The relationship between the open-circuit potential of a galena electrode and the dissolved lead concentration

HydrometaUurgy, 23 (1990) 341-352

341

Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands

The Relationship b e t w e e n the Open-Circuit P o t e n t i a l of a Galena Electrode and the D i s s o l v e d Lead Concentration M.D. PRITZKER* and R.H. YOON

Department of Mining and Minerals Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061 (U.S.A.) ( Received January 22, 1988; revised and accepted December 23, 1988)

ABSTRACT Pritzker, M.D. and Yoon, R.H., 1990. The relationship between the open-circuit potential of a galena electrode and the dissolved lead concentration. HydrometaUurgy, 23: 341-352. Electrochemical experiments and thermodynamic mass balance calculations have been conducted to determine the relationship between the open-circuit potential of a galena electrode and the dissolved lead concentration at pH = 0, 1.1 and 4.6. The experiments have been performed in such a way that the potential covers the range from reducing values where Pb ° is present on the electrode surface to oxidizing ones where the anodic dissolution of PbS takes place. The results indicate that the response of this system is characterized by a region at low potentials where the electrode behaves essentially as a Pb ° electrode and another at higher potentials where the electrode has reverted to its original PbS character. The transition between these two regions is sharp and occurs when all ( p H = 0 and 1.1 ) or most (pH=4.6) of the Pb ° has dissolved from the surface. The pH has also been found to have a significant effect on the reversibility of the system. At pH = 0, the potential obeys Nernstian behavior along both portions of the electrode response. Raising the pH to 1.1 causes the observed potentials along the lower Pb°-like segment to deviate anodically from the reversible values. When a pH of 4.6 is reached, the upper segment shows an anodic shift as well.

INTRODUCTION

In the analysis of data obtained from electrochemical experiments, the Nernst equation is often used to relate the electrode potential to the electrolyte composition. However, there have been relatively few studies in which the concentration of an electro-active species is monitored as a function of the potential. One of the few such studies on a sulfide system was that done by Brodie [ 1 ] *Present address: Department of Chemical Engineering, University of Waterloo, Waterloo, Ont. N2L 3G1 (Canada).

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© 1990 Elsevier Science Publishers B.V.

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M.D. PRITZKER AND R.H. YOON

who was able to vary the open-circuit potential of a galena electrode immersed in 1.0 M HCI04 solution ( p H = 0 ) and measure the concentration of lead in the solution resulting from the dissolution of the electrode. One objective of this communication is to compare the relationship between the potential and the lead concentration determined experimentally by Brodie to the one predicted on the basis of mass balance calculations assuming conditions of thermodynamic equilibrium. A similar attempt was made by Pritzker and Yoon [ 2 ], but the activity coefficients of the lead-bearing species were not considered. Additional experiments have been conducted in the present work in 0.1 M HC104 (pH = 1.1 ) and 0.5 M CH3COOH/0.5 M CH3COONa ( p H = 4.6) solutions to see whether or not a galena electrode obeys Nernstian behavior in these electrolytes of different pH values. EXPERIMENTAL

Details concerning the galena sample, electrode preparation and the electrochemical instrumentation have been reported elsewhere [2,3]. The experiments were carried out either in 0.1 M HC1Q (pH = 1.1 ) or 0.5 M CH3COOH/ 0.5 M CH3COONa (pH--4.6) solutions. Precautions were taken to deoxygenate the solutions by purging them with high-purity nitrogen for at least one hour before each test and throughout the experiment. Following the method described by Brodie [ 1 ] and Pritzker and Yoon [2 ], the galena electrode was polarized cathodically in an electrolyte solution at a current density of 1 mA cm -2 for one hour. This reduced the electrode, leaving behind a layer of metallic lead on the surface and releasing H2S into the solution. The electrode was then transferred to another vessel containing a fresh, de-aerated solution of the same electrolyte. An anodic current of 1 mA cm -2 was applied for a short period of time (on the order of one minute) and then switched off. During this relaxation period while the circuit was open, the electrode potential was continually monitored until a steady-state value was reached and then a 5 ml aliquot of the solution was withdrawn for analysis of lead using a plasma emission spectrometer. This entire procedure was repeated over and over again, and in so doing, it was possible to increase the steady-state potential each time and to relate it to the dissolved lead concentration. RESULTS AND DISCUSSION

pH=O.O The experimental results obtained by Brodie [ 1 ] are shown as open circles in Fig. 1. In the early stages of the anodic polarization, the rest potential remains almost constant in the range of - 2 7 0 to - 2 4 0 mV, while the [Pb 2+ ] increases from 2.5 to 20 ppm. Beyond this point, the potential rises sharply as

