For the reaction $2N_2O_5 \rightarrow 4NO_2 + O_2$,the rate constant is $3.0 \times 10^{-5} \ s^{-1}$. If the rate of reaction is $2.40 \times 10^{-5} \ mol \ L^{-1} \ s^{-1}$,calculate the concentration of $N_2O_5$ in $mol \ L^{-1}$.

After how many seconds will the concentration of the reactant in a first order reaction be halved if the rate constant is $1.155 \times 10^{-3} \ s^{-1}$?

What is the slope of the graph plotted between half-life $(t_{1/2})$ and initial concentration $(a)$ for a $1^{st}$ order reaction?

$A$ flask contains a mixture of compounds $A$ and $B.$ Both compounds decompose by first-order kinetics. The half-lives for $A$ and $B$ are $300 \ s$ and $180 \ s,$ respectively. If the concentrations of $A$ and $B$ are equal initially,the time required for the concentration of $A$ to be four times that of $B$ (in $s$): (Use $\ln 2 = 0.693$)

$A_{(g)} \rightarrow 2B_{(g)}$. Initially,$2 \ mol$ of $A$ are taken in a $5 \ L$ vessel. After $20 \ min$,$[A]_t = \frac{[B]_t}{2}$. Find the half-life time of $A$ in the first-order reaction in $\min$.

In a first order reaction,the concentration of the reactant decreases from $0.8 \ M$ to $0.4 \ M$ in $15 \ min$. The time taken for the concentration to change from $0.1 \ M$ to $0.025 \ M$ is .......... $min$.