A reaction takes place in three steps with activation energy ${\mathrm{E}}_{{\mathrm{a}}_1}=180$ kJ/mol, ${\mathrm{E}}_{{\mathrm{a}}_2}=80$ kJ/mol and ${\mathrm{E}}_{{\mathrm{a}}_3}=50$ kJ/mol respectively.
Overall rate constant of the reaction is $\mathrm{k}={\left[\frac{{\mathrm{k}}_1{\mathrm{k}}_2}{{\mathrm{k}}_3}\right]}^{2/3}$ .
The activation energy of the reaction will be