Time required for completion of $99.9 \%$ of a First order reaction is . . . . . . times of half life $(t_{1/2})$ of the reaction.

For a first-order reaction,the time taken for the concentration of the reactant to reach $3/4$ of its initial value is $t_{1/4}$. If the rate constant for the reaction is $K$,then $t_{1/4}$ can be expressed as: (in $/K$)

For a first order reaction,the time required for completion of $90 \%$ reaction is '$x$' times the half life of the reaction. The value of '$x$' is $........$. (Given: $\ln 10 = 2.303$ and $\log 2 = 0.3010$)

The half-life of a substance in a certain enzyme-catalysed reaction is $138 \; s$. The time required for the concentration of the substance to fall from $1.28 \; mg \; L^{-1}$ to $0.04 \; mg \; L^{-1}$ is ....... $s$.

The decomposition reaction $2N_2O_{5(g)} \xrightarrow{\Delta} 2N_2O_{4(g)} + O_{2(g)}$ is started in a closed cylinder under isothermal isochoric conditions at an initial pressure of $1 \ atm$. After $Y \times 10^3 \ s$,the pressure inside the cylinder is found to be $1.45 \ atm$. If the rate constant of the reaction is $5 \times 10^{-4} \ s^{-1}$,assuming ideal gas behavior,the value of $Y$ is. . . . . . . .

Half-life period of a first order reaction is $1386 \ s$. The specific rate constant of the reaction is