[alanjz]

I can't understand the answer for a rate law question:

Ozone in the earth's atmosphere decomposes according to the equation: 2 O3(g) → 3 O2(g). This reaction is thought to occur via the two-step mechanism:
Step 1: O3(g) O2(g) + O(g) Fast, reversible
Step 2: O3(g) + O(g) → 2 O2(g) Slow
What rate law is consistent with this mechanism?
(A) –∆[O3]/∆t = k[O3]
(B) –∆[O3]/∆t = k[O3]²
(C) –∆[O3]/∆t = k[O3]²/[O2]
(D) –∆[O3]/∆t = k[O3]²/[O2]³

I chose B. I've never gotten negative orders just from the reaction mechanism (only in charts showing rates after changes in concentration) so I'd like to know where it comes from. Thanks.

[Corribus]

The negative sign just means that the rate decreases as the reactants are consumed.

Usually you see it on the opposite side of the equal sign, e.g. d[O₃]/dt = -k[O₃]².

The reaction order is the exponent above the concentration dependency.  In this case, the order is 2 (second order).