Consider the following reaction

$2N{O}_2(g)+F_2(g)2N{O}_{2}F(g)$

Someone suggests that its mechanism involves the following two elementary steps:

$(1)N{O}_2(g)+F_2(g){}_{k_{-1}}^{k_1}N{O}_{2}F(g)+F(g)$

$(2)N{O}_2(g)+F(g)k_{2}N{O}_{2}F(g)$

$($a$)$ State which species is the intermediate in the mechanism.

$($b$)$ Use the steady$-$state approximation to write down the time derivative of the concentration of the intermediate $(d\frac{?}{d}t)$ that you have identified in part $($a$).$

$($c$)$ Express the concentration of the intermediate without any derivatives.

$($d$)$ Find the time derivative of i$.$e$.,($:$\frac{d[N{O}_2(F)((g))]}{dt}\}$ without $F(g)$ in the answer.

$($e$)($Bonus $2$ points. Possible to get $102\%$ in this assignment$)$ Try to simplify your answer if $k_2{k}_1.$ What is the overall order of the reaction?