For a reaction involving substances $x$,$y$,and $z$,if the overall order of the reaction is $0.5$,which of the following rate laws is applicable?

For the elementary reaction $M \rightarrow N$,the rate of disappearance of $M$ increases by a factor of $8$ upon doubling the concentration of $M$. The order of the reaction with respect to $M$ is :

For the reaction $2 NO_{(g)} + Cl_{2_{(g)}} \rightarrow 2NOCl_{(g)}$,when the concentration of $Cl_2$ is doubled,the rate of the reaction becomes twice the original rate. When the concentration of $NO$ is doubled,the rate becomes four times the original rate. What is the overall order of the reaction?

Define the following terms:
$(1)$ Elementary reaction
$(2)$ Complex reaction

During the kinetic study of the reaction,$2A + B \rightarrow C + D,$ the following results were obtained:

$Run$	$[A] / mol \ L^{-1}$	$[B] / mol \ L^{-1}$	Initial rate of formation of $D / mol \ L^{-1} \ min^{-1}$
$I.$	$0.1$	$0.1$	$6.0 \times 10^{-3}$
$II.$	$0.3$	$0.2$	$7.2 \times 10^{-2}$
$III.$	$0.3$	$0.4$	$2.88 \times 10^{-1}$
$IV.$	$0.4$	$0.1$	$2.40 \times 10^{-2}$

Based on the above data,which one of the following is correct?

Write the unit of the rate constant for the following reactions:
$1.$ Fourth order
$2.$ Third order