58G
W. 1,. FRKYRERGER ANI) P. L. DE RRUYN
carbon, the lowering of the heat of chlorination is 15 k c d ; with a cyclobutene the lowering is 20 kcal. A chlorine atom is less effective if only one
Wol. 01
is present, One gives a lowering of 8.5 kcal. but two on the same carbon gives a lowering of 16.2 kcal.
THE ELECTROCHEMICAL DOUBLE LAYER ON SILVER SULFIDE‘ BY W. L.FREYBERGER AND P. L. DE BRUYN
.
Department of Metallurgy, Massachusetts Instilute of Technology, Cambridge, Massachueella Received October N.1868
Adsorption densities of silver and Nulfide ions at the silver sulfide-solution interface were determined as a function of Silver and sulfide ions were identified as the potential determining ions for this system. The aero- )oinbof-charge for silver sulfide in solutions containing sodium acetate and sodium metaborate was observed to he tit pkg 10. This zero-point-of-charge was also shown to be independent of the concentration of hydrosulfide ions below 10 mole/liter and of pH in the pII range 4.7 to 9.2. From the adsor tion data the magnitude of the changes in free energy fit, tho solid-liquid interface was calculated at different pAg values. #he differential capacity of the double layer was determined from the adRorption curves. The results indicated that the capacity values were in good agreement with those found for d v r r iodide and mercury except at high positive polarization of the surface, p A g ant1 ionic strength.
Introduction I n the separation of a valuable mineral from the wort’hless solids by means of the froth flotation proiwsa, reactions a t the solid-solution and solid-air interfaven are very important.2 The reagents used in flotnt,ionvary widely in their chemical nature and in the effects they produce a t the solid interfaces. The niechanisms by which these changes are accomplished are not clearly understood and have been tthe subject of much investigation in recent years. One tippoach to this problem would be t o attempt, R correlation between the electrical properties of a xpecific solid-liquid interface under a given set of conditions and the flotation behavior of the same solid under identical conditions. The desirability of such a correlation has been recognized for a long while and a few experiments have been carried oiit.s-6 However, the success of this approach until now has been limited by the lack of quantitative knowledge of the electrical properties of the solid-liquid system except for the mercurysolution’ and silver iodide-solution system.8 Neither one of these two systems is of much practical interest from a flotation standpoint. A program of research was initiated to study the electrical and electrochemical properties of a solidliquid system which is more closely allied t o flotation practice. The solid chosen was silver sulfide and this paper reports the results of an electrochemical study of the adsorption of silver and sulfur-bearing ions a t the silver sulfide-solution interface in the presence of controlled concentrations of an indifferent electrolyte. Silver sulfide was chosen as the solid because it is a heavy metal sulfide typical of the ore-forming (1) Based on a dissertation submitted by W. L. Freyberger in partial fulfillment of the requirements for the degree of Doctor of Soienoe,
MIT. (2) P. L. de Bruyn, J. Th. 0.Overbeek and R. Schuhmann, Jr., Trans. Am. Inst. Min. & Mal. Enora., 199, 519 (1954). (3) D, Talmud and N. M. Lubman, Kolloid-Z., 60, 163 (1930). (4) P. A. Lintern and N. K. Adam, Trans. Faraday Sac., 81, 504 (1935). (5) B. Kemienskl, 2. phyeik. Chem., AlS8, 441 (1932). (6) 0. Jo, J . Minine Inst. Japan, 88, 439 (1952). (7) D. C.Orahame, Chsm. Reus., 41, 441 (1947). (8) E. L. Mackor, Reo. lrav. ohim., TO, 703 (1951).
metal sulfides; because in contact with silver it forms a reversible electrode of the second kind; because it can be prepared as & well flocculated precip itate with high specific surface and because silver has only one important valence state, which simplifies greatly the interpretation of electrochemical results.
