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title: "The gas-phase oxidation of nitric oxide proceeds according to the following overall balanced equation:  \\[ 2\\text{ NO}(g) + \\text{O}_2(g) \\rightarrow 2\\text{ NO}_2(g) \\]  A proposed two-step reaction mechanism for the process is shown below:  Step 1 (fast equilibrium): \\[ 2\\text{ NO}(g) \\underset{k_{-1}}{\\overset{k_1}{\\rightleftharpoons}} \\text{N}_2\\text{O}_2(g) \\]  Step 2 (slow): \\[ \\text{N}_2\\text{O}_2(g) + \\text{O}_2(g) \\xrightarrow{k_2} 2\\text{ NO}_2(g) \\]  At a certain temperature, the elementary rate constants have the values \\(k_1 = 4.0 \\times 10^3\\text{ M}^{-1}\\text{s}^{-1}\\), \\(k_{-1} = 2.0 \\times 10^2\\text{ s}^{-1}\\), and \\(k_2 = 5.0 \\times 10^1\\text{ M}^{-1}\\text{s}^{-1}\\). The overall rate law is expressed as \\(\\text{Rate} = k_{\\text{obs}} [\\text{NO}]^2 [\\text{O}_2]\\). What is the value of the observed rate constant, \\(k_{\\text{obs}}\\)?"
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url: "https://nerd-notes.com/ubq/123662/"
date_modified: "2026-09-28T12:01:56+00:00"
---

# The gas-phase oxidation of nitric oxide proceeds according to the following overall balanced equation:

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

A proposed two-step reaction mechanism for the process is shown below:

Step 1 (fast equilibrium):
\[ 2\text{ NO}(g) \underset{k_{-1}}{\overset{k_1}{\rightleftharpoons}} \text{N}_2\text{O}_2(g) \]

Step 2 (slow):
\[ \text{N}_2\text{O}_2(g) + \text{O}_2(g) \xrightarrow{k_2} 2\text{ NO}_2(g) \]

At a certain temperature, the elementary rate constants have the values \(k_1 = 4.0 \times 10^3\text{ M}^{-1}\text{s}^{-1}\), \(k_{-1} = 2.0 \times 10^2\text{ s}^{-1}\), and \(k_2 = 5.0 \times 10^1\text{ M}^{-1}\text{s}^{-1}\). The overall rate law is expressed as \(\text{Rate} = k_{\text{obs}} [\text{NO}]^2 [\text{O}_2]\). What is the value of the observed rate constant, \(k_{\text{obs}}\)?

The gas-phase oxidation of nitric oxide proceeds according to the following overall balanced equation:

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

A proposed two-step reaction mechanism for the process is shown below:

Step 1 (fast equilibrium):
\[ 2\text{ NO}(g) \underset{k_{-1}}{\overset{k_1}{\rightleftharpoons}} \text{N}_2\text{O}_2(g) \]

Step 2 (slow):
\[ \text{N}_2\text{O}_2(g) + \text{O}_2(g) \xrightarrow{k_2} 2\text{ NO}_2(g) \]

At a certain temperature, the elementary rate constants have the values \(k_1 = 4.0 \times 10^3\text{ M}^{-1}\text{s}^{-1}\), \(k_{-1} = 2.0 \times 10^2\text{ s}^{-1}\), and \(k_2 = 5.0 \times 10^1\text{ M}^{-1}\text{s}^{-1}\). The overall rate law is expressed as \(\text{Rate} = k_{\text{obs}} [\text{NO}]^2 [\text{O}_2]\). What is the value of the observed rate constant, \(k_{\text{obs}}\)?

- **A.** \(2.5\text{ M}^{-2}\text{s}^{-1}\)
- **B.** \(2.0 \times 10^1\text{ M}^{-2}\text{s}^{-1}\)
- **C.** \(1.0 \times 10^3\text{ M}^{-2}\text{s}^{-1}\)
- **D.** \(2.0 \times 10^5\text{ M}^{-2}\text{s}^{-1}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123662/*