For a first-order reaction,the time taken for the concentration of the reactant to reach $3/4$ of its initial value is $t_{1/4}$. If the rate constant for the reaction is $K$,then $t_{1/4}$ can be expressed as: (in $/K$)

For a first order reaction $A \to B$,the reaction rate at reactant concentration of $0.01 \ M$ is found to be $2.0 \times 10^{-5} \ M \ sec^{-1}$. The half-life period of the reaction is .......... $sec$.

The decomposition of the smog component peroxyacetyl nitrate $(PAN)$ follows a first-order reaction into peroxyacetyl radical and $NO_{2(g)}$,with a half-life of $32 \ min$.
$CH_3COONO_2 \to CH_3COO^{\bullet} + NO_2$
If the initial concentration of $PAN$ in an air sample is $5.0 \times 10^{14} \ molecules/L$,what will be the concentration after $1.5 \ hr$?

$A_{(g)} \rightarrow 2B_{(g)}$. Initially,$2 \ mol$ of $A$ are taken in a $5 \ L$ vessel. After $20 \ min$,$[A]_t = \frac{[B]_t}{2}$. Find the half-life time of $A$ in the first-order reaction in $\min$.

The half-life period of a first-order reaction is $138.6 \ min$. The rate constant of the reaction is: (in $min^{-1}$)

$A$ first order reaction is $75\%$ completed in $100 \ min$. How long will it take for its $87.5\%$ completion? (in $\min$)