Experimental
The experimental techni ue adopted in this reaearah is similar to that used by Mazora for his studies on silver iodide. This technique consists of adding measured quantities of silver acetate to an aqueous suspension of finely divided silver sulfide and then determining electroche+ally the concentration of silver ion in solution after equilibrium has been reached. The amount adsorbed at the solid Butface is determined by difference. Materials.-Fine1 divided silver sulfide was prep-wed by precipitation wit[ hydrogen sulfide from an ammoniacal solution of silver hydroxide.@ After precipitation, the silver sulfide was allowed to stand overni h t in contact with the saturated hydrosulfide solution. Tfe precipitate was then washed free of foreign electrolytes by decantation. The precipitation and subsequent washings were carried out as murh as possible in a nitrogen atmosphere. Chemical analyses o two of the precipitates gave 86.99 and.86:12% silver and 13.48 and 12.96% sulfur, respectively. Stolchiometrically, silver sulfide should analyze 87.1% silver and 12.9% sulfur. X-Ray diffraction patterns of these two precipitates checked with the data listed by the A.S.T.M. for &silver siilfide, the low temperature form of silver sulfide. A value of #7.32g./cm.’ was used for the density of silver sulfide. The aging characteristics of several precipitates were checkkd by measuring electrochemically the change In silver ion aoncentration in a solution in contact with the precipitdte for periods up to six days. This check was necessary because the experimental technique required that the solid should not chan e its specific surface by recrystalhzation at a rapid rate. $he aging tests showed that during the time of testing, the precipitates decreased in surface area by only a few hundredths of one per cent. A precipitate was used in an experiment for about fourteen days and was not re-used. Tank prepurified nitrogen which was further purified, provided an inert atmosphere for the electrochemical titrations aiid was used to remove dissolved oxygen from the solutions. The tank nitrogen was urified by passing i t over hot co per punchings, then tirough a solution of chromous chkride, next over activated charcoal and finally through a suspension of silver sulfide of the same composition as the one being titrated a t that time. Tank hydro en sulfide, purified according to the recommendation .of bodd and Robinson,m was used as a source of (9) W. L. Freyberger, Sc.D. Thesis, Maaa. Inst. of Tech., 1955. (10) R. E. Dodd and P. L. Robinson, “ExperimtaI Inorganic Chemistry,” Elsevier Publishing Co., New Yorf, N. Y.. 1964.
. J
sulfido for all expcrimenta. The water used in t,he teats was rtdistillotl in a bloc:k-t,in at.ill from an alkaline pcrmangnnnt'e t;nliit,ion. No wrbtcr wns used which had a specific conohm-' cm.-l. dii(:t,nncegrc:tter than 0.7 X ISxoept for silver acetate and sodium hydroxide, all the chemical reagcnts were of reagent grade and were not purified. Silver acetate of rm unspecified purity was recrystallized once from water and was stored in a dark bottle after IJeirig pum ed dry in a vacuum desiccator. The s d t anaIpzcd 64.1 silver as compared to the theoretical value of 64.6%. Rotliuin hydroxide, free from sodium cnrhonate, WLS preparcd :tccording to the method of Kolthoff and Sandellll and was used immediately after preparation. Apparatus.-The titrations of the silver sulfide suspension8 were conducted in a Pyrex glass vessel having a total voliime of nhorit 500 ml. Normally 250 ml. of suspension was med in a test. A rubber stopper Realed the vessel and provided rntranrc for the silver sulfide electrodes, the referwr.r electrode, a thermometer, two microburets and an inlet and an outlet for nitrogen gas. The suspension was stirred with a magnetic stirrer and the temperature of the suspension was maintained between 20 and 25" by placin a copper p h t e carrying a water coil between the vessel and t%estirrer. The elcctromotive force of the cell was measured by means of a Leeds and Northrup Student Potentiometer with a Vibrating Reed Electrometer serving as a null-point indicator. F.m.f. mensurement,s were accurate to 1 0 . 