LITMIR.BIZ

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href="#ulink_fdbeb15a-cbaf-5b06-a562-649a03c4e6ac">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 H_2(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 = E⁰_cathode – E⁰_anode, 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 E_h 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 a_H+ 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:

(1.14)

      which is given by the sum of Reaction 1.7 (H⁺/H₂ redox couple: the anode) and the following half‐reaction (the cathode):

(1.15)

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:

(1.16)

(1.17)

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:

(1.18)

      where a and f denote activity and fugacity, respectively, pH = –loga_H+ and it is considered that aO₂ = fO₂/fO₂⁰ with fO₂⁰ = 1 bar.

      Similarly, the redox potential related to Reaction 1.7 is then:

(1.19)

Equations 1.18 and 1.19, which can also be derived for Reactions 1.16 and 1.17, can be used to trace E‐pH diagrams (also called Pourbaix or predominance diagrams; Casey, 2017) limiting the stability field of water (Figure 1.1) and of any other systems in which E‐pH relationships can be established from the reactions of intervening species (Figure 1.2). E‐pH diagrams are most used for understanding the geochemical formation, corrosion and passivation, leaching and metal recovery, water treatment precipitation, and adsorption.

      For the set of species of interest, E‐pH diagrams show boundaries that are given by:

      1 lines of negative slope that limit the stability field of water (Equations 1.18 and 1.19) or related to solid–solid phase changes in which paired electron–proton exchanges occur because the ligand (water) participates in reaction, such as in the case of the hematite–magnetite boundary in Figure 1.2:Figure 1.1 E‐pH diagram reporting the stability of water at T = 25°C and P = 1 bar for different partial pressure of H2 and O2 (log‐values).(1.20) Note that boundary slope is negative because protons and electrons appear on the same side of reaction. The protons/electrons ratio determines the slope value.

      2 (rare) pH‐dependent lines of positive slopes, and associated with electron–proton exchanges involving, for example, reduction of dissolved cations to the oxide with a lower oxidation number, e.g.(1.21) Boundary slope is positive because protons and electons appear on different sides of reaction.

      3 horizontal lines (pure electron

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