For a first order reaction $R \longrightarrow P$,the rate constant is $k$. If the initial concentration of $R$ is $[R_0]$,the concentration of $R$ at any time $t$ is given by the expression:

Drug $X$ becomes ineffective after $50 \%$ decomposition. The original concentration of drug in a bottle was $16 \ mg/mL$ which becomes $4 \ mg/mL$ in $12 \ months$. The expiry time of the drug in months is $..........$ Assume that the decomposition of the drug follows first order kinetics.

At $500\,^oC$,cyclopropane isomerizes to propene. This reaction is first order with a rate constant of $6.7 \times 10^{-4}\,s^{-1}$. If the initial concentration of cyclopropane is $0.05\, M$,what will be the molarity of cyclopropane after $30\, min$ (in $, M$)?

$A$ molecule undergoes two independent first order reactions whose respective half-lives are $12 \ min$ and $3 \ min$. If both the reactions are occurring simultaneously,the time taken for the $50 \%$ consumption of the reactant is $.......... \ min$ (Nearest integer).

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

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

For the decomposition of azomethane,$CH_3N_2CH_{3(g)} \rightarrow CH_3CH_{3(g)} + N_{2(g)}$,a first order reaction,the variation in partial pressure with time at $600 \ K$ is given as shown in the graph. The value of the rate constant $k$ in $s^{-1}$ is $x \times 10^4$. Find the value of $x$.