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Thermodynamics of materials

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?

  1. AAll the ΔG° values become positive and lie above the temperature axis, so the scale is easier to read
  2. BThe vertical distance between 2 lines is directly equal to the ΔG° of the reaction in which one metal reduces the other's oxide
  3. CThe ΔS° that sets the slope becomes equal for all oxides, so the lines can be compared as parallel lines
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Answer: B. The vertical distance between 2 lines is directly equal to the ΔG° of the reaction in which one metal reduces the other's oxide

With normalization per mol of O₂, taking the difference between, for example, 4/3 Al + O₂ → 2/3 Al₂O₃ and 2Fe + O₂ → 2FeO cancels the O₂, and the ΔG° of 2FeO + 4/3 Al → 2Fe + 2/3 Al₂O₃ can be read directly as the vertical distance between the 2 lines. The metal of the lower line can reduce the oxide of the upper line at that temperature. The ΔG° of oxide formation is almost always negative, and the normalization does not change its sign. The slopes are set by the ΔS° of each reaction, so they do not become equal even when normalized per mol of O₂. In metal oxidation, 1 mol of gaseous O₂ is consumed in every case, which only makes the slopes similar.

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More Thermodynamics of materials questions

  1. 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.
  2. 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.
  3. 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.
  4. Which statement about the activity of a component in a solution (a liquid or a solid solution) is correct?
  5. At a certain temperature, let p₀ be the equilibrium oxygen partial pressure at which pure Cr and Cr₂O₃ coexist. At the same temperature, about how many times p₀ is the equilibrium oxygen partial pressure at which an alloy with a Cr activity of 0.10 coexists with pure Cr₂O₃? Take the reaction as 4/3 Cr + O₂ → 2/3 Cr₂O₃.