Identify the correct statement regarding the order of reaction from the following.

Consider the following single step reaction in gas phase at constant temperature.
$2 \ A_{(g)} + B_{(g)} \rightarrow C_{(g)}$
The initial rate of the reaction is recorded as $r_1$ when the reaction starts with $1.5 \ atm$ pressure of $A$ and $0.7 \ atm$ pressure of $B$. After some time,the rate $r_2$ is recorded when the pressure of $C$ becomes $0.5 \ atm$. The ratio $r_1 : r_2$ is $\qquad$ $\times 10^{-1}$.
(Nearest integer)

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:

The following data is given for the reaction between $A$ and $B$:

$S.NO.$	$[A] \ mol \ L^{-1}$	$[B] \ mol \ L^{-1}$	$Rate \ mol \ L^{-1} \ sec^{-1}$
$I$	$1 \times 10^{-2}$	$2 \times 10^{-2}$	$2 \times 10^{-4}$
$II$	$2 \times 10^{-2}$	$2 \times 10^{-2}$	$4 \times 10^{-4}$
$III$	$2 \times 10^{-2}$	$4 \times 10^{-2}$	$8 \times 10^{-4}$

Which of the following are correct statements?
$(a)$ Rate constant of the reaction is $1 \ mol^{-1} \ L \ sec^{-1}$.
$(b)$ Rate law of the reaction is $k[A][B]$.
$(c)$ Rate of reaction increases four times on doubling the concentration of both the reactants.

What is the order of reaction for $A + B \to C$?

$Observation$	$[A] \ (mol \ L^{-1})$	$[B] \ (mol \ L^{-1})$	$Rate \ (mol \ L^{-1} \ sec^{-1})$
$1$	$0.1$	$0.1$	$2 \times 10^{-3}$
$2$	$0.2$	$0.1$	$4 \times 10^{-3}$
$3$	$0.1$	$0.2$	$8 \times 10^{-3}$

Identify the reaction order from each of the following rate constants.
$(i)$ $k = 2.3 \times 10^{-5} \, L \, mol^{-1} \, s^{-1}$
$(ii)$ $k = 3 \times 10^{-4} \, s^{-1}$