For the reaction $A \to \text{Products}$,the rate of reaction becomes one-fourth when the concentration of $A$ is halved. What is the order of the reaction?

The rate law expression for the reaction $aA + bB \to P$ is $\text{rate} = K [A]^p [B]^q$. The order of the reaction is

The order of the reaction occurring by the following mechanism should be:
$(i)$ $A_2 \to A + A$ (fast)
$(ii)$ $A + B_2 \to AB + B$ (slow)
$(iii)$ $A + B \to AB$ (fast)

The rate of the reaction $x + y \rightarrow \text{product}$ is $5.4 \times 10^{-2} \ mol \ dm^{-3} \ sec^{-1}$. When $[x] = 0.2 \ mol \ dm^{-3}$ and $[y] = 0.1 \ mol \ dm^{-3}$,calculate the rate constant of the reaction if it is first order in $X$ and second order in $Y$.

The reaction of hydrogen and iodine monochloride is given as
$H_{2(g)} + 2ICl_{(g)} \to 2HCl_{(g)} + I_{2(g)}$
This reaction is of first order with respect to $H_{2(g)}$ and $ICl_{(g)}$. Which of the following mechanisms is consistent with the given information?
Mechanism $A$:
$H_{2(g)} + 2ICl_{(g)} \to 2HCl_{(g)} + I_{2(g)}$
Mechanism $B$:
$H_{2(g)} + ICl_{(g)} \to HCl_{(g)} + HI_{(g)}$ (Slow)
$HI_{(g)} + ICl_{(g)} \to HCl_{(g)} + I_{2(g)}$ (Fast)

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