According to the Arrhenius equation, $\log \frac{k_2}{k_1} = \frac{E_a}{2.303 R} \left[ \frac{T_2 - T_1}{T_1 T_2} \right]$ Given: $T_1 = 27^{\circ}\text{C} = 27 + 273 = 300 \text{ K}$ $T_2 = 57^{\circ}\text{C} = 57 + 273 = 330 \text{ K}$ $\frac{k_2}{k_1} = 4$ (since the rate quadruples) $\log 4 = \frac{E_a}{2.303 \times 8.314} \left[ \frac{330 - 300}{300 \times 330} \right]$ $0.6021 = \frac{E_a}{19.147} \left[ \frac{30}{99000} \right]$ $0.6021 = \frac{E_a}{19.147} \times \frac{1}{3300}$ $E_a = 0.6021 \times 19.147 \times 3300$ $E_a = 38044.1 \text{ J mol}^{-1} \approx 38.04 \text{ kJ mol}^{-1}$.