The equilibrium potential is then given by: It can be represented in an E-pH diagram for equal activity in and by a decreasing line in Fig. 15. Fig. 15 Partial E-pH diagram for the + 8H + + 6e - + 2H 2 O reaction Above the line, there is a region in which is predominantly stable but in equilibrium with smaller activities of . Below the line, is predominantly stable, with smaller quantities of . Pure Acid-Base Reactions. The previous computations showed that there are possible equilibria between the metal and its ions (such as Ni 2+ /Ni) and between the metal and its oxide (NiO/Ni). In the case of cobalt it is possible, as shown in Fig. 16, to determine the equilibria for Co 2+ /Co and for CoO/Co. The two equilibrium potential lines meet at some point P, and above them are two domains of stability for Co 2+ and CoO. These two species are submitted to an acid-base chemical reaction: Co 2+ + H 2 O € CoO + 2H + (Eq 18) which does not involve electrons. It does not depend, then, on the potential, and it will be represented by a vertical line. Point P in Fig. 16 is one point on that line located at a pH 6.3 for an activity of 1 in Co 2+ ions. Fig. 16 Partial E -pH diagram for Co 2+ /Co and CoO/Co The pH value of that line can also be computed from the chemical equilibrium, with the general equation: ∆G° = -RT In K or (Eq 19) where K is a constant, ν R is the stoichiometric coefficient of the reactants, ν P is the stoichiometric coefficient of the product, μ° R is the standard chemical potential of the reactant, and μ° p is the standard chemical potential of the product. In this case, the equilibrium as given in Eq 18 can be written: By assuming that (CoO) and (H 2 O) both have activities of 1 and by replacing the standard chemical potentials by their values given in the Atlas of Electrochemical Equilibria (Ref 13), it is possible to write: (Eq 20) and finally: log (Co 2+ ) = 12.6 - 2 pH (Eq 21) for (Co 2+ ) = 1 or pH = 6.3. This verifies the value obtained by tracing the two equilibrium lines. Figure 17(a) shows a partial E-pH diagram in which only three chemical species--Co, Co 2+ , and CoO--are considered. There are, however, other possible chemical species, such as CoO 2 and , that must be considered. This introduces new equilibria that modify the diagram to give Fig. 17(b). Fig. 17(a) Partial E-pH diagram for cobalt Fig. 17(b) E-pH diagram for cobalt The Water E-pH Diagram. Pourbaix diagrams are traced for equilibrium reactions taking place in water; consequently, the water E-pH diagram always must be considered at the same time as the system under investigation. Water can be decomposed into oxygen and hydrogen, according to the following reactions: 2H + + 2e - →H 2 and H 2 O → O 2 + 2H + + 2e - There are then two possible electrochemical equilibria for which the equilibrium potential can be determined by using the Nernst equation (Eq 12). For hydrogen: where (H + ) is the activity of H + in water, and p is the pressure of hydrogen near the electrode. Because, by convention, E° = O, the above equation can be rewritten as follows: (Eq 22) The equilibrium potential for the system H 2 /H 2 O can be represented in Fig. 18 by line a, which decreases with the pH. Fig. 18 The water E-pH diagram of 1 atm The equilibrium potential for the oxygen/water reaction is given by the Nernst equation: where p equals the pressure of O 2 near the electrode. The activity is, as usual , assumed to be 1, and the standard potential for 0 2 /H 2 O is computed to be 1.23 V. The following can then be written: (Eq 23) Equation 23 is represented under 1 atm pressure by line b in Fig. 18. It is interesting to note that the pressures of hydrogen and oxygen in the vicinity of the electrode are usually identical and nearly equal to the pressure that exists in the electrochemical cell. To be rigorous, the water vapor pressure should be taken into account, but it is frequently neglected as not being very significant. When the pressure increases, line b in Fig. 18 is displaced upward in the diagram, and line a is lowered. The result is that the domain of water stability increases with increasing pressure. The water diagram is so important for a good understanding of the corrosion behavior of a metal that it is usually represented by dotted lines in all Pourbaix diagrams (Ref 13). Practical Use of E-pH Diagrams The E-pH diagram is an important tool for understanding electrochemical phenomena. It provides much useful thermodynamics information in a simple figure. A few cases are presented here to illustrate its