A reaction takes place in three steps with activation energy $E_{a_{1}} = 180$ kJ/mol, $E_{a_{2}} = 80$ kJ/mol and $E_{a_{3}} = 50$ kJ/mol respectively.
Overall rate constant of the reaction is $k = {[\frac{k_{1} k_{2}}{k_{3}}]}^{2 / 3}$ .
The activation energy of the reaction will be

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The rate of constant of the reaction is k = k 1 k 2 k 3 2 / 3 Activation energy of the reaction will be E a = 2 3 [ E a 1 + E a 2 - E a 3 ] = 2 3 [ 180 + 80 - 50 ] = 140 kJ/mol.

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