Ozone depletion takes place as :
`2O_(3)(g)rarr3O_(2)(g)`
Step1: `O_(3)(g)overset(k)hArrO_(2)(g)+O(g)" "`(fast)
Step2 : `O_(3)(g)+[O]overset(k)rarr2O_(2)(g)" "` (slow)
order of the reaction will be :

Options

A. 1
B. 2
C. 3
D. unpredictable

Answer

To determine the order of the reaction for the given ozone depletion process, we will analyze the provided steps and focus on the rate-determining step.

### Step-by-Step Solution:

**Step 1: Identify the Rate-Determining Step**
- The reaction consists of two steps:
- Step 1 (Fast): \( O_3(g) \rightleftharpoons O_2(g) + O(g) \)
- Step 2 (Slow): \( O_3(g) + [O] \rightarrow 2O_2(g) \)

- The slow step is the rate-determining step, which means that the rate of the overall reaction is determined by this step.

**Step 2: Write the Rate Law for the Slow Step**
- For the slow step, the rate can be expressed as:
\[ \text{Rate} = k [O_3][O] \]
where \( k \) is the rate constant for the slow step.

**Step 3: Identify the Intermediate**
- In the slow step, \( [O] \) is an intermediate. It is produced in the fast step and consumed in the slow step. Since intermediates do not appear in the overall balanced equation, we need to eliminate \( [O] \) from our rate expression.

**Step 4: Relate the Intermediate to the Reactants**
- From the fast step, we can express \( [O] \) in terms of \( [O_3] \) and \( [O_2] \):
\[ O_3 \rightleftharpoons O_2 + O \]
This implies that:
\[ [O] = \frac{[O_3] - [O_2]}{1} \]
However, for simplicity in the rate law, we can assume that \( [O] \) is proportional to \( [O_3] \) since \( O_2 \) is also produced.

**Step 5: Substitute the Intermediate into the Rate Law**
- Substituting \( [O] \) back into the rate law:
\[ \text{Rate} = k [O_3] \left( \frac{[O_3]}{K} \right) \]
where \( K \) is the equilibrium constant for the fast step.

**Step 6: Simplify the Rate Expression**
- This gives us:
\[ \text{Rate} = k' [O_3]^2 \]
where \( k' = \frac{k}{K} \).

**Step 7: Determine the Order of the Reaction**
- The overall order of the reaction is determined by the sum of the powers of the concentration terms in the rate law. Here, the order is 2 (from \( [O_3]^2 \)).

### Conclusion
- The order of the reaction is **2**.