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?

$A$ complex reaction takes place in the following steps:
$NO_2Cl_{(g)} \longrightarrow NO_{2(g)} + Cl_{(g)}$ (slow)
$NO_2Cl_{(g)} + Cl_{(g)} \longrightarrow NO_{2(g)} + Cl_{2(g)}$ (fast)
Identify the rate law equation for this reaction.

For the reaction $Cl_{2(aq)} + H_2S_{(aq)} \to S_{(s)} + 2H^{+}_{(aq)} + 2Cl^{-}_{(aq)}$,the rate law is $r = K[Cl_2][H_2S]$. Which of the following mechanisms is/are consistent with this rate law?
$A. \ H_2S \rightleftharpoons H^{+} + HS^{-}$ (fast)
$Cl_2 + HS^{-} \to 2Cl^{-} + H^{+} + S$ (slow)
$B. \ Cl_2 + H_2S \to H^{+} + Cl^{-} + Cl^{+} + HS^{-}$ (slow)
$Cl^{+} + HS^{-} \to H^{+} + Cl^{-} + S$ (fast)

$A$ bacterial infection in an internal wound grows as $N(t) = N_0 \exp(t)$,where the time $t$ is in hours. $A$ dose of antibiotic,taken orally,needs $1 \ hour$ to reach the wound. Once it reaches there,the bacterial population decreases as $\frac{dN}{dt} = -5N^2$. What will be the plot of $\frac{N_0}{N}$ vs. $t$ after $1 \ hour$?

Fill in the blanks:
$1.$ The rate of reaction depends on the ........... step.
$2.$ In a bimolecular reaction,the reaction takes place with ........... species and ........... .
$3.$ The order of reaction is determined by ...........

For the reaction $aA \to xP$,the rate is $2.4 \ mMs^{-1}$ when $[A] = 2.2 \ M$. When the concentration of $A$ is halved,the rate becomes $0.6 \ mMs^{-1}$. Determine the order of the reaction with respect to $A$.