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 mechanism provided indicates that the second step (A2 + B → P) is the slow step, which means it is the rate-determining step. The rate law for the overall reaction will be based on this step.

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

### Step 3: Express \( [A_2] \) in Terms of \( [A] \)
From the first step of the mechanism (2A ⇌ A2), we can derive the equilibrium expression. At equilibrium, we have:
\[ K_{eq} = \frac{[A_2]}{[A]^2} \]
Thus, we can express \( [A_2] \) as:
\[ [A_2] = K_{eq} [A]^2 \]
where \( K_{eq} \) is the equilibrium constant for the first step.

### Step 4: Substitute \( [A_2] \) into the Rate Law
Now, we substitute \( [A_2] \) back into the rate law:
\[ \text{Rate} = k [A_2][B] = k (K_{eq} [A]^2)[B] \]
This simplifies to:
\[ \text{Rate} = k K_{eq} [A]^2 [B] \]

### Step 5: Determine the Overall Order of the Reaction
In the rate law \( \text{Rate} = k K_{eq} [A]^2 [B] \), the order of the reaction is determined by the sum of the powers of the concentrations:
- The power of \( [A] \) is 2.
- The power of \( [B] \) is 1.

Thus, the overall order of the reaction is:
\[ 2 + 1 = 3 \]

### Final Answer
The order of the reaction is **3**.

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