The experimental data for the reaction $2A + B_2 \longrightarrow 2AB$ is given below:

Exp.	$[A] \ (mol \ L^{-1})$	$[B_2] \ (mol \ L^{-1})$	Rate $(mol \ L^{-1} \ S^{-1})$
$1$	$0.50$	$0.50$	$1.6 \times 10^{-4}$
$2$	$0.50$	$1.00$	$3.2 \times 10^{-4}$
$3$	$1.00$	$1.00$	$3.2 \times 10^{-4}$

Determine the rate law for the reaction.

The reaction $2NO + O_2 \rightarrow 2NO_2$ is an example of which order of reaction?

Write the unit of the rate constant for the following reactions:
$1.$ $5/2$ order
$2.$ $n$ order

What is the molecularity of the following reactions?
$1.$ $NH_4NO_2(s) \rightarrow N_2(g) + 2H_2O(l)$
$2.$ $2HI(g) \rightarrow H_2(g) + I_2(g)$
$3.$ $2NO(g) + O_2(g) \rightarrow 2NO_2(g)$

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

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:

At what concentration of the reactant (in $M$) are the rate constants for first-order,second-order,and third-order reactions equal?