$A$ 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).

Which is a correct integrated rate equation for a first-order reaction?

The rate constant of a first order reaction is $1.15 \times 10^{-3} \ s^{-1}$. How long will $5 \ g$ of reactant take to reduce to $3 \ g$ (in $s$)?

For the decomposition of $N_2O_5$ according to the equation $2N_2O_5(g) \to 4NO_2(g) + O_2(g)$,the reaction is of first order. After $30 \, \min$ from the start of the reaction in a closed vessel,the total pressure is $305.5 \, mm \, Hg$,and at the end of complete decomposition,the total pressure is $587.5 \, mm \, Hg$. Calculate the rate constant of the reaction.

Consider the following first order gas phase reaction at constant temperature:
$A_{(g)} \rightarrow 2B_{(g)} + C_{(g)}$
If the total pressure of the gases is found to be $200 \ torr$ after $23 \ s$ and $300 \ torr$ upon the complete decomposition of $A$ after a very long time,then the rate constant of the given reaction is . . . . . . $\times 10^{-2} \ s^{-1}$ (nearest integer).
[Given: $\log_{10}(2) = 0.301$]

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	$200$