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

Explanation

To determine the overall order of the hypothetical reaction \( X_2 + Y_2 \rightarrow 2XY \) given the mechanism, we will analyze each step of the reaction and focus on the rate-determining step.

### Step 1: Write the Rate Law for the Overall Reaction
The overall reaction is:
\[ X_2 + Y_2 \rightarrow 2XY \]

The rate of the overall reaction can be expressed as:
\[ R = k [X_2]^A [Y_2]^B \]
where \( A \) and \( B \) are the orders with respect to \( X_2 \) and \( Y_2 \), respectively.

### Step 2: Identify the Rate-Determining Step
From the given mechanism:
1. \( X_2 \rightarrow X + X \) (fast)
2. \( X + Y_2 \rightleftharpoons XY + Y \) (slow)
3. \( X + Y \rightarrow XY \) (fast)

The slow step is the rate-determining step. Therefore, we will use this step to derive the rate law.

### Step 3: Write the Rate Law for the Slow Step
For the slow step \( X + Y_2 \rightleftharpoons XY + Y \), the rate can be expressed as:
\[ R = k' [X][Y_2] \]
where \( k' \) is the rate constant for the slow step.

### Step 4: Express Concentration of \( X \)
From the first step, we can express the concentration of \( X \) in terms of \( [X_2] \):
\[ X_2 \rightarrow X + X \]
This implies that:
\[ [X] = \frac{1}{2} [X_2] \]

### Step 5: Substitute \( [X] \) into the Rate Law
Now, substituting \( [X] \) into the rate law for the slow step:
\[ R = k' \left(\frac{1}{2} [X_2]\right) [Y_2] \]
This simplifies to:
\[ R = \frac{k'}{2} [X_2] [Y_2] \]

### Step 6: Determine the Overall Rate Law
The overall rate law can now be expressed as:
\[ R = k [X_2]^{1/2} [Y_2]^1 \]
where \( k \) is a new rate constant that incorporates the factor of \( \frac{1}{2} \).

### Step 7: Calculate the Overall Order of the Reaction
The overall order of the reaction is the sum of the powers of the concentration terms in the rate law:
\[ \text{Overall Order} = \frac{1}{2} + 1 = \frac{3}{2} \]

### Conclusion
Thus, the overall order of the reaction is:
\[ \text{Overall Order} = 1.5 \]