most acidic natural waters, so we need not deal with reactions between H+, SO42–, HSO4–, and H2SO4, and need not consider the latter two in our list of species. Similarly, though many natural waters contain Na+ and Cl–, NaCl will precipitate only from concentrated brines, so we generally need not consider reactions between NaCl, Na+, and Cl–.
Carbonate is a somewhat different matter. Over the range of compositions of natural waters, H2CO3,
3.11 OXIDATION AND REDUCTION
An important geochemical variable that we have not yet considered is the oxidation state of a system. Many elements exist in nature in more than one valence state. Iron and carbon are the most important of these because of their abundance. Other elements, including transition metals such as Ti, Mn, Cr, Ce, Eu, and U, and nonmetals such as N, S, and As, are found in more than one valence state in nature. The valence state of an element can significantly affect its geochemical behavior. For example, U is quite soluble in water in its oxidized state, U6+, but is much less soluble in its reduced state, U4+. Many uranium deposits have formed when an oxidized, U-bearing solution was reduced. Iron is reasonably soluble in reduced form, Fe2+, but much less soluble in oxidized form, Fe3+. The same is true of manganese. Thus, iron is leached from rocks by reduced hydrothermal fluids and precipitated when these fluids mix with oxidized seawater. Eu2+ in magmas substitutes readily for Ca in plagioclase, whereas Eu3+ does not. Nitrogen is the element most critical to life after C, H, and O and is abundant in the atmosphere and dissolved in natural waters as N2. Plants and algae, however, can utilize N only in its reduced or oxidized states (such as ammonium or nitrate). The mobility of pollutants, particularly toxic metals, will depend strongly on whether the environment is reducing or oxidizing. Thus, the oxidation state of a system is an important geochemical variable.
The valence number of an element is defined as the electrical charge an atom would acquire if it formed ions in solution. For strongly electronegative and electropositive elements that form dominantly ionic bonds, valence number corresponds to the actual state of the element in ionic form. However, for elements that predominantly or exclusively form covalent bonds, valence state is a somewhat hypothetical concept. Carbon, for example, is never present in solution as a monatomic ion. Because of this, assignment of valence number can be a bit ambiguous. A few simple conventions guide assignment of valence number:
The valence number of all elements in pure form is 0.
The sum of valence numbers assigned to atoms in molecules or complex species must equal the actual charge on the species.
The valence number of hydrogen is +1, except in metal hydrides, when it is −1.
The valence number of oxygen is −2 except in peroxides, when it is −1.
The valence state in which an element will be present in a system is governed by the availability of electrons. Oxidation–reduction (redox) reactions involve the transfer of electrons and the resultant change in valence. Oxidation is the loss of electrons; reduction is the gain of electrons.‡ An example is the oxidation of magnetite (which consists of 1 Fe2+ and 2 Fe3+) to hematite:
(3.101)
The Fe2+ in magnetite loses an electron in this reaction and is thereby oxidized; conversely, oxygen gains an electron and is thereby reduced.
We can divide the elements into electron donors and electron acceptors; this division is closely related to electronegativity, as you might expect. Electron acceptors are electronegative; electron donors are electropositive. Metals in 0 valence state are electron donors, nonmetals in 0 valence state are usually electron acceptors. Some elements, such as carbon and sulfur, can be either electron donors or receptors. Oxygen is the most common electron acceptor, hence the term oxidation. It is nevertheless important to remember that oxidation and reduction may take place in the absence of oxygen.
A reduced system is one in which the availability of electrons is high, due to an excess of electron donors over electron acceptors. In such a system, metals will be in a low valence state (e.g., Fe2+). Conversely, when the availability of electrons is low, due to an abundance of electron acceptors, a system is said to be oxidized. Since it is the most common electron acceptor, the abundance 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
