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and main group elements (e.g., N, halogens, O, S, C) have multiple oxidation states and important redox chemistry, which affect element distribution within the geochemical shells on Earth but also through the boundaries between such shells (e.g., Moretti et al., 2020a). For instance, it is the redox state of metals and ligands that complex them, which then determines (i) their “unlocking” from pristine reservoirs (e.g. minerals in which they occur at trace level); (ii) their mobility on Earth through carriers such as magma, water, or vapor; and eventually (iii) their accumulation and precipitations in new phases making up ore deposits.

      Redox reactions involve a coupled transfer of electrons, so for any oxidation (loss of electrons) a reciprocal reduction (gain of electrons) occurs. Moreover, redox reactions naturally occurring on Earth involve a net chemical change that can be described not only via the exchange of electrons between ions or their complexes, but also of oxygen and/or hydrogen atoms and compounds that these can form (e.g., Cicconi et al., 2020a and references therein). Here are some examples:

(1.1)

      (1.2)

(1.3)

(1.4)

(1.5)

      In which the subscripts s, m, aq, and g refer to solid, melt, aqueous, and gas (including supercritical fluids) phases, respectively. In the five examples above, O_2(g), H₂O_(g), Fe³⁺_(aq), O_2(g) and SO_2(g) are oxidizing agents, whereas Fe_(s), FeO_(l), H_2(g), Fe²⁺_(aq) are the reducing agents.

The word oxidation was introduced by Antoine Lavoisier (1777) and indicates the chemical mechanisms in which oxygen is consumed and added to a compound. The parallel mechanism in which some other compounds loose oxygen was called reduction. The oxidation number of reaction components in Reactions 1.1 to 1.5 shows that some elements have a greater affinity for electrons than others and that oxygen tends to appear with oxidation number –II in its compounds (including the O^2– species in its ionic compounds). In contrast, hydrogen tends to appear with oxidation number I. Besides, hydrogen and oxygen atoms and their compounds in reaction are related to ligands making up the most important matrixes on Earth, such as aqueous solutions (including highly concentrated saline solution), supercritical fluids and gases, silicate melts or oxide, and silicate minerals making up rocks. Except for rocks, these matrixes are also important transport agents and thus redox carriers within Earth geochemical reservoirs and throughout their boundaries. Therefore, nearly all redox exchanges on Earth are related to chemical transfers involving hydrogen‐ and/or oxygen‐based half‐reactions such as (Cicconi et al., 2020a,b):

(1.6)

(1.7)

that we will call henceforth oxygen and hydrogen electrodes (e.g., Cicconi et al., 2020a; Moretti, 2020) and in which the electron exchange is made explicit. For example, Reaction 1.1 can be written as the sum of Reaction 1.6 and:

      (1.8)

      plus the formation of FeO oxides from its ions,

      (1.9)

      in which oxidation numbers and then formal charges of involved atoms do not vary.

      In ore geochemistry, but also in metallurgical practice, a special mention must be made to redox mechanisms involving chalcophile elements and sulfide. Most often, relevant equilibria are written without the involvement of the medium in which they actually occur. Pyrite formation can result from the hydrothermal alteration of igneous pyrrhotite, but their equilibrium can be simply written in the sole Fe–S system as (Barton, 1970):

(1.10)

      In 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:

(1.11)

(1.12)

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 E_cathode – E_anode) 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:

(1.13)

with a_i the activity of the i^th 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

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