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Overall activation energy from a composite rate constant

This type of question, asked 3 times: 29 Jan 2024, 4 Apr 2024, 24 Jan 2025. All 3 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    29 Jan 2024

    53
    For a reaction taking place in three steps at same temperature, overall rate constant K=K1 K2 K3K =\frac{K_{1}{\text{ }K}_{2}}{{\text{ }K}_{3}}. If Ea1,Ea2Ea_{1},Ea_{2} and Ea3Ea_{3} are 40,50 and 60 kJ/mol60\text{ }kJ/mol respectively, the overall Ea is ____ kJ/molkJ/mol.

  2. Question 2

    4 Apr 2024

    57
    Consider the following transformation involving first order elementary reaction in each step at constant temperature as shown below.
    A+B⇌ Step 1 Step 3C→ Step 2PA + B\overset{\text{~Step~}3}{\overset{\text{~Step~}1}{\rightleftharpoons}}C\overset{\text{~Step~}2}{\rightarrow}P
    Some details of the above reaction are listed below.
    StepRate constant
    (sec⁡−1)\left( \sec^{- 1} \right)
    		Activation energy (kJ mol−1)\left( {kJ\text{ }mol}^{- 1} \right)
    1
    k1k_{1}
    		300
    2
    k2k_{2}
    		200
    3
    k3k_{3}
    Ea3Ea_{3}
    If the overall rate constant of the transformation (k)(k) is given as k=k1k2k3k =\frac{k_{1}k_{2}}{k_{3}} and the overall activation energy (Ea)\left( E_{a} \right) is 400 kJ mol−1400\text{ }kJ{\text{ }mol}^{- 1}, then the value of Ea3Ea_{3} is _____ kJmol−1kJmol^{- 1} (nearest integer)

  3. Question 3

    24 Jan 2025

    123
    Consider a complex reaction taking place in three steps with rate constants k1,k2k_{1},k_{2} and k3k_{3} respectively. The overall rate constant kk is given by the expression k=k1k3k2k =\sqrt{\frac{k_{1}k_{3}}{k_{2}}}. If the activation energies of the three steps are 60,30 and 10 kJ mol−110\text{ }kJ{\text{ }mol}^{- 1} respectively, then the overall energy of activation in kJmol−1kJmol^{- 1} is ______\_\_\_\_\_\_ . (Nearest integer)