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title: "The direct decomposition of solid titanium(IV) oxide into its elements is thermodynamically unfavorable at \\(298\\text{ K}\\), as represented by the following equation:  \\[\\text{TiO}_2\\text{(s)} \\rightarrow \\text{Ti(s)} + \\text{O}_2\\text{(g)} \\quad \\Delta G^\\circ_{298} = +890\\text{ kJ/mol}_{\\text{rxn}}\\]  To produce \\(1.0\\text{ mol}\\) of \\(\\text{Ti(s)}\\), the decomposition reaction is coupled with one of three auxiliary oxidation processes at \\(298\\text{ K}\\), shown in the table below.  | Auxiliary process | Balanced chemical equation | \\(\\Delta G^\\circ_{298}\\text{ (kJ/mol}_{\\text{rxn}}\\text{)}\\) | | :— | :— | :— | | Process X | \\(2\\,\\text{Mg(s)} + \\text{O}_2\\text{(g)} \\rightarrow 2\\,\\text{MgO(s)}\\) | \\(-1140\\) | | Process Y | \\(\\text{Ca(s)} + \\frac{1}{2}\\,\\text{O}_2\\text{(g)} \\rightarrow \\text{CaO(s)}\\) | \\(-600\\) | | Process Z | \\(2\\,\\text{CO(g)} + \\text{O}_2\\text{(g)} \\rightarrow 2\\,\\text{CO}_2\\text{(g)}\\) | \\(-510\\) |  Which of the following correctly ranks the three coupled processes in order of thermodynamic favorability for the production of \\(1.0\\text{ mol}\\) of \\(\\text{Ti(s)}\\) at \\(298\\text{ K}\\), from most favorable to least favorable?"
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url: "https://nerd-notes.com/ubq/123953/"
date_modified: "2026-09-28T12:32:35+00:00"
---

# The direct decomposition of solid titanium(IV) oxide into its elements is thermodynamically unfavorable at \(298\text{ K}\), as represented by the following equation:

\[\text{TiO}_2\text{(s)} \rightarrow \text{Ti(s)} + \text{O}_2\text{(g)} \quad \Delta G^\circ_{298} = +890\text{ kJ/mol}_{\text{rxn}}\]

To produce \(1.0\text{ mol}\) of \(\text{Ti(s)}\), the decomposition reaction is coupled with one of three auxiliary oxidation processes at \(298\text{ K}\), shown in the table below.

| Auxiliary process | Balanced chemical equation | \(\Delta G^\circ_{298}\text{ (kJ/mol}_{\text{rxn}}\text{)}\) |
| :— | :— | :— |
| Process X | \(2\,\text{Mg(s)} + \text{O}_2\text{(g)} \rightarrow 2\,\text{MgO(s)}\) | \(-1140\) |
| Process Y | \(\text{Ca(s)} + \frac{1}{2}\,\text{O}_2\text{(g)} \rightarrow \text{CaO(s)}\) | \(-600\) |
| Process Z | \(2\,\text{CO(g)} + \text{O}_2\text{(g)} \rightarrow 2\,\text{CO}_2\text{(g)}\) | \(-510\) |

Which of the following correctly ranks the three coupled processes in order of thermodynamic favorability for the production of \(1.0\text{ mol}\) of \(\text{Ti(s)}\) at \(298\text{ K}\), from most favorable to least favorable?

The direct decomposition of solid titanium(IV) oxide into its elements is thermodynamically unfavorable at \(298\text{ K}\), as represented by the following equation:

\[\text{TiO}_2\text{(s)} \rightarrow \text{Ti(s)} + \text{O}_2\text{(g)} \quad \Delta G^\circ_{298} = +890\text{ kJ/mol}_{\text{rxn}}\]

To produce \(1.0\text{ mol}\) of \(\text{Ti(s)}\), the decomposition reaction is coupled with one of three auxiliary oxidation processes at \(298\text{ K}\), shown in the table below.

| Auxiliary process | Balanced chemical equation | \(\Delta G^\circ_{298}\text{ (kJ/mol}_{\text{rxn}}\text{)}\) |
| :--- | :--- | :--- |
| Process X | \(2\,\text{Mg(s)} + \text{O}_2\text{(g)} \rightarrow 2\,\text{MgO(s)}\) | \(-1140\) |
| Process Y | \(\text{Ca(s)} + \frac{1}{2}\,\text{O}_2\text{(g)} \rightarrow \text{CaO(s)}\) | \(-600\) |
| Process Z | \(2\,\text{CO(g)} + \text{O}_2\text{(g)} \rightarrow 2\,\text{CO}_2\text{(g)}\) | \(-510\) |

Which of the following correctly ranks the three coupled processes in order of thermodynamic favorability for the production of \(1.0\text{ mol}\) of \(\text{Ti(s)}\) at \(298\text{ K}\), from most favorable to least favorable?

- **A.** \(\text{Process X} > \text{Process Y} > \text{Process Z}\)
- **B.** \(\text{Process X} > \text{Process Z} > \text{Process Y}\)
- **C.** \(\text{Process Z} > \text{Process X} > \text{Process Y}\)
- **D.** \(\text{Process Y} > \text{Process X} > \text{Process Z}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123953/*