of oxygen usually controls the oxidation state of a system, but this need not be the case.
To predict the equilibrium oxidation state of a system, we need a means of characterizing the availability of electrons, and the valence state of elements as a function of that availability. Low-temperature geochemists and high-temperature geochemists do this in different ways. The former use electrochemical potential while the latter use oxygen fugacity. We will consider both.
3.11.1 Redox in aqueous solutions
The simplest form of the chemical equation for the reduction of ferric iron would be:
(3.102)
Figure 3.18 Electrode reactions in the Daniell cell.
where the subscript aq denotes the aqueous species. This form suggests that the energy involved might be most conveniently measured in an electrochemical cell.
The Daniell cell pictured in Figure 3.18 can be used to measure the energy involved in the exchange of electrons between elements, for example, zinc and copper:
(3.103)
where the subscript s denotes the solid. Such a cell provides a measure of the relative preference of Zn and Cu for electrons. In practice, such measurements are made by applying a voltage to the system that is just sufficient to halt the flow of electrons from the zinc plate to the copper one. What is actually measured, then, is a potential energy, denoted E, and referred to as the electrode potential, or simply the potential of the reaction.
If we could measure the potential of two separate half-cell reactions:
we could determine the energy gain/loss in the transfer of an electron from an individual element. Unfortunately, such measurements are not possible (nor would these reactions occur in the natural environment: electrons are not given up except to another element or species§). This requires the establishment of an arbitrary reference value. Once such a reference value is established, the potential involved in reactions such as 3.102 can be established.
3.11.1.1 Hydrogen scale potential, EH
The established convention is to measure potentials in a standard hydrogen electrode cell (at standard temperature and pressure). The cell consists on one side of a platinum plate coated with fine Pt powder that is surrounded by H2 gas maintained at a partial pressure of 1 atm and immersed in a solution of unit H+ activity. The other side consists of the electrode and solution under investigation. A potential of 0 is assigned to the half-cell reaction:
(3.104)
where the subscript g denotes the gas phase. The potential measured for the entire reaction is then assigned to the half-cell reaction of interest. Thus, for example, the potential of the reaction:
is –0.763 V. This value is assigned to the reaction:
(3.105)
Table 3.3 EH° and pε° for some half-cell reactions.
| Half-cell reaction | EH° (V) | pε° |
| Li+ + e– ⇌ Li | −3.05 | −51.58 |
| Ca2+ + 2 e– ⇌ Ca | −2.93 | −49.55 |
| Th4+ + 4e– ⇌ Th | −1.83 | −30.95 |
| U4+ + 4e– ⇌ U | −1.38 | −23.34 |
| Mn2+ +2e– ⇌ Mn | −1.18 | −19.95 |
| Zn2+ + 2e– ⇌ Zn | −0.76 | −12.85 |
| Cr3+ +3e– ⇌ Cr | −0.74 | −12.51 |
| CO2(g) + 4H+ + 4e– ⇌ CH2O*+2H2O | −0.71 | −12.01 |
| Fe2+ + 2e– ⇌ Fe | −0.44 | −7.44 |
| Eu3+ + e– ⇌ Eu2+ | −0.36 | −6.08 |
| Ni2+ + 2e– ⇌ Ni | −0.26 | −4.34 |
| Pb2+ + 2e– ⇌ Pb | −0.13 | −2.2 |
| CrO42− + 4H2O +3e– ⇌ Cr(OH)3 + H2O | −0.13 | −2.2 |
| 2H+ + 2e– ⇌ H2(g) | 0 | 0 |
| N2(g) + 6H+ + 6e– ⇌ 2NH3 | 0.093 | 1.58 |
| Cu2+ + 2e– ⇌ Cu | 0.34 | 5.75 |
| UO22+ + 2e– ⇌ UO2 | 0.41 | 6.85 |
| S + 2e– ⇌ S2− | 0.44 | 7.44 |
| Cu+ + e– ⇌ Cu |
0.52
|