The NO oxidation reaction has been studied extensively and several reaction mechanisms have been proposed. Considering $(1)$ the termolecular reaction or $(2)$ the pre$-$equlibrium mechanism with $N{O}_3$ as an intermediate, the following rate equations were derived.

After simplifying the rate equations, $NO$ decomposition $($or $N{O}_2$ formation$)$ rate could be expressed by the following equation.

$-\frac{d[NO]}{dt}=+\frac{d[N{O}_2]}{dt}=2k[NO{]}^2[O_2]$

$($Q$)$ Please explain the reason to use $"2k"$ instead of using $"k".$ You need to check the reference$($s$)$ that related to the NO oxidation reaction and fully explain the reason$($s$).$