Select the rate law for the reaction $A + B \longrightarrow C$ based on the following data:

$Exp$	$[A]$	$[B]$	$Rate$
$1$	$0.012$	$0.035$	$0.10$
$2$	$0.024$	$0.070$	$0.80$
$3$	$0.024$	$0.035$	$0.10$
$4$	$0.012$	$0.070$	$0.80$

$[A]_0 / \text{mol } L^{-1}$	$t_{1/2} / \text{min}$
$0.100$	$200$
$0.025$	$100$

For a given reaction $R \rightarrow P$,$t_{1/2}$ is related to $[A]_0$ as given in the table:
Given: $\log 2 = 0.30$
Which of the following is true?
$A.$ The order of the reaction is $1/2$.
$B.$ If $[A]_0$ is $1 \text{ M}$,then $t_{1/2}$ is $200 \sqrt{10} \text{ min}$.
$C.$ The order of the reaction changes to $1$ if the concentration of reactant changes from $0.100 \text{ M}$ to $0.500 \text{ M}$.
$D.$ $t_{1/2}$ is $800 \text{ min}$ for $[A]_0 = 1.6 \text{ M}$.
Choose the correct answer from the options given below:

For any reaction,the rate constant $K = 2.3 \times 10^{-5} \ mol^{-3/2} \ L^{3/2} \ S^{-1}$. The order of the reaction is . . . . . . .

The rate for the reaction $A + B \rightarrow \text{product}$ is $1.8 \times 10^{-2} \ mol \ dm^{-3} \ s^{-1}$. Calculate the rate constant if the reaction is second order in $A$ and first order in $B$,given $[A] = 0.2 \ M$ and $[B] = 0.1 \ M$.

The reaction,$X + 2Y + Z \to N$ occurs by the following mechanism:
$(i)$ $X + Y \rightleftharpoons M$ (very rapid equilibrium)
$(ii)$ $M + Z \to P$ (slow)
$(iii)$ $P + Y \to N$ (very fast)
What is the rate law for this reaction?

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.