The chemical reaction 2O₃ → 3O₂ proceeds as:  

O₃ ⇋ O₂ + O (Fast)

O + O₃ → 2O₂ (slow)

The rate law expression for this reaction should be: 

CONCEPT:

Rate Law Expression

• The rate law expression for a chemical reaction relates the rate of the reaction to the concentration of reactants raised to specific powers (determined experimentally).
• For a multi-step reaction mechanism, the rate law is determined by the slowest step in the mechanism (rate-determining step).
• If an intermediate appears in the rate law, it must be replaced using the equilibrium relationship from the fast step of the reaction mechanism.

EXPLANATION:

• In the given reaction mechanism:
  • Fast step: O₃ ⇋ O₂ + O
  • Slow step: O + O₃ → 2O₂
• The slow step determines the rate law. The rate of the reaction is proportional to the concentration of O and O₃:

  Rate = k[O][O₃]

• However, O (an intermediate) is not stable and its concentration needs to be expressed in terms of the reactants.
• From the fast equilibrium step:

  O₃ ⇋ O₂ + O

  The equilibrium constant K_eq = [O][O₂] / [O₃]

  Rearranging for [O]: [O] = K_eq[O₃] / [O₂]

• Substitute [O] into the rate law expression:

  Rate = k[O₃] × (K_eq[O₃] / [O₂])

  Rate = kK_eq[O₃]² / [O₂]

• Since kK_eq is a constant, we represent it as K (overall rate constant). Thus:

  Rate = K[O₃]²[O₂]^-1

Therefore, the correct rate law expression is: r = K[O₃]²[O₂]^-1.