The oxidation state of an atom in a molecule is a concept helpful in keeping account of electrons. In many cases it is an indication of the number of electrons involved in bonding, but this is not always true and the oxidation state (or oxidation number) need not have any physical meaning. The oxidation state is equivalent to the charge on a positive or negative ion in an ionic substance, while for a covalent compound it is arrived at arbitrarily by assigning the electrons in a bond to the most electronegative atom. Electrons forming bonds between two atoms of the same electronegativity are shared equally in the assignment.6
Reactions that involve changes of oxidation states, called oxidation-reduction (redox) reactions, are governed by the oxidation potentials of the systems involved. The potential E of the redox couple or half-cell, M/Mn+, is given a numerical value based in principle on an electrochemical cell in which M is in equilibrium with its ions:
The potential is measured against a reference couple, the primary one being H2/H+, which is defined to have a standard potential value of exactly zero volts. The potential E is related to the free energy change of the process;
where F is the Faraday constant, 96,500 coulombs (C), and n is the number of electrons transferred. Positive potentials and negative AG values are characteristic of spontaneous processes.
Standard potentials E° refer to values where the reactants are at unit concentration (strictly, unit activity). Values are tabulated as the electromotive
60xidation state is conventionally expressed in parenthetical roman numerals after the symbol or name for the element [e.g., Fe(II)].
series, usually as reduction potentials, that is, for the process as written in reaction (9-37). The potential varies with concentration according to the Nernst equation. For the process given in reaction (9-37), we have
RT 1 0 059
at 25°C (R is the gas constant, F is the Faraday constant, and T is the absolute temperature.) Potentials on this scale are sometimes given the symbol EH to indicate that values are on the hydrogen scale.
It is often desirable to express the oxidizing or reducing properties of a system in terms of the concept of pE, which is analogous to pH. That is, in a formal sense, pE = — log (concentration of electrons).7 Although there are no free electrons in typical chemical systems, the value of pE provides a measure of the oxidizing or reducing properties of a solution. Alternatively, pE serves as a quantitative indication of the oxidizing or reducing conditions necessary for a given oxidation state of an element to be stable. The quantity pE gives a unitless scale analogous to pH, while EH is a scale measured in volts. In practice, pE is evaluated from the expression pE =(RT/FE) ln 10 = 0059 at225 °C (9-40)
The pE value for oxygen in aqueous media can be evaluated for illustration. The oxygen half-cell reaction in acid solution is8
Under conditions of equilibrium with the atmosphere, where the partial pressure of 02 is 0.21 atm, we have pE = 1229 + 4(—ph)+ log°.21 (9-43)
At a pH value of 8, in the range reasonable for natural waters, pE = 12.6. This will vary with pH and the oxygen partial pressure. In the absence of other oxidizing agents, the oxidizing power in a body of water is in fact determined by the concentration of dissolved oxygen. If the water is not saturated with
7More properly, pH = — log (activity of H+); then pE = — log (activity of electrons).
8In basic solution, the reaction is
The acid and base reactions are related by the ion product of water, and either can be used under all conditions.
oxygen, equation (9-42) should have the value of the oxygen partial pressure that would be in equilibrium with the actual O2 concentration according to Henry's law.
When used to describe a set of conditions or an environment, "oxidizing'' and "reducing'' are relative terms; that is, they have meaning only with respect to the reaction or compound being considered. Conditions that exhibit low values of pE will favor reductions of many elements and compounds, and the lower the value, the greater the number of materials that can be reduced. High pE values will favor oxidation similarly.
Oxidizing or reducing power in aqueous solution is limited by the fact that water itself can be oxidized or reduced according to the reactions
respectively. [Reaction (9-44) is just the reverse of (9-41).] The pE values of these reactions set the limits of strength for oxidizing or reducing substances that can be stable in water. The values are dependent on the pH and on the oxygen or hydrogen concentrations (or equilibrium partial pressures).
