The rate constant of the decomposition of hydrogen peroxide is $0.0204 \text{ min}^{-1}$. Calculate the half-life of the reaction. (in $\text{ min}$)

Calculate the rate constant of a first-order reaction if the concentration of the reactant decreases by $90 \%$ in $30 \ minutes$.

In a $1^{st}$ order reaction,$75\%$ of the reactant is consumed in $1.388 \, h$. Find the rate constant of the reaction.

$A$ first order reaction is found to have a rate constant,$k = 5.5 \times 10^{-14} \ s^{-1}$. The half life of reaction is . . . . . . .

The reaction,$X \to$ product follows first order kinetics. In $40 \, min$ the concentration of $X$ changes from $0.1 \, M$ to $0.025 \, M$. Then the rate of reaction when concentration of $X$ is $0.01 \, M$ is:

$t_{1/4}$ for a first-order reaction is given as: