Ruthenium redox equilibria: 3. Pourbaix diagrams for the systems Ru-H2O and Ru-Cl--H2O doi:10.5599/jese.229 145 J. Electrochem. Sci. Eng. 6(1) (2016) 145-153; doi: 10.5599/jese.229 Open Access : : ISSN 1847-9286 www.jESE-online.org Original scientific paper Ruthenium redox equilibria 3. Pourbaix diagrams for the systems Ru-H2O and Ru-Cl - -H2O Igor Povar, Oxana Spinu Institute of Chemistry of the Academy of Sciences of Moldova, 3 Academiei str., MD 2028, Chisinau, Moldova Corresponding Author: ipovar@yahoo.ca; Tel.: +373 22 73 97 36; Fax: +373 22 73 97 36 Received: September 30, 2015; Accepted: February 18, 2016 Abstract On the basis of selected thermodynamic data, the standard electrode potentials of pos- sible half reactions in the Ru-H2O and Ru-Cl - -H2O systems have been calculated. Using the thermodynamic approach developed by the authors, the potential - pH and potential - pCl diagrams for the considered system have been built. Keywords Potential - pH diagram; Standard electrode potential; Soluble and insoluble ruthenium species. Introduction Thermodynamic analysis is a valuable and powerful tool in predicting, comprehending, and rationalizing the stability relations in redox reaction systems. In order to create an integrated picture of the thermodynamic properties of compounds of the element in its different valence states in both aqueous and solid phases, the diagrams potential - pH (or so-called Pourbaix diagrams) are generally used [1-16]. Pourbaix diagram is very important in predicting the thermo- dynamic equilibrium phases of an aqueous electrochemical system. These diagrams allow the gra- phical presentation of the thermodynamic properties of compounds of the given element based on the solution pH and the overall metal ion concentration in solution. The diagrams E(pH) are compact and contain a large quantity of information, which led to their wide application in various fields of science and technology, particularly in electrochemistry [1-9], hydrometallurgy [10-13] analytical chemistry [14,15], etc. In the presence of a small number of species in the redox system the construction of such diagrams does not present difficulties. The increase in the number of components and, in particular, the appearance of poly-nuclear species, calculating chemical and electrochemical equilibria becomes laborious. Authors [16] proposed an original procedure of http://www.jese-online.org/ mailto:ipovar@yahoo.ca J. Electrochem. Sci. Eng. 6(1) (2016) 145-153 RUTHENIUM REDOX EQUILIBRIA: 3. POURBAIX DIAGRAMS 146 calculation. Firstly, on the basis of the tabulated thermodynamic data, the thermodynamic stability areas of chemical species, depending on the solution pH for each valence state (degree of oxi- dation), are determined [17,18]. These areas are demarcated on diagrams by vertical lines. Then, a system of independent electrochemical equations for electrode reactions between chemical speci- es with varying degrees of oxidation, the predominance areas of which overlap, are drawn up. The electrode potentials of these reactions are linear functions of pH, which are depicted on diagrams. The potential - pH (Pourbaix) diagram constitutes an effective method of graphical representation of chemical and electrochemical equilibria, especially for systems under protolytic processes and contains as valence states oxides and hydroxides in the solid phase, protonated particles or hydroxo- complexes in solution. In addition to the "metal-water" system of a complexing agent that forms stable complexes with metal ions, the electrode potential often depends decisively on the ligand concentration CL 0 in solution. In this case, the Pourbaix diagrams are less informative because of a large number of lines as CL 0 functions and then the more useful are diagrams representing the dependence of the potential on CL 0 or log CL 0 . The ligand usually is taken in large excess relative to the metal ion (CL 0 >> CM 0 ) and therefore CL 0 . In particular, the influence of a number of such factors, as the medium acidity, the complexation and precipitation processes of the redox species is necessary to examine. This article has done some work in order to extend the usefulness of the Frost diagram. Since some equilibria are also some functions of the metal ion concentration CL 0 and the solution pH, for the construction of the diagram E(log [L]) the conditions CL 0 = const and pH = const are assumed. In this paper, the following procedure of calculating E-pH diagram is proposed: 1. Firstly, the predominance areas of different valence forms in function of pH, 0 M logC or 0 L log C are calculated; 2. On the basis of the diagrams ΔGr(n) [17-18], the thermodynamic stability of different valence forms toward disproportionation conditions is determined; 3. The system of electrochemical equations for electrode reactions between chemical species in different valence states, the predominance areas of which overlap, is composed; Based on standard thermodynamic data of participating species in specific reactions, the electrode potential is calculated by the equation E 0 ΔGr 0 /nF, where ΔGr 0 is the value of the standard Gibbs energy of electrode reaction; The electrode potentials of these processes are calculated as a function of 0 L C , respecting the conditions CM 0 = const and pH = const. The first two steps have been carried out in [17]. Theoretical considerations The Pourbaix diagram for the Ru-H2O system is presented in [1], but it suffers from a number of drawbacks: a. It is carried out on the basis of outdated thermodynamic data and their interpretation may lead to erroneous conclusions; b. The formation of solid phases is not taken into account; c. It is calculated for on metal ion concentration only. This paper aims to remove such deficiencies and calculating diagrams E-pH [16] on the basis of selected thermodynamic data [19]. In [18] it was shown that for ruthenium the disproportionation reactions are characteristic, in particular for the Ru(II), Ru(VI) and Ru(VII). In this paper the Frost diagrams are designed as a preliminary step for building E-pH diagrams. We will examine in detail the calculation of the E-pH diagram for CRu 0 =10 -4 mol/L. In the range 0 < pH < 14 ruthenium for the degree of oxidations Ru(II), Ru(V), Ru(VI) and Ru(VII) is represented I. Povar et al. J. Electrochem. Sci. Eng. 6(1) (2016) 145-153 doi:10.5599/jese.229 147 by single species, Ru 2+ , Ru2O5 (s), RuO4 2- , RuO4 - correspondingly, while for the valence states Ru(III), Ru(IV) and Ru(VIII), the hydrolysis is characteristic with formation of hydroxocomplexes. Ru(II) and Ru(IV), within a wide range of pH and CRu 0 , form also poorly soluble hydroxides. Authors [17,18] determined the thermodynamic stability areas of the following species for consecutive degrees of oxidation: Ru(VIII) H2RuO5 0.00 < pH < 11.53 HRu(OH)5 - 11.53 < pH < 14.00 Ru(IV) Ru(OH)2 2+ 0.00 < pH < 2.55 Ru4(OH)12 4+ 2.55 < pH < 4.43 RuO2 ∙ H2O (s) 4.43 < pH < 14.00 Ru(III) Ru 3+ 0.00 < pH < 1.76 Ru(OH)2 + 1.76 < pH < 4.42 Ru(OH)3 (s)∙H2O 4.42 < pH < 14.00 We will examine the calculation of respective values pHD for CRu 0 =10 -6 mol/L. From the ΔGr(n) diagram it follows that the reaction of disproportionation of Ru(V) to Ru(VIII) and Ru(IV) occurs between the pH values 1 and 3. This process is described by the equation: 2Ru2O5 (s) + H2O + 6H + = 3Ru(OH)2 2+ + H2RuO5 (1) The standard Gibbs energy variation 0 r G is equal to Gr 0 =Gf 0 (H2RuO5) + 3Gf 0 (Ru(OH)2 2+ - 2Gf 0 (Ru2O5 (s)) Gf 0 (H2O) = 70.59 kJ For reaction (1) the isotherm equation takes the form Gr =Gr 0 – 6RT ln[H + ] + 4RT ln CRu 0 The pHD value corresponds to the beginning of disproportionation, provided by the condition ΔGr = 0. Wherein, pH(ΔGr = 0) = 1.94 (the point A on the diagram E-pH). In the same way, we determine pHD for the following redox couples: 3RuO4 - + ½ H2O + 3H + = ½ Ru2O5 (s) + H2RuO5 , Gr 0 = 136.0 kJ Gr = Gr 0 + 3RT ln[H + ] + RT ln CRu 0 , pHD(Gr=0) = 5.94 (point B) 2RuO4 - + 3H + = ½ Ru2O5 (s) + RuO4 2- + 3/2 H2O, Gr 0 = 215.18 kJ Gr = Gr 0 + 3RT ln[H + ] + RT ln CRu 0 , pHD(Gr=0) = 10.57 (point C) Ru2O5 (s) + 3H2O = RuO4 2- + RuO2 2H2O + H + , Gr 0 = 158.97.18 kJ Gr = Gr 0 + 2RT ln[H + ] + RT ln CRu 0 , pHD(Gr=0) = 10.92 (point D). Next, we will analyze the equilibria between chemical species in solution and solid phase. We will consider only the electrode potentials of redox couples, the predominance of areas of which overlap. So we get: Ru(III) – Ru(0) Ei 0 / V 1. Ru 3+ +3e = Ru 0.00 < pH < 1.76 0.599 2. Ru(OH)2 + + 2H + + 3e = Ru + 2H2O 1.76 < pH < 4.42 0.668 3. Ru(OH)3 (s)×H2O + 3H + + 3e = Ru + 4H2O 4.42 < pH < 14.0 0.631 J. Electrochem. Sci. Eng. 6(1) (2016) 145-153 RUTHENIUM REDOX EQUILIBRIA: 3. POURBAIX DIAGRAMS 148 Ru(IV) – Ru(III) 4. Ru(OH)2 2+ + 2H + + e = Ru 3+ + 2H2O 0.0 < pH < 1.76 0.831 5. Ru(OH)2 2+ + e = Ru(OH)2 + 1.76 < pH < 2.55 0.612 6. ¼ Ru4(OH)12 4+ + H + + e = Ru(OH)2 + + H2O 2.55 < pH < 4.42 0.506 7. ¼ Ru4(OH)12 4+ + H2O + e = Ru(OH)3 (s)×H2O 4.42 < pH < 4.43 0.617 8. RuO2 (s)×2H2O + H + + e = Ru(OH)3 (s)×H2O 4.43 < pH < 14.0 0.777 Ru(V) – Ru(IV) 9. ½ Ru2O5 (s) + 3H + + e = Ru(OH)2 2+ + ½ H2O 1.94 < pH < 2.55 1.222 10. ½ Ru2O5 (s) + ½ H2O + 2H + + e = ¼ Ru(OH)12 4+ 2.55 < pH < 4.43 1.328 11. ½ Ru2O5 (s) + 3/2 H2O + H + + e = RuO2 (s) + 2 H2O 4.43 < pH < 10.92 1.168 Ru(VI) – Ru(V) 12. RuO4 2- + 3H + + e = ½ Ru2O5 (s) + 3/2 H2O 10.57 < pH < 10.92 2.816 Ru(VI) – Ru(IV) 13. RuO4 2- + 4H + + 2e = RuO2 (s) + 2H2O 10.92 < pH < 14.00 1.992 Ru(VII) – Ru(V) 14. RuO4 - + 3H + + 2e = ½ Ru2O5 (s) + 3/2 H2O 5.94 < pH < 10.57 1.701 Ru(VII) – Ru(VI) 15. RuO4 - + e = RuO4 2- 10.57 < pH < 14.00 0.586 Ru(VIII) – Ru(IV) 16. H2RuO5 + 6H + + 4e = RuOH2 2+ + H2O 0.00 < pH < 1.94 1.405 Ru(VIII) – Ru(V) 17. H2RuO5 + 3H + + 3e = ½ Ru2O5(S) + 5/2 H2O 1.94 < pH < 5.94 1.466 Ru(VIII) Ru(VII) 18. H2RuO5 + e = RuO4 - + H2O 5.94 < pH < 11.53 0.996 19. HRuO5 - + H + + e = RuO4 - + H2O 11.53 < pH < 14.00 1.678 The following expressions for electrode potentials (within the respective pH ranges) correspond to these electrode processes: Ru(III) – Ru(0) E1 = E1 0 + RT / 3F ln CRu 0 0.00 < pH < 1.76 E2 = E2 0 + RT / 3F ln CRu 0 + RT / 3F ln [H + ] 1.76 < pH < 4.42 E3 = E3 0 + RT / F ln [H + ] 4.42 < pH < 14.0 Ru(IV) – Ru(III) E4 = E4 0 + 2 RT / F ln [H + ] 0.00 < pH < 1.76 E5 = E5 0 1.76 < pH < 2.55 E6 = E6 0 + RT / F ln [H + ] - 3RT / 4F ln CRu 0 – ¼ RT / ln 4 2.55 < pH < 4.42 E7 = E7 0 + RT / 4F ln CRu 0 – ¼ RT / ln 4 4.42 < pH < 4.43 E8 = E8 0 + RT / F ln [H + ] 4.43 < pH < 14.0 Ru(V) – Ru(IV) E9 = E9 0 + 3 RT / F ln [H + ] - 3RT / 4F ln CRu 0 1.94 < pH < 2.55 E10 = E10 0 + 2RT / F ln [H + ] - RT / 4F ln CRu 0 – ¼ RT / ln 4 2.55 < pH < 4.43 E11 = E11 0 + RT / F ln [H + ] 4.43 < pH < 10.92 Ru(VI) – Ru(V) E12 = E12 0 + 3 RT / F ln [H + ] + RT / F ln CRu 0 10.57 < pH < 10.92 Ru(VI) – Ru(IV) E13 = E13 0 + 2 RT / F ln [H + ] + RT / 2F ln CRu 0 10.92 < pH < 14.00 Ru(VII) – Ru(V) E14 = E14 0 + 3 RT / 2F ln [H + ] + RT / 2F ln CRu 0 5.94 < pH < 10.57 I. Povar et al. J. Electrochem. Sci. Eng. 6(1) (2016) 145-153 doi:10.5599/jese.229 149 Ru(VII)– Ru(VI) E15 = E15 0 10.57 < pH < 14.00 Ru(VIII)-Ru(IV) E16 = E16 0 + 3 RT / 2F ln [H + ] 0 < pH < 1.94 Ru(VIII) –Ru(V) E17 = E17 0 + RT / F ln [H + ] + RT / 3F ln CRu 0 1.94 < pH < 5.94 Ru(VIII)-Ru(VII) E18 = E18 0 5.94 < pH < 11.53 E19 = E19 0 + RT / F ln [H + ] 11.53 < pH < 14.00 Results and discussion From the selected thermodynamic data [19], the standard electrode potentials of possible half- reactions in the Ru–Cl - -H2O system have been also calculated. The calculation results of redox equilibria and the areas of predominance of chemical species in the examined system are shown in the form of diagrams potential-log[Cl - ]. Er 0 represents the standard electrode potential for respective redox couple, calculated in the basis of thermodynamic data [19] by the formula. Er 0 = - Gr0. Finally, the E-pH diagrams for CRu 0 = 10 -4 and CRu 0 = 10 -6 mol/L are shown in Fig. 1 and 2. On their basis the following conclusions can be made: 1. With increasing of the total concentration of ruthenium: a. The areas of stability of Ru(OH)2 + , Ru(OH)2 2+ , RuO4 2- , RuO4 - significantly narrow; b. The thermodynamic stability areas of the solid phase Ru(OH)3∙H2O(S), RuO2∙H2O(S) and Ru2O5(S) increase; Ru(II) is thermodynamically unstable to dismutation in Ru and Ru(III) within the entire range of pH and CRu0 values. In [19] it is assumed that Ru2+ does not participate in the disproportionation process due to the preponderance of the kinetics conditions on the thermodynamic inhibition. Figure 1. The potential – pH diagrams for ruthenium compounds in the system Ru-H2O, CRu 0 = 10 -4 mol/L . 