elimination mechanism.
4. Step 4: Compare the leaving group and base strength. Bromine is a good leaving group in both reactions. However, the base strength differs significantly. Lithium diethylamide is much stronger than ethylamine, which makes the E2 reaction faster due to the increased rate of elimination.
5. Step 5: Justify the faster reaction. The E2 reaction is faster because it involves a stronger base (Et₂NLi) and is less affected by steric hindrance compared to the SN2 reaction. The SN2 reaction is slower due to the secondary alkyl halide and the moderate nucleophilicity of ethylamine.

Key Concepts

S_N2 Reactions

S_N2 (substitution nucleophilic bimolecular) reactions involve a single concerted step where the nucleophile attacks the electrophile, leading to the displacement of a leaving group. The reaction rate depends on the concentration of both the nucleophile and the substrate, making it a second-order reaction. S_N2 reactions are favored in primary substrates and polar aprotic solvents, resulting in inversion of configuration.

E2 Reactions

E2 (elimination bimolecular) reactions are characterized by a single concerted step where a base abstracts a proton while a leaving group departs, forming a double bond. The reaction rate is dependent on both the substrate and the base, making it second-order as well. E2 reactions typically occur with secondary and tertiary substrates and require strong bases, often leading to the formation of alkenes.

Reaction Conditions and Mechanism

The choice of reaction conditions, such as the strength of the nucleophile or base and the nature of the substrate, significantly influences the rate of S_N2 and E2 reactions. For instance, strong bases favor E2 mechanisms, while good nucleophiles promote S_N2 pathways. Additionally, steric hindrance and substrate structure (primary, secondary, or tertiary) play crucial roles in determining which reaction will proceed faster.