RELATIONSHIP BETWEEN POTENTIAL OF GALENAELECTRODE AND LEAD CONCENTRATION

pH LU

0.0

: o ~(~ i

200

"lco

343

io io o

Brodie

(1969)

Ii i i d i

calculated

i i i

0 i

oi

-200

I 10

Total

Pb concentration

100

, ppm

Fig. 1. Effect of potential on the dissolution of a galena electrode t h a t has been cathodically polarized and immersed in a stirred 1 M HC104 solution. T h e solid line represents the results of t h e r m o d y n a m i c calculations and the vertical dashed line represents the complete dissolution of P b ° formed during the cathodic polarization.

the lead concentration levels off at about 28 ppm. This continues until a potential of 240 mV is reached, whereupon [Pb 2+ ] begins to increase again sharply with small changes in the open-circuit potential. Brodie was able to match the flat portions of the curve with the equilibrium potentials for the reactions: P b S = P b 2+ + S o + 2e

(1)

above E h - - 2 4 0 mV, and: Pb ° = Pb 2+ + 2e

(2)

below Eh = - 240 mV. Furthermore, he reasoned that the region in which the potential rises steeply corresponds to the galena surface going from one which is saturated with P b ° to one which is saturated with S °. This can occur while the dissolved lead concentration in the solution remains essentially constant because a variation of about 10 -6 mol% of lead (or sulfur) in the galena composition is all that is needed for the transition from the one type of surface to the other. Although Brodie was able to account for the flat portions of his curve in terms of equilibrium thermodynamics, he did not attempt to predict the lead concentration [Pb 2+ ] at which the transition from a Pb°-saturated surface to a S°-saturated one occurs. The question therefore remains as to whether the entire curve can be predicted by bulk equilibrium thermodynamics. In previous work, mass balance calculations were carried out for the P b S - H 2 0 system which yielded the relationship between Eh and [Pb 2+ ] assuming conditions of thermodynamic equilibrium [2,4]. It will be interesting to compare the results of calculations of this type to the experimental data obtained by Brodie, focusing attention on the steep portion of the curve.

344

M.D. PRITZKER AND R.H. Y 0 0 N

When both PbS and Pb ° are present, the mass balance equations for lead and sulfur can be written as: lead

npbs +nebo +2:(Pb) =Npb

(3)

sulfur

n,bS +2:(S) =Ns

(4)

where npbs and npbo are the number of moles of PbS and Pb °, respectively, present per liter of solution, X(Pb) and X(S) are the total concentrations of lead- and sulfur-bearing soluble species, and Npb and Ns are the total lead and sulfur content in the system. Subtracting Eq. 4 from Eq. 3 yields: npbo +2:(Pb) - X ( S ) =Npb --Ns

(5)

We can simplify this expression by recognizing that the last remaining elemental lead on the galena surface disappears when the vertical portion of the curve is reached (i.e., npbo = 0). The value of Npb--Ns on the right-hand side of Eq. 5 corresponds to the deviation from the ideal 1 : 1 lead/sulfur stoichiometry of pure galena resulting from the initial cathodic polarization and transfer into fresh electrolyte. Since the decomposition of each mole of PbS during cathodic polarization leads to the formation of one mole of Pb ° on the surface and the release of one mole of H2S to the solution, the value of N p b - - Ns will just be equal to the number of moles of Pb ° produced, i.e. Xpb. The treatment of Eq. 5 can be further simplified by the fact that at pH = 0, all of the soluble lead- and sulfur-bearing species are in the form of Pb 2+ and H2S. Substitution of all of these modifications into Eq. 5 leads to the following expression: [Pb 2+ ] - [HeS(aq) ] - [H2S (g)] -~-Xpb

(6)

The concentrations of the species Pb 2+, HeS (aq) and H2S ( g ) are related by the equilibrium conditions for the reactions: PbS + 2H + = P b 2+ + H2 S(aq)

(7)

and: H2S(g) =H2S(aq)

(8)

Using the free energy data for the species in Eqs. 7 and 8 [2], we can write [H2S (aq) ] and [HzS (g) ] in terms of [Pb 2+ ], and in so doing convert Eq. 6 to an equation with only one unknown: [pbz + ] _ 3.681× 10 -s [pb2 +] =Xpb

