The thermodynamic effective concentration of a component in a solution or solid solution, satisfying μ = μ° + RT ln a. It is 1 for the pure substance and equals the mole fraction in an ideal solution.
Japanese name: 活量
Activity appears in 3 practice questions across 1 topic, including Thermodynamics of materials.
Field: Thermodynamics of materials
When the chemical potential of component i in a solution is written μi = μi° + RT ln ai, ai is the activity. μi° is the chemical potential in the reference state; in materials science the pure solid or liquid at the same temperature is often taken as the reference (ai = 1), and for gases the partial pressure divided by the standard pressure corresponds to the activity. In an ideal solution ai = xi (the mole fraction) by Raoult's law, and for real solutions one writes ai = γi·xi, with the activity coefficient γi expressing the deviation from ideality. Equilibrium constant expressions contain activities in place of concentrations.
When unlike atoms attract each other more weakly than like atoms, the component escapes from the solution more easily, giving γ > 1 (positive deviation from Raoult's law), and in extreme cases the solution separates into 2 phases. Conversely, when unlike atoms attract strongly, γ < 1 (negative deviation), indicating a tendency toward ordering or compound formation. In the regular solution model, it can be written RT ln γA = Ω(1 − xA)² using the interaction parameter Ω. In the dilute range of a solute, γ becomes nearly constant, and Henry's law, in which activity is proportional to concentration, holds.
The equilibrium of metal oxidation 2M + O₂ → 2MO is expressed by ΔG° = −RT ln K with K = a(MO)² ÷ (a(M)² × pO₂). If the activity of metal M in an alloy is less than 1, the equilibrium oxygen partial pressure is higher for the same ΔG°, and M becomes harder to oxidize. Conversely, if the oxide formed dissolves in another oxide and its activity falls, oxidation proceeds more easily. Removing impurity oxides by dissolving them into slag in smelting, and finding the amount of hydrogen or nitrogen dissolved in a molten metal from the gas partial pressure (Sieverts' law), are also based on equilibrium thinking with activities.
Answer: C. About 3×10⁻¹⁶ bar
At equilibrium ΔG = ΔG° + RT ln(1/pO₂) = 0, so ΔG° = RT ln pO₂. Then log pO₂ = ΔG°/(2.303RT) = −298000/(2.303 × 8.314 × 1000) ≈ −15.6, and pO₂ ≈ 3×10⁻¹⁶ bar. If the oxygen partial pressure of the atmosphere is higher than this, Ni is oxidized; if it is lower, NiO is reduced. About 1×10⁻³⁶ bar mistakes ΔG°/RT ≈ −35.8 for a common logarithm instead of a natural logarithm. About 2×10⁻⁸ bar takes ΔG° per mol of NiO (−149 kJ/mol), drops the exponent 1/2 on pO₂, and sets it equal to RT ln pO₂.
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.
Concentration expresses how much of a component is present, while activity expresses how strongly that component acts in chemical reactions and phase equilibria. In an ideal solution the mole fraction and activity coincide, but in real solutions with atomic interactions they differ by the activity coefficient. It is activity that is used in the expressions for equilibrium constants and chemical potentials.
Because the pure solid itself is chosen as the reference state. If the chemical potential of the reference state is μ°, then for the pure substance μ = μ°, so ln a = 0, that is, a = 1. Choosing another reference changes the value, but in equilibrium calculations ΔG° is put on the same reference, so the result does not change.
With the pure substance as the reference, it does not exceed 1 in a solution in stable equilibrium. If it did, the free energy would be lowered by precipitating that component as the pure substance. In supersaturated states, or with another reference based on Henry's law (such as a dilute 1 wt% solution), values above 1 can occur.
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.
Which statement about the activity of a component in a solu…Cr in the alloy becomes harder to oxidize to the extent that its activity is lowered, and a higher oxygen partial pressure is needed.
At a certain temperature, let p₀ be the equilibrium oxygen …Equilibrium oxygen partial pressure Chemical potential Stainless steel Ellingham diagram Entropy of mixing Gibbs energy Regular solution Spinodal decomposition