The following data are obtained for the decomposition of N$2$O$5$ at $45\backslash$deg C:

$2$N$2$O$5($g$)->4$NO$2($g$)+$ O$2($g$)$

$(102$s$)$

$02\mathrm{.}004\mathrm{.}006\mathrm{.}008\mathrm{.}00$

$$N$2$O$5($Bar$)$

$2\mathrm{.}502\mathrm{.}221\mathrm{.}961\mathrm{.}731\mathrm{.}53$

$($a$)$ Use these data to determine the order of the decomposition process.

$($b$)$ Determine the rate constant, including appropriate units.

k $=$

$5\mathrm{.}94$

$\backslash$times $10$

$-4$

s$-1.$

$($c$)$ What is the pressure of N$2$O$5$ after $1900$ s$?$

p $=$

$($d$)$ How long will it take for the pressure to decrease to $0\mathrm{.}200$ bar?