T1 = 293K, T2 = 313K
According to Arrhenius equation,
\(log\frac{k_2}{k_1}= \frac{E_a}{2.303\,R} [\frac{T_2\,-\,T_1}{T_1\,T_2}]\)
∴ \(E_a= 2.303\,R\,\times[ \frac{T_1\,T_2}{T_2\,-\,T_1}]log \frac{k_2}{k_1}\)
∴ \(E_a= 2.303\,\times\,8.314\,JK^{-1}\,mol^{-1}\,\times\)\([\frac{293 \times 313}{313\,-\,293}]log\frac{4}{1}\)
= 2.303 × 8.314 J K-1 mol-1 × 4585.45 K × 0.6021
= 52863.33 J mol-1
= 52.86 kJ mol-1