For the chemical reaction $2O_3 \rightarrow 3O_2$,the mechanism is given below. What will be the rate law expression?
$O_3 \rightleftharpoons O_2 + O$ ...... (fast)
$O + O_3 \rightarrow 2O_2$ ...... (slow)

For the non-stoichiometric reaction $2A + B \rightarrow C + D,$ the following kinetic data were obtained in three separate experiments,all at $298 \, K.$

Initial Concentration $(A)$	Initial Concentration $(B)$	Initial rate of formation of $C$ $(mol \, L^{-1} \, s^{-1})$
$0.1 \, M$	$0.1 \, M$	$1.2 \times 10^{-3}$
$0.1 \, M$	$0.2 \, M$	$1.2 \times 10^{-3}$
$0.2 \, M$	$0.1 \, M$	$2.4 \times 10^{-3}$

The rate law for the formation of $C$ is:

Under a given set of experimental conditions,with an increase in the concentration of the reactants,the rate of a chemical reaction

The hydrolysis of an ester is catalyzed by dilute acids $A$ and $B$. The rate constants for the two processes are $K_A$ and $K_B$ respectively. If $K_A > K_B$,which of the following statements is correct?

The rate constants for the following reactions are:
Reaction $1$: $A \xrightarrow{\text{catalyst } 1} P_1, k_1 = 1 \ s^{-1}$
Reaction $2$: $A \xrightarrow{\text{catalyst } 2} P_2, k_2 = 0.1 \ L \ mol^{-1} \ s^{-1}$
Reaction $3$: $A \xrightarrow{\text{catalyst } 3} P_3, k_3 = 0.01 \ L^2 \ mol^{-2} \ s^{-1}$
What is the correct relation between the rates of the reactions at $[A] = 1 \ M$?

$t_{1/2} =$ constant confirms the first order reaction. If $a^2 t_{1/2} =$ constant,it confirms that the order of reaction is ($a =$ initial concentration of reactant).