$A$ first order reaction is $25 \%$ completed in $40 \ min$. What is the rate constant $k$ for the reaction?

For a first order reaction,the initial concentration of a reactant is $0.05 \ M$. After $45 \ minutes$,it is decreased by $0.015 \ M$. Calculate the half-life period $(t_{1/2})$ (in $min$)?

The following is a first-order reaction:
$N_2O_5 \text{ (solution)} \rightarrow 2 NO_2 \text{ (solution)} + \frac{1}{2} O_2 \text{ (g)}$
In this reaction,$CCl_4$ is the solvent. The rate constant is $k = 5.0 \times 10^{-4} \ s^{-1}$. The initial concentration of $N_2O_5$ is $0.25 \ mol \ L^{-1}$.
$(i)$ What will be the initial rate of reaction?
$(ii)$ Calculate the half-life $(t_{1/2})$.
$(iii)$ How much time is required to complete $75\%$ of the reaction?
$(iv)$ Calculate the concentration of $N_2O_5$ and $NO_2$ after $30 \ min$.

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)

For a first order reaction,the rate constant is given as $\log_{10} K = 12 - \frac{6 \times 10^3}{T}$. What will be the value of temperature if its half-life period is $6.93 \times 10^{-3} \, \text{min}$ (in $, K$)?

The half-life period of a first-order reaction is $138.6 \ min$. The rate constant of the reaction is: (in $min^{-1}$)