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Thermodynamics of materials

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.

  1. AAbout 10 times
  2. BAbout 22 times
  3. CAbout 100 times
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Answer: B. About 22 times

At equilibrium ΔG° = −RT ln K, with K = a(Cr₂O₃) to the power 2/3 ÷ (a(Cr) to the power 4/3 × pO₂). At the same temperature ΔG° and K are the same, so with a(Cr₂O₃) = 1, a(Cr) to the power 4/3 × pO₂ is constant. Therefore pO₂ = p₀ × 0.10 to the power −4/3 ≈ 21.5 p₀, about 22 times. Cr in the alloy becomes harder to oxidize to the extent that its activity is lowered, and a higher oxygen partial pressure is needed. About 10 times takes the coefficient 4/3 of Cr as 1, and about 100 times takes it as 2. In this way, the activities of alloying elements and the oxygen partial pressure let you judge which element is selectively oxidized at the surface of a stainless steel.

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