For a first-order reaction involving gaseous reactants and gaseous products,what will be the unit of its rate constant?

For which order reaction is a straight line parallel to the $x-$axis obtained by plotting a graph between half-life $(t_{1/2})$ and initial concentration '$a$'?

For the thermal decomposition of $N_2O_{5(g)}$ at constant volume,the following table can be formed for the reaction mentioned below:
$2N_2O_{5(g)} \rightarrow 2N_2O_{4(g)} + O_{2(g)}$

$S.NO$	$Time/s$	Total pressure $(atm)$
$1.$	$0$	$0.6$
$2.$	$100$	$X$

$X = . . . . . . \times 10^{-3} \ atm$ [nearest integer]
Given: Rate constant for the reaction is $4.606 \times 10^{-2} \ s^{-1}$.

Following data was obtained for the first order decomposition of $SO_2Cl_{2(g)}$ at constant volume:
$SO_2Cl_{2(g)} \to SO_{2(g)} + Cl_{2(g)}$

$S. No.$	$Time$ $(s)$	$Total$ $pressure$ $(atm)$
$1$	$0$	$0.5$
$2$	$100$	$0.6$

Calculate the rate constant.

For a first order reaction $A \rightarrow B$, the data is provided in the table below. Find $x$ in minutes. (Nearest integer)

$t/\text{min}$	$[A]/M$
$0$	$0.6500$
$x$	$0.0650$
$20$	$0.00065$

The half-life for radioactive decay of $^{14}C$ is $5730$ years. An archaeological artifact containing wood had only $80 \%$ of the $^{14}C$ found in a living tree. Estimate the age of the sample.