(9)

which can be readily solved once Xpb is specified. In deriving this expression, we have taken into account deviations from ideal solution behavior by using the Davies equation to estimate activity coefficients, ~ [5]:

RELATIONSHIP BETWEEN POTENTIAL OF GALENA ELECTRODE AND LEAD CONCENTRATION

log Yi = - AZ~ [[ 1 Ti~/2 ~/e

0.2i 1

345

(10)

where A is a constant that depends on temperature and solvent (A =0.51 for water at 25 ° C), Zi is the valence of the ion and I is the ionic strength of the solution. According to his experimental procedure, Brodie cathodically polarized the galena at 1 mA cm -2 for one hour. Assuming a current efficiency of 100% for the reduction of galena, we estimate Xeb to be 1.27 × 10-4 mol l-1 (26.3 ppm ). Substitution of this value into Eq. 9 yields [Pb2+] =2.66× 10 -4 M (or 55.0 ppm). This is then plotted as the vertical segment between the lines corresponding to the Nernst equations for reactions 1 and 2 to yield the solid lines in Fig. 1. It should be noted that in a previous publication [2], a similar calculation was carried out and the results were compared to the experimental data of Brodie. However, at that time, Yiwas assumed to be equal to unity for all species. The effect of incorporating non-ideal activity coefficients has been to shift the steep portion of the theoretical curve toward the right. As can be seen, thermodynamics predicts that the mineral solubility along the vertical portion should be about twice as large as is actually observed (55.0 ppm versus 28 ppm). Apparently, the view of the three phases, i.e. the PbS substrate, the Pb ° layer on the surface and the electrolyte, being in equilibrium with each other does not adequately describe the observed behavior. Just what may explain the situation better becomes more obvious when it is noted that the lead concentration at which the open-circuit potential is observed to rise steeply, i.e. 28 ppm, is very close to the value Xpb (26.3 ppm). The close agreement between these two values implies that up to this point in the experiment, electro-dissolution of the electrode has only involved the layer of elemental lead, but not the galena underneath. As long as Pb ° is present, the application of anodic current causes it to dissolve reversibly according to the Pb°/Pb 2+ couple. This corresponds to the lower inclined line segment below [Pb 2+ ] = 28 ppm in Fig. 1. The galena is not in thermodynamic equilibrium with the Pb°/ electrolyte interface and acts essentially as an electrical contact between the external circuit and the outer surface. Thus, the galena electrode behaves as if it is a Pb ° electrode until all the Pb ° is dissolved. For this reason, one can predict the critical lead ion concentration (vertical dashed line) from the amount of Pb ° formed during cathodic polarization. When the final amount of Pb ° has just disappeared, the electrode reverts to its galena-like character. However, the potential is initially too low ( ~ - 2 4 0 mV in Fig. 1 ) for galena to oxidize and, consequently, it rapidly rises until it reaches a value where reaction 1 can begin to occur (i.e. ~ 240 mV). This rapid rise, of course, constitutes the steep portion of the curve. The match between the calculated line and the data obtained by Brodie above 240 mV indicates

M.D.PRITZKERANDR.H.YOON

346

that the electrode is behaving reversibly at this pH once reaction 1 begins to proceed.

pH=l.1 Two experiments were conducted on the galena electrode immersed in a 0.1 M HC104 solution at pH--1.1. The procedure of the first one was essentially the same as that used by Brodie, with the exception that the galena was cathodically polarized at a current of -0.92 mA cm -2 for 75 min. In the second test, an additional and more important modification to the original procedure was made. Instead of transferring the electrode to a fresh electrolyte immediately after cathodic polarization, we kept the galena in the same solution for both the cathodic and anodic portions of the experiment. The idea behind this was to try to preserve the 1:1 lead/sulfur stoichiometry of pure galena in the entire system. (It should be noted that the reaction vessel was kept airtight to minimize the loss of H2S to the atmosphere.) Comparison with the first test would show whether the H2S present in the electrolyte from the reduction of galena would have an effect on the E h - [ Pb 2+ ] relationship during the subsequent anodic polarization. The experimental results are shown along with those calculated from the mass balance thermodynamic calculations in Fig. 2. Two sets of calculations have been performed to simulate the different experiments that were conducted. For the one corresponding to the experiment in which the electrode was transferred to a fresh solution after cathodic polarization, the computation was carried out in a similar manner as for the case o f p H - - 0 (Fig. 1). For the other, it was assumed that none of the H2S produced during the cathodic poI

300

pH 1.1

w

•

1:1 P b / S

o

excess Pb

100 --

calculated

g I00 0

excess Pb

J 1:1 P b / S

o. J --O

-300 ]

10

I 100

Total Pb c o n c e n t r a t i o n , ppm

Fig. 2. Anodic dissolution of a galena electrode immersed in a stirred 0.1 M H C I Q solution at pH = 1.1. The solid lines represent two cases of thermodynamic calculations.

