In the sequence of reaction `A to^(k_1) B to^(k_2) C to^(k_3) D`, it is know that `k_3 gt k_2 gt k_1`. Then the rate determining step of the reaction is:

Options

A. `A to B`
B. `C to D`
C. `B to C`
D. `A to D`

Answer

To determine the rate-determining step in the sequence of reactions \( A \xrightarrow{k_1} B \xrightarrow{k_2} C \xrightarrow{k_3} D \), we need to analyze the given rate constants \( k_1, k_2, \) and \( k_3 \).

### Step-by-Step Solution:

1. **Identify the Rate Constants**:
We have three rate constants for the reactions:
- \( k_1 \) for the reaction \( A \to B \)
- \( k_2 \) for the reaction \( B \to C \)
- \( k_3 \) for the reaction \( C \to D \)

2. **Understand the Meaning of Rate Constants**:
The rate constant \( k \) is a measure of the speed of a reaction. A higher value of \( k \) indicates a faster reaction, while a lower value indicates a slower reaction.

3. **Analyze the Given Information**:
We are given that \( k_3 > k_2 > k_1 \). This means:
- The reaction \( C \to D \) (with rate constant \( k_3 \)) is the fastest.
- The reaction \( B \to C \) (with rate constant \( k_2 \)) is faster than \( A \to B \).
- The reaction \( A \to B \) (with rate constant \( k_1 \)) is the slowest.

4. **Identify the Rate-Determining Step**:
The rate-determining step is the slowest step in the reaction sequence. Since \( k_1 \) is the smallest among \( k_1, k_2, \) and \( k_3 \), the reaction \( A \to B \) is the slowest step.

5. **Conclusion**:
Therefore, the rate-determining step of the reaction sequence is \( A \to B \).

### Final Answer:
The rate determining step of the reaction is \( A \to B \).

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