What is the order of reaction for the decomposition of gaseous acetaldehyde?

Calculate the overall order of a reaction which has the rate expression:
$(a)$ $\text{Rate} = k[A]^{1/2}[B]^{3/2}$
$(b)$ $\text{Rate} = k[A]^{3/2}[B]^{-1}$

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)

For a reaction $A \rightarrow 2 B + C$ the half-lives are $100 \ s$ and $50 \ s$ when the concentration of reactant $A$ is $0.5 \ mol \ L^{-1}$ and $1.0 \ mol \ L^{-1}$ respectively. The order of the reaction is (Nearest Integer).

Identify the reaction intermediate of the following reaction sequence:
$(i)$ $2 SO_{2(g)} + 2 NO_{2(g)} \rightarrow 2 SO_{3(g)} + 2 NO_{(g)}$
$(ii)$ $2 NO_{(g)} + O_{2(g)} \rightarrow 2 NO_{2(g)}$
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Overall: $2 SO_{2(g)} + O_{2(g)} \rightarrow 2 SO_{3(g)}$

If $a$ is the initial concentration of the reactant,the half-life period of the reaction of $n^{th}$ order is inversely proportional to