RELATIONSHIP BETWEEN POTENTIAL OF GALENA ELECTRODE AND LEAD CONCENTRATION

347

larization is lost to the atmosphere and, consequently, the right-hand side of Eq. 5 was set equal to zero. It is evident that with the exception of an anodic shift in the lower segment of the curves, the presence of H2S in the electrolyte does not affect the measured relationship between Eh and [ Pb 2+ ]. The potential begins to rise steeply when the dissolved lead concentration reaches 7.1 ppm in both cases. Comparison of both of these sets of data with the calculated results (shown as solid lines) shows that there is poor quantitative agreement between them. For one thing, the inclined segments at low potential for both calculations coincide and are considerably cathodic to those determined experimentally. Secondly, the calculations predict the steep rise portion to occur at a position considerably different from what is observed. Moreover, unlike the actual measurements, the position of the vertical segment depends very much on the overall lead/ sulfur stoichiometry in the system (i.e. Xpb in Eq. 6). The vertical segment occurs at [Pb e+ ] = 3.7 ppm for the case of 1:1 lead/sulfur stoichiometry, but at 9.1 ppm when we allow for a sulfur deficiency equivalent to the amount of H2S released during cathodic polarization. It is interesting to note that the experimentally determined vertical segment lies between the two theoretical ones for the different stoichiometries. One might argue that in the case of the experiment where the H2S released during cathodic polarization is kept in the system, the results do follow equilibrium behavior for some lead/sulfur stoichiometry intermediate to the extremes for which the calculations have been performed. However, this does not explain why the steep rise portions for both experiments coincide. As in the case of the data for pH = 0, a better explanation for the observed behavior becomes apparent when we consider that the position of the vertical segment is determined by the Pb 2+ concentration at which all of the Pb ° produced during the cathodic polarization subsequently dissolves according to reaction 2. Assuming 100% current efficiency during the reduction of galena, we would expect that the dissolved lead concentration should be 7.3 ppm when all of the Pb ° has been removed by the anodic polarization. This agrees quite well with the location of the steep rise at [Pb e+ ] =7.1 ppm from our observations. As is the case at pH -- 0, reaction 2 is apparently the only dissolution process which takes place until all of the elemental lead has disappeared from the surface. Although it is possible that the Pb ° can also be removed from the surface by another anodic reaction, i.e., Pb°+H2S

, P b S + 2 H + +2e

(11)

its kinetics must be much slower than that of reaction 2, which explains why the vertical segments obtained for the two experiments coincide. Data from voltammetry experiments conducted in our laboratory at this and other acidic pH values have also shown this to be the case [3,4]. An important aspect concerning the results obtained at pH--1.1 is the an-

348

M.D. PRITZKER AND R.H. YOON

odic shift in the observed potentials during the electrodissolution of Pb ° in relation to what is expected from the Nernst equation. Such a shift in the opencircuit potential indicates that reaction 2 is being retarded to some extent by an interfering effect, although it is not clear what that might be. This behavior is different from what we have seen at p H = 0 (Fig. 1) where apparently no such interference exists and the observed potentials agree exactly with the reversible potentials for reaction.

pH=4.6 The experimental data obtained in an acetate solution at pH = 4.6 are compared with the theoretical values in Fig. 3. Details concerning these results that are worth noting are that the cathodic polarization was carried out at a current of - 1 mA cm-2 for one hour and that the electrode was transferred immediately to a fresh electrolyte after being cathodically polarized. The mass balance calculations at this pH are complicated by the fact that the acetate in the electrolyte used can readily form complexes with lead. A recent voltammetric study in our laboratory [3] has shown that this can have a noticeable effect on the electrode response of galena. Nevertheless, this can be taken into account by using free energy data from Martell and Smith [6] and the Davies equation [5] to determine the percentage distribution of the possible soluble lead-bearing species. The composition is given in Table 1. It should be noted that because of the stoichiometries of the different species and the fact that the oxidation state of lead remains the same in all of them, the breakdown is not affected by the total lead concentration or the potential. As can be seen, Pb (CH3COO) 2 and Pb (CH3 CO0 ) ~- are the most abundant speI 200

pH 4.6

W

2: o9

o

o

- -

excess Pb

i

calculated

o

i i

c ~D 200

0 13...