5 mv. The titration vetwe1 was placed inside a grounded copper box and shielded cabIe was used in the circuit to prevent interference from electrical pick-up. The clect8rodr systcm for determining t.he concentration ofsilver ion in aoliit,ion consisted of a reference electrode and 11, Rilver-silver sulfide indicating electrodo. Two different mfcrcnc.e electrodes were used depending on the pH of the suspension. A t a p H of ahout 5 , i t was ossible to use a g l n ~ dectrodc a8 reference electrode. 'Wien the pH was Imffered at, I), thc glass electrode was sluggish in its response so :t saturat,ed calomel electrode connected to the system by means of n salt bridge, was used. The salt bridge wm ropied from t8he one described by Mackor.0 The liquid jiinct,ion solution in the bridge was 2 N ",NOS. Silver-Rilver sulfide indicnt,ing electrodes were prepared by firat plating a platinum wire with silver and then anodizing eleotjrically the silver in the presence of a solution of sodium ~ u l f i d e . ~Several sets of these electrodes were re pared. Kach set, contained two or three electrodes wl!ich were used Nimriltancously during a titration. From measurements .of the standard potcntial of the silver--silver sulfide: RlasR electrode couple, the standnrd poten(,id(R) of the hrtlf rcll reac4ion 2Ag(s) P(:q) J_ AgzS(s) 2e(1) \vas c-:ilrrilnt,trd, Thc n,vrrap;c!of 23 determinations wit,height iliffiwrit silvcr-silver aiilfide clertrodes indicated that a t
Eantoa~ornei
+
22.5O
E " A ~ ( ~ ) /= A~ 0.7180 , R ( ~f ) 0.0035 volt (2) 7'11~slantlard I)otonti:d of the glass clcct.rodcs was determ i n d to be EOEinfi#= -0.7040 & 0.0044 volt (3) (A)
1 1
M R ) AgzS(s)
or (R) Ada) ..
.
Ag,S(s) .- . .
1 1
-
_-
indifferent electrolyte and small concn. of Ag+, S-, H + , rtc.
+ 0.00076[t("C.)- 251 volt,
(5)
A check on the stabilit,y of the indicating electrodes wa8 obtained by measuring the standard )otent8ialof a pair OF electrodes three times over a period *{three months. During this time the standard potential varied by nbout three millivolts. Procedure.-At the start of an experiment, a suspension of freshly prepared silver sulfide reci itate in an aqueous solution of reagents needed to fix t i e p!I and ionic strength, was introduced into the titration vessel. Experiments were run a t either pH 4.7 or H 9.2 and a t several values of ionic t p H 4.7 the electrolyte used to fix skength of solution. I the ionic strength was sodium acetate and the solution was buffered by maintaining equal molar concentrations of acetic acid and sodium acetclte. At p H 9.2 boric acid and sodium hydroxide in the molar ratio of 2: 1 werc! used to give e ual concentrntions of boric acid and Aodium metaborate. %he latter salt fixed the ionic strength. Aqueous solutions of silver acetate and sodium hydrosulfide to be used as titrating agents, were prepared esAentially free of oxygen and were stored under nitrogen in a modified 5-ml. Koch microburet, from which they were added to the suspension when required. The sodium hydrosulfide sohtion was preparcd by bubbling purified HzS through a sohtion of approximately 0.1 N sodium hydroxide. Titrations were run by measuring the equilibrium tial of the silver-silver sulfide electrode agalnst the re erence electrode. Then a measured number of moles of silver acetate was added and the new equilibrium e.m.f. value was determined. Equilibrium was usually attained in less than four hours after the addition of silver acetate. The additions of silver acetate were made stepwise until the pAg value was just leas than 4. Below pAg 4, the measurements became exceedingly inaccurate because small changes in cell e.m.f. were produced by relatively large .additions of silver acetate. A t this point su cient sodium hydrosulfide was added to raise the pAg to a f?out 13. I t proved impractical to carry out the addition of sodium hydrosulfide stepwise as was done with the silver acetate addition because in spite of all precautions taken Has gas continually escaped from the sodium hydrosulfide solution thereby changing the concentration of the solution. The titration procedure was then repeated, usually three times, until enough points have been obtained to establish the curve of the cell e.m.f. versus moles of silver acetate added for a particular value of the ionic strength. The pAg was then again adjusted to about, 13 a.nd the ionic strength of the systcm was increased and the whole sequcnce was repeated.