practical use in corrosion. Acid Corrosion of Nickel. A rod of nickel is immersed in an aqueous deaerated acid solution with a pH of 1 that contains 10 -4 g ion/L of Ni 2+ ions. The system is under 1 atm pressure. These conditions make it possible to simplify the E-pH diagram, as shown in Fig. 19. Fig. 19 E-pH diagram for nickel At the metallic nickel/water interface, two electrochemical reactions are possible, and their equilibrium potentials can be computed: Ni →Ni 2+ + 2e - with E Ni = -0.25 + 0.03 log a , which for concentration a = 10 -4 gives E Ni = -0.37 V (see Fig. 13). It follows that: 2H + + 2e - →H 2 with E H = -0.06 pH. At pH = 1, E H = -0.06 V. The nickel equilibrium potential is then more active than that of hydrogen, and electrons tend to flow from the negative nickel to the more positive hydrogen. Because both reactions occur on the same electrode surface, the electrons can go directly from the nickel to the hydrogen. The two reaction then tend to proceed under a common electrode potential of mixed potential, with a value somewhere between the nickel and hydrogen equilibrium potentials. The mixed potential E M is then above the Ni 2+ /Ni equilibrium potential in the region of Ni 2+ stability (Fig. 19). Nickel is then not stable at low pH in water, and it tends to oxidize or corrode, producing Ni 2+ , according to the reaction: Ni →Ni 2+ + 2e - This charge separation could stop the ionization reaction if there were not another chemical reaction--the reduction of H + . The mixed potential E M is located below the H + /H 2 equilibrium potential in a region where H 2 is stable (Fig. 19). As a result, H + can accept the electrons and is reduced according to 2H + + 2e - →H 2 , producing H 2 gas. The Pourbaix diagram explains the tendency for nickel to corrode in strong acid solutions. It does not indicate the rate of corrosion, however. This important information has to be obtained from a kinetic experiment, for example, by measuring the corrosion current in a polarization experiment. The Pourbaix diagram can also show that when the pH increases the difference between the nickel and the hydrogen equilibrium potential decreases in magnitude and that, consequently, the corrosion tendency becomes less important. For pHs between 6 and 8, Fig. 19 shows that hydrogen is more active than nickel. Under this condition, H + /H 2 can no longer accept the electrons from nickel. Moreover, the potential of the system is in this case below the equilibrium potential of nickel in the region of metal immunity. In pure water at room temperature, nickel does not corrode for pHs between 6 and 8. Moreover, an increase in pressure according to Eq 22 lowers the equilibrium line of H + /H 2 and does not change the equilibrium line of nickel. As a result, an increase in pressure favors the corrosion resistance of nickel. This behavior of nickel makes the metal slightly noble, and it is expected from the diagram to resist corrosion better than iron or zinc. The presence of elements, such as chloride, not considered in Fig. 19 may increase the corrosion tendency of nickel. For pHs higher than 8, NiO, Ni(OH) 2 , or Ni 3 O 4 can form, as can be seen in Fig. 19. These oxides may in some cases protect the metal by forming a protective layer that prevents or mitigates further corrosion. This phenomenon is called passivation (passivation is described in detail in the article "Kinetics of Aqueous Corrosion" in this Volume). The presence of chloride is dangerous here, because it may attack the protective layer and then favor corrosion. Figure 19 also illustrates that for very strong alkaline solutions nickel may corrode as when the potential is made anodic. Corrosion of Copper. Observation of the copper E-pH diagram in Fig. 20 immediately reveals that the corrosion of copper immersed in deaerated acid water is not likely to occur. The H + /H 2 equilibrium potential represented by line a is always more active than the Cu 2+ /Cu equilibrium potential. The H + ions are then always in contact with immune copper metal that cannot corrode. Fig. 20 Partial E-pH diagram for copper The presence of dissolved oxygen in nondeaerated solutions introduces another possible reaction--O 2 /H 2 O reduction, with an equilibrium potential more noble than that of Cu 2+ /Cu. The O 2 /H 2 O system is then a good acceptor for the electrons abandoned by copper oxidation. The two electrochemical reactions: O 2 + 2H + + 2e - →H 2 O and Cu →Cu 2+ + 2e - take place at the same metal/solution interface at a common mixed