For a first-order reaction, if the initial concentration $[A]_0 = 1.0 \text{ M}$ and the concentration after time $t = 276 \text{ s}$ is $[A]_t = 0.25 \text{ M}$, find the value of the rate constant $(k)$. (in $\text{ s}^{-1}$)

Which of the following plots is(are) correct for the given reaction? $( [P]_0$ is the initial concentration of $P$ $)$

In a reaction $A + B \rightarrow C$,initial concentrations of $A$ and $B$ are related as $[A]_0 = 8[B]_0$. The half-lives of $A$ and $B$ are $10 \ min$ and $40 \ min$,respectively. If they start to disappear at the same time,both following first-order kinetics,after how much time will the concentration of both the reactants be the same (in $min$)?

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 $, K$)?

What is the value of the rate constant of a first-order reaction if the slope of the graph between $\log_{10} \frac{[A]_0}{[A]_t}$ ($y$-axis) and time ($x$-axis) is $1 \times 10^{-3}$?

In a first order reaction,$60 \%$ of the reactant converts into product in $45 \ minutes$. Calculate the rate constant of the reaction.