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

The rate for a first order reaction is $0.6932 \times 10^{-2} \, mol \, L^{-1} \, min^{-1}$ and the initial concentration of the reactants is $1 \, M$. The half-life $T_{1/2}$ is equal to ........ $min$.

The gaseous reaction $A_{(g)} \to 2B_{(g)} + C_{(g)}$ is a first-order reaction. If the initial pressure $P_A = 90 \ mm \ Hg$ and the total pressure after $10 \ min$ is $180 \ mm \ Hg$,calculate the rate constant of the reaction.

$PCl_{5(g)} \rightarrow PCl_{3(g)} + Cl_{2(g)}$
In the above first order reaction,the concentration of $PCl_{5}$ reduces from an initial concentration of $50 \ mol \ L^{-1}$ to $10 \ mol \ L^{-1}$ in $120 \ minutes$ at $300 \ K$. The rate constant for the reaction at $300 \ K$ is $X \times 10^{-2} \ min^{-1}$. The value of $X$ is $......$
$[$ Given $\log 5 = 0.6989 ]$

In a first-order reaction,the concentration of reactant $X$ decreases from $0.1 \, M$ to $0.005 \, M$ in $40 \, min$. What will be the rate of reaction when the concentration of $X$ is $0.01 \, M$?

The rate constant for a first order reaction is $60 \ s^{-1}$. How much time will it take to reduce the initial concentration of the reactant to its $1/16^{th}$ value?