$A \rightarrow$ products is a first-order reaction. The following data is obtained for this reaction at $T \ K$. The value of $x : y$ is:

Rate $(\text{mol } L^{-1} \ \text{min}^{-1})$	$[A]$
$0.2$	$0.02 \ M$
$0.4$	$x \ M$
$1.0$	$y \ M$

$N_2O_5$ decomposes to $NO_2$ and $O_2$ and follows first order kinetics. After $50 \, min$,the pressure inside the vessel increases from $50 \, mm \, Hg$ to $87.5 \, mm \, Hg$. The pressure of the gaseous mixture after $100 \, min$ at constant temperature will be ........... $mm \, Hg$

The rate equation for a first-$order$ reaction is given by $R = R_0 e^{-kt}$. $A$ straight line with positive slope is obtained by plotting which of the following? ($R_0 =$ Initial concentration of the reactant,$R =$ concentration of the reactant at time $t$)

$A$ first order reaction takes $40 \ min$ for $20 \%$ decomposition. Calculate its rate constant.

The rate constant of a first order reaction whose half-life is $480 \ s$,is

For the $1^{st}$ order reaction,the half-life is $5 \ minutes$ when $[A] = 0.1 \ M$. If the concentration of $[A]$ becomes twice,then the half-life becomes: