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Thermodynamics of materials

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.

  1. A−320 kJ/mol; it proceeds in the direction of aluminum reducing Cr₂O₃
  2. B+320 kJ/mol; it proceeds in reverse, in the direction of chromium reducing Al₂O₃
  3. C−1380 kJ/mol; it proceeds in the direction of aluminum reducing Cr₂O₃
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Answer: A. −320 kJ/mol; it proceeds in the direction of aluminum reducing Cr₂O₃

The required reaction is the Al₂O₃ formation equation minus the Cr₂O₃ formation equation, and the O₂ cancels. ΔG° = (−850) − (−530) = −320 kJ/mol is negative, so the reaction proceeds in the direction of aluminum reducing Cr₂O₃ to give metallic chromium. This corresponds to the Al₂O₃ line lying below the Cr₂O₃ line in the Ellingham diagram, and it is the principle of making metallic chromium by the aluminothermic process. +320 kJ/mol reverses the order of subtraction and gets the sign wrong; because Al₂O₃ is the more stable oxide, chromium does not reduce Al₂O₃. −1380 kJ/mol is the value obtained by adding the 2 ΔG° values.

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More Thermodynamics of materials questions

  1. 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.
  2. 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.
  3. Which statement about the activity of a component in a solution (a liquid or a solid solution) is correct?
  4. 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.
  5. Which statement about the Gibbs energy of mixing of an ideal solution (ideal solid solution), ΔG_mix = RT[x ln x + (1 − x) ln(1 − x)], is correct? x is the mole fraction of one component.