If decomposition reaction $A\left(g\right)\to B\left(g\right)$ follows first order kinetics then the graph of rate conformation $\left(B\right)$ of $B$ against time t will be:

For the first order decomposition of ${\mathrm{SO}}_2{\mathrm{Cl}}_2\left(\mathrm{g}\right)$,

$\left[{\mathrm{SO}}_2{\mathrm{Cl}}_2\left(\mathrm{g}\right)\to {\mathrm{SO}}_2\left(\mathrm{g}\right)+{\mathrm{Cl}}_2\left(\mathrm{g}\right)\right]$

a graph of $\log \left({\mathrm{a}}_0-\mathrm{x}\right)$ vs $\mathrm{t}$ is shown in figure. What is the rate constant $\left({\sec }^{-1}\right)$ ?

Consider the reaction $\mathrm{A}⟶\mathrm{B}$, graph between half life $\left({\mathrm{t}}_{1/2}\right)$ and initial concentration (a) of the reactant is

Hence, graph between$-\frac{\mathrm{d}\left[\mathrm{A}\right]}{\mathrm{dt}}$ And time will be

Consider the following first order competing reactions :

$\mathrm{X}\stackrel{{\mathrm{k}}_{\mathrm{I}}}{⟶}\mathrm{A}+\mathrm{B}$  and  $\mathrm{Y}\stackrel{{\mathrm{k}}_2}{\to }\mathrm{C}+\mathrm{D}$

If  $50\%$ of the reaction of $\mathrm{X}$ was completed when $96\%$ of the reaction of$\mathrm{Y}$ was completed, the ratio of their rate constants $\left({\mathrm{k}}_2/{\mathrm{k}}_1\right)$ is :

Consider this reaction. $2{\mathrm{NO}}_{2\left(\mathrm{g}\right)}+{\mathrm{O}}_{3\left(\mathrm{g}\right)}\to {\mathrm{N}}_2{\mathrm{O}}_{5\left(\mathrm{g}\right)}+{\mathrm{O}}_{2\left(\mathrm{g}\right)}$

The reaction of nitrogen dioxide and ozone represented in first order in ${\mathrm{NO}}_{2\left(\mathrm{g}\right)}$ and ${\mathrm{O}}_{3\left(\mathrm{g}\right)}$. Which of these possible reaction mechanisms is consistent with the rate law? 

$\begin{array}{ccccc}\mathrm{Mechanism} \mathrm{I}.& & {\mathrm{NO}}_2+{\mathrm{O}}_3\to {\mathrm{NO}}_3+{\mathrm{O}}_2& & \mathrm{slow}\\ & & {\mathrm{NO}}_3+{\mathrm{NO}}_2\to {\mathrm{N}}_2{\mathrm{O}}_5& & \mathrm{fast}\end{array}$

$\begin{array}{ccccc}\mathrm{Mechanism} \mathrm{II}.& & {\mathrm{O}}_3\rightleftharpoons {\mathrm{O}}_2\to \mathrm{O}& & \mathrm{fast}\\ & & {\mathrm{NO}}_2+\mathrm{O}\to {\mathrm{NO}}_3& & \mathrm{slow}\\ & & {\mathrm{NO}}_3+{\mathrm{NO}}_2\to {\mathrm{N}}_2{\mathrm{O}}_5& & \mathrm{fast}\end{array}$