An organic compound undergoes first order decomposition. If the time taken for the $60 \%$ decomposition is $540 \ s$,then the time required for $90 \%$ decomposition will be $.......... \ s$. (Nearest integer). Given : $\ln 10 = 2.3 ; \log 2 = 0.3$

The half-life period for a first order reaction is $693 \ sec$. The rate constant for this reaction would be: (in $sec^{-1}$)

The initial concentration of $N_2O_5$ in the following first order reaction $N_2O_{5(g)} \rightarrow 2NO_{2(g)} + 1/2O_{2(g)}$ was $1.24 \times 10^{-2} \, mol \, L^{-1}$ at $318 \, K$. The concentration of $N_2O_5$ after $60 \, minutes$ was $0.20 \times 10^{-2} \, mol \, L^{-1}$. Calculate the rate constant of the reaction at $318 \, K$.

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

Calculate the half-life of a first order reaction from the rate constants given below:
$(i) \ 200 \ s^{-1}$
$(ii) \ 2 \ min^{-1}$
$(iii) \ 4 \ years^{-1}$

For a first order reaction,show that the time required for $99 \%$ completion is twice the time required for the completion of $90 \%$ of the reaction.