For a reaction $A + B \to$ product,it was found that the rate of reaction increases four times if the concentration of $A$ is doubled,but the rate of reaction remains unaffected if the concentration of $B$ is doubled. Hence,the rate law for the reaction is

The half-life for a second-order reaction is $30 \ min$. If the initial concentration is $0.1 \ M$,then the value of the rate constant will be $............ \ M^{-1} \ min^{-1}$.

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:

For a reaction $A + B \rightarrow \text{Product}$,the order with respect to $A$ is $2$ and with respect to $B$ is $3$. If the concentration of both is doubled,by how much will the rate increase?

The three experimental data sets for determining the differential rate of the reaction $2 NO_{(g)} + Cl_{2_{(g)}} \rightarrow 2 NOCl_{(g)}$ at a definite temperature are given below. (Note: The data table was missing in the input,assuming standard values for this reaction: $Exp 1: [NO]=0.1, [Cl_2]=0.1, Rate=0.18$; $Exp 2: [NO]=0.1, [Cl_2]=0.2, Rate=0.36$; $Exp 3: [NO]=0.2, [Cl_2]=0.1, Rate=0.72$).
$(a)$ Derive the differential rate law of the reaction.
$(b)$ Calculate the order of the reaction.
$(c)$ Calculate the value of the rate constant.

The mechanism of the reaction $2NO_2 + F_2 \to 2NO_2F$ is given by:
$(i)$ $NO_2 \xrightarrow{slow} NO + O$
$(ii)$ $F_2 + O + NO \xrightarrow{fast} NO_2F + F$
$(iii)$ $F + NO_2 \xrightarrow{fast} NO_2F$
Select the correct statement.