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(A) Solvolysis reactions typically proceed via an $S_N1$ mechanism,which involves the formation of a carbocation intermediate as the rate-determining

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$II > I > III$

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(A) Solvolysis reactions typically proceed via an $S_N1$ mechanism,which involves the formation of a carbocation intermediate as the rate-determining step.The stability of the carbocation formed determines the reactivity of the substrate. More stable carbocations are formed faster,leading to higher reactivity.$1$. In compound $(I)$,the carbocation formed is a benzylic carbocation: $Ph-C^+(CH_3)_2$.$2$. In compound $(II)$,the carbocation formed is $p-CH_3O-C_6H_4-C^+(CH_3)_2$. The methoxy group $(-OCH_3)$ is a strong electron-donating group by resonance ($+M$ effect),which significantly stabilizes the carbocation.$3$. In compound $(III)$,the carbocation formed is $p-O_2N-C_6H_4-C^+(CH_3)_2$. The nitro group $(-NO_2)$ is a strong electron-withdrawing group by both inductive $(-I)$ and resonance $(-M)$ effects,which destabilizes the carbocation.Comparing the stability: The carbocation from $(II)$ is the most stable due to the $+M$ effect of $-OCH_3$. The carbocation from $(I)$ is intermediate. The carbocation from $(III)$ is the least stable due to the $-I$ and $-M$ effects of $-NO_2$.Therefore,the decreasing order of reactivity is $II > I > III$.

The decreasing order of reactivity of the compounds given below towards solvolysis under identical conditions is:

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Conversion of $I$ to $II$:

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