The rate of reaction $A + 2B \to 3C$ becomes $72$ times when the concentration of $A$ is tripled and the concentration of $B$ is doubled. The order of reaction with respect to $A$ and $B$ respectively is:

In a reaction between $A$ and $B$,the initial rate of reaction $(r_0)$ was measured for different initial concentrations of $A$ and $B$ as given below:

$A / mol \ L^{-1}$	$0.20$	$0.20$	$0.40$
$B / mol \ L^{-1}$	$0.30$	$0.10$	$0.05$
$r_0 / mol \ L^{-1} \ s^{-1}$	$5.07 \times 10^{-5}$	$5.07 \times 10^{-5}$	$1.43 \times 10^{-4}$

What is the order of the reaction with respect to $A$ and $B$?

The three experimental data sets for determining the differential rate of the reaction $2 NO_{(g)} + Cl_{2_{(g)}} \rightarrow 2 NOCl_{(g)}$ at a definite temperature are given below. (Note: The data table was missing in the input,assuming standard values for this reaction: $Exp 1: [NO]=0.1, [Cl_2]=0.1, Rate=0.18$; $Exp 2: [NO]=0.1, [Cl_2]=0.2, Rate=0.36$; $Exp 3: [NO]=0.2, [Cl_2]=0.1, Rate=0.72$).
$(a)$ Derive the differential rate law of the reaction.
$(b)$ Calculate the order of the reaction.
$(c)$ Calculate the value of the rate constant.

The hypothetical reaction : $2A + B \to C + D$ is catalyzed by $E$ as indicated in the possible mechanism below -
Step-$1$ : $A + E \rightleftharpoons AE$ (fast)
Step-$2$ : $AE + A \to A_2 + E$ (slow)
Step-$3$ : $A_2 + B \to C + D$ (fast)
What rate law best agrees with this mechanism?

For a reaction $A \rightarrow \text{Product}$,the rate constant is $6.93 \times 10^{-3} \ hour^{-1}$. What is the order of the reaction?

For the reaction $A \to B$,the rate increases by a factor of $2.25$ when the concentration of $A$ is increased by $1.5$. What is the order of the reaction?