Consider the gaseous reaction, $$ A_2+B_2 \longrightarrow 2 A B $$ The following data was obtained for the above reaction.

[A₂]₀	[B₂]₀	Initial rate of formation of AB (mol L⁻¹ s⁻¹)
0.1 M	0.1 M	2.5 × 10⁻⁴
0.2 M	0.1 M	5.0 × 10⁻⁴
0.2 M	0.1 M	1.0 × 10⁻³

The value of rate constant for the above reaction is

For a first order reaction, a plot of $\ln k\left(Y\right.$-axis) and $\frac{1}{T}$ $(X$-axis) gave the straight line with slope equal to $-10^3 \mathrm{~K}$ and intercept equal to 2.303 ( on $Y$-axis). What is the activation energy ( $E_a$ in $\mathrm{kJ} \mathrm{mol}^{-1}$ ) of the reaction? (Given, $R=8314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$ )