Q6(d). Order of SN1 solvolysis in aqueous formic acid

Introduction. Aqueous formic acid is a highly ionising, weakly nucleophilic solvent: substitution goes by SN1. The rate-determining step is ionisation to the carbocation, so the rate follows the stability of the carbocation (and of the transition state that resembles it).

Scheme: The two benzylic cations; the positive charge spreads into the ring(s).

1. Bromodiphenylmethane, Ph₂CHBr: the benzhydryl cation is delocalised over two benzene rings. Fastest.
2. 1-Bromo-1,2,3,4-tetrahydronaphthalene: a secondary benzylic cation; the ring fusion holds the empty p orbital parallel to the aromatic π system, so delocalisation into one ring is effective.
3. 1-Bromo-1-methylcyclohexane: a tertiary alkyl cation, stabilised only by hyperconjugation and induction from three alkyl groups; comparable to, but below, a benzylic cation that is held planar.
4. 1-Bromo-3-methylbutane, (CH₃)₂CHCH₂CH₂Br: primary; a primary cation is too unstable to form, so no SN1. It reacts only by a very slow SN2 with the weak nucleophiles water/formic acid (any ionisation would be accompanied by a hydride shift). Slowest by far.

Conclusion. Decreasing rate: Ph₂CHBr > 1-bromotetralin > 1-bromo-1-methylcyclohexane ≫ (CH₃)₂CHCH₂CH₂Br, the order of carbocation stability (doubly benzylic > benzylic > tertiary ≫ primary).

Application. Solvolysis rates in aqueous formic acid or ethanol (Grunwald–Winstein) are used to measure carbocation stability; benzhydryl and trityl groups are used as acid-labile protecting groups for this reason.