Mechanism of a hypothetical reaction
`X_(2) + Y_(2) rarr 2XY` is given below:
(i) `X_(2) rarr X + X` (fast)
(ii) `X+Y_(2) hArr 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`

Explanation

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

### Step-by-Step Solution:

1. **Identify the Rate-Determining Step**:
The slow step of the reaction mechanism is:
\[ \text{(ii)} \quad X + Y_2 \rightleftharpoons XY + Y \]
Since this step is slow, it will dictate the rate of the overall reaction.

2. **Write the Rate Law for the Slow Step**:
The rate law for the slow step can be expressed as:
\[ \text{Rate} = k [X][Y_2] \]
where \( k \) is the rate constant for this step.

3. **Express [X] in terms of [X₂]**:
From the first step of the mechanism:
\[ \text{(i)} \quad X_2 \rightarrow X + X \]
This step is fast and establishes an equilibrium. The concentration of \( X \) can be derived from the equilibrium expression:
\[ K_{eq} = \frac{[X]^2}{[X_2]} \]
Rearranging gives:
\[ [X] = \sqrt{K_{eq} [X_2]} \]

4. **Substitute [X] into the Rate Law**:
Now substitute \( [X] \) back into the rate law:
\[ \text{Rate} = k [X][Y_2] = k \left(\sqrt{K_{eq} [X_2]}\right)[Y_2] \]
This simplifies to:
\[ \text{Rate} = k \sqrt{K_{eq}} [X_2]^{1/2} [Y_2] \]

5. **Determine the Overall Order of the Reaction**:
The rate law can now be expressed as:
\[ \text{Rate} = k' [X_2]^{1/2} [Y_2] \]
where \( k' = k \sqrt{K_{eq}} \). The overall order of the reaction is the sum of the powers of the concentration terms in the rate law:
\[ \text{Overall Order} = \frac{1}{2} + 1 = \frac{3}{2} = 1.5 \]

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

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