LECTURE 12 - Redox Potentials and Equilibria Note: Slide numbers refer to the PowerPoint presentation which accompanies the lecture. Redox, slide 1 here INTRODUCTION Redox, slide 2 here The problem of equilibrium in geochemistry may be approached in several ways. Equilibrium may be treated by a free energy approach (ΔG = ΔH - TΔS) or with equilibrium constants. A third method, which applies to many geochemical problems, uses oxidation and reduction reactions. These reactions are often written as half-cells, or two reactions, one involving an oxidation step and another involving a reduction step. The half-cell reactions can be combined into a single reaction and, if the appropriate data is available, an equilibrium constant can be calculated. Redox, slide 3 here Oxidation occurs when an atom or ion gives up one or more electrons, so that its formal valance state increases. 12-1 The symbol e - will be used to represent an electron. Reduction occurs when an atom or ion accepts electrons, so that its formal valance is reduced. 12-2 These reactions can be combined by adding the equations and eliminating the electrons: 12-3 Redox, slide 4 here The video shows the processes of oxidation and reduction. Redox, slide 5 here 1
This video shows the rational for simple reactions, the burning of methane, the burning of hydrogen, and iron in hydrochloric acid. Redox, slide 6 here 12-4 Here, one reduction step (Cr 6+ Cr 3+ ), one oxidation step (Fe 2+ Fe 3+ ) and one step involving neither oxidation nor reduction (H + H 2 O) exists. Redox, slide 7 here This video shows a step by step process for balancing redox reactions, first in acid solution, than in basic solution. Redox, slide 8 here Measuring the absolute value of the potential for an ion to gain or lose an electron is impossible. Therefore, an arbitrary standard is chosen: 12-5 Redox, slide 9 here This has an arbitrary standard potential (at standard conditions [H 2 ] = 1 atm. and 25 C) E = 0.00 volts. The symbol E specifically denotes standard potential, whereas E would denote a potential at other than standard conditions. Redox, slide 10 here Once a standard is chosen, all other half-cell reactions can be defined in terms of the standard. Example: Thus, 12-6 12-7 2
Choice of a plus or minus sign was originally arbitrary, and unfortunately both choices have been used. The literature is divided approximately fifty-fifty. The choice is not important, if it is used consistently. When reading the literature, knowing which convention the author is using is important. Krauskopf (1979) chooses to express any reaction that is more reducing than H (able to reduce H) as negative, and we will use that convention in this course. Redox, slide 11 here A table of electrode potentials (these are readily available) can be used to judge which reactions are thermodynamically favorable. A reduced ion will react with any oxidized species less negative than itself. Redox, slide 12 here Thus, uranium U 3+ will reduce tin Sn 2+, 12-8 but not magnesium, Redox, slide 13 here 12-9 12-10 Redox, slide 14 here A reaction's potential difference can be found by combining two half cell reactions: 12-11 12-12 Equation 12-9 was reversed and added to two times equation 12-8 to get equation 12-11. Note that doubling a reaction does not affect the potential. Potential is an intensive variable like density or temperature. Intensive variables do not depend on the amount of material present. When a reaction is reversed, the listed potential must be subtracted, not added. 3
Redox, slide 15 here The potential for a reaction may be related to the free energy of the reaction through the equation: 12-13 where n = # of electrons transferred, f = Faraday constant = 23,061 calories/volt, E is the potential in volts (Note that the Faraday constant may also be expressed as 96,420 coulombs if the energies are to be given as volt-coulombs, which equal joules.) Redox, slide 16 here 12-14 Thus, for equation 12-11, if the reaction is at standard conditions the standard potential, E, is used to calculate the standard free energy, ΔG. The standard free energy can be used to calculate the equilibrium constant, as shown in equation 12-15. Redox, slide 17 here R is the gas-law constant and is equal to 1.987 cal/ mole or 8.314 joules/mole. T is the absolute temperature, in Kelvin. ( C + 273.15 = Kelvin). K is the equilibrium constant. The 2.303 factor is introduced to convert a natural logarithm to a base ten logarithm. This equation is a specific case of the Nernst equation shown in equation 12-16. 12-15 4
Redox, slide 18 here 12-16 Redox, slide 19 here The relationship of E to K eq can easily be derived: 12-17 12-18 Values of E can be determined for solutions of geologic interest. Thus, in a complex situation, the overall tendency of the solution to oxidize or reduce can be measured. Redox, slide 20 here The usual method of determining E is to insert two electrodes into the solution of interest. One electrode is platinum, and the other is hydrogen. A hydrogen electrode can be made by allowing hydrogen at one atmosphere to bubble over a platinum electrode (see Drever, 1988, pp.282-285, for a discussion of electrodes). This technique s advantage is that we do not need to know the exact reactions taking place. Potential determined in this way is known as the redox potential, E h. E h and ph are similar: Redox, slide 21 here ph: E h : Measures the ability of a solution to accept or donate hydrogen ion Measures the ability of a solution to accept electrons from a reducing agent, or supply electrons to an oxidizing agent Redox, slide 22 here 5
