For a reaction the activation energy is zero. What is the value of rate constant at $300 \mathrm{K}$.
[Given ${\mathrm{k}}_{280 \mathrm{K}}=1.6\times {10}^6{ \mathrm{s}}^{-1};\mathrm{R}=8.314{\mathrm{Jmol}}^{-1}{ \mathrm{K}}^{-1}$ ]

Given ${\mathrm{T}}_1=280 \mathrm{K},{\mathrm{k}}_1=1.6\times {10}^6{ \mathrm{s}}^{-1},{\mathrm{k}}_2=?,{\mathrm{E}}_{\mathrm{a}}=0,{ \mathrm{T}}_2=300 \mathrm{K}$.
By Arrhenius equation,

$$\begin{gathered} \log \frac{{\mathrm{k}}_1}{{\mathrm{k}}_1}=\frac{{\mathrm{E}}_{\mathrm{a}}}{2.303\mathrm{R}}\left[\frac{{\mathrm{T}}_2-{\mathrm{T}}_1}{{ \mathrm{T}}_2{ \mathrm{T}}_1}\right] \\ \mathrm{As},{\mathrm{E}}_{\mathrm{a}}=0 \\ \mathrm{or} \frac{{\mathrm{k}}_2}{{\mathrm{k}}_1}=1\text{or}{\mathrm{k}}_2={\mathrm{k}}_1 \\ \text{Thus, the rate constant at}300\mathrm{K}\text{is}1.6\times {10}^6{\mathrm{s}}^{-1} \end{gathered}$$