For a first order reaction $A_5 \rightarrow 5 B_2$,the concentration vs time plot is as shown. The half-life of the reaction is

$A$ substance $A$ decomposes by a first order reaction starting initially with $[A]_0 = 2.00 \, M$ and after $200 \, \min$,$[A]_t = 0.15 \, M$. For this reaction,what is the value of the rate constant $k$?

For an elementary reaction,$X_{(g)} \rightarrow Y_{(g)} + Z_{(g)}$,the $t_{1/2}$ is $10 \text{ minutes}$. In what period of time would the concentration of $X$ be reduced to $10 \%$ of its original concentration?

The reaction $A \rightarrow B$ follows first-order kinetics. If it takes $1 \text{ hour}$ to convert $0.8 \text{ mol}$ of $A$ to $0.6 \text{ mol}$ of $B$,how many hours will it take to convert $0.9 \text{ mol}$ of $A$ to $0.675 \text{ mol}$ of $B$?

Dissociation of $N_2O_5$ dissolved in $CCl_4$ at constant temperature: $N_2O_{5(soln)} \to 2NO_{2(soln)} + \frac{1}{2}O_{2(g)}$. This is a first order reaction. The velocity constant is $5.0 \times 10^{-4} \ s^{-1}$. The initial concentration of $N_2O_5$ is $0.25 \ mol \ L^{-1}$. How much time is required to produce $0.20 \ mol \ L^{-1}$ concentration of $NO_2$ (in $s$)?

Time required to decompose $SO_{2}Cl_{2}$ to half of its initial amount is $60 \ minutes$. If the decomposition is a first order reaction,calculate the rate constant of the reaction.