Exams › JEE Advanced › Chemistry
A reaction proceeds in three steps with activation energies Ea1 = 180 kJ/mol, Ea2 = 80 kJ/mol, and Ea3 = 50 kJ/mol respectively. The overall rate constant is given by k = (k1*k2/k3)^(2/3), where k1, k2, k3 are the rate constants of the first, second, and third steps. What is the overall activation energy of the reaction?
- 140 kJ/mol
- 150 kJ/mol
- 43.44 kJ/mol
- 100 kJ/mol
Correct answer: 140 kJ/mol
Solution
Since k proportional to exp(-Ea/RT), taking ln: ln k = (2/3)(ln k1 + ln k2 - ln k3). Therefore Ea_overall = (2/3)(Ea1 + Ea2 - Ea3) = (2/3)(180 + 80 - 50) = (2/3)(210) = 140 kJ/mol.
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