An example of the use of pE is shown by consideration of the equilibrium between sulfate S(IV) and sulfide S(-II) [reaction (9-46)], where the conditions under which SO44 or sulfide predominates in solution can be related to the pE value.
Under most conditions of pH that are of interest environmentally, the predominant form of sulfide is HS4. Other sulfur species (e.g., sulfite, SO24, and elemental sulfur) will be ignored for simplicity; in much, but not all, of the aqueous chemistry of sulfur compounds, they are not important. For reaction (9-46), E° is 0.25 V. Therefore,
particular pH. At a pH of 8, we have
4.24 + 1log 1SO04 9pH
One can consider how the ratio of [SO4 ] to [HS ] varies with pE at a pE = 44.76 + 1log ISO^ (9-48)
From this, it can be seen that the concentrations of SO4 and HS will be equal at pE = —4.76. On the other hand, at the pE of oxygen-saturated water, 12.6, the ratio [SO4— ]/[HS—] is very large (log [SO2—]/[HS—] = 138.9), and hence SO2— is the stable form. Plots can be made for [SO^] and [HS— ] as a function of E or pE (the slopes of the plots are easily established, as was the plot of pH vs log concentration for weak acids) at a particular total concentration of SO4— plus HS— to show the behavior graphically (see Section 10.4).
Plots of potential E vs pH that show the regions in which particular species are stable are called Pourbaix or predominance area diagrams. An example for sulfur is given in Figure 9-15. Each region represents the conditions of E and pH necessary for a particular species to be stable. There is a small region in which elemental sulfur is favored; this is not included in the foregoing discussion. A vertical line on this diagram represents an equilibrium reaction that is independent of potential, that is, an acid-base reaction. It is the value of pK. A horizontal line represents a redox reaction that is independent of pH, and is simply the E° value, while sloping lines represent redox reactions that are pH dependent; the slope depends on the number of electrons and the number of hydrogen ions involved in the reaction. A line representing equilibria between soluble species marks conditions at which concentrations are equal: one species or the other predominates on either side of the line. If only one species is soluble, it is necessary to specify what solution concentration will be necessary for "predominance"—in other words, what level of concentration
will be deemed important—and draw the plot accordingly. The upper and lower limits in this diagram are the stability limits for water; they are not limits on the existence of particular states in the absence of water.
Potentials are based on thermodynamics and represent equilibrium situations; they say nothing about how fast equilibrium will be reached. Many redox reactions have multistep and complex mechanisms. Kinetic limitations may make reactions slow even when they are strongly favored thermodynam-ically. This book would be carbon dioxide and water now if it were not for kinetics! Many electrode reactions require a larger potential than calculated to overcome a kinetic barrier (the overpotential). Redox reactions involving oxo anions often take place slowly, the more so the higher the oxidation state of the central element, and the smaller it is. Thus, the perchlorate ion, ClO4— is reduced more slowly than chlorate, ClO—, and chlorate more slowly than iodate, IO—. Reactions involving many diatomic molecules such as 02 also tend to be slow.
There are two general mechanisms for redox reactions. In the outer sphere mechanism, the reactants must approach each other to allow the electron to be transferred, but no direct bonding takes place between them. In the inner sphere mechanism, a bonded intermediate must form first (although it may be transient and unstable). This process involves the same needs for activation, and so on as the kinetics of other chemical reactions. Even outer sphere processes may require an activation of the reactants before the electron can be transferred. Many redox reactions do not involve transfer of electrons as such, but rather transfer of an atom. The oxidation state changes because of our definition. An example is the reaction between the common oxidizing agent hypochlorous acid and the nitrite ion,
where the oxygen atom originally on the Cl in ClOH is transferred to the nitrogen. In other reactions involving oxo ions, the first step is protonation of one of the oxygens to form water, which dissociates to leave an electron-deficient species that can bond to a lone pair on the reducing agent Not only are the potentials of such reactions affected by pH according to the Nernst equation, but so are the rates at which they can occur.
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