Thermodynamics of materials
Check the Gibbs energy and the condition for spontaneous change, how to read Ellingham diagrams, equilibrium oxygen partial pressures and H₂/H₂O ratios, activity and activity coefficients, the free energy of mixing of ideal and regular solutions, and spinodal decomposition with multiple-choice questions. Calculation questions come with worked explanations.
Thermodynamics of materials: key points
At constant temperature and pressure, a change proceeds in the direction that lowers the Gibbs energy G = H − TS, and equilibrium is reached at ΔG = 0. The Ellingham diagram, which compares the stability of oxides, plots the ΔG° of formation per mol of O₂ against temperature; the lower its line, the more stable the oxide a metal forms, and that metal can reduce the oxides of the lines above. From ΔG° = RT ln pO₂, the equilibrium oxygen partial pressure at which a metal and its oxide coexist can be found.
Activity is the effective concentration of a component in a solution or solid solution; in an ideal solution it equals the mole fraction, and deviations are expressed by the activity coefficient. The free energy of a solid solution is set by the balance between the decrease due to the entropy of mixing and the enthalpy of mixing, and when unlike atoms repel each other in the regular solution model, a miscibility gap appears at low temperature. The equilibrium compositions of 2 phases are set by the common tangent, and spinodal decomposition occurs inside the gap.
All Thermodynamics of materials questions (15)
- At constant temperature and pressure, which quantity and condition correctly determine whether a change in a closed system proceeds spontaneously?
- Which statement is correct for a reaction with ΔH > 0 and ΔS > 0 (for example, the thermal decomposition of a carbonate)? Assume ΔH and ΔS do not depend on temperature.
- For the decomposition of calcium carbonate, CaCO₃(s) → CaO(s) + CO₂(g), take the standard reaction enthalpy as ΔH° = +178 kJ/mol and the standard reaction entropy as ΔS° = +161 J/(mol·K), both independent of temperature. Which value is closest to the temperature at which decomposition starts to proceed spontaneously in the standard state with a CO₂ partial pressure of 1 bar (the temperature at which ΔG° = 0)?
- In an Ellingham diagram, what is the main reason why the ΔG° line for the oxidation of most metals, 2M(s) + O₂(g) → 2MO(s), slopes upward, with ΔG° becoming larger (closer to 0) at higher temperature?
- Which statement correctly describes the line for the carbon reaction 2C(s) + O₂(g) → 2CO(g) in an Ellingham diagram?
- 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?
- 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.
- 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.
- 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.
- Which statement about the activity of a component in a solution (a liquid or a solid solution) is correct?
- 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.
- 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.
- 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).
- 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?
- A solid solution with a miscibility gap was quenched from the single-phase state at high temperature and held at a temperature inside the gap. Which statement about spinodal decomposition is correct?