For the decomposition of azomethane,$CH_3N_2CH_{3(g)} \rightarrow CH_3CH_{3(g)} + N_{2(g)}$,a first order reaction,the variation in partial pressure with time at $600 \ K$ is given as shown in the graph. The value of the rate constant $k$ in $s^{-1}$ is $x \times 10^4$. Find the value of $x$.

The following is a first-order reaction:
$N_2O_5 \text{ (solution)} \rightarrow 2 NO_2 \text{ (solution)} + \frac{1}{2} O_2 \text{ (g)}$
In this reaction,$CCl_4$ is the solvent. The rate constant is $k = 5.0 \times 10^{-4} \ s^{-1}$. The initial concentration of $N_2O_5$ is $0.25 \ mol \ L^{-1}$.
$(i)$ What will be the initial rate of reaction?
$(ii)$ Calculate the half-life $(t_{1/2})$.
$(iii)$ How much time is required to complete $75\%$ of the reaction?
$(iv)$ Calculate the concentration of $N_2O_5$ and $NO_2$ after $30 \ min$.

$A$ reaction is $50\%$ complete in $2 \ hours$ and $75\%$ complete in $4 \ hours$. The order of reaction is

The half-life period of a $1^{st}$ order reaction is $60 \ minutes$. What percentage will be left over after $240 \ minutes$ (in $\%$)?

The slope of a graph $\log [A]_t$ versus '$t$' for a first-order reaction is $-2.5 \times 10^{-3} \,s^{-1}$. Find the rate constant of the reaction.

The gaseous reaction $A_{(g)} \to 2B_{(g)} + C_{(g)}$ is a first-order reaction. If the initial pressure $P_A = 90 \ mm \ Hg$ and the total pressure after $10 \ min$ is $180 \ mm \ Hg$,calculate the rate constant of the reaction.