If the rate expression for a chemical reaction is given by $\text{Rate} = k[A]^m[B]^n$,what is the order of the reaction?

$A$ student has studied the decomposition of a gas $AB_3$ at $25^{\circ} C$. He obtained the following data.

$p \ (mm \ Hg)$	$50$	$100$	$200$	$400$
Relative $t_{1/2} \ (s)$	$4$	$2$	$1$	$0.5$

The order of the reaction is

For the reaction $2A + B \rightarrow \text{Product}$,the following mechanism is given. What is the order of the reaction?
$2A \rightleftharpoons A_2$ (fast)
$A_2 + B \rightarrow P$ (slow)

The reaction $3ClO^{-} \rightarrow ClO_{3}^{-} + 2Cl^{-}$ occurs in the following two steps:
$(i)$ $ClO^{-} + ClO^{-} \xrightarrow{K_{1}} ClO_{2}^{-} + Cl^{-}$ (Slow step)
$(ii)$ $ClO_{2}^{-} + ClO^{-} \xrightarrow{K_{2}} ClO_{3}^{-} + Cl^{-}$ (Fast step)
Then the rate of the given reaction is equal to . . . . . . .

Calculate the overall order of a reaction which has the rate expression:
$(a)$ $\text{Rate} = k[A]^{1/2}[B]^{3/2}$
$(b)$ $\text{Rate} = k[A]^{3/2}[B]^{-1}$

For the reaction $2 A + B \longrightarrow D + E$,the following mechanism has been proposed: $A + B \longrightarrow C + D$ (slow) and $A + C \longrightarrow E$ (fast). Determine the rate law.