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Thermodynamics of materials

In an Ellingham diagram, what is the main reason why the ΔG° line for the oxidation of most metals, 2M(s) + O₂(g) → 2MO(s), slopes upward, with ΔG° becoming larger (closer to 0) at higher temperature?

  1. AGaseous O₂ is consumed to form a solid oxide, so the entropy change ΔS° is negative
  2. BAs temperature rises, the heat ΔH° released by oxidation grows
  3. CAs temperature rises, faster diffusion in the metal increases the oxidation rate
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Answer: A. Gaseous O₂ is consumed to form a solid oxide, so the entropy change ΔS° is negative

An Ellingham diagram plots ΔG° = ΔH° − TΔS° for oxide formation per mol of O₂ against temperature, and if ΔH° and ΔS° are roughly constant, the slope of the line is −ΔS°. In metal oxidation, high-entropy gaseous O₂ is taken into a solid, so ΔS° is negative, around −0.2 kJ/(mol·K), and the slope is positive (upward). In other words, oxides become less stable at higher temperature. ΔH° depends little on temperature and only sets the height of the line. Diffusion and oxidation rates belong to kinetics and have nothing to do with the slope of the Ellingham diagram, which represents the equilibrium ΔG°. At the temperatures where a metal or oxide melts or boils, ΔS° changes and the line bends.

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More Thermodynamics of materials questions

  1. Which statement correctly describes the line for the carbon reaction 2C(s) + O₂(g) → 2CO(g) in an Ellingham diagram?
  2. In an Ellingham diagram, the formation reactions of all oxides are drawn with ΔG° normalized per mol of O₂. What is the main advantage of doing so?
  3. At 1000℃, take ΔG° for 4/3 Al + O₂ → 2/3 Al₂O₃ as −850 kJ/mol and ΔG° for 4/3 Cr + O₂ → 2/3 Cr₂O₃ as −530 kJ/mol (both per mol of O₂). Which combination of the ΔG° of 2/3 Cr₂O₃ + 4/3 Al → 2/3 Al₂O₃ + 4/3 Cr and the direction in which the reaction proceeds is correct? Assume all substances are pure.
  4. At 1000 K, ΔG° for 2Ni(s) + O₂(g) → 2NiO(s) is −298 kJ/mol. Which value is closest to the equilibrium oxygen partial pressure at which Ni and NiO coexist? Treat Ni and NiO as pure solids (activity 1), and take the standard pressure as 1 bar, the gas constant as 8.314 J/(mol·K), and ln 10 = 2.303.
  5. At 1000 K, take ΔG° for 2H₂(g) + O₂(g) → 2H₂O(g) as −385 kJ/mol and ΔG° for 2Ni(s) + O₂(g) → 2NiO(s) as −298 kJ/mol. When nickel is annealed in an H₂–H₂O gas mixture, which value is closest to the partial pressure ratio pH₂O/pH₂ at which Ni and NiO are in equilibrium (Ni is not oxidized if the ratio is smaller than this)? Take the gas constant as 8.314 J/(mol·K), and treat Ni and NiO as pure solids.