The reaction `2A+Bto` product follow the mechanism :-
`2AhArrA_(2)("fast")`
`A_(2)+BtoP(slow)`
`The order of the reaction is

Options

A. 1.5
B. 3
C. 1
D. 2

Explanation

To determine the order of the reaction given the mechanism, we can follow these steps:

### Step 1: Identify the Rate-Determining Step
The slow step in the reaction mechanism is the rate-determining step. Here, the slow step is:
\[ A_2 + B \rightarrow P \]

### Step 2: Write the Rate Law for the Slow Step
The rate law for the slow step can be expressed as:
\[ \text{Rate} = k[A_2][B] \]
where \( k \) is the rate constant for this step.

### Step 3: Express \( [A_2] \) in Terms of \( [A] \)
Since \( A_2 \) is formed from \( A \) in the fast step:
\[ 2A \rightleftharpoons A_2 \]
The equilibrium expression for this step can be written as:
\[ K = \frac{[A_2]}{[A]^2} \]
Thus, we can express \( [A_2] \) as:
\[ [A_2] = K[A]^2 \]

### Step 4: Substitute \( [A_2] \) in the Rate Law
Now, we can substitute \( [A_2] \) back into the rate law:
\[ \text{Rate} = k[K[A]^2][B] \]
This simplifies to:
\[ \text{Rate} = k' [A]^2 [B] \]
where \( k' = kK \) is a new rate constant.

### Step 5: Determine 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:
- The order with respect to \( A \) is 2.
- The order with respect to \( B \) is 1.

Thus, the overall order \( n \) is:
\[ n = 2 + 1 = 3 \]

### Conclusion
The order of the reaction is 3.

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