2. The most stable valence state of ruthenium is Ru(IV). These results are in good agreement with existing experimental data [19]. 1 0 2 4 6 8 10 12 14 -0,2 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 Ru(OH) 2 + R u (O H ) 2 2 + Ru 2 O 5(am) Ru(OH) 3 . H 2 O (am) Ru 4 (OH) 12 4+ Ru 3+ Ru RuO 2  2H 2 O (am) RuO 4 2- RuO 4 - HRuO 5 -H 2 RuO 5 E , V pH 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 E / V J. Electrochem. Sci. Eng. 6(1) (2016) 145-153 RUTHENIUM REDOX EQUILIBRIA: 3. POURBAIX DIAGRAMS 150 Figure 2. The potential – pH diagrams for ruthenium compounds in the system Ru-H2O, CRu 0 = 10 -6 mol/L . We will now examine the equilibrium between species in different valence states. Along with the reaction equation, the calculated standard electrode potential E 0 is indicated: Ru(III) – Ru(0) Ei 0 / V 1. Ru 3+ + 3e = Ru log[Cl - ] < -2.17 0.599 2. RuCl 2+ + 3e = Ru + Cl - -2.17 < log[Cl - ] < -1.57 0.566 3. RuCl2 + + 3e = Ru + 2Cl - -1.57 < log[Cl - ] < -0.54 0.525 4. RuCl3 0 + 3e = Ru + 3Cl - -0.54 < log[Cl - ] < 0.15 0.514 5. RuCl4 - + 3e = Ru + 4Cl - 0.15 < log[Cl - ] < 0.30 0.517 6. RuCl5 2- + 3e = Ru + 5Cl - 0.30 < log[Cl - ] < 0.40 0.523 7. RuCl6 3- + 3e = Ru + 6Cl - 0.40 < log[Cl - ] < 0.50 0.531 Ru(IV) – Ru(III) 8. Ru(OH)2 2+ + 2H + + e = Ru 3+ + 2H2O log[Cl - ] < -2.17 0.821 9. Ru(OH)2 2+ + 2H + + Cl - + e = RuCl 2+ + 2H2O -2.17 < log[Cl - ] < -1.57 0.950 10. Ru(OH)2 2+ + 2H + + 2Cl - + e = RuCl + + 2H2O -1.57 < log[Cl - ] < -1.39 1.043 11. Ru(OH)2Cl + + 2H + + Cl - + e = RuCl2 + + 2H2O -1.39 < log[Cl - ] < -0.54 0.961 12. Ru(OH)2Cl + + 2H + + 2Cl - + e = RuCl3 + 2H2O -0.54 < log[Cl - ] < -0.44 0.993 13. Ru(OH)2Cl4 2+ + 2H + + e = RuCl3 + Cl - + 2H2O -0.44 < log[Cl - ] < 0.15 0.915 14. Ru(OH)2Cl4 2+ + 2H + + e = RuCl4 - + 2H2O 0.15 < log[Cl - ] < 0.30 0.906 15. Ru(OH)2Cl4 2+ + 2H + + Cl - + e = RuCl5 2- + 2H2O 0.30 < log[Cl - ] < 0.40 0.888 16. Ru(OH)2Cl4 2+ + 2H + + 2Cl - + e = RuCl6 3- + 2H2O 0.40 < log[Cl - ] < 0.50 0.865 Ru(VIII) – Ru(IV) 17. H2RuO5 + 6H + + 4e = Ru(OH)2 2+ + 3H2O -2.50 < log[Cl - ] < -1.39 1.405 18. H2RuO5 + 6H + + Cl - + 4e = Ru(OH)2Cl + + 3H2O -1.39 < log[Cl - ] < -0.44 1.425 19. H2RuO5 + 6H + + 4Cl - + 4e = Ru(OH)2Cl4 2- + 3H2O -0.44 < log[Cl - ] < 0.50 1.445 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 -0,2 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 Ru(OH) 3 . H 2 O (am) Ru Ru(OH) 2 + Ru 5+ RuO 4 2-RuO2 . 2H 2 O R u 4 (O H ) 12 4+ Ru(OH) 2 2+ Ru 2 O 5(am) RuO 4 - HRuO 5 -H 2 RuO 5 E , V pH 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 E / V I. Povar et al. J. Electrochem. Sci. Eng. 6(1) (2016) 145-153 doi:10.5599/jese.229 151 Finally, the electrode potential depending on the Cl - concentration is calculated: Ru(III) – Ru(0) (= (RT / 3F) ln10) E1 = E1 0 +  logCRu 0 log[Cl - ] < -2.17 E2 = E2 0 +  logCRu 0 -  log[Cl - ] -2.17 < log[Cl - ] < -1.57 E3 = E3 0 +  logCRu 0 - 2 log[Cl - ] -1.57 < log[Cl - ] < -0.54 E4 = E4 0 +  logCRu 0 - 3 log[Cl - ] -0.54 < log[Cl - ] < 0.15 E5 = E5 0 +  logCRu 0 - 4 log[Cl - ] 0.15 < log[Cl - ] < 0.30 E6 = E6 0 +  logCRu 0 - 5 log[Cl - ] 0.30 < log[Cl - ] < 0.40 E7 = E7 0 +  logCRu 0 - 6 log[Cl - ] 0.40 < log[Cl - ] < 0.50 Ru(IV) – Ru(III) (= (RT / F) ln10) E8 = E8 0 + 2 log [H + ] log[Cl - ] < -2.17 E9 = E9 0 + 2 log [H + ] +  log[Cl - ] -2.17 < log[Cl - ] < -1.57 E10 = E10 0 + 2 log [H + ] + 2 log[Cl - ] -1.57 < log[Cl - ] < -1.39 E11 = E11 0 + 2 log [H + ] +  log[Cl - ] -1.39 < log[Cl - ] < -0.54 E12 = E12 0 + 2 log [H + ] + 2 log[Cl - ] -0.54 < log[Cl - ] < -0.44 E13 = E13 0 + 2 log [H + ] -  log[Cl - ] -0.44 < log[Cl - ] < 0.15 E14 = E14 0 + 2 log [H + ] 0.15 < log[Cl - ] < 0.30 E15 = E15 0 + 2 log [H + ] +  log[Cl - ] 0.30 < log[Cl - ] < 0.40 E16 = E16 0 + 2 log [H + ] + 2 log[Cl - ] 0.40 < log[Cl - ] < 0.50 Ru(VIII) – Ru(IV) (= (RT / 4F) ln10) E17 = E17 0 + 6 log [H + ] -2.50 < log[Cl - ] < -1.39 E18 = E18 0 + 6 log [H + ] +  log[Cl - ] -1.39 < log[Cl - ] < -0.44 E19 = E19 0 + 6 log [H + ] + 4 log[Cl - ] -0.44 < log[Cl - ] < -0.50 These functions along with predominance areas of the species in solution are diagrammatically shown in Fig. 3 as the potential – log [L] diagram. Compared with diagrams E - pH, on the E (log [L]) diagram a considerable number of chemical species of ruthenium(IV) is outside of the thermodynamic stability area of water (the dotted line a). Within the entire range of the [Cl - ] values, -2.20 < log[Cl - ] < 0.50, the valence states of ruthenium Ru(II), Ru(V), Ru(VI) and Ru(VII) are unstable with respect to dismutation processes. J. Electrochem. Sci. Eng. 6(1) (2016) 145-153 RUTHENIUM REDOX EQUILIBRIA: 3. POURBAIX DIAGRAMS 152 Figure 3. The potential - log[L] diagram for the system Ru-Cl - -H2O, pH 0, CRu0 = 10 -6 mol/L. Conclusions 1. On the basis of the thermodynamic data, the area of thermodynamic stability of Ru chemical species as a function of pH (or pCl) for each degree of oxidation has been determined. 2. Based on the Gr = f(n)diagrams calculated for several values of pH, a narrow pH value is determined, in which the dismutation of appropriate form takes place. Based on thermody- namic analysis, the exact pHD value of the beginning of disproportionation (or compropor- tionation) is found. After that, the diagrams of heterogeneous chemical equilibria, developed by us earlier, as a function of pH and the total concentration of metal ion in solution, are built. 3. It is derived a system of electrochemical equations of electrode reactions between chemical species in different degrees of oxidation, the predominance areas of which are overlapped. Finally, the dependenceGr or E on pH (or pCl) is calculated for different redox pairs. Depending on pH and pE, as well as the total concentration of inorganic ligands, the Ru compounds may undergo various transformations to produce a whole range of chemical forms in solution. The potential—pH and potential-pCl diagrams of the Ru-H2O and Ru-Cl - -H2O systems have been constructed. The calculated Pourbaix diagrams within our approach agree well with the previously reported experimental data. 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