The rate constant for a first order reaction is $20 \, min^{-1}$. The time required for the initial concentration of the reactant to reduce to its $\frac{1}{32}$ level is $........ \times 10^{-2} \, min$. (Nearest integer) (Given: $\ln 10 = 2.303, \log 2 = 0.3010$)

Thermal decomposition of $HCOOH$ is a first order reaction and the rate constant at $T(K)$ is $4.606 \times 10^{-3} \ s^{-1}$. The time required to decompose $90 \%$ of initial quantity of $HCOOH$ at $T(K)$ in seconds is

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 $0.3 \ M$?

In the following first order reactions $A$ $\xrightarrow{K_1} B$ $\xrightarrow{K_2} \text{Product}$,find the ratio $K_1/K_2$ if $90\%$ of $A$ has been reacted in time $t$ while $99\%$ of $B$ has been reacted in time $2t$.

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

For the given first order reaction $A \rightarrow B$,the half-life of the reaction is $0.3010 \ min$. The ratio of the initial concentration of reactant to the concentration of reactant at time $2.0 \ min$ will be equal to $........$ (Nearest integer).