The following graph is obtained for a first order reaction $(A \rightarrow P)$. The activation energy ( $E_a$ in $\left.\mathrm{kJ} \mathrm{mol}^{-1}\right)$ and heat of reaction $\left(|\Delta H|\right.$ in $\left.\mathrm{kJ} \mathrm{mol}^{-1}\right)$ for this reaction are respectively

$\left(x=\right.$ reaction coordinate; $y=E$ in $\left.\mathrm{kJ} \mathrm{mol}^{-1}\right)$

For a first order reaction, the ratio between the time taken to complete $\frac{3}{4}$ th of the reaction and time taken to complete half of the reaction is

The following equation is obtained for a first order reaction at 300 K

$$ \log _{10} \frac{k}{A}=0.00174 $$

What is the activation energy (in $\mathrm{J} \mathrm{mol}^{-1}$ ) of the reaction?

$$ \left(R=8314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\right) $$

$A \rightarrow B$ is a first order reaction. The concentration of $A$ is decreased from $x \mathrm{~mol} \mathrm{~L}^{-1}$ to $y \mathrm{~mol} \mathrm{~L}^{-1}$ in 100 min . What is the average velocity of the reaction in $\mathrm{mol} \mathrm{L}^{-1} \min ^{-1}$ ?