Chemical Kinetics Question 5
Question 5 - 2024 (29 Jan Shift 1)
For a reaction taking place in three steps at same temperature, overall rate constant $\mathrm{K}=\frac{\mathrm{K}{1} \mathrm{~K}{2}}{\mathrm{~K}{3}}$. If $\mathrm{Ea}{1}, \mathrm{Ea}{2}$ and $\mathrm{Ea}{3}$ are 40,50 and $60 \mathrm{~kJ} / \mathrm{mol}$ respectively, the overall $\mathrm{Ea}$ is _______ $\mathrm{kJ} / \mathrm{mol}$.
Show Answer
Answer (30)
Solution
$K=\frac{K_{1} \cdot K_{2}}{K_{3}}=\frac{A_{1} \cdot A_{2}}{A_{3}} \cdot e^{-\frac{\left( E_{a_{1}}+E_{a_{2}}-E_{a_{3}}\right)}{R T}}$
$A \cdot e^{-E_{a} / R T}=\frac{A_{1} A_{2}}{A_{3}} \cdot e^{-\frac{\left(E_{a_{1}} +E_{a_{2}}-E a_{3}\right)}{R T}}$
$\mathrm{E}{\mathrm{a}}=\mathrm{E}{\mathrm{a}{1}}+\mathrm{E}{\mathrm{a}{2}}-\mathrm{E}{\mathrm{a}_{3}}=40+50-60=30 \mathrm{~kJ} / \mathrm{mole}$
