The rate law for the chemical reaction `2NO_2Cl rarr 2NO_2 +Cl_2 + Cl_2 = k [ NO_2 Cl]` is rate The rate determining step is

Options

A. `2NO_2Cl rarr 2NO_2 + 2Cl`
B. `NO_2 + Cl_2 rarr NO_2Cl + Cl`
C. `NO_2 Cl + Cl rarr NO_2 + Cl_2`
D. `NO_2 Cl rarr NO_2 + Cl`

Answer

To solve the problem, we need to analyze the given reaction and determine the rate-determining step (RDS) based on the provided rate law.

### Step-by-Step Solution:

1. **Identify the Reaction**: The reaction given is:
\[ 2 \text{NO}_2\text{Cl} \rightarrow 2 \text{NO}_2 + \text{Cl}_2 \]
However, there is an extra \(\text{Cl}_2\) mentioned in the question. The correct interpretation is:
\[ 2 \text{NO}_2\text{Cl} \rightarrow 2 \text{NO}_2 + \text{Cl}_2 \]

2. **Write the Rate Law**: The rate law given is:
\[ \text{Rate} = k [\text{NO}_2\text{Cl}] \]
This indicates that the rate of the reaction depends on the concentration of \(\text{NO}_2\text{Cl}\).

3. **Understanding the Rate Determining Step**: The rate determining step (RDS) is the slowest step in a reaction mechanism that dictates the overall rate of the reaction. The rate law reflects the stoichiometry of the RDS.

4. **Analyzing the Stoichiometry**: The stoichiometric coefficient for \(\text{NO}_2\text{Cl}\) in the reaction is 2, but the rate law suggests that the reaction behaves as if it is first order with respect to \(\text{NO}_2\text{Cl}\). This implies that the RDS must involve one molecule of \(\text{NO}_2\text{Cl}\).

5. **Proposing the Rate Determining Step**: To satisfy the rate law, we can propose that the RDS is:
\[ \text{NO}_2\text{Cl} \rightarrow \text{NO}_2 + \text{Cl} \]
This step involves one \(\text{NO}_2\text{Cl}\) molecule, which aligns with the rate law indicating first-order dependence.

6. **Selecting the Correct Option**: Among the provided options, we need to find one that matches the proposed RDS:
- The correct option is:
\[ \text{NO}_2\text{Cl} \rightarrow \text{NO}_2 + \text{Cl} \]

### Conclusion:
The rate-determining step (RDS) for the reaction is:
\[ \text{NO}_2\text{Cl} \rightarrow \text{NO}_2 + \text{Cl} \]