potential. This discussion assumes that the solution does not contain chloride or other compounds capable of forming soluble complexes with copper. In the presence of such impurities, another diagram must be traced for copper that in some conditions reveals different corrosion behavior. The diagram gives valuable information if all the substances present in the actual system under investigation are taken into account when it is traced. References 1. L. Pauling, General Chemistry, W.H. Freeman, 1964, p 338-360 2. J. O'M. Bokris and A.K.N. Reddy, Modern Electrochemistry, Vol 1, Plenum Press, 1977 3. J.M. Smith and H.C. Van Hess, Introduction to Chemical Engineering Thermodynamics, McGraw-Hill, 1975, p 159-162 4. K. Denbigh, Principles of Chemical Equilibrium, 2nd ed., Cambridge Press, 1981, p 133-186 5. M.G. Fontana, Corrosion Engineering, 2nd ed., McGraw-Hill, 1978, p 297-303 6. A.J. Bard, R. Parsons, and J. Jordan, Standard Potentials in Aqueous Solutions, Marcel Dekker, 1985 7. W.M. Latimer, Oxidation Potentials, Prentice-Hall, 1964 8. F.L. La Que, Corrosion Handbook, H.H. Uhlig, Ed., John Wiley & Sons, 1948, p 416 9. M.G. Fontana, Corrosion Engineering, 2nd ed., McGraw-Hill, 1978, p 12 10. Thermodynamique des Solutions Aqueuses Diluées, Potentiel D'oxydo-Réduction; (résumé de conférence), Bull. Soc. Chim. Belgique, Vol 48, Dec 1938 11. M. Pourbaix, Thermodynamics of Dilute Aqueous Solutions, Arnold Publications, 1949 12. R.W. Staehle, Marcel J.N. Pourbaix--Palladium Award Medalist, J. Electrochem. Soc., Vol 123, 1976, p 23C 13. M. Pourbaix, Atlas of the Electrochemical Equilibria, NACE, 1974 Kinetics of Aqueous Corrosion D. W. Shoesmith, Fuel Waste Technology Branch, Atomic Energy of Canada Ltd. Introduction THE AQUEOUS CORROSION of metal is an electrochemical reaction. For metal corrosion to occur, an oxidation reaction (generally a metal dissolution or oxide formation) and a cathodic reduction (such as proton or oxygen reduction) must proceed simultaneously. For example, the corrosion of iron in acid solutions is expressed as follows: Oxidation (anodic) Fe →Fe 2+ + 2e - (Eq 1) Reduction (cathodic) 2H + + 2e →H 2 (Eq 2) Overall reaction Fe + 2H + →Fe 2+ + H 2 (Eq 3) As a second example, for the corrosion of iron in a solution containing dissolved oxygen, the following expressions are used: Oxidation (anodic) Fe →Fe 2+ + 2e - Reduction (cathodic) O 2 + 4H + + 4e - →2H 2 O (Eq 4) Overall reaction 2Fe + O 2 + 4H + →2Fe 2+ + 2H 2 O (Eq 5) The reaction for metal dissolution (M →M n+ ) driven by the cathodic reaction O R, is: M + O →M n+ + R (Eq 6) where M is a metal, O is oxygen or another oxidizing reagent, n+ is the multiple of the charge, and R is the reduced species or reduction. The corrosion process has been written as two separate reactions occurring at two distinct sites on the same surface (Fig. 1a). These two sites are known as the anode, or metal dissolution site, and the cathode, or the site of the accompanying reduction reaction. Fig. 1 Schematics of two distinct corrosion processes. (a) The corrosion process M + O →M n+ + R showing the separation of anodic and cathodic sites. (b) The corrosion process involving two cathodic reactions. As shown in Fig. 1(a), the corroding metal is equivalent to a short-circuited energy-producing cell in which the energy is dissipated during the consumption of cathodic reagent and the formation of corrosion products. To maintain a mass balance, the amount of cathodic reagent consumed must be equal, in chemical and electrochemical terms, to the amount of corrosion product formed. Because electrons are liberated by the anodic reaction and consumed by the cathodic reaction, corrosion can be expressed in terms of an electrochemical current. Expressing the mass balance requirement in electrochemical terms, it can be stated that the total current flowing into the cathodic reaction must be equal, and opposite in sign to, the current flowing out of the anodic reaction (Fig. 1b). If measurable, this current can be taken as a gage of the rate of the corrosion process and therefore the rate of metal wastage. The current, known as the corrosion current, i corr , and the amount of metal corroded are related by Faraday's law: (Eq 7) . two distinct corrosion processes. (a) The corrosion process M + O →M n+ + R showing the separation of anodic and cathodic sites. (b) The corrosion process. indicate the rate of corrosion, however. This important information has to be obtained from a kinetic experiment, for example, by measuring the corrosion current