Calculate the time needed for a reactant to decompose $99.9 \%$ if the rate constant of a first-order reaction is $0.576 \ min^{-1}$.

$A$ substance $A$ decomposes by a first order reaction starting initially with $[A]_0 = 2.00 \, M$ and after $200 \, \min$,$[A]_t = 0.15 \, M$. For this reaction,what is the value of the rate constant $k$?

What is the value of the slope when a graph is plotted of $\log \frac{[R]_0}{[R]}$ versus $t$ (time) for a first-order reaction?

If the half-life of a first-order reaction is $4 \ min$,then after how many minutes will the reaction be $99.9 \%$ complete?

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 $, K$)?

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