The rate constants of a reaction are \(1 × 10^{−3}s^{−1}\) and \(2 × 10^{−3}s^{−1}\) at 27°C and 37°C respectively. What will be the activation energy of the reaction?
Answer & explanation
Correct answer: option 2
The correct answer is option 2. 53.6 kJ mol−1
Given, \(k_1 = 1 × 10^{−3}s^{−1}\),
\(k_2 = 2 × 10^{−3}s^{−1}\)
\(T_1 = 27^oC = 300 K\)
\(T_2 = 37^oC = 310 K\)
According to Arrhenius equation,
\(log\frac{k_2}{k_1} = \frac{E_a}{2.303R}\left(\frac{T_2 − T_1}{T_1T_2}\right)\)
⇒ \(log\frac{2 × 10^{−3}}{1 × 10^{−3}} = \frac{E_a}{2.303 × 8.314 \text{ J K}^{−1}}\left(\frac{310 − 300}{300 × 310}\right)\)
⇒ \(log(2)= \frac{E_a}{19.147}\left(\frac{10}{300 × 310}\right)\)
⇒ \(E_a = 0.301 × 19.147 ×310 ×30\)
⇒ \(E_a = 53598.19 J mol^{−1}\)
∴ \(E_a = 53.6 kJ mol^{−1}\)