If the rate constant of a first-order reaction is $0.6932 \ hr^{-1}$,then its half-life period is .......... $hr$.

For a first-order reaction,the time taken for the initial concentration to decrease to $1/4$ of its value is $20 \ min$. The time taken for the initial concentration to decrease to $1/16$ of its value will be $......... \ min$.

The following results are obtained in one pseudo first order reaction:

Time $(s)$	$0$	$30$	$60$	$90$
Concentration $(mol \ L^{-1})$	$0.551$	$0.312$	$0.173$	$0.085$

$(a)$ Calculate the average rate of reaction between $30$ and $60$ seconds.
$(b)$ Calculate the rate constant $(k)$ of this first order reaction.

Identify True $(T)$ and False $(F)$ statements for the first order reaction $R \rightarrow P$ given below:
$I. \ k = \frac{1}{t} \ln \frac{[R]_0}{[R]}$
$II. \ k = \frac{1}{t} \ln \frac{[R]}{[R]_0}$

For the first-order isomerization reaction $A \rightarrow B$,the rate constant is $4.5 \times 10^{-3} \ min^{-1}$. If the initial concentration of $A$ is $1 \ M$,find the rate of the reaction after $1 \ hour$.

The integrated rate equation for a first-order reaction is: