Consider the following transformation involving first order elementary reaction in each step at constant temperature as shown below. A+B [ Step 3]…

Consider the following transformation involving first order elementary reaction in each step at constant temperature as shown below. $$A+B \xrightleftharpoons[\text { Step } 3]{\text { Step 1 }} C \xrightarrow{\text { Step 2 }} P $$ Some details of the above reactions are listed below.

Step	Rate constant $\displaystyle \left(\mathrm{sec}^{-1}\right)$	Activation energy ( $\displaystyle \mathrm{kJ} \mathrm{mol}^{-1}$ )
$\displaystyle 1$	$\displaystyle \mathrm{k}_1$	$\displaystyle 300$
$\displaystyle 2$	$\displaystyle \mathrm{k}_2$	$\displaystyle 200$
$\displaystyle 3$	$\displaystyle \mathrm{k}_3$	$\displaystyle \mathrm{Ea}_3$

If the overall rate constant of the above transformation (k) is given as $\displaystyle \mathrm{k}=\frac{\mathrm{k}_1 \mathrm{k}_2}{\mathrm{k}_3}$ and the overall activation energy $\displaystyle \left(\mathrm{E}_{\mathrm{a}}\right)$ is $\displaystyle 400 \mathrm{~kJ} \mathrm{~mol}^{-1}$, then the value of $\displaystyle \mathrm{Ea}_3$ is $\displaystyle \_\_\_\_$ $\displaystyle \mathrm{kJ} \mathrm{mol}^{-1}$ (nearest integer)