Ruthenium redox equilibria 3 . Pourbaix diagrams for the systems RuH 2 O and Ru-Cl-- H 2 O

On the basis of selected thermodynamic data, the standard electrode potentials of possible 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.


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][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16].Pourbaix diagram is very important in predicting the thermodynamic equilibrium phases of an aqueous electrochemical system.These diagrams allow the graphical 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][2][3][4][5][6][7][8][9], hydrometallurgy [10][11][12][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 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 oxidation), 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 species 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 hydroxocomplexes 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 C L 0 in solution.In this case, the Pourbaix diagrams are less informative because of a large number of lines as C L 0 functions and then the more useful are diagrams representing the dependence of the potential on C L 0 or log C L 0 . The ligand usually is taken in large excess relative to the metal ion (C L 0 >> C M 0 ) and therefore C L 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 C L 0 and the solution pH, for the construction of the diagram E(log [L]) the conditions C L 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 logC are calculated; 2. On the basis of the diagrams ΔG r (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 ΔG r 0 /nF, where ΔG r 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 C M 0 = const and pH = const.The first two steps have been carried out in [17].

Theoretical considerations
The Pourbaix diagram for the Ru-H 2 O 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 C Ru 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 by single species, Ru 2+ , Ru 2 O 5 (s), RuO 4 2-, RuO 4 -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 C Ru 0 , form also poorly soluble hydroxides.Authors [17,18] determined the thermodynamic stability areas of the following species for consecutive degrees of oxidation: 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: The standard Gibbs energy variation 0 r G  is equal to 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: The following expressions for electrode potentials (within the respective pH ranges) correspond to these electrode processes:

Results and discussion
From the selected thermodynamic data [19], the standard electrode potentials of possible halfreactions in the Ru-Cl --H 2 O 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 -].E r 0 represents the standard electrode potential for respective redox couple, calculated in the basis of thermodynamic data [19] by the formula.E r 0 = -Gr0.Finally, the E-pH diagrams for C Ru 0 = 10 -4 and C Ru 0 = 10 -6 mol/L are shown in Fig. 1 and 2.
On their basis the following conclusions can be made: 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.2. The most stable valence state of ruthenium is Ru(IV).These results are in good agreement with existing experimental data [19].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:

1 . 2 +
With increasing of the total concentration of ruthenium: a.The areas of stability of Ru(OH) thermodynamic stability areas of the solid phase Ru(OH) 3 •H 2 O (S) , RuO 2 •H 2 O (S) and Ru 2 O 5(S)increase;