For example, let us consider a solution with a measured E h of 0.48 volts. This solution is known be acidic and to contain iron. However, we wish to know whether ferrous or ferric ion is present. The potential for the oxidation of ferrous ion to ferric ion is: 12-19 Since our measured potential is more reducing than this value, we qualitatively expect that ferrous ion will dominate. To calculate the ratio of ferric to ferrous ion: 12-20 Redox, slide 23 here 12-21 12-22 In our water sample, for each ferric ion, there are more than 82,000 ferrous ions. This calculation assumes that no complexes are formed which may not always be true, especially if organic anions are present. Redox, slide 24 here One problem with the use of measured E h values is the speed of the reactions. As previously seen, kinetic barriers may keep a reaction from proceeding quickly to completion. If the reaction is slow, the measured E h value will be less than the equilibrium values and will usually be too low. Reactions involving oxygen often have this problem. Such reactions often involve a series of steps, one of which is very slow. Use of the platinum electrode often results in erroneously low values of E h for slow reactions. Thus, E h values may be used to set limits on the types of processes that are possible but may not precisely define the exact process. USE OF REDOX POTENTIALS IN GEOCHEMISTRY 6
The application of redox potentials to geologically and geochemically useful situations usually involves the simultaneous determination of E h and ph. The use of these two parameters allows the theoretical predication of the behavior of systems. These predications are often useful and the exercise is therefore deemed to have merit. Redox, slide 25 here One method of using E h and ph values is to plot a diagram of E h versus ph. The ph is plotted on the abscissa with 0 on the left and 14 on the right. E h is plotted on the ordinate, with negative values at the bottom increasing toward positive values at the top. This type of representation is primarily useful for low temperature environments in which water is stable and ph is a useful parameter. In environmental geochemistry, this condition is easily met, so we find such diagrams to be of value. Sedimentary processes also may be treated with E h -ph diagrams. Before considering the actual use of such diagrams, we should consider some limits found in most terrestrial environments. Pure oxygen is the strongest oxidizing agent. If an agent, stronger than oxygen, existed in nature, it would react with water to liberate oxygen. This reaction is: Redox, slide 26 here 12-23 The Nernst equation for this reaction is: Redox, slide 27 here 12-24 At the earth's surface we may use 0.2 atm for the oxygen concentration and rewrite equation 12-24 in terms of ph: 12-25 Empirically, it is found that the value of 1.22 is too high and Baas Becking et al. (1960) suggest a working value of 1.04. 7
Redox, slide 28 here Reducing agents in nature cannot be stronger than hydrogen since they would reduce water and liberate hydrogen. 12-26 Redox, slide 29 here The Nernst equation for this reaction is: 12-27 Since [H 2 ] cannot exceed one atmosphere near the surface, equation 12-27 reduces to: Redox, slide 30 here 12-28 The limits on ph are easier to set. Often, the ph in natural systems ranges between 4 and 9 but we have seen exceptions to that rule. Using limits of 4 to 9 for the ph allows us to draw a parallelogram in E h -ph space. The boundaries of this parallelogram are the natural limits of most aqueous systems. Redox, slide 31 here Figure 12-1 illustrates the general appearance of E h -ph diagrams and outlines the range of values we can expect to see in natural waters. In using the Nernst equation we should use activity products instead of concentration products. 8
Redox, slide 32 here Activity is a thermodynamic concept that considers the actual reactivity instead of the concentration. Activity may be thought of as an effective concentration. Activities are harder to determine than concentrations and the formalism of E h in terms of activities may require the conversion to and from volts and activities. To overcome this disadvantage, the concept of pe was introduced. Redox, slide 33 here By analogy with ph, pe = - log a e - (Hostettler, 1984). To see how we can apply the formalism of pe to a real situation consider the following equation: Redox, slide 34 here Figure 12-1 12-29 9
We can write an expression for the equilibrium constant as follows: 12-30 Redox, slide 35 here 12-31 12-32 Redox, slide 36 here K eq may be calculated from standard thermodynamic data (see Krauskopf, 1979, p.561 or Drever, 1988, p. 410). 12-33 Redox, slide 37 here 12-34 10
12-35 Redox, slide 38 here 12-36 From equation 12-32 it follows that: 12-37 Redox, slide 39 here Generalizing this for the reduction of an oxidized species with n electrons: 12-38 12-39 Redox, slide 40 here Thus, expressing the activity of electrons in solution in units of volts (E h ) or in units of electron activity (as either a e - or pe) is possible. The two quantities may be related: 12-40 Redox, slide 41 here At 25 C, pe = 16.9 E h and E h = 0.059 pe (Drever, 1988, p.285). 11
REFERENCES L.G.M. Baas Becking, I.R. Kaplan, and D. Moore, Limits of the natural environment in terms of ph and oxidation-reduction potentials, Jour. Geol., 68, 243-284, 1960. James I. Drever, The Geochemistry of Natural Waters, second edition, Prentice Hall, Englewood Cliffs, 1988. J.D. Hostettler, Electrode electrons, aqueous electrons, and redox potentials in natural waters, Am. J. Sci., 284, 734-759, 1984. Konrad B. Krauskopf, Introduction to Geochemistry, McGraw-Hill, New York, 1979. 4241LN12_PP_F16.wpd October 11, 2016 12