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Thermodynamics of materials

Which statement about the activity of a component in a solution (a liquid or a solid solution) is correct?

  1. AActivity is always equal to the molar concentration (mol/L), and the activity coefficient does not depend on the kind of solution
  2. BThe activity coefficient is greater than 1 (positive deviation from Raoult's law) when unlike atoms attract each other more strongly than like atoms
  3. CTaking the pure solid or liquid as the reference (activity 1), the activity of a component in an ideal solution is equal to its mole fraction
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Answer: C. Taking the pure solid or liquid as the reference (activity 1), the activity of a component in an ideal solution is equal to its mole fraction

Activity a is a "thermodynamic effective concentration" defined so that the chemical potential of a component in a solution can be written μ = μ° + RT ln a. With the pure substance as the reference state, the activity of a pure solid or liquid is 1, and in an ideal solution a = x (the mole fraction) by Raoult's law. For real solutions one writes a = γx, and the activity coefficient γ expresses the deviation from ideality. When unlike atoms attract each other more weakly than like atoms, the component escapes from the solution more easily, giving γ > 1 (positive deviation) and a tendency toward phase separation. When unlike atoms attract strongly, γ < 1, indicating a tendency toward ordering or compound formation. Treating activity as the molar concentration is only an approximation for dilute aqueous solutions.

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  1. 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.
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