For a first order reaction $A \to B$,the reaction rate at reactant concentration of $0.01 \ M$ is found to be $2.0 \times 10^{-5} \ mol \ L^{-1} \ s^{-1}$. The half-life period of the reaction is .......... $sec$.

For a first order reaction,the ratio of the time for $75 \% $ completion of a reaction to the time for $50 \% $ completion is $....$ . (Integer answer)

Calculate the rate constant of the first order reaction if $80 \%$ of the reactant reacted in $15 \ minute$.

If the rate constant for a first order reaction is $2.303 \times 10^{-3} \ s^{-1}$,find the time required to reduce $4 \ g$ of the reactant to $0.2 \ g$. (in $hours$)

$A$ first order reaction is $50 \%$ complete in $16 \ min$. How much time is required to complete $87.5 \%$ of the reaction (in $min$)?

Which of the following represents the integrated rate law equation for the gas-phase first-order reaction,$A_{(g)} \rightarrow B_{(g)} + C_{(g)}$? If $P_{i}$ is the initial pressure of $A$ and $P$ is the total pressure of the reaction mixture at time $t$.