English
Menu

Thermodynamics of materials

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.

  1. AAbout 1×10⁻³⁶ bar
  2. BAbout 2×10⁻⁸ bar
  3. CAbout 3×10⁻¹⁶ bar
Show answer and explanation

Answer: C. About 3×10⁻¹⁶ bar

At equilibrium ΔG = ΔG° + RT ln(1/pO₂) = 0, so ΔG° = RT ln pO₂. Then log pO₂ = ΔG°/(2.303RT) = −298000/(2.303 × 8.314 × 1000) ≈ −15.6, and pO₂ ≈ 3×10⁻¹⁶ bar. If the oxygen partial pressure of the atmosphere is higher than this, Ni is oxidized; if it is lower, NiO is reduced. About 1×10⁻³⁶ bar mistakes ΔG°/RT ≈ −35.8 for a common logarithm instead of a natural logarithm. About 2×10⁻⁸ bar takes ΔG° per mol of NiO (−149 kJ/mol), drops the exponent 1/2 on pO₂, and sets it equal to RT ln pO₂.

Report an error

Practice this topic Back to topic

More Thermodynamics of materials questions

  1. 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.
  2. Which statement about the activity of a component in a solution (a liquid or a solid solution) is correct?
  3. 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.
  4. 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.
  5. In the regular solution model, the enthalpy of mixing is taken as ΔH_mix = Ωx(1 − x) (Ω is an interaction parameter independent of temperature), and the entropy of mixing is the same as for an ideal solution. For Ω = +20 kJ/mol, which value is closest to the critical temperature Tc = Ω/(2R) at which the region where the solid solution separates into 2 phases (the miscibility gap) disappears? Take the gas constant as 8.314 J/(mol·K).