In the rigorous unimolecular solvolysis of a generic tertiary alkyl halide () dissolved in a polar p — Haloalkanes and Haloarenes Chemistry Question
Question
In the rigorous unimolecular solvolysis of a generic tertiary alkyl halide ($R_3C-X$) dissolved in a polar protic solvent, let the variable $m$ equal the molecularity of the shared rate-determining step, and let the variable $n$ equal the absolute total number of distinct, competing primary product pathways that directly and immediately consume the resulting reactive intermediate. What is the precise integer value of the mathematical sum $(m + n)$?
💡 Solution & Explanation
The rate-determining step for purely unimolecular solvolysis is the initial heterolytic cleavage of the polar $C-X$ bond to form a carbocation. This slow step formally involves only one single reactant molecule (the alkyl halide itself), so its absolute molecularity is $m = 1$. The resulting high-energy carbocation intermediate can then rapidly undergo exactly two primary competing reactions: it can be attacked directly by a lone pair on a solvent molecule to yield a substitution product ($S_N1$), or it can lose an adjacent $\beta$ -proton to a solvent molecule to yield an alkene elimination product ($E1$). Thus, the number of distinct competing pathways is $n = 2$. The sum $(m + n) = 1 + 2 = 3$.