-

400

--C-

J 10

100

Total Pb c o n c e n t r a t i o n , ppm

Fig. 3. Anodic dissolution of a galena electrode immersed in a stirred 0.5 M CH3COOH/0.5 M CH3COONa solution at pH = 4.6.

RELATIONSHIP BETWEEN POTENTIAL OF GALENAELECTRODE AND LEADCONCENTRATION

349

TABLE 1 Equilibrium composition of lead-bearing species in 0.5 M CHaCOOH/0.5 M CHaCOONa electrolyte at pH = 4.6 Mol % P b ( CHACO0 ) 2 P b (CHaCO0)~PbCHaCO0 ÷ Pb (CHaCOO)~Pb 2+

62.6 24.3 10.4 2.5 0.2

cies, representing 62.6% and 24.3%, respectively, of the total lead on a molar basis. Thus, the thermodynamics predict that essentially all of the lead should be complexed. As in the case of pH = 0 and 1.1, the lower segment of the curves in Fig. 3 are attributed to the anodic dissolution of the elemental lead on the galena electrode. Since Pb(CHaCOO)2 is now the predominant soluble species, the expected reaction is: Pb°+2CHaCO0 -

, Pb(CHaCOO)2+2e

Eo=-0.247

(12)

The Nernst relationship for this reaction corresponding to the experimental conditions of this study is found to be: E h = -0.219+0.0296 log [Pb(CHaCO0)2]

(13)

where the concentration is to be expressed as mol 1-' and Eh in V (SHE). It is more convenient to express the potential in terms of the total soluble lead content since this is what is actually being measured by plasma emission spectrometry. This can be done very simply from Table I to obtain: Eh-- -0.225+0.0296 log [Z(Pb) ]

(14)

where X ( Pb ) is the total lead solubility. (Since all of the species are considered to be in equilibrium with each other, the anodic reaction 12 could just as easily be written so that another lead compound is being produced. After converting concentration from that of the particular species to that of the total lead, an expression identical to the one given by Eq. 14 would be obtained.) The line corresponding to Eq. 14, which is shown in Fig. 3, lies below the one obtained experimentally, as was found at pH-- 1.1 (see Fig. 2 ), and also rises more steeply with lead concentration. The upper segment, which is due to the anodic oxidation of PbS, can be treated in an analogous way. The most likely reaction is: PbS+2CH3COO-

, Pb(CHaCOO)2+S°+2e

Eo=0.254 V

(15)

and the theoretical relationship between the potential and the lead solubility becomes:

350

M.D. PRITZKER AND R.H. YOON

Eh--0.275+0.0296 log [X(Pb)]

(16)

Note that the dissolution of PbS is shifted by approximately 30 mV toward the anodic direction from the equilibrium potentials calculated using Eq. 16. These shifts might be attributed to oxygen reduction, but it is not certain why the same has not been observed at lower pH values. The position of the vertical segment can be calculated in a similar manner to what has been done for the other pH values, i.e. by utilizing Eq. 5. One modification, of course, is that the lead acetate complexes must now be included in the X(Pb) term in the expression. Solving Eq. 5, one can predict that the steep rise should occur at a total soluble lead concentration of 6.3 ppm (see Fig. 3). Unlike the situation at p H = 0 and 1.1, this value is the same as that calculated from the amount of elemental lead formed during the cathodic polarization. The reason for this correspondence becomes readily apparent when the thermodynamics of the system is examined more closely. Below the potential where the anodic oxidation of PbS is possible, dissolution of PbS can occur only by a chemical reaction such as Eq. 7 or: P b S + 2 H + +2CH~COO-

, Pb(CH3COO)2 +H2S

(17)

