For the reaction $\mathrm{A}\to \mathrm{B},$ the rate constant $k\left(in{s}^{-1}\right)$ is given by ${\log }_{10}\mathrm{k}=20.35-\frac{\left(2.47\times {10}^3\right)}{\mathrm{T}}$.The energy of activation in  $kJmo{l}^{-1}$ is _____[Given: $R=8.314J{K}^{-1}mo{l}^{-1}$ ]
 

According to Arrhenius equation

$k=A{e}^{-E_a/RT}$

$\log k=\log A-\frac{E_a}{2.303RT}\_\_\_\_\_\left(i\right)$

$\log k=20.35-\frac{2.47\times {10}^3}{T}\_\_\_\_\_\left(ii\right)$

Comparing (i) and (ii)

$\frac{E_a}{2.303R}=2.47\times {10}^3,$

$E_a=2.47\times {10}^3\times R\times 2.303=2.47\times 8.314\times {10}^3\times 2.303$

$=47\times {10}^{3}J/molor47kJ/mol$