$t_{1/2} =$ constant confirms the first order reaction. If $a^2 t_{1/2} =$ constant,it confirms that the order of reaction is ($a =$ initial concentration of reactant).

For the reaction $2A + B \to C$,the values of initial rate at different reactant concentrations are given in the table below: The rate law for the reaction is

$[A] \ (mol \ L^{-1})$	$[B] \ (mol \ L^{-1})$	Initial Rate $(mol \ L^{-1} \ s^{-1})$
$0.05$	$0.05$	$0.045$
$0.10$	$0.05$	$0.090$
$0.20$	$0.10$	$0.72$

For the reaction $A + B \longrightarrow \text{product}$,the rate law equation is $\text{rate} = k[A]^2[B]$. If the rate of reaction is $0.22 \ mol \ L^{-1} \ s^{-1}$,calculate the rate constant $k$. Given: $[A] = 1 \ mol \ L^{-1}, [B] = 0.25 \ mol \ L^{-1}$.

An example of a pseudo-$unimolecular$ reaction is

The results given in the below table were obtained during kinetic studies of the following reaction:
$2 A + B \longrightarrow C + D$

Experiment	$[A] / mol \ L^{-1}$	$[B] / mol \ L^{-1}$	Initial rate / $mol \ L^{-1} \ min^{-1}$
$I$	$0.1$	$0.1$	$6.00 \times 10^{-3}$
$II$	$0.1$	$0.2$	$2.40 \times 10^{-2}$
$III$	$0.2$	$0.1$	$1.20 \times 10^{-2}$
$IV$	$X$	$0.2$	$7.20 \times 10^{-2}$
$V$	$0.3$	$Y$	$2.88 \times 10^{-1}$

$X$ and $Y$ in the given table are respectively :

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