English
Menu

Thermodynamics of materials

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.

  1. AAbout 5.3×10⁻³
  2. BAbout 190
  3. CAbout 3.5×10⁴
Show answer and explanation

Answer: B. About 190

Taking the difference of the 2 equations gives 2Ni + 2H₂O → 2NiO + 2H₂, with ΔG° = (−298) − (−385) = +87 kJ/mol. At equilibrium ΔG° = −RT ln K with K = (pH₂/pH₂O)², so (pH₂O/pH₂)² = exp(87000/(8.314 × 1000)) = exp(10.46) ≈ 3.5×10⁴, and pH₂O/pH₂ ≈ 190. As long as the water vapor pressure is less than about 190 times that of hydrogen, Ni is not oxidized. About 3.5×10⁴ forgets that H₂ and H₂O each appear as 2 mol in the equation and omits the square root, and about 5.3×10⁻³ inverts the ratio to pH₂/pH₂O.

Report an error

Practice this topic Back to topic

More Thermodynamics of materials questions

  1. Which statement about the activity of a component in a solution (a liquid or a solid solution) is correct?
  2. 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.
  3. 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.
  4. 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).
  5. At constant temperature and pressure, which is the correct condition for an α phase and a β phase of a binary system to coexist in equilibrium?