At $30^{\circ}C$,the half-life for the decomposition of $AB_{2}$ is $200\,s$ and is independent of the initial concentration of $AB_{2}$. The time required for $80\%$ of the $AB_{2}$ to decompose is $....s$ (Given: $\log 2 = 0.30; \log 5 = 0.70$)

The slope of a graph $\log [A]_t$ versus '$t$' for a first-order reaction is $-2.5 \times 10^{-3} \,s^{-1}$. Find the rate constant of the reaction.

The decomposition of substance $A$ follows first-order kinetics. Flask $I$ contains $1 \ L$ of $1 \ M$ solution of $A$,and flask $II$ contains $100 \ mL$ of $0.6 \ M$ solution of $A$. After $8 \ hours$,the concentration of $A$ in flask $I$ becomes $0.25 \ M$. How many hours will it take for the concentration of $A$ in flask $II$ to become $0.3 \ M$?

The time required for a first-order reaction to be $90\%$ complete is approximately .........

Calculate the half-life of the first-order reaction $C_2H_4O_{(g)} \to CH_{4(g)} + CO_{(g)}$. If the initial pressure of $C_2H_4O_{(g)}$ is $80 \ mm$ and the total pressure at the end of $20 \ minutes$ is $120 \ mm$,find the half-life in $\text{min}$.

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 : $\ln 10 = 2.3 ; \log 2 = 0.3$