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: $[A] = 1 \ mol \ L^{-1}, [B] = 0.25 \ mol \ L^{-1}$.

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)

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 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 $............ \ M^{-1} \ min^{-1}$.

The reaction $CH_{3}COF + H_{2}O \rightleftharpoons CH_{3}COOH + HF$ is studied under two conditions:
Condition $I$: $[H_{2}O]_{0} = 1.00 \ M$,$[CH_{3}COF]_{0} = 0.01 \ M$
Condition $II$: $[H_{2}O]_{0} = 0.02 \ M$,$[CH_{3}COF]_{0} = 0.80 \ M$

Time $(t)$ min (Condition $I$) / $[CH_{3}COF]$ $M$	Time $(t)$ min (Condition $II$) / $[H_{2}O]$ $M$
$0$ / $0.01000$	$0$ / $0.0200$
$10$ / $0.00867$	$10$ / $0.0176$
$20$ / $0.00735$	$20$ / $0.0156$
$40$ / $0.00540$	$40$ / $0.0122$

Determine the overall order of the reaction and calculate the rate constant.

For the reaction $A + B \rightarrow$ product,the rate of reaction is $3.6 \times 10^{-2} \ mol \ dm^{-3} \ sec^{-1}$. When $[A] = 0.2 \ mol \ dm^{-3}$ and $[B] = 0.1 \ mol \ dm^{-3}$,find the rate constant of the reaction if it is second order with respect to both reactants.