For a reaction of $n^{th}$ order,the plot of $t_{1/2}$ versus initial concentration $[A]_0$ is a straight line. When the initial concentration is $2 \ mol \ L^{-1}$,the reaction takes $10 \ min$ to complete $50\%$. If the reaction takes $t \ min$ to complete $50\%$ when the initial concentration is $4 \ mol \ L^{-1}$,find $n$ and $t$ respectively.

For a certain reaction,$10\%$ of the reactant dissociates in $1 \ hour$,$20\%$ of the reactant dissociates in $2 \ hour$,and $30\%$ of the reactant dissociates in $3 \ hour$. What are the units of the rate constant?

$A$ reaction $2A \to$ products is found to follow zero order kinetics,then

For a reaction $A \to$ Products,a plot of $\log\,t_{1/2}$ versus $\log\,a_0$ is shown in the figure. If the initial concentration of $A$ is represented by $a_0,$ the order of the reaction is

Consider the reaction $aX \to bY$,for which the rate constant at $30^\circ C$ is $1 \times 10^{-3} \text{ mol L}^{-1} \text{ s}^{-1}$. Which of the following statements are true?
$A$. When concentration of $X$ is increased to four times,the rate of reaction becomes $16$ times.
$B$. The reaction is a second order reaction.
$C$. The half-life period is independent of the concentration of $X$.
$D$. Decomposition of $N_2O_5$ is an example of the above reaction.
$E$. $\ln \frac{[R]_0}{[R]}$ vs time is valid for the above reaction.

Half life of zero order reaction $A \rightarrow \text{product}$ is $1 \ \text{hour}$,when initial concentration of reactant is $2.0 \ \text{mol L}^{-1}$. The time required to decrease concentration of $A$ from $0.50$ to $0.25 \ \text{mol L}^{-1}$ is: