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 $\text{ s}^{-1}$)

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

For the reaction $R \rightarrow P$,the half-life is independent of the initial concentration of the reactant,$R$. Which one of the following graphs is not correct for this reaction?

Calculate the half-life of a first-order reaction in minutes if the rate constant is $1 \times 10^{-3} \ sec^{-1}$.

The reaction $2N_2O_5 \,(g) \to 4NO_2 \,(g) + O_2 \,(g)$ follows first order kinetics. The pressure of a vessel containing only $N_2O_5$ was found to increase from $50 \, mmHg$ to $87.5 \, mmHg$ in $30 \, min$. The pressure exerted by the gases after $60 \, min$ will be .......... $mmHg$ (assume temperature remains constant).

When the value of rate constant $(k)$ is $2.0 \text{ min}^{-1}$, then what will be the half-life of the reaction $(t_{1/2})$ in seconds?