Determine the rate law and the rate constant for the reaction below given the data presented in the table.

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

Experiment

Initial $[$O$2]$

Initial $[$N$2]$

Initial Rate $($M$/$s$)$

$1$

$0\mathrm{.}040$

$0\mathrm{.}020$

$707$

$2$

$0\mathrm{.}040$

$0\mathrm{.}010$

$500$

$3$

$0\mathrm{.}010$

$0\mathrm{.}010$

$125$