Mechanism of a hypothetical reaction
`X_(2) + Y_(2) rarr 2XY` is given below:
(i) `X_(2) hArr X + X` (fast)
(ii) `X+Y_(2)rarr XY+Y` (slow)
(iii) `X + Y rarr XY` (fast)
The overall order of the reaction will be :

Options

A. 2
B. 0
C. 1.5
D. 1

Answer

To determine the overall order of the reaction given the mechanism, we will analyze each step of the reaction mechanism and derive the rate law from the slow step.

### Step-by-Step Solution:

1. **Identify the Steps of the Reaction Mechanism:**
- Step (i): \( X_2 \rightleftharpoons X + X \) (fast)
- Step (ii): \( X + Y_2 \rightarrow XY + Y \) (slow)
- Step (iii): \( X + Y \rightarrow XY \) (fast)

2. **Determine the Rate Law from the Slow Step:**
- The rate of a reaction is determined by its slowest step (rate-determining step). In this case, the slow step is Step (ii):
\[ \text{Rate} = k[X][Y_2] \]
Here, \( k \) is the rate constant, and \( [X] \) and \( [Y_2] \) are the concentrations of the reactants.

3. **Handle the Intermediate:**
- In this mechanism, \( X \) is an intermediate, which means its concentration cannot be directly measured. We need to express \( [X] \) in terms of the other reactants.
- From Step (i), we know that \( X_2 \) dissociates to form \( X \):
\[ K_{eq} = \frac{[X]^2}{[X_2]} \]
Rearranging gives:
\[ [X]^2 = K_{eq} [X_2] \]
Thus,
\[ [X] = \sqrt{K_{eq} [X_2]} \]

4. **Substitute \( [X] \) into the Rate Law:**
- Substitute \( [X] \) back into the rate law:
\[ \text{Rate} = k \cdot \sqrt{K_{eq} [X_2]} \cdot [Y_2] \]
- This can be rewritten as:
\[ \text{Rate} = k' [X_2]^{1/2} [Y_2] \]
where \( k' = k \cdot \sqrt{K_{eq}} \).

5. **Determine the Overall Order of the Reaction:**
- The overall order of the reaction is the sum of the exponents in the rate law:
\[ \text{Overall order} = \frac{1}{2} + 1 = \frac{3}{2} = 1.5 \]

### Conclusion:
The overall order of the reaction is **1.5**.