The following mechanism has been proposed for the exothermic catalyzed cmplex reaction:
`A + B overset("Fast")rarr IABoverset(k_(1))rarrAB+Ioverset(k_(2))rarrP+A`
If `k_(1)` is much smaller than `k_(2)`, the most suitable qualitative plot of potential energy `(PE)` versus reaction coordinates for the above reaction is

Options

A.
B.
C.
D.

Explanation

To solve the problem regarding the potential energy (PE) versus reaction coordinates for the given reaction mechanism, we will follow these steps:

### Step 1: Understand the Reaction Mechanism
The reaction mechanism provided is:
1. \( A + B \overset{\text{Fast}}{\rightarrow} IAB \)
2. \( IAB \overset{k_1}{\rightarrow} AB + I \)
3. \( AB \overset{k_2}{\rightarrow} P + A \)

Here, \( k_1 \) is much smaller than \( k_2 \), indicating that the first step is slow compared to the second step.

### Step 2: Identify the Nature of the Reaction
The problem states that the reaction is exothermic. This means that the enthalpy of the products is lower than that of the reactants. Therefore, the potential energy of the products will be lower than that of the reactants in the PE vs. reaction coordinate graph.

### Step 3: Analyze Activation Energies
- Since \( k_1 \) is much smaller than \( k_2 \), the activation energy for the step involving \( k_1 \) (the formation of \( IAB \)) will be higher than that for the step involving \( k_2 \) (the conversion of \( AB \) to \( P + A \)).
- The first step is fast, indicating that it has a low activation energy, while the second step has a higher activation energy.

### Step 4: Evaluate the Graph Options
- **Graph A**: Shows a lower potential energy for products compared to reactants and has a reasonable activation energy for the first step.
- **Graph B**: Shows a higher potential energy for products, which is incorrect for an exothermic reaction.
- **Graph C**: Shows a high activation energy for the first step, which is not consistent with the fast reaction.
- **Graph D**: Also shows a high activation energy for the first step, which is not consistent with the fast reaction.

### Conclusion
Given the analysis, the most suitable qualitative plot of potential energy versus reaction coordinates for the reaction is **Graph A**.

### Final Answer
The correct option is **A**.

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