&
+
-0.2415
poten
Calculation of the Adsorption Density of SiIver ions.-To obtain the amount of silver adsorbed at a given pAg value and fixed ionic strength fr m the experimental e.m.f. values and the known &ount of silver added t o the system, it is necessary to account for the various forma in which silver might, exist in sohition. Depending on the reference electrode used, the electrical cell whose e.m.f. is measured corresponds t o either
/I
HCI (dil. aq.)
l
AgCl(s)
l
Ag(s)
iudiffcrcnt, clectrolyt,e and small concn. of Ag+, S; I T + , etc.
Determination8 were made with the Ralt bridge-calomel electrode assembly in order to evaluate the effect of the liquid junction potcntial. The average of 41 such determinationa with 13 different Ag/AgZS electrodes gave at 22.5" EoAg(e)/AatE(a)/lis, Junalion = 0.7090 f 0.0028 Volt (4) The potential of the a:tturated caloniel electrode was taken adz (11) I. M. Kolthoff and E. 13. Sandoll, "Textbook of Qumtitative Inorganic Analysin," The Maemillan Co., New York, N. Y.. 1936. (12) 8. Glasstonc, "An Introduction to ElrrtrochemiRtry," n. Van Nostrand Co., New York, N . Y., 1942.
For cell A it is apparent that provided the pH is held constant, any change in cell e.m.f. ( E ) can be related directly to changes in the chemical potential ( p ) of the sulfide ion, the hydrosulfide ion and the HzS rnolecule, by the relation F dE
I/Z~CLS-
= '/zdrns- = I/idpREs
(6)
The same interpretation can be given to changes in the e.m.f. of cell B provided the liquid junction potential between the cell soliition and the salt bridge does not vary.
588
W.I,.
PREY~ERGER AND
I3 using the relation expressing the solubility pro uct of silver sulfide
d
dpb+
5
- '/&e-
(7)
-
Equation 6 may be written aa F dE - d p ~ & + -RT d In ah8+ (8) where, R is the gas constant, T,the absolute temerature and C Z A ~ + ,the activity of the silver ion. brom equation 8 the activity of the free silver ion in solution is obtained. The other forms that silver could assume in the system include insoluble precipitates, adsorbed ions a t the solid-liquid interface, complex ions and undissociated molecules in solution. Care was taken to avoid precipitation of insoluble compounds except, of course, silver sulfide. Possible insoluble compounds that could be formed are silver acetate (AgAc), silver hydroxide and silver metaborate. The concentrations of sulfide ion, hydrosulfide ion and undissociated h drogen sulfide were calculated from the measuredy silver ion activity and the equilibrium constants at 22.5"
-
+ S-(aq); K rH+(aq) + HS-(aq); Hd(aq) I K HS-bq) _C H+(s4) + S'(aq); AgsS(6) I r2Ag+(aq)
-
1.96 X
1.00 X lo-'
P. r,.
Ag+(aq)
Vol. 01
DE RRUYN
+ IWXaq) J_ AgHS(aq) + Ii+(aq); IC = 1.78 X 10' (16)
The concentjrations of AgS- and AgIIS were never of any significance under the conditions used in this investigation. To convert the ionic activities calculated from the above equilibrium constants to ionic concentrations the ionic activity coefficients were estimated from the Debye-I-fiickol rehtion
(9)
where fi is the activity coefficient of ion i of valence zi a t ionic strength I , was used in these calculations. The calculated increaae in the amount of free silver ion and in the amount of silver ion tied up in solution in the various forms discussed above are subtracted from the total amount of silver added to the system in passing from one pAg value to a lower value. The difference thus obtained is assumed to represent the amount of silver adsorbed. The adsorption densities were thus calculated in moles of silver per gram of solid as a function of the silver ion activity in solution and also of ionic strength.
