For an $n^{th}$ order reaction,the rate law is given by $\frac{dx}{dt} = K[A]^n$. Which parameter can be determined from the logarithmic plot?

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

For a chemical reaction $A \rightarrow B$,the rate of the reaction is $2 \times 10^{-3} \ mol \ dm^{-3} \ s^{-1}$,when the initial concentration is $0.05 \ mol \ dm^{-3}$. The rate of the same reaction is $1.6 \times 10^{-2} \ mol \ dm^{-3} \ s^{-1}$ when the initial concentration is $0.1 \ mol \ dm^{-3}$. The order of the reaction is

For the reaction $2A + B \to C$,the values of initial rate at different reactant concentrations are given in the table below: The rate law for the reaction is

$[A] \ (mol \ L^{-1})$	$[B] \ (mol \ L^{-1})$	Initial Rate $(mol \ L^{-1} \ s^{-1})$
$0.05$	$0.05$	$0.045$
$0.10$	$0.05$	$0.090$
$0.20$	$0.10$	$0.72$

The rate for the reaction $2 A + B \rightarrow \text{product}$ is $6 \times 10^{-4} \ mol \ dm^{-3} \ s^{-1}$. Calculate the rate constant if the reaction is first order in $A$ and zeroth order in $B$,given $[A] = [B] = 0.3 \ M$.

For the reaction:
$2NO_{2(g)} + O_{3(g)} \to N_2O_{5(g)} + O_{2(g)}$
The rate law is $R = K[NO_2]^1 [O_3]^1$.
Which of these possible reaction mechanisms is consistent with the rate law?
Mechanism $I$:
$NO_{2(g)} + O_{3(g)} \to NO_{3(g)} + O_{2(g)}$ (slow)
$NO_{3(g)} + NO_{2(g)} \to N_2O_{5(g)}$ (fast)
Mechanism $II$:
$O_{3(g)} \rightleftharpoons O_{2(g)} + [O]$ (fast)
$NO_{2(g)} + [O] \to NO_3$ (slow)
$NO_{3(g)} + NO_{2(g)} \to N_2O_5$ (fast)