The rate constant value for a reaction is $1.75 \times 10^2 \ L^2 \ mol^{-2} \ sec^{-1}$. The half-life period $t_{1/2} \propto$ . . . . . . .

The order of a reaction is said to be $2$ with respect to a reactant $X$,when

The rate law equation for a reaction between $A$,$B$ and $C$ is $r = k[A][B][C]^2$. What will be the new rate of reaction if the concentration of both $A$ and $B$ are doubled (in $r$)?

The half-life of a reaction is found to be inversely proportional to the cube of its initial concentration. The order of the reaction is:

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

$2 \ NO + 2 \ H_2 \rightarrow N_2 + 2 \ H_2O$
The above reaction has been studied at $800^{\circ} C$. The related data are given in the table below.

Reaction serial number	Initial pressure of $H_2$ / $kPa$	Initial Pressure of $NO$ / $kPa$	Initial rate $(-\frac{dp}{dt}) / (kPa \ s^{-1})$
$1$	$65.6$	$40.0$	$0.135$
$2$	$65.6$	$20.1$	$0.033$
$3$	$38.6$	$65.6$	$0.214$
$4$	$19.2$	$65.6$	$0.106$

The order of the reaction with respect to $NO$ is $...........$