Comparison of SN1 Reactivity and Carbocation Stability

To evaluate the correctness of both statements regarding $S_N1$ reactivity and carbocation stability, let us analyze the factors involved:

1. Analysis of Statement (I): In a unimolecular nucleophilic substitution ($S_N1$) reaction, the rate-determining step (RDS) is the heterolytic cleavage of the carbon-halogen bond to form a carbocation intermediate: $\text{R-Cl} \xrightarrow{\text{slow (RDS)}} \text{R}^+ + \text{Cl}^-$

The rate of an $S_N1$ reaction is directly proportional to the stability of the intermediate carbocation $\text{R}^+$ formed in this step: $\text{Rate of } S_N1 \propto \text{Stability of Carbocation Intermediate}$

• Benzyl chloride ($\text{C}_6\text{H}_5\text{CH}_2\text{Cl}$): Ionization produces the benzyl carbocation ($\text{C}_6\text{H}_5\text{CH}_2^+$). The positive charge on the benzylic carbon is delocalized over the aromatic ring through resonance (4 resonance structures involving the ortho and para positions), leading to high stabilization.
• Ethyl chloride ($\text{CH}_3\text{CH}_2\text{Cl}$): Ionization produces the ethyl carbocation ($\text{CH}_3\text{CH}_2^+$), which is a $1^\circ$ primary carbocation stabilized only by hyperconjugation (3 $\alpha$-hydrogens) and weak inductive ($+I$) effect.

Because the resonance-stabilized benzyl carbocation is much more stable than the hyperconjugation-stabilized ethyl carbocation, benzyl chloride undergoes $S_N1$ reaction significantly faster than ethyl chloride.

Thus, Statement (I) is true.

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2. Analysis of Statement (II):

• The stabilization energy provided by extended $\pi$-electron resonance (as seen in the benzyl carbocation, $\text{C}_6\text{H}_5\text{CH}_2^+$) is generally far greater than the stabilization energy provided by hyperconjugation from a single methyl group with 3 $\alpha$-hydrogens (as seen in the ethyl carbocation, $\text{CH}_3\text{CH}_2^+$).
• Therefore, the ethyl carbocation is less stabilized by hyperconjugation than the benzyl carbocation is by resonance.

Thus, Statement (II) is true.

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Conclusion: Both Statement (I) and Statement (II) are true statements.

Correct Answer: Option A (Both Statement I and Statement II are true)