The reaction 2 CO(g) + O₂(g) → 2 CO2(g) is described by this rate law: rate = k[CO]²[0₂] Which of the following mechanisms are consistent with this rate law? (Think carefully.) (a) CO+O₂ CO₂ + O Slow O + CO - CO₂ Fast (b) CO+O2CO3 Fast equilibrium CO3 + CO2 CO2 Slow Slow C202 +02 C204 Fast C204-2 CO2 Fast (d) 2 CO→ C₂02 Fast equilibrium (c) 2 CO-C₂02 C₂O2 CO2 + O Slow

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**Reaction Mechanism and Rate Law Analysis: An Educational Overview**

The given reaction: 
\[ 2 \text{CO}(g) + \text{O}_2(g) \rightarrow 2 \text{CO}_2(g) \]
is described by the following rate law:
\[ \text{rate} = k[\text{CO}]^2[\text{O}_2] \]

To determine which of the following mechanisms are consistent with this rate law, consider the step-by-step reaction processes and their respective speeds.

**Mechanisms:**

(a) 
\[ \text{CO} + \text{O}_2 \rightarrow \text{CO}_2 + \text{O} \quad (\text{Slow}) \]
\[ \text{O} + \text{CO} \rightarrow \text{CO}_2 \quad (\text{Fast}) \]

(b) 
\[ \text{CO} + \text{O}_2 \rightarrow \text{CO}_3 \quad (\text{Fast equilibrium}) \]
\[ \text{CO}_3 + \text{CO} \rightarrow 2 \text{CO}_2 \quad (\text{Slow}) \]

(c) 
\[ 2 \text{CO} \rightarrow \text{C}_2\text{O}_2 \quad (\text{Slow}) \]
\[ \text{C}_2\text{O}_2 + \text{O}_2 \rightarrow \text{C}_2\text{O}_4 \quad (\text{Fast}) \]
\[ \text{C}_2\text{O}_4 \rightarrow 2 \text{CO}_2 \quad (\text{Fast}) \]

(d) 
\[ 2 \text{CO} \rightarrow \text{C}_2\text{O}_2 \quad (\text{Fast equilibrium}) \]
\[ \text{C}_2\text{O}_2 \rightarrow \text{CO}_2 + \text{O} \quad (\text{Slow}) \]
\[ \text{O} + \text{CO} \rightarrow \text{CO}_2 \quad (\text{Fast}) \]

**Analysis:**

To determine which mechanism corresponds to the given rate law (\( \text{rate} = k[\text{CO}]^2[\text{O}_2] \)), we need to identify
Transcribed Image Text:**Reaction Mechanism and Rate Law Analysis: An Educational Overview** The given reaction: \[ 2 \text{CO}(g) + \text{O}_2(g) \rightarrow 2 \text{CO}_2(g) \] is described by the following rate law: \[ \text{rate} = k[\text{CO}]^2[\text{O}_2] \] To determine which of the following mechanisms are consistent with this rate law, consider the step-by-step reaction processes and their respective speeds. **Mechanisms:** (a) \[ \text{CO} + \text{O}_2 \rightarrow \text{CO}_2 + \text{O} \quad (\text{Slow}) \] \[ \text{O} + \text{CO} \rightarrow \text{CO}_2 \quad (\text{Fast}) \] (b) \[ \text{CO} + \text{O}_2 \rightarrow \text{CO}_3 \quad (\text{Fast equilibrium}) \] \[ \text{CO}_3 + \text{CO} \rightarrow 2 \text{CO}_2 \quad (\text{Slow}) \] (c) \[ 2 \text{CO} \rightarrow \text{C}_2\text{O}_2 \quad (\text{Slow}) \] \[ \text{C}_2\text{O}_2 + \text{O}_2 \rightarrow \text{C}_2\text{O}_4 \quad (\text{Fast}) \] \[ \text{C}_2\text{O}_4 \rightarrow 2 \text{CO}_2 \quad (\text{Fast}) \] (d) \[ 2 \text{CO} \rightarrow \text{C}_2\text{O}_2 \quad (\text{Fast equilibrium}) \] \[ \text{C}_2\text{O}_2 \rightarrow \text{CO}_2 + \text{O} \quad (\text{Slow}) \] \[ \text{O} + \text{CO} \rightarrow \text{CO}_2 \quad (\text{Fast}) \] **Analysis:** To determine which mechanism corresponds to the given rate law (\( \text{rate} = k[\text{CO}]^2[\text{O}_2] \)), we need to identify
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