---
title: "The direct thermal decomposition of a solid metal oxide, \\(\\text{MO}_2\\text{(s)}\\), into its pure elements is thermodynamically unfavorable at \\(298\\text{ K}\\):  \\[ \\text{MO}_2\\text{(s)} \\rightarrow \\text{M(s)} + \\text{O}_2\\text{(g)} \\quad \\Delta G^\\circ = +460\\text{ kJ/mol}_{rxn} \\]  To drive the extraction of pure \\(\\text{M(s)}\\), this unfavorable decomposition can be coupled with an oxidation reaction through the shared intermediate \\(\\text{O}_2\\text{(g)}\\). Thermodynamic data for three candidate oxidation reactions at \\(298\\text{ K}\\) are shown in the table below.  | Reaction | Chemical equation | \\(\\Delta G^\\circ_{298}\\ (\\text{kJ/mol}_{rxn})\\) | |—|—|—| | 1 | \\(2\\,\\text{C(s)} + \\text{O}_2\\text{(g)} \\rightarrow 2\\,\\text{CO(g)}\\) | \\(-274\\) | | 2 | \\(\\text{C(s)} + \\text{O}_2\\text{(g)} \\rightarrow \\text{CO}_2\\text{(g)}\\) | \\(-394\\) | | 3 | \\(2\\,\\text{CO(g)} + \\text{O}_2\\text{(g)} \\rightarrow 2\\,\\text{CO}_2\\text{(g)}\\) | \\(-514\\) |  Which of the following balanced chemical equations represents an overall coupled process that is thermodynamically favorable at \\(298\\text{ K}\\)?"
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url: "https://nerd-notes.com/ubq/123938/"
date_modified: "2026-09-28T12:32:20+00:00"
---

# The direct thermal decomposition of a solid metal oxide, \(\text{MO}_2\text{(s)}\), into its pure elements is thermodynamically unfavorable at \(298\text{ K}\):

\[
\text{MO}_2\text{(s)} \rightarrow \text{M(s)} + \text{O}_2\text{(g)} \quad \Delta G^\circ = +460\text{ kJ/mol}_{rxn}
\]

To drive the extraction of pure \(\text{M(s)}\), this unfavorable decomposition can be coupled with an oxidation reaction through the shared intermediate \(\text{O}_2\text{(g)}\). Thermodynamic data for three candidate oxidation reactions at \(298\text{ K}\) are shown in the table below.

| Reaction | Chemical equation | \(\Delta G^\circ_{298}\ (\text{kJ/mol}_{rxn})\) |
|—|—|—|
| 1 | \(2\,\text{C(s)} + \text{O}_2\text{(g)} \rightarrow 2\,\text{CO(g)}\) | \(-274\) |
| 2 | \(\text{C(s)} + \text{O}_2\text{(g)} \rightarrow \text{CO}_2\text{(g)}\) | \(-394\) |
| 3 | \(2\,\text{CO(g)} + \text{O}_2\text{(g)} \rightarrow 2\,\text{CO}_2\text{(g)}\) | \(-514\) |

Which of the following balanced chemical equations represents an overall coupled process that is thermodynamically favorable at \(298\text{ K}\)?

The direct thermal decomposition of a solid metal oxide, \(\text{MO}_2\text{(s)}\), into its pure elements is thermodynamically unfavorable at \(298\text{ K}\):

\[
\text{MO}_2\text{(s)} \rightarrow \text{M(s)} + \text{O}_2\text{(g)} \quad \Delta G^\circ = +460\text{ kJ/mol}_{rxn}
\]

To drive the extraction of pure \(\text{M(s)}\), this unfavorable decomposition can be coupled with an oxidation reaction through the shared intermediate \(\text{O}_2\text{(g)}\). Thermodynamic data for three candidate oxidation reactions at \(298\text{ K}\) are shown in the table below.

| Reaction | Chemical equation | \(\Delta G^\circ_{298}\ (\text{kJ/mol}_{rxn})\) |
|---|---|---|
| 1 | \(2\,\text{C(s)} + \text{O}_2\text{(g)} \rightarrow 2\,\text{CO(g)}\) | \(-274\) |
| 2 | \(\text{C(s)} + \text{O}_2\text{(g)} \rightarrow \text{CO}_2\text{(g)}\) | \(-394\) |
| 3 | \(2\,\text{CO(g)} + \text{O}_2\text{(g)} \rightarrow 2\,\text{CO}_2\text{(g)}\) | \(-514\) |

Which of the following balanced chemical equations represents an overall coupled process that is thermodynamically favorable at \(298\text{ K}\)?

- **A.** \(\text{MO}_2\text{(s)} + 2\,\text{C(s)} \rightarrow \text{M(s)} + 2\,\text{CO(g)}\)
- **B.** \(\text{MO}_2\text{(s)} + \text{C(s)} \rightarrow \text{M(s)} + \text{CO}_2\text{(g)}\)
- **C.** \(\text{MO}_2\text{(s)} + 2\,\text{CO(g)} \rightarrow \text{M(s)} + 2\,\text{CO}_2\text{(g)}\)
- **D.** \(\text{MO}_2\text{(s)} + 2\,\text{CO}_2\text{(g)} \rightarrow \text{M(s)} + 2\,\text{CO(g)} + 2\,\text{O}_2\text{(g)}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123938/*