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, $R=8314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$ )

A possible mechanism for the gaseous reaction $2 \mathrm{H}_2+2 \mathrm{NO} \longrightarrow 2 \mathrm{H}_2 \mathrm{O}+\mathrm{N}_2$ is

Step 1:2 $\mathrm{NO} \rightleftharpoons \mathrm{N}_2 \mathrm{O}_2$

Step 2 : $\mathrm{N}_2 \mathrm{O}_2+\mathrm{H}_2 \longrightarrow \mathrm{~N}_2 \mathrm{O}+\mathrm{H}_2 \mathrm{O}$ (slow)

Step 3: $\mathrm{N}_2 \mathrm{O}+\mathrm{H}_2 \longrightarrow \mathrm{~N}_2+\mathrm{H}_2 \mathrm{O}$

The rate law for this reaction is

The rate law for the decomposition of hydrogen iodide is $-\frac{d[\mathrm{HI}]}{d t}=k[\mathrm{HI}]^2$. The units of rate constant $k$ are

For a zero order reaction $A \rightarrow$ product, a plot of $[A]$ (on $y$-axis) and time (on $x$-axis) gave a straight line with slope equal to $-3 \times 10^{-3} \mathrm{M} \mathrm{min}^{-1}$ and intercept equal to $2 \times 10^{-2} \mathrm{M}$ (on y -axis). What is the rate constant (in M $\mathrm{min}^{-1}$ ) of this reaction?