The following data were obtained during the first-order decomposition of $2 A_{(g)} \rightarrow B_{(g)} + C_{(s)}$ at a constant volume and at a particular temperature. The rate constant in $min^{-1}$ is:

$S$.no.	Time	Total pressure in Pascal
$1.$	At the end of $10 \ min$	$300$
$2.$	After completion	$200$

The half-life period for a first-order reaction is . . . . . . .

$A$ first order reaction is $50 \%$ complete in $16 \ min$. How much time is required to complete $87.5 \%$ of the reaction (in $min$)?

The decomposition of substance $A$ in a solution follows first-order kinetics. Vessel-$I$ contains $1 \ L$ of $1 \ M$ solution of $A$. Vessel-$II$ contains $100 \ mL$ of $0.6 \ M$ solution of $A$. If the concentration of $A$ in Vessel-$I$ becomes $0.25 \ M$ in $8 \ hr$,then the time required for the concentration of $A$ in Vessel-$II$ to become $0.3 \ M$ is ......... $hr$.

If $50\%$ of a reaction occurs in $100 \ s$ and $75\%$ of the reaction occurs in $200 \ s$,the order of this reaction is

$A \rightarrow P$ is a first order reaction. At $300 \ K$,this reaction was started with $[A] = 0.5 \ mol \ L^{-1}$. The rate constant of the reaction was $0.125 \ min^{-1}$. The same reaction was started separately with $[A] = 1 \ mol \ L^{-1}$ at $300 \ K$. The rate constant (in $min^{-1}$) now is: