In the series reaction
`Aoverset(K_(2))(rarr)Boverset(K_(2))(rarr)Coverset(K_(2))(rarr)D` , if `K_(1)gtK_(2)gtK_(3)` then the rate determing step of the reaction is

Options

A. `ArarrB`
B. `CrarrD`
C. `BrarrC`
D. Any step

Answer

To determine the rate-determining step in the series reaction \( A \overset{k_1}{\rightarrow} B \overset{k_2}{\rightarrow} C \overset{k_3}{\rightarrow} D \), we need to analyze the given rate constants \( k_1 \), \( k_2 \), and \( k_3 \).

### Step-by-Step Solution:

1. **Understand the Concept of Rate-Determining Step**:
- The rate-determining step (RDS) is the slowest step in a reaction mechanism. It controls the overall rate of the reaction.

2. **Identify the Given Information**:
- We have the series of reactions with their respective rate constants:
- \( k_1 \) for the reaction \( A \rightarrow B \)
- \( k_2 \) for the reaction \( B \rightarrow C \)
- \( k_3 \) for the reaction \( C \rightarrow D \)
- The relationship between the rate constants is given as \( k_1 > k_2 > k_3 \).

3. **Analyze the Rate Constants**:
- Since \( k_1 \) is the largest, the step \( A \rightarrow B \) is the fastest.
- \( k_2 \) is slower than \( k_1 \) but faster than \( k_3 \), indicating that \( B \rightarrow C \) is slower than the first step but faster than the last step.
- \( k_3 \) is the smallest, which means \( C \rightarrow D \) is the slowest step in the series.

4. **Conclude the Rate-Determining Step**:
- Since \( k_3 \) is the smallest, the step \( C \rightarrow D \) is the rate-determining step of the reaction.

### Final Answer:
The rate-determining step of the reaction is \( C \rightarrow D \).