Determine the rate law and the value of $k$ for the following reaction using the data provided.

$2N_2{O}_5(g)4N{O}_2(g)+O_2(g),[N_2{O}_5]i(M)$ Initial Rate $(\frac{M}{s})$

$,0\mathrm{.}093,4\mathrm{.}84{10}^{-4}$

$,0\mathrm{.}174,9\mathrm{.}05{10}^{-4}$

$,0\mathrm{.}224,1\mathrm{.}16{10}^{-3}$