Question #44807

The photochemical dechlorination of chlorobenzene ($\ce{C6H5Cl}$) in hexane at $298 \text{ K}$ is driven by continuous UV irradiation ($\lambda = 254 \text{ nm}$). The strong C-Cl bond, stabilized by resonance ($+M$ effect of Cl), necessitates this high-energy initiation. The reaction mixture absorbs UV photons at a constant rate of $1.0 \times 10^{-3} \text{ Einstein L}^{-1} \text{ s}^{-1}$. Given that the quantum yield ($\Phi$) for the formation of phenyl radicals is $0.10$ and the reaction follows zero-order kinetics with respect to the substrate, determine the rate constant $k$ in $\text{mol L}^{-1} \text{ min}^{-1}$ and the half-life ($t_{1/2}$) of the reaction if the initial concentration of $\ce{C6H5Cl}$ is $0.12 \text{ M}$.