For a first order reaction,the ratio between the time taken to complete $\frac{3}{4}$ th of the reaction and time taken to complete half of the reaction is

At $27^{\circ} C$ temperature,the time required for $75 \%$ completion of a first order reaction is $20 \ s$. What will be its rate constant?

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. . . . . . . .

If the half-life $(t_{1/2})$ for a first order reaction is $1 \text{ minute}$,then the time required for $99.9\%$ completion of the reaction is closest to

In a first order reaction,the concentration of the reactant decreases from $0.6 \ M$ to $0.3 \ M$ in $15 \ min$. The time taken for the concentration to change from $0.1 \ M$ to $0.025 \ M$ in minutes is

For a first order reaction,the half-life period is