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

For a first order reaction $R \longrightarrow P$,the rate constant is $k$. If the initial concentration of $R$ is $[R_0]$,the concentration of $R$ at any time $t$ is given by the expression:

For a first order reaction, the half-life is $5 \text{ hour}$. What time is required to reduce $10 \text{ g}$ of reactant to $2.5 \text{ g}$ (in $\text{ hour}$)?

$A_{(g)} \xrightarrow{\Delta} P_{(g)} + Q_{(g)} + R_{(g)}$ follows first-order kinetics with a half-life of $69.3 \ s$ at $500^{\circ}C$. Starting from the gas '$A$' enclosed in a container at $500^{\circ}C$ and at a pressure of $0.4 \ atm$,the total pressure of the system after $230 \ s$ will be (in $atm$)

If benzene diazonium chloride undergoes first order decomposition at $T \ K$ with a rate constant of $6.93 \times 10^{-2} \ min^{-1}$,the time for completion of $90 \%$ of the reaction (in $min$) is (nearest integer) $(\log 2 = 0.30, \log 3 = 0.477)$.

For a first order reaction $A \to \text{products}$,the concentration of $[A]$ is reduced from $2 \ M$ to $0.125 \ M$ in one hour. The $t_{1/2}$ of this reaction (in $\text{min}$) is: