The rate constant k1 and k2 for two different reactions are 1016⋅e−2000/T and 1015⋅e−1000/T respectively. The temperature at which k1=k2 is:

$k_{1} = 10^{16} \cdot e^{- 2000 / T}; k_{2} = 10^{15} \cdot e^{- 1000 / T}$

The temperature at which $k_{1} = k_{2}$ will be :

$10^{16} \cdot e^{- 2000 / T} = 10^{15} \cdot e^{- 1000 / T}; or \frac{10^{15}}{10^{16}} = \frac{e^{- 2000 / T}}{e^{- 1000 / T}}$

or $\begin{aligned} 10^{- 1} = e^{- 1000 / T} \\ \log_{e} e^{- 1000 / T} = \log_{e} 10^{- 1} \end{aligned}$

$2.303 \log_{10} e^{- 1000 / T} = 2.303 \log_{10} 10^{- 1}$

or $- \frac{1000}{T} \log_{10} e = - 1 . So, T = \frac{1000}{2.303} K .$

The rate constant $k_{1}$ and $k_{2}$ for two different reactions are $10^{16} \cdot e^{- 2000 / T}$ and $10^{15} \cdot e^{- 1000 / T}$ respectively. The temperature at which $k_{1} = k_{2}$ is: