In a first order reaction,the concentration of the reactant is reduced to $(1/8)^{th}$ of its initial concentration in $23.03 \ min$. What is the half-life period of the reaction (in $min$)?

For the first-order reaction $N_2O_5 \text{ (in } CCl_4) \rightarrow 2NO_2 + \frac{1}{2}O_{2(g)}$,the rate constant is $6.2 \times 10^{-4} \, s^{-1}$. What will be the rate of reaction when $[N_2O_5] = 1.25 \, mol \, L^{-1}$?

For an elementary reaction,$X_{(g)} \rightarrow Y_{(g)} + Z_{(g)}$,the $t_{1/2}$ is $10 \text{ minutes}$. In what period of time would the concentration of $X$ be reduced to $10 \%$ of its original concentration?

If the rate constant for a first order reaction is $k$,the time $(t)$ required for the completion of $99 \%$ of the reaction is given by

$A$ reaction which is of first order with respect to reactant $A$,has a rate constant $6 \, min^{-1}$. If we start with $[A] = 0.5 \, mol \, L^{-1}$,when would $[A]$ reach the value of $0.05 \, mol \, L^{-1}$?

Azo isopropane decomposes according to the equation:
$((CH_3)_2CHN)_2N_{2(g)} \xrightarrow{250 - 290 \ ^oC} N_{2(g)} + C_6H_{14(g)}$
It is found to be a first order reaction. If the initial pressure is $P_o$ and the total pressure of the mixture at time $t$ is $P_t$,then the rate constant $K$ is given by: