For a first order reaction,the rate constant is $0.6932 \ hr^{-1}$,then the half-life for the reaction is ......... $hr$.

For a first order reaction $A_{(g)} \rightarrow 2B_{(g)} + C_{(g)}$ at constant volume and $300 \ K$,the total pressure at the beginning $(t=0)$ and at time $t$ are $P_0$ and $P_t$,respectively. Initially,only $A$ is present with concentration $[A]_0$,and $t_{1/3}$ is the time required for the partial pressure of $A$ to reach $1/3^{rd}$ of its initial value. The correct option$(s)$ is (are) (Assume that all these gases behave as ideal gases)

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

$A$ first-order reaction is $50\%$ complete in $45 \text{ minutes}$. How many hours will it take for the reaction to be $99.9\%$ complete?

The reaction $A \rightarrow B$ follows first-order kinetics. If it takes $1 \text{ hour}$ to convert $0.8 \text{ mol}$ of $A$ to $0.6 \text{ mol}$ of $B$,how many hours will it take to convert $0.9 \text{ mol}$ of $A$ to $0.675 \text{ mol}$ of $B$?

The integrated rate equation for a first-order reaction,$A \rightarrow \text{product}$,is