The first$-$order rate constant for the decomposition of $N_2{O}_5,$ given below, at $70C$ is $6\mathrm{.}82{10}^{-3}{s}^{-1}.$ Suppose we start with $0\mathrm{.}0500$mol of $N_2{O}_5(g)$ in a volume of $4\mathrm{.}5L.$

$2N_2{O}_5(g)4N{O}_2(g)+O_2(g)$

$($a$)$ How many moles of $N_2{O}_5$ will remain after $3\mathrm{.}0$ min?

mol

$($b$)$ How many minutes will it take for the quantity of $N_2{O}_5$ to drop to $0\mathrm{.}005$ mol?

min

$($c$)$ What is the half$-$life of $N_2{O}_5$ at $70C?$

min