Question #45060

The electrophilic addition of \ce{HCl(g)} to 3,3-dimethylbut-1-ene in anhydrous \ce{CH2Cl2} proceeds via a secondary carbocation intermediate. This intermediate faces a kinetic competition: it can either undergo direct nucleophilic capture by \ce{Cl^-} to form product $P_1$, or undergo a 1,2-methyl shift followed by capture to form product $P_2$. The activation energy for the direct capture is $E_{a,cap} = 15.0 \text{ kJ/mol}$, while the activation energy for the rearrangement is $E_{a,rearr} = 27.45 \text{ kJ/mol}$. The ratio of their pre-exponential factors is $\frac{A_{rearr}}{A_{cap}} = e^{10}$. Assuming $R = 8.3 \text{ J K}^{-1} \text{mol}^{-1}$, identify the major product formed at $100 \text{ K}$ and $300 \text{ K}$ respectively, along with its stereochemical nature.