the Fe–S system, pyrite is not at the liquidus (pyrite does not melt), but as a conceptual exercise we can still relate its formation to the occurrence of the following fictitious half‐reactions in the solid phase involving sulfide and polysulfide anions:
and their combination with iron, which appears in its cationic form Fe2+ in both sides of Reaction 1.10. In the liquid state, melts in which sulfide is the main or the sole anionic ligand are very scarcely represented on Earth and segregate from reducing sulfur oversaturated magmatic silicate melts (e.g., Li and Ripley, 2013 and references therein). Instead, sulfide melts are of interest in extractive metallurgy (e.g., Sokhanwaran et al., 2016).
1.1.2. The Redox Potential in Solutions and the Ligand Role
In redox reactions a potential difference drives the transfer electrons from an anode (negative electrode) to a cathode (positive electrode): oxidation occurs at the anode and reduction occurs at the cathode. Reactions are spontaneous in the direction of ΔG < 0, which is also the direction in which the potential (defined as Ecathode – Eanode) is positive. In a redox reaction the anode is then the half‐reaction written with electrons on the right and the cathode is the half‐reaction with electrons appearing on the left side.
The electric work done by a spontaneous redox reaction, like in a galvanic cell (E > 0), is the (measurable) electromotive force of the reacting systems and equals the Gibbs free energy change (e.g. Ottonello, 1997) via the Nernst equation:
with ai the activity of the ith component participating in the redox exchange, F as the Faraday constant (96,485 Coulomb per mole), n the number of transferred electrons, and Q the activity product. In writing redox reactions, complete electrolytes are often used because the activity coefficients are measured without extra thermodynamic assumptions, but Equation 1.13 is normally used for reactions based on individual ions. To establish a potential scale for half‐reactions, we keep using the convention that electrons are reported on the left‐hand side of the reaction, that is, in the sense of reduction. The potentials of half‐reactions can be added and subtracted, like free energies, to give an overall value for the reaction. It is also worth noting that by convention, it was decided to use a hydrogen‐electrode‐scale electric potential, by setting E0 = 0.0 V for reaction 1.7 with the constituents in their standard state (e.g., Casey, 2017). This arbitrary decision implies that (i) the Gibbs energy for H+(aq), the electron (e–), and H2(g) are all 0.0 kJ/mol, and (ii) potential difference of reactions involving the hydrogen electrode (Reaction 1.7) are given by the other half‐reaction completing the redox exchange.
The electrode potential values (E0) hold at standard conditions: by definition, standard conditions mean that any dissolved species have concentrations of 1 m, any gaseous species have partial pressures of 1 bar, and the system is 25°C. Standard potentials represent the case where no current flows and the electrode reaction is reversible. Measuring a voltage is an indication that the system is out of equilibrium. Nernstian processes are characterized by fast electron transfer and are rate‐limited by the diffusion of the electron‐active species into the electrolyte. The system then spontaneously approaches equilibrium because negative and positive charged species can flow in opposite directions. At equilibrium, the voltage drops to zero and the current stops, like in dead batteries. The magnitude of the cell potential, E0 = E0cathode – E0anode, may be viewed as the driving force for current flow in the circuit.
The hydrogen‐electrode scale electric potential so defined, E (also indicated as Eh in aqueous solutions), is a measure of the oxidation state of a system at equilibrium relative to a hydrogen electrode. E is not a constant (for given T and P) but depends on the system composition via activities of ions entering a half redox reaction. When coupled to a compositional parameter of the system related to the activity of the ligand making up the solvent of interest, such as aH+ for aqueous solutions, E can be used to establish a kind of phase diagram that shows which species (dissolved ion species, gases, or solids) will predominate among a chosen set in the system of interest (a solution) for a given temperature.
To easily understand all this, we can look at the reaction leading to the formation of liquid water:
which is given by the sum of Reaction 1.7 (H+/H2 redox couple: the anode) and the following half‐reaction (the cathode):
which is governed by the O2/H2O redox couple. The presence of protons in both Reactions 1.7 and 1.15 shows that the overall Reaction 1.14 is defined for acidic conditions (pH < 7). For neutral or basic conditions (pH ≥ 7), Reaction 1.14 can be obtained from the following two half‐reactions for H2O/H2 and O2/OH– couples, respectively:
Let us now deal with Reactions 1.7 and 1.15 occurring in the acidic medium (see, for example, Ottonello, 1997). The standard potential of Reaction 1.15 is E016 = 1.228 V and refers to a standard state of water in equilibrium at T = 25°C and P = 1 bar with an atmosphere of pure O2. From Equation 1.13 we obtain:
where a and f denote
