Question

For a reaction taking place in three steps at the same temperature, the overall rate constant $K = \frac{K_1 K_2}{K_3}$. If $E_{a1}$, $E_{a2}$, and $E_{a3}$ are 40, 50, and 60 kJ/mol respectively, the overall $E_a$ is ____ kJ/mol.

Answer 1

For the overall rate constant:

$K = \frac{K_1 \cdot K_2}{K_3} = \frac{A_1 \cdot A_2}{A_3} \cdot e^{\left(\frac{E_{a1} + E_{a2} - E_{a3}}{RT}\right)}$

Therefore,

$K = \frac{A \cdot e^{-E_a/RT}}{A_3} = \frac{A_1 A_2}{A_3} \cdot e^{\left(\frac{E_{a1} + E_{a2} - E_{a3}}{RT}\right)}$

Given:

$E_a = E_{a1} + E_{a2} - E_{a3} = 40 + 50 - 60 = 30 \, \text{kJ/mol}$

So, the correct answer is: 30