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 (RDS) 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 Reaction Steps and Rate Constants:**
- The reactions are:
- Step 1: \( A \xrightarrow{k_1} B \)
- Step 2: \( B \xrightarrow{k_2} C \)
- Step 3: \( C \xrightarrow{k_3} D \)
- The rate constants are given as \( k_3 > k_2 > k_1 \).

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

3. **Analyze the Given Information:**
- Since \( k_3 \) is the largest, the reaction \( C \xrightarrow{k_3} D \) is the fastest.
- Since \( k_1 \) is the smallest, the reaction \( A \xrightarrow{k_1} B \) is the slowest.

4. **Determine the Rate Determining Step (RDS):**
- The rate determining step is the slowest step in the sequence of reactions because it limits the overall rate of the reaction.
- Therefore, since \( k_1 \) is the smallest, the reaction \( A \xrightarrow{k_1} B \) is the rate determining step.

5. **Conclusion:**
- The rate determining step of the reaction sequence is \( A \xrightarrow{k_1} B \).

### Final Answer:
The rate determining step of the reaction is \( A \xrightarrow{k_1} B \).

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