For a first-order reaction,the ratio of the time required for $99.9\%$ completion to the time required for $50\%$ completion is:

Which is the correct relation between rate constant and half-life of a first-order reaction?

$N_2O_5 \rightarrow 2NO_{2(g)} + \frac{1}{2}O_{2(g)}$ is a first order reaction. $k = 5 \times 10^{-4} \ s^{-1}$. The initial concentration of $N_2O_5 = 0.2 \ mol \ L^{-1}$. After how much time will its concentration be $25 \%$ of the initial concentration (in $s$)?

For a first-order reaction $SO_2Cl_2 \to SO_2 + Cl_2$ at $320\, ^\circ C$,the rate constant is $2.2 \times 10^{-5}\, s^{-1}$. What percentage $(\%)$ of $SO_2Cl_2$ will decompose upon heating for $90\, min$?

If the rate constant for a first order reaction is $k$,then find the time required for completion of $80 \%$ of the reaction.

$N_{2}O_{5(g)} \rightarrow 2NO_{2(g)} + \frac{1}{2}O_{2(g)}$
In the above first order reaction,the initial concentration of $N_{2}O_{5}$ is $2.40 \times 10^{-2} \ mol \ L^{-1}$ at $318 \ K$. The concentration of $N_{2}O_{5}$ after $1 \ hour$ was $1.60 \times 10^{-2} \ mol \ L^{-1}$. The rate constant of the reaction at $318 \ K$ is $..... \times 10^{-3} \ min^{-1}$. (Nearest integer)
[Given: $\log 3 = 0.477, \log 5 = 0.699$]