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 $mol \ L^{-1}$.

$A$ flask is filled with equal moles of $A$ and $B$. The half-lives of $A$ and $B$ are $100 \, s$ and $50 \, s$ respectively and are independent of the initial concentration. The time required for the concentration of $A$ to be four times that of $B$ is $.... \, s.$
(Given : $\ln 2 = 0.693$ )

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.

$A$ first order reaction which is $30\%$ complete in $30 \ min$ has a half-life period of .............. $min.$ (in $.2$)

The integrated rate equation for a first-order reaction is:

Consider the following two first order reactions occurring at $298 \ K$ with same initial concentration of $A$: $(1)$ $A \rightarrow B$; rate constant,$k=0.693 \ min^{-1}$ $(2)$ $A \rightarrow C$; half-life,$t_{1/2}=0.693 \ min$. Choose the correct option.