For the elementary reaction $M \rightarrow N$,the rate of disappearance of $M$ increases by a factor of $8$ upon doubling the concentration of $M$. The order of the reaction with respect to $M$ is :

For the reaction $2H_2 + 2NO \to N_2 + 2H_2O$,the following mechanism has been proposed:
$I$. $2NO \rightleftharpoons N_2O_2$ (fast)
$II$. $N_2O_2 + H_2 \xrightarrow{k_2} N_2O + H_2O$ (slow)
$III$. $N_2O + H_2 \to N_2 + H_2O$ (fast)
What will be the rate law of this reaction?

Find the rate law for the reaction,$CHCl_{3(g)} + Cl_{2(g)} \rightarrow CCl_{4(g)} + HCl_{(g)}$ if the order of reaction with respect to $CHCl_{3(g)}$ is $1$ and with respect to $Cl_{2(g)}$ is $1/2$.

The possible mechanism for the reaction $2NO + Br_2 \to 2NOBr$ is:
$NO + Br_2 \rightleftharpoons NOBr_2$ (Fast)
$NOBr_2 + NO \to 2NOBr$ (Slow)
The rate law expression is:

The three experimental data for determining the differential rate of reaction $Cl_{2(g)} + 2NO_{(g)} \rightarrow 2NOCl_{(g)}$ at $310 \ K$ temperature are provided. $(a)$ Derive the differential rate of reaction. $(b)$ Calculate the order of reaction. $(c)$ Calculate the value of the rate constant.

For a reaction $A \to B$,the rate of reaction quadrupled when the concentration of $A$ is doubled. The rate expression of the reaction is $r = K[A]^n$. The value of $n$ is