SN\(_1\) vs. SN\(_2\) Reactions:
1. SN\(_1\) reactions proceed in two steps, with the rate-determining step being carbocation formation. SN\(_2\) reactions are single-step processes involving backside attack on the carbon attached to the leaving group.
2. Polar protic solvents, which stabilize carbocations, favor SN\(_1\) reactions. Polar aprotic solvents, which do not heavily solvate the nucleophile, favor SN\(_2\) reactions by enhancing nucleophilic attack.
Faster SN\(_1\) Reaction:
The compound \( \text{C}_6 \text{H}_5 \text{CH}_2 \text{Cl} \) will react faster via SN\(_1\). This is due to the resonance stabilization of the resulting benzyl carbocation by the aromatic ring. In contrast, the cyclohexyl carbocation is less stable, leading to a slower SN\(_1\) reaction rate.