(10)
Results Zero-polnt-of-charge.-Experimentally, it is only
possible to determine the change in adsorption density of silver ion with pAg. In order to plot an adsorption isotherm, it is necessary to know the absolute value for the adsorption density a t at least one pAg value. From the experimental m l t a TAFJLB I therefore, an adsorption isotherm can be constructed BTANDARDFREEENERGY OF FORMATION OF SILVER SULFIDE, only with adsorption density in arbitrary units SILVER, SIJLFIDSO AND HYDROSULFIDE IONBAND HYDRO- veraua pAg. These adsorption curves are shown in Figs. 1 and 2. Figure 1 shows a series of adsorption SULFURIC ACID AT 25' AFO, APo curves a t pH 4.7 and a t five different ionic substance cal./mole Subatanoe cal./mble strengths: 2 X 10-8, 5 X lo-*, 5 X 0.1 nil A g 8 (0) -9,68218 Ag+ (aq.) 18,44814 0.2 N . Figure 2 shows a series of a d w p t i n '8 (as.) 23,450" H S (as.) -8,490" curves a t pH 9.2 and a t ionic strengths 5 X lo-', HS- (aq.) 2,98014 5 X 10-2 and 0.2 N . The set of curves in each Equilibrium data on complexes involving silver figure was obtained on the same precipitate: the and acetate are given by MacDougall and Topol.16 titration was started a t the lowest ionic strength. The horizontal dotted lines connecting successive The equilibrium constants for these complexes are curves indicate the changes in pAg when the ionic AgAc(aq) Ag+(aq) + Ac-(aq); K = 0.186 (12) strength was increased a t constant total silver and sulfide content of the system. These lines are AgAct-(aq) 1_ Ag+(aq) 2Ao-(rtq); drawn horizontally and are therefore lines of conK = 0.230 (13) stant adsorption density because the solutions The concentrations of these complexes were appre- were so dilute with respect to silver and sulfide ion ciable under conditions of high silver and acetate concentration that no measurable change in adconcentrations but, in this investigation, the cor- sorption density would be expected to take place rections never exceeded 15% of the total amount of even though the pAg value changed at times by as silver added to the system. much as one-half a unit. Concentrations of complex ions of silver and sulIt will be seen from Figs. 1 and 2 that the arbifide or hydrosulfide ions were calculated from data trary adsorption curves do not cross exact1 a t one given by Treadwell and Hepenstrick. point but that the intersecting points ie very close to a pAg value of 10 for both sets of curves AgHS(sq) _r H+(aq) AgS-(aq); with the exception of the curve at ionic strength 2 K E 6 X 10-0 (14) X lo-* N in Fig. 1. (13) J. R. Ooales, A. 0.Cole. E. L. Qray and N. D. Faux, J . A n . Even,though the curve a t 2 X lo-* N ionic Clem. Sat.. 78, 707 (1951). strength does not intersect the other curves in the (14) "Handbook of Chemistry and Phyaics," 34th Ed., Chemicnl Rubher Publishin8 Company, Cleveland, 1052. vicinity of pAg 10, its shape, nevertheless, has been 60, 1090 (16) i. XI. MnoDougaIl and L. E. Topol, THISJOURNAL, determined quite accurate1 . The anomalous be(1962). havior of this curve must e attributed to an ex(le) W. D. Treadwell ond €1, Ilcpcnatrick, N o h . Chin,. A d o , 8% perimental error wllicli occurred when changing the 1872 (1049).
K = 7.08 x 10-14 (11) The free energy data used for calculating these constants are given in Table I.
.*
+
3!