The equilibrium positions of these reactions are strongly dependent upon the pH and rapidly shift to the left as the pH rises. Although a considerable amount of chemical dissolution can occur at pH = 0 and 1.1, virtually none is possible at pH-- 4.6. Regardless of whether the PbS beneath the Pb ° layer is in thermodynamic equilibrium or not, it will not contribute very much to the dissolution into the solution. Consequently, the layer of Pb ° will be the only source of lead in the solution until the vertical segment is reached, explaining the excellent agreement between the two sets of calculations. An important observation concerning the results obtained at pH = 4.6 is that on the experimentally-obtained curve, the vertical segment occurs at a lead solubility of 4.8 ppm, which is significantly less than the 6.3 ppm expected if all of the elemental lead on the galena surface has dissolved. This is unlike the observations made at pH = 0 and 1.1 in that the position of the steep rise depends on the amount of Pb ° formed during the cathodic polarizations. One explanation for the discrepancy may be that the assumption of 100% current efficiency during the cathodic polarization is not valid at pH = 4.6. There may be a competing cathodic reaction that would limit the amount of elemental lead formed on the surface. Another reason may be related to differences in the way in which the elemental lead comes off the surface in the various experiments. At pH = 0 and 1.1, the elemental lead layer may dissolve away fairly uniformly and consequently almost all of the metal will have to be removed before the underlying PbS becomes uncovered. On the other hand, if the Pb ° comes off in patches at pH -- 4.6, then some might still be left on the electrode when enough PbS becomes exposed for the electrode to revert to its galena-

RELATIONSHIP BETWEEN POTENTIAL OF GALENAELECTRODE AND LEADCONCENTRATION

351

like character. This difference in behavior may be attributed to the fact that at the lower pH values perchloric acid was used, while at pH = 4.6 the more reactive acetic acid/sodium acetate mixture was used as the electrolyte. Future experiments involving direct microscopic analyses of the electrode surface are needed to test this hypothesis. CONCLUSIONS

By first cathodically polarizing the electrode and then intermittently oxidizing it for short periods of time, the behavior of galena in acid solutions at pH = 0, 1.1 and 4.6 has been studied over a potential range from reducing values where Pb ° is present on the surface to oxidizing ones where the anodic dissolution of PbS takes place. In general, the open-circuit potential varies slowly with the dissolved lead concentration in two separate regions, one at low and the other at high potentials. These two regions are joined by a segment in which the potential changes very rapidly with concentration. Closer analysis, however, reveals that the pH does have a significant effect on the behavior of the system. Comparison of the experimental results with those predicted by the Nernst equation indicates that at pH = 0, the electrode behaves as a reversible lead electrode until all the metal present on the electrode has dissolved from the surface. Once this occurs, the electrode reverts to its original PbS character and behaves reversibly. With a rise in the pH, the system begins to behave less reversibly. At pH = 1.1, the anodic dissolution of Pb ° occurs at potentials about 30 mV higher than predicted by the Nernst equation, while that of PbS shows approximately Nernstian behavior. A further increase in the pH to 4.6 causes both Pb ° and PbS dissolution to deviate from reversibility. In addition, the steep rise no longer occurs at a lead concentration corresponding to that predicted assuming that all the Pb ° originally deposited has been removed. ACKNOWLEDGEMENTS

The authors acknowledge the financial support of the National Science Foundation (Grant No. CPE-8303860 ) and the Virginia Mining and Minerals Resources Research Institute. They also wish to thank Beth Dillinger Howell for her attention to the manuscript.

REFERENCES 1 Brodie, J.B., 1969. Electrochemical dissolution of galena. M.S. thesis, Univ. British Columbia, Vancouver, B.C.

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2 Pritzker, M.D. and Yoon, R.H., 1984. Thermodynamic calculations on sulfide flotation systems. I. Galena-ethyl xanthate system in the absence of metastable species. Int. J. Miner. Process., 12: 95-125. 3 Pritzker, M.D. and Yoon, R.H., 1987. A voltammetric study of galena immersed in acetate solution at pH 4.6. J. Appl. Electrochem., 18: 323-332. 4 Pritzker, M.D., 1985. Thermodynamic and kinetic studies of galena in the presence and absence of potassium ethyl xanthate. Ph.D. dissertation, Virginia Polytechnic Inst. State Univ., Blacksburg, Va. 5 Blackburn, T.R., 1969. Equilibrium. A Chemistry of Solutions. Holt, Rinehart, New York, N.Y. 6 Martell, A.E. and Smith, R.M., 1977. Critical Stability Constants. Organic Ligands, Vol. 3. Plenum Press, New York, N.Y.