Given the following two mechanisms, one with catalyst and the other without catalyst.
(i) `A + B rarr C` (slow)
(ii) `C +B rarr F + A` (fast)
(iii) `B + B rarr F` (slow)
Which mechanism use the catalyst and what is it ?

Options

A. Step (i), `A`
B. Step (ii), `B`
C. Step (iii), `F`
D. Steps (i) and (ii), `C`

Explanation

To determine which mechanism uses a catalyst and identify the catalyst, let's analyze the given reactions step by step.

### Step 1: Identify the reactions and their rates
We have three reactions:
1. **Reaction 1**: \( A + B \rightarrow C \) (slow)
2. **Reaction 2**: \( C + B \rightarrow F + A \) (fast)
3. **Reaction 3**: \( B + B \rightarrow F \) (slow)

### Step 2: Analyze the role of each reactant
- In **Reaction 1**, reactants \( A \) and \( B \) produce \( C \). Since this is a slow reaction, it likely determines the rate of the overall mechanism.
- In **Reaction 2**, \( C \) reacts with \( B \) to produce \( F \) and regenerate \( A \). This reaction is fast, indicating that it quickly consumes \( C \) and produces \( F \) while also regenerating \( A \).
- In **Reaction 3**, \( B \) reacts with itself to produce \( F \), which is also a slow reaction.

### Step 3: Identify the catalyst
A catalyst is defined as a substance that increases the rate of a reaction and is not consumed in the process. It is regenerated at the end of the reaction sequence.

- In **Reaction 2**, \( A \) is produced again after being consumed in **Reaction 1**. This means that \( A \) is not permanently consumed in the reaction sequence; instead, it is regenerated.
- Therefore, \( A \) acts as a catalyst in this mechanism because it facilitates the conversion of \( C \) to \( F \) and is regenerated in the process.

### Conclusion
The mechanism that uses a catalyst is the one involving the reactions of \( A \), \( B \), and \( C \). The catalyst in this case is **A**.

### Summary
- **Mechanism using the catalyst**: The first mechanism (involving \( A + B \rightarrow C \) and \( C + B \rightarrow F + A \)).
- **Catalyst**: \( A \)

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