The ascending order of relative rate of solvolysis of following compounds is :

Solution

Chemistry ma’am · 3 steps

Solvolysis goes by SN1, so rank the four carbocations; the more stable the cation, the faster the rate.

1. Mechanism first. In solvolysis the solvent is a weak nucleophile, so the reaction follows SN1. The slow step is loss of Br⁻ to form a carbocation, so the rate depends only on how stable that carbocation is.

   Compound	Carbocation formed	Stabilised by	Rank
   (D)	2° alkyl, on C-2 of 3-methylpentane	hyperconjugation and +I from alkyl groups only	slowest
   (A)	3° alkyl, on the ring carbon carrying CH₃	more hyperconjugation than a 2° alkyl cation	second
   (B)	2° benzylic, next to the fused benzene ring	resonance with one benzene ring	third
   (C)	diphenylmethyl (C₆H₅)₂CH⁺	resonance with two benzene rings	fastest

2. Resonance beats hyperconjugation. Delocalising the positive charge into a benzene ring stabilises it more than the extra alkyl groups of a 3° cation can. So the 2° benzylic cation from (B) is more stable than the 3° cation from (A), and two rings in (C) stabilise it even more.
3. So. The ascending order of solvolysis rate is (D) < (A) < (B) < (C), which is option (b).

The idea to keep. For SN1 and solvolysis, ignore crowding and just rank the carbocations. Resonance with benzene rings beats extra alkyl groups, and each extra ring adds more stability.

Answer from the NTA final answer key. Solution by PrepWiser.