Explanation

(b)
We know,
Given, $T_{1} = 27 + 273 = 300\ KK_{1} = k$
$T_{2} = 37 + 273 = 310K\ K_{2} = 2k$
$R = 8.314 \times 10^{- 3}\ kJ$
$2.303\log{\frac{k_{2}}{k_{1}} = \frac{E_{a}}{R}\left( \frac{T_{2} - T_{1}}{T_{1} - T_{2}} \right)}$
$2.303\log{\frac{2k}{k} =}\frac{E_{a}}{8.314 \times 10^{- 3}} \times \left( \frac{310 - 300}{310 \times 300} \right)$
$2.303\log{2 = \frac{E_{a}}{8.314 \times 10^{- 3}} \times \frac{10}{93000}}$
$2.303{\times 0.3010}{= \frac{E_{a}}{8.314 \times 10^{- 3}} \times 0.000108}$
$E_{a} = \frac{2.303 \times 0.3010 \times 8.314 \times 10^{- 3}}{0.000108}$
$\ = \frac{5.7633 \times 10^{- 3}}{0.000108}$
$E_{a} = 53.363\ kJ$