The rate law for 2 NO(g) + O2(g) → 2 NO,(g) is rate = k[NO]?[0,]. The following mechanisms have been proposed: I. 2 NO(g) + O2(g)→ 2 NO2(g) П. 2 NO(g) = N,02(g) [fast] N,O2(g) + O2(g) → 2 NO2(g) [slow] 2 NO(g) = N2(g)+ O2(g) N2(g) + 2 O2(g) –→ 2 NO2(g) III. [fast] [slow] (a) Which of these mechanisms is consistent with the rate law? Check all that apply II. III. None of the above

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### Reaction Rate Law Analysis

#### Provided Reaction and Rate Law
Be sure to answer all parts.

The rate law for the reaction:

\[ 2 \text{NO}(g) + \text{O}_2(g) \rightarrow 2 \text{NO}_2(g) \]

is given by:

\[ \text{rate} = k[\text{NO}]^2[\text{O}_2] \]

#### Proposed Mechanisms
The following mechanisms have been proposed to explain this rate law:

**Mechanism I:**

\[ 2 \text{NO}(g) + \text{O}_2(g) \rightarrow 2 \text{NO}_2(g) \]

**Mechanism II:**

1. \[ 2 \text{NO}(g) \rightleftharpoons \text{N}_2\text{O}_2(g) \] \[ \text{[fast]} \]
2. \[ \text{N}_2\text{O}_2(g) + \text{O}_2(g) \rightarrow 2 \text{NO}_2(g) \] \[ \text{[slow]} \]

**Mechanism III:**

1. \[ 2 \text{NO}(g) \rightleftharpoons \text{N}_2(g) + \text{O}_2(g) \] \[ \text{[fast]} \]
2. \[ \text{N}_2(g) + 2 \text{O}_2(g) \rightarrow 2 \text{NO}_2(g) \] \[ \text{[slow]} \]

#### Question
(a) Which of these mechanisms is consistent with the rate law? Check all that apply.

- [x] I.
- [x] II.
- [ ] III.
- [ ] None of the above

---

**Explanation:**
1. **Mechanism I** directly converts \( \text{NO} \) and \( \text{O}_2 \) into \( \text{NO}_2 \), consistent with the rate law \( \text{rate} = k[\text{NO}]^2[\text{O}_2] \).

2. **Mechanism II** consists of a fast pre-equilibrium step forming \( \text{N}_2\text{O}_2 \) followed by a slow step
Transcribed Image Text:### Reaction Rate Law Analysis #### Provided Reaction and Rate Law Be sure to answer all parts. The rate law for the reaction: \[ 2 \text{NO}(g) + \text{O}_2(g) \rightarrow 2 \text{NO}_2(g) \] is given by: \[ \text{rate} = k[\text{NO}]^2[\text{O}_2] \] #### Proposed Mechanisms The following mechanisms have been proposed to explain this rate law: **Mechanism I:** \[ 2 \text{NO}(g) + \text{O}_2(g) \rightarrow 2 \text{NO}_2(g) \] **Mechanism II:** 1. \[ 2 \text{NO}(g) \rightleftharpoons \text{N}_2\text{O}_2(g) \] \[ \text{[fast]} \] 2. \[ \text{N}_2\text{O}_2(g) + \text{O}_2(g) \rightarrow 2 \text{NO}_2(g) \] \[ \text{[slow]} \] **Mechanism III:** 1. \[ 2 \text{NO}(g) \rightleftharpoons \text{N}_2(g) + \text{O}_2(g) \] \[ \text{[fast]} \] 2. \[ \text{N}_2(g) + 2 \text{O}_2(g) \rightarrow 2 \text{NO}_2(g) \] \[ \text{[slow]} \] #### Question (a) Which of these mechanisms is consistent with the rate law? Check all that apply. - [x] I. - [x] II. - [ ] III. - [ ] None of the above --- **Explanation:** 1. **Mechanism I** directly converts \( \text{NO} \) and \( \text{O}_2 \) into \( \text{NO}_2 \), consistent with the rate law \( \text{rate} = k[\text{NO}]^2[\text{O}_2] \). 2. **Mechanism II** consists of a fast pre-equilibrium step forming \( \text{N}_2\text{O}_2 \) followed by a slow step
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