Chemistry - Chemical Kinetics Question with Solution | TestHub

According to Arrhenius equation, $\log k=\log A-\frac{E_a}{2.303RT}...(i)$ For $1^{\text{st }}$ order reaction, $k=\frac{0.693}{t_{1/2}}=\frac{0.693}{600s}=1.1\times 10^{-3}{\mathrm{s}}^{-1}$ Substitute the value of $k$ in Eq. (i) $log\left(1.1\times 10^{-3}\right)=\log \left(4\times 10^{13}\right)-\frac{98.6\times 10^3}{2.303\times 8.314\times T}$ Solving for $T$, $T=311.15\mathrm{K}$