For the reaction sequence

$N_5{O}_5{k}_{1}N{O}_2+N{O}_3$

$N{O}_2+N{O}_3{k}_2{N}_2{O}_5$

$N{O}_2+O_3{k}_{3}N{O}_3+O_2$

$2N{O}_3{k}_{4}2N{O}_2+O_2$

$($a$)$ Write equations for the rates of formation of $N_2{O}_5,N{O}_2,N{O}_3,O_2,$ and $O_3.$

$($b$)$ Assume that the species $N{O}_2$ and $N{O}_3$ are in steady state. Solve for their concentrations.

$($c$)$ What do the results of the steady$-$state assumption imply with respect to the rate of $N_2{O}_5$ formation?