Identify the reaction order from each of the following rate constants.
$(i)$ $k = 2.3 \times 10^{-5} \, L \, mol^{-1} \, s^{-1}$
$(ii)$ $k = 3 \times 10^{-4} \, s^{-1}$

For the reaction:
$2NO_{2(g)} + O_{3(g)} \to N_2O_{5(g)} + O_{2(g)}$
The rate law is $R = K[NO_2]^1 [O_3]^1$.
Which of these possible reaction mechanisms is consistent with the rate law?
Mechanism $I$:
$NO_{2(g)} + O_{3(g)} \to NO_{3(g)} + O_{2(g)}$ (slow)
$NO_{3(g)} + NO_{2(g)} \to N_2O_{5(g)}$ (fast)
Mechanism $II$:
$O_{3(g)} \rightleftharpoons O_{2(g)} + [O]$ (fast)
$NO_{2(g)} + [O] \to NO_3$ (slow)
$NO_{3(g)} + NO_{2(g)} \to N_2O_5$ (fast)

Which one of the following is wrong about molecularity of a reaction?

If the concentration of reactant $A$ is increased by $10$ times,the rate of reaction becomes $100$ times. What is the order of reaction if the rate law is,$\text{rate} = k[A]^{x}$?

For the reaction $A + B \to C + D$,if the concentration of $A$ is doubled without affecting the concentration of $B$,the rate doubles. If the concentration of $B$ is increased $9$ times without affecting the concentration of $A$,the rate becomes $3$ times. Determine the order of the reaction.

Rate law for a reaction is $r=k[A]^2[B]$. If rate constant is $6.25 \ mol^{-2} \ dm^6 \ s^{-1}$,what is the rate of reaction when $[A]=1 \ mol \ dm^{-3}$ and $[B]=0.2 \ mol \ dm^{-3}$?