English
Menu

Thermodynamics of materials

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?

  1. AEach component has the same chemical potential in the α and β phases
  2. BThe Gibbs energy per mole of the α phase is equal to that of the β phase
  3. CThe α and β phases have equal compositions, with no difference in concentration between them
Show answer and explanation

Answer: A. Each component has the same chemical potential in the α and β phases

At equilibrium, moving a small amount of any component from the α phase to the β phase must not change G, so μA(α) = μA(β) and μB(α) = μB(β) hold for components A and B respectively. When the molar Gibbs energy is plotted against composition, this corresponds to drawing a tangent common to the 2 curves, and the 2 points of tangency give the compositions of the 2 phases in equilibrium. The values at the ends of the tangent (x = 0 and x = 1) are the chemical potentials of the respective components. The molar Gibbs energies of the 2 phases are generally not equal, and the compositions at the 2 ends of the common tangent differ. Equal molar G is the equilibrium condition only when the 2 phases have the same composition, as in the melting of a pure substance.

Report an error

Practice this topic Back to topic

More Thermodynamics of materials questions

  1. 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?
  2. At constant temperature and pressure, which quantity and condition correctly determine whether a change in a closed system proceeds spontaneously?
  3. 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.
  4. 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)?
  5. 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?