An organic compound undergoes first order decomposition. If the time taken for the $60 \%$ decomposition is $540 \ s$,then the time required for $90 \%$ decomposition will be $.......... \ s$. (Nearest integer). Given : $\ln 10 = 2.3 ; \log 2 = 0.3$

The decomposition of dinitrogen pentoxide $(N_2O_5)$ follows first order rate law. What will be the rate constant from the given data?
At $t = 800 \ s$,$[N_2O_5] = 1.45 \ mol \ L^{-1}$
At $t = 1600 \ s$,$[N_2O_5] = 0.88 \ mol \ L^{-1}$

For a first-order reaction $A \to B$,the rate of reaction at a reactant concentration of $0.01 \, M$ is $2.0 \times 10^{-5} \, mol \, L^{-1} \, s^{-1}$. The half-life period of the reaction is .... $s$.

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 $30 \ min$.

$A$ radioactive substance decomposes such that after $100 \ min$,its concentration becomes $1/8$ of the original concentration. Calculate the rate constant $(k)$ and half-life time $(t_{1/2})$.

Calculate the rate constant of the first order reaction if $80 \%$ of the reactant decomposes in $60 \ minutes$.