+
t
%
ionic strength from 2 x N to 2 x N. A more recent investigation of this system under the same conditions as to pH and nature of indifferent el~ctrolyte'~ has shown that even a t an ionic strength of N , the adsorption curve intersects at p h g 10. Since it has been demonstrated that the adsorption density of silver is a function of ionic strength as well as pAg (see Figs. 1 and 2), the point common to all the adsorption curves must represent the oint of zero charge on the silver sulfide surface. bor silver sulfide there is, therefore, no excess of silver or sulfur-bearing ions a t the surface a t pAg 10. With the zero-point-of-charge established, the absolute adsorption curves can be plotted. The reproducibility of the ciirves shown in Figs. 1 and 2 has been illustrated by redetermining the curves under identical conditions but by using different precipitates. Adsorption Isotherms.-To express the adsorption density in terms of charge per cm.2,the specific surface of the silver sulfide precipitates must be known. Several attempts to measure the surface area by the B.E.T. nitrogen adsorption method gave unsatisfactory results. The specific surfaces obtained by this method indicate that the average particle size lies between one and three microns whereas observations with the electron microscope showed that the maximum particle size was less than half a p. The specific surface of the silver sulfide prccipitates waa estimated by the same method used by Mack09 in determining the surface area of silver iodide. This method involves the assumption that the minimum differential capacity of the double layer for silver sulfide in contact with an aqueous solution of an indifferent electrolyte a t low ionic strength has the same value as the minimum differential capacity of mercury in contact with an aqueous solution of sodium fluoride a t the same ionic strength. The differential capacity is defined as the differential change in charge with change in potential at constant ionic strength. The change in charge is calculated from the experimental data and the change in potential is measured by the change in pAg. The validity of this method of arriving at the surface area depends on satisfactory proof that the electrolyte (sodium acetate or sodium metaborate) which fixes the ionic strength of the system is not specifically adsorbed at the interface and that the ionic strength is low enough so that the Gouy model of a diffuse double layer' is applicable. If these two conditions are met, then the differential capacity of the double layer should have only a very slight dependence on the chemical nature of the solid surface. From Figs. 1 and 2 it follows that the electrolytes, NaAc and NaB02, act as indifferent electrolytes since all the curves cross in a narrow p h g region. A specifically adsorbed clectrolyte corild cause a shift in the zcro-point-of-cliarge of as much as two or three p A g units as the electrolyte concentration is varied. Furthermore, at the lowest ionic strength, 2 X N used in these experiments, the diffuse layer model should apply reason(17) Unprililisli~rlrenriltn by T. Twnqnki, M n w . Tnst. o l Trrli.
7
I1 13 16 PAIS. Fig. 1.-Adsorption dnnsity of potential determining ion@ on silver srilfide (EB a function of the p A g . Adsorption density calculated directly from tho titration data. Indifferent electrolyte: sodium acetate; pH 4.G4. 0
I
8
1
I
1
12 14 PAU. Fi 2 Adaorption dcnsity of potential determining ions on sikei8ulfide as a function of the p A g . Adsorption calculated directly from the titration data. Indiffcrcnt elcctrolytc, sodium metaborate; pH 9.19. 10
ably well. Grahame18 obtained an experimental value of 7.6 p farads per cm.z for the minimum differential capacity at this ionic strength. By using this value and knowing the total capacity for a given weight of silver sulfide, specific surfaces varying from 25,000 to 65,000 cm.2/g. were calculated. In Fig. 3 adsorption density expressed in p COUlombs per cm.2 is plotted against pAg at an ionic strength of 0.2 N , to show that pH has no effect on the adsorption density of silver or sulfide ions in the pII range 4.7 to 9.2. Similar results were obtained N. a t ionic strengths 5 X lo-%N and 5 X Figure 4 combines all the experimental results in the form of one series of adsorption isotherms for different ionic strengths. The individual curves have been adjusted to cross a t pAg 10, the established zero-point-of-charge. Adjustments were made only in the value of the ordinate since the pAg value was established by the experimentally determined e.m.f. of the cell. The curves at ionic strength 5 X 10-8, 5 X 10-2 and 0.2 N have been ohtained at PIE 4.7 and pII 0.2; t,he curves at the other ionic strengths were determined only a t pH 4.7. It is interesting to note the unsymmetrical nature of the adsorption isotherm. A smaller change in pAg below the zero-point-of-charge than above this point gives the same adsorption density. (18) D. C. Cmlisrno, J . A m . Chem. Sac,, 76, 4819 (1961).
