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Thermodynamics of materials

At constant temperature and pressure, which quantity and condition correctly determine whether a change in a closed system proceeds spontaneously?

  1. AThe Gibbs energy change ΔG is negative
  2. BThe enthalpy change ΔH is negative (exothermic)
  3. CThe entropy change ΔS of the system alone is positive
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Answer: A. The Gibbs energy change ΔG is negative

At constant temperature and pressure, a change proceeds spontaneously in the direction that lowers the Gibbs energy of the system, G = H − TS (ΔG < 0), and equilibrium is reached at ΔG = 0. This rewrites the second law, "the entropy of the system plus its surroundings increases", in terms of quantities of the system alone, and the form ΔG = ΔH − TΔS takes both enthalpy and entropy into account. Even an exothermic reaction with negative ΔH does not proceed at high temperature if its entropy falls sharply. Even if the ΔS of the system is positive, a strongly endothermic change does not proceed at low temperature. The entropy of the system alone decides the matter only for an isolated system, which exchanges neither heat nor work with its surroundings.

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More Thermodynamics of materials questions

  1. 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.
  2. 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)?
  3. 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?
  4. Which statement correctly describes the line for the carbon reaction 2C(s) + O₂(g) → 2CO(g) in an Ellingham diagram?
  5. 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?