Question #44222

Consider the $S_N1$ solvolysis of the optically active alkyl halide (2S,3S)-2-chloro-3-methylpentane in \ce{H2O} at 298 K. The reaction proceeds via an initial carbocation $C_1^+$ which undergoes a rapid 1,2-shift to form a more thermodynamically stable carbocation $C_2^+$, ultimately yielding the major product $P$. The global enthalpy path shifts due to the superior hyperconjugative stabilization of $C_2^+$.

Let $n_1$ and $n_2$ be the number of hyperconjugable $\alpha$-hydrogens in $C_1^+$ and $C_2^+$, respectively. Identify the major product $P$, its optical activity, and the difference in hyperconjugable hydrogens ($\Delta n = n_2 - n_1$) that provides the thermodynamic driving force ($\Delta H_{\text{rearr}} < 0$) for the shift.