It takes $1 \, h$ for a first order reaction to go to $50 \, \%$ completion. The total time required for the same reaction to reach $87.5 \, \%$ completion will be $..... \, h$.

For a first order reaction $A \rightarrow B$,the rate constant,$k = 5.5 \times 10^{-14} \, s^{-1}$. The time required for $67 \, \%$ completion of reaction is $x \times 10^{-1}$ times the half life of reaction. The value of $x$ is $....$ (Nearest integer)

For the first order reaction $A \to \text{Product}$ $(t_{1/2} = 10 \ \text{min})$,the fraction of reactant degraded after an hour from the reaction has started is

Calculate the time needed for a reactant to decompose $99.9 \%$ if the rate constant of a first-order reaction is $0.576 \ min^{-1}$.

The first order rate constant for the decomposition of $N_2O_5$ is $6.2 \times 10^{-4} \ s^{-1}$. The half-life period for this decomposition in seconds 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.