The depletion of ozone involves the following steps :
Step 1 : `O_3underset(K_1)overset(K_2)hArrO_2+O` (fast)
Step 2 : `O_3+Ounderset(K)rarr2O_2` (slow)
The predicted order of the reaction will be

Options

A. First
B. 1.5
C. `-1.5`
D. Zero

Answer

To determine the order of the reaction involving the depletion of ozone, we need to analyze the given steps of the reaction and focus on the slow step, as the rate of the overall reaction is determined by this step.

### Step-by-Step Solution:

1. **Identify the Steps**:
- Step 1: \( O_3 \underset{K_1}{\overset{K_2}{\rightleftharpoons}} O_2 + O \) (fast)
- Step 2: \( O_3 + O \underset{K}{\rightarrow} 2O_2 \) (slow)

2. **Determine the Rate Law from the Slow Step**:
- The rate of the reaction is determined by the slow step. For the slow step \( O_3 + O \rightarrow 2O_2 \), the rate law can be written as:
\[ \text{Rate} = k [O_3]^1 [O]^1 = k [O_3][O] \]

3. **Express Concentration of Intermediate**:
- The species \( O \) is an intermediate and is not present in the overall reaction. We need to express its concentration in terms of the reactants. We can use the fast equilibrium from Step 1 to do this.
- From Step 1, at equilibrium:
\[ K_{eq} = \frac{[O_2][O]}{[O_3]} \]
- Rearranging gives:
\[ [O] = K_{eq} \frac{[O_3]}{[O_2]} \]

4. **Substitute the Expression for \( O \) into the Rate Law**:
- Substitute \( [O] \) into the rate law:
\[ \text{Rate} = k [O_3] \left(K_{eq} \frac{[O_3]}{[O_2]}\right) \]
- This simplifies to:
\[ \text{Rate} = k K_{eq} \frac{[O_3]^2}{[O_2]} \]

5. **Determine the Overall Order of the Reaction**:
- The rate expression is now:
\[ \text{Rate} = k' \frac{[O_3]^2}{[O_2]} \]
- Here, \( k' = k K_{eq} \) is a new rate constant.
- The order of the reaction is the sum of the powers of the concentrations in the rate law:
- The power of \( [O_3] \) is 2.
- The power of \( [O_2] \) is -1 (since it is in the denominator).
- Therefore, the overall order is:
\[ 2 + (-1) = 1 \]

### Conclusion:
The predicted order of the reaction is **1**.