The rate of a first-order reaction is $1.5 \times 10^{-2} \, mol \, L^{-1} \, min^{-1}$ when the concentration of the reactant is $0.5 \, M$. Find the half-life $(t_{1/2})$ of the reaction in $min$.

For the first-order reaction $2N_2O_{5(g)} \rightarrow 4NO_{2(g)} + O_{2(g)}$,which of the following statements is incorrect?

$[A] \rightarrow [B]$. If the formation of compound $[B]$ follows first-order kinetics and after $70 \ min$ the concentration of $[A]$ was found to be half of its initial concentration,then the rate constant of the reaction is $x \times 10^{-6} \ s^{-1}$. The value of $x$ is $......$ (Nearest Integer).

The integrated rate equation for a first-order reaction is:

For an elementary reaction,$X_{(g)} \rightarrow Y_{(g)} + Z_{(g)}$,the $t_{1/2}$ is $10 \text{ minutes}$. In what period of time would the concentration of $X$ be reduced to $10 \%$ of its original concentration?

For a first-order reaction,it takes $20 \, \text{min}$ for the concentration to decrease from $1 \, M$ to $0.6 \, M$. How much time is required for the concentration to decrease from $0.6 \, M$ to $0.36 \, M$?