Apossible mechanism for the overall reaction br2 (g) + 2no (g) → 2nobr (g) is no (g) + br2 (g) nobr2 (g) (fast) nobr2 (g) + no (g) k2→ 2nobr (slow) the rate law for formation of nobr based on this mechanism is rate = a possible mechanism for the overall reaction br2 (g) + 2no (g) 2nobr (g) is no (g) + br2 (g) nobr2 (g) (fast) nobr2 (g) + no (g) 2nobr (slow) the rate law for formation of nobr based on this mechanism is rate = k1[br2]1/2 (k2k1/k-1)[no][br2]2 (k1/k-1)2[no]2 k1[no]1/2 (k2k1/k-1)[no]2[br2]

The overall reaction is:
Br₂(g) + 2 NO(g) ↔ 2 NOBr(g)
rate law = k [Br₂][NO]²

The first step of the overall reaction is:
NO(g) + Br₂(g)   K₁⇄⇄K-1  NOBr₂(g)
rate law 1 = k₁ [Br₂][NO] or 
rate law 2 = k-1 [NOBr₂]

The second step of the overall reaction is:
NOBr₂(g) + NO(g)  →K₂→ 2 NOBr
rate law 3 = k₂[NOBr₂][NO]

So, rate law of overall reaction can be obtained as follows:
(rate law 1)*(rate law 3) / (rate law 2)
= [(k₁[Br₂][NO])* (K₂[NOBr₂][NO])] / k₋₁[NOBr₂]
= [k₁k₂/k₋₁][NO]²[Br₂]
So the correct answer is:
[k₁k₂/k₋₁][NO]² [Br₂]