Differences between SN\(_1\) and SN\(_2\) reactions:
1. In SN\(_1\) reactions, the rate-determining step is the formation of a carbocation intermediate, and the reaction proceeds via a two-step mechanism. In contrast, SN\(_2\) reactions occur in a single step and involve a backside attack on the carbon bearing the leaving group.
2. SN\(_1\) reactions are favored by polar protic solvents, which help stabilize the carbocation intermediate, whereas SN\(_2\) reactions are favored by polar aprotic solvents, which do not solvate the nucleophile as much and allow better nucleophilic attack.
Which compound undergoes SN\(_1\) reaction faster?
The compound with the benzene ring (\( \text{C}_6 \text{H}_5 \text{CH}_2 \text{Cl} \)) will undergo the SN\(_1\) reaction faster. This is because the benzyl carbocation formed after the departure of the leaving group (Cl\(^-\)) is stabilized by resonance with the aromatic ring, making it more stable and favorable for the SN\(_1\) mechanism. The cyclohexyl group, on the other hand, does not stabilize the carbocation as effectively and thus would not undergo the SN\(_1\) reaction as quickly.