The silver-water system, fully thermodynamic per Bard Table 6. Two triple points organize the diagram: TP₁ = 3.43 − log[Ag⁺] (Lines D, E, F meet, AgO band emerges) and TP₂ = 6.32 − log[Ag⁺] (Lines A = B and C = E meet, Ag⁺ / Ag₂O vertical boundary). At default 0.1 M Ag: TP₁ = 4.43, TP₂ = 7.32.
S = 0.05916 V (RT·ln10/F at 25 °C). All E° from Bard, Standard Potentials in Aqueous Solution, Table 6 (nonhydrated oxides). Solid activities = 1. Lines are drawn as continuous paths between their thermodynamic crossings, no Ksp constraint imposed (the Ag⁺ / Ag₂O boundary at pH 7.32 is where Line A meets Line B, the true thermodynamic boundary).
| Line | Half-reaction | E° (V) | Nernst expression | Bard # |
|---|---|---|---|---|
| A | Ag⁺ + e⁻ → Ag(s) | +0.7991 | E = 0.7991 + S·log[Ag⁺] | #5 |
| B | Ag₂O(s) + 2H⁺ + 2e⁻ → 2Ag(s) + H₂O | +1.173 | E = 1.173 − S·pH | #7ᵃ |
| C | 2AgO(s) + 2H⁺ + 2e⁻ → Ag₂O(s) + H₂O | +1.398 | E = 1.398 − S·pH | #10ᵃ |
| D | Ag₂O₃(s) + 2H⁺ + 2e⁻ → 2AgO(s) + H₂O | +1.569 | E = 1.569 − S·pH | #11 |
| E | AgO(s) + 2H⁺ + e⁻ → Ag⁺ + H₂O | +1.772 | E = 1.772 − 2S·pH − S·log[Ag⁺] | #15 |
| F | Ag₂O₃(s) + 6H⁺ + 4e⁻ → 2Ag⁺ + 3H₂O | +1.670 | E = 1.670 − 1.5S·pH − 0.5S·log[Ag⁺] | #12 |
| pH range | Phases (top to bottom) |
|---|---|
| 0 to 4.43 (below TP₁) | Ag₂O₃ | Ag⁺ | Ag (Line F bounds Ag₂O₃ from Ag⁺ directly) |
| 4.43 to 7.32 (between triple points) | Ag₂O₃ | AgO | Ag⁺ | Ag (full acidic stack) |
| 7.32 to 14 (above TP₂) | Ag₂O₃ | AgO | Ag₂O | Ag (alkaline stack) |
The vertical line at TP₂ connects A=B (0.740 V) up to C=E (0.965 V). Above that elevation only Ag₂O₃ and AgO are present and the diagram is continuous. The thermodynamic boundary at pH 7.32 (where Line A meets Line B) is NOT the Ksp dissolution pH 11.15. These describe different chemical conditions, and the Pourbaix uses the redox-coupled criterion. Ag²⁺ (Bard #16) is omitted because it has no real stability region at unit activity. Ag₂O₃ is included as the Ag(III) endpoint per Bard's table.