Question #44234

Consider the gas-phase heterolytic cleavage of 2-chloro-3-methylbutane ($\ce{C5H11Cl}$) to form the thermodynamically most stable rearranged carbocation intermediate ($R'^+$) and a chloride ion ($\ce{Cl^-}$) at 298 K.

Given the following thermodynamic parameters: $\bullet$ Standard enthalpy of formation of $\ce{C5H11Cl} (g)$, $\Delta H_f^\circ = -140 \text{ kJ/mol}$ $\bullet$ Standard enthalpy of formation of $\ce{Cl^-} (g)$, $\Delta H_f^\circ = -230 \text{ kJ/mol}$ $\bullet$ The theoretical standard enthalpy of formation of the localized (un-hyperconjugated) $3^\circ$ carbocation $R'^+$ is $+880 \text{ kJ/mol}$. $\bullet$ The hyperconjugative stabilization energy is $12 \text{ kJ/mol}$ per $\alpha$-C-H bond.

Calculate the actual enthalpy of reaction ($\Delta H_{rxn}^\circ$) for this heterolytic cleavage, accounting for the hyperconjugative stabilization of the final rearranged carbocation.