Which of the following is a first order reaction:

Options

A. `NH_5 NO_2 (s) to N_2+ 2H_2O`
B. `2HI to H_2 + I_2`
C. `2NO_2 to 2NO + O_2`
D. `2NO + O_2 to 2NO_2`

Answer

To determine which of the given reactions is a first-order reaction, we need to analyze each option based on their rate laws and the order of the reactions. The order of a reaction is defined as the sum of the powers of the concentration terms in the rate law expression.

### Step-by-Step Solution:

1. **Understand the Definition of Reaction Order**:
- The order of a reaction is the sum of the exponents of the concentration terms in the rate law equation.

2. **Analyze Option 1**:
- Given reaction: \( nH_5NO_2 \rightarrow N_2 + 2H_2O \)
- Rate law: \( \text{Rate} = k [nH_5NO_2]^1 \)
- Here, the exponent of \( [nH_5NO_2] \) is 1.
- Therefore, the order of the reaction is \( 1 \) (first-order).

3. **Analyze Option 2**:
- Given reaction: \( 2HI \rightarrow H_2 + I_2 \)
- Rate law: \( \text{Rate} = k [HI]^2 \)
- Here, the exponent of \( [HI] \) is 2.
- Therefore, the order of the reaction is \( 2 \) (second-order).

4. **Analyze Option 3**:
- Given reaction: \( 2NO_2 \rightarrow 2NO + O_2 \)
- Rate law: \( \text{Rate} = k [NO_2]^2 \)
- Here, the exponent of \( [NO_2] \) is 2.
- Therefore, the order of the reaction is \( 2 \) (second-order).

5. **Conclusion**:
- From the analysis, only **Option 1** is a first-order reaction.

### Final Answer:
- The first-order reaction is **Option 1**: \( nH_5NO_2 \rightarrow N_2 + 2H_2O \).