For a given reaction $t_{1/2} = \frac{1}{Ka}$. The order of the reaction is

The reaction,$X + 2Y + Z \to N$ occurs by the following mechanism:
$(i)$ $X + Y \rightleftharpoons M$ (very rapid equilibrium)
$(ii)$ $M + Z \to P$ (slow)
$(iii)$ $P + Y \to N$ (very fast)
What is the rate law for this reaction?

For the reaction $A + B \rightarrow$ products,it is observed that
$(i)$ on doubling the initial concentration of $A$ only,the rate of reaction is also doubled and
$(ii)$ on doubling the initial concentration of both $A$ and $B$,there is a change by a factor of $8$ in the rate of the reaction.
The rate of this reaction is given by

The following mechanism has been proposed for the reaction of $NO$ with $Br_2$ to form $NOBr$:
$NO_{(g)} + Br_{2(g)} \rightleftharpoons NOBr_{2(g)}$
$NOBr_{2(g)} + NO_{(g)} \longrightarrow 2NOBr_{(g)}$
If the second step is the rate-determining step,the order of the reaction with respect to $NO_{(g)}$ is:

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:

For the reaction ${H_{2(g)} + I_{2(g)} \to 2HI_{(g)}}$,the possible mechanism is given below:
$I_2 \underset{k_{-1}}{\stackrel{k_1}{\rightleftharpoons}} 2 I$ (fast step)
${2I + H_2 \xrightarrow{K_2} 2HI}$ (slow step)
Determine the rate law for the reaction.