The mechanism of the reaction $A + 2B \to D$ is given by:
$2B \xrightarrow{k} B_2$ [Slow]
$B_2 + A \to D$ [Fast]
The rate law expression,order with respect to $A$,order with respect to $B$,and overall order are respectively:

The half-life periods of decomposition of $PH_3$ for different initial pressures are given below $:$

Initial Pressure $p$ (torr)	$707$	$79$	$37.5$
Half-life $t_{1/2}$ (min)	$84$	$84$	$84$

Determine the order of the reaction.

$A \rightarrow$ products ($1^{st}$ order reaction). Three sets of experiment were performed for a reaction under similar experimental conditions. Run $1 \Rightarrow 100 \ mL$ of $10 \ M$ solution of reactant $A$. Run $2 \Rightarrow 200 \ mL$ of $10 \ M$ solution of reactant $A$. Run $3 \Rightarrow 100 \ mL$ of $10 \ M$ solution of reactant $A + 100 \ mL$ of $H_2O$ added. The correct variation of rate of reaction is:

The data for the reaction $A + B \to C$ is given below. The rate law corresponding to the above data is:

$Exp.$	$[A]_0$	$[B]_0$	Initial rate
$(1)$	$0.012$	$0.035$	$0.10$
$(2)$	$0.024$	$0.070$	$0.80$
$(3)$	$0.024$	$0.035$	$0.10$
$(4)$	$0.012$	$0.070$	$0.80$

The decomposition of ozone in the upper atmosphere is catalyzed by nitric oxide. The mechanism of the reaction is as follows:
$2NO \rightleftharpoons N_2O + [O]$
$O_3 + [O] \to 2O_2$ (slow)
Determine the order of the reaction.

For a hypothetical reaction $A + B \rightarrow C$,the following data is provided from three different experiments:
$1$. $[A] = 0.01 \ M$,$[B] = 0.01 \ M$ - Rate of reaction $= 1.0 \times 10^{-4} \ M \ s^{-1}$.
$2$. $[A] = 0.01 \ M$,$[B] = 0.03 \ M$ - Rate of reaction $= 9.0 \times 10^{-4} \ M \ s^{-1}$.
$3$. $[A] = 0.03 \ M$,$[B] = 0.03 \ M$ - Rate of reaction $= 2.70 \times 10^{-3} \ M \ s^{-1}$.
Determine the rate law.