w.L. FREYBERGER AND P. 1,. DE R R U Y N
590
Vol. 01
Discussion Thermodynamical Considerations.-?y appl ing the well-known Oibbs adsorption equation a n i by making use of the general theory of the electrochemical doubfe layer Grahaine,' Mackold Kruyt and O ~ e r b e e k 'have ~ succeeded in improving our understanding of interactions a t the solid-solu tion interface. The general form of the Gibbs equation
1 1
dr
I-
--ridpi
(17)
where y is the interfacial free energy, 1'1 the adsorption density of component i, and /.6j the chemical potential of component i in the bulk solution, may he expanded for silver sulfide in contact with a solution of sodium acetate at constant pH and constant ionic strength to yield - rap+ dpAg+ - I'R- dps- - I"e- ~ ~ L H-S -rae dpHe dr
- r A g A c dPADAc - rAgAar-
dpAgAoi.
- r&B-
dp.488-
II&As dpA.se
0
8
10
12
14
10
17.k
ViK. 3. --Adwrption density of otential detorminin ions on silvcr siilfitlo n~ a function o r the pAg. Curve 8etermincd ti,t two p€I valiies with two different electrolytes nt lhe mmz) ionic Rtrength.
0 h
"
2
2
4
i
EJ
3
8a
6
v
.* 3
8
10
1
12
a -4
-
(18)
Equation 18 may he simplified if the assumption is made that, the adsorption density of the silver acetate and silver sulfido complexes is negligible. Thie amumption is reasonnhle because the activities of these complexes were always kept very low. Furthermore, by making use of the definition of the solubility product of AgzS (equation 7) and by realizing that at, constant, pT-I dpm- = d w f i = tipsdr =
-(rnp+
- 2 [ W + I'm- + rn@])dphl)+ (20)
When working at constant pH there is no means of distinguishing among the adsorptions of 5-, HSand H2S. Experimentally, only the total charge due to an excess of sulfur-bearing species over silver ion at the interface is ,obtained. However, equation 20 can be sim lified further and the specific rolw of the S- and S- ions and the IIzS molecule will be clarified by recalling that identical adsorption isotherms for a fixed ionic strength but two different p R values were obtained (see Figs. 3 and 4). At, a given pAg, the sulfide ion concentration is fixed regardless of the pH, but the HS- ion activity in going from pH 4.7 to p H 9.2 changes by a factor of lo4. The experiments at different pH values therefore indicate that I'm- and rH,S are negligibly small or perhaps zero and that the sulfide ion alone dcterrnines the adsorption density at, pAg values above the zero-point-of-charge. Equation 20, therefore, reduces t o d r = -(rAg+ - 2 r g - ) d p ~ + (211 Ry introducing now the electrochemical relation
4
R
14
P d E = -dpAg+
16
which defines the change in free energy of the reversible cell used in this investigation at constant pII, equation 21 reduces to
18
20
.
(10)
Equation 18 simplifies to
d r = +P(I'Al*
- 2rs-)dE
(8)
(22)
i
I
The silver and sulfide ions are common to both t,he solid phase and the solution phase; furthermore t>hesoions are irivolvcd in the electrode reaction a t l h a Ag/Ag,S eleutrotle. As :t consequence these (I!))11. 11. Kniyt, "ColltJid Srivnn.." N , ' \ ' , , 1952.
f ' o . , N ~ b r r \'III'I,,
Vol. I , 1Clacvit.r
1'iiOll~liiiig
I
May, 1957
ELECTROCHEMICAL D O U ~ LLAYER E ON SILVER SULFIDE
ions are known as potential determining ions hectiiisc their activity in solution det,ermines the change in the potential difference (Nernst potential) between the solid and liquid. It should be realizcd that a t constant pH the electrode reaction at, the hg/Ag2S electrode can also be written in terms of H2S or HS- and under such conditione t,heRe species could also be considered as potential tletcrmining. However, by changing the pH at constant ionic strength, the role of the Sa ion as the only potential determining anion has been estabIishad. Since adsorbed silver and sulfide ions cannot be tlistinguished from the silver and sulfide ions constittiting the silver sulfide crystal lattice, the term F(rