The mechanism of the reaction, `2NO+O_(2)rarr2NO_(2)` is
`NO+NO underset(k_(-1))overset(k_(1))rarr N_(2)O_(2)` (fast)
`N_(2)O_(2)+O_(2)overset(k_(2))rarr2NO_(2)` (slow) The rate constant of the reaction is

Options

A. `k_(2)`
B. `k_(2)k_(1)(k_(-1))`
C. `k_(2)k_(1)`
D. `k_(2)((k_(1))/(k_(-1)))`

Explanation

Slow step is the rate detremining step (RDS) and `(N_(2)O_(2))` is the reactive intermediate.
`therefore r = k_(2)[N_(2)O_(2)][O_(2)]` ….(i)
From reversible reaction, `[N_(2)O_(2)]` is : `(k_(1))/(k_(-1)) = ([N_(2)O_(2)])/([NO]^(2))` …(ii)
Substitute `[N_(2)O_(2)]` in Eq. (i), `r = k_(2)((k_(1))/(k_(-1)))[NO]^(2)[O_(2)]`. Hence, rate constant `= k_(2)((k_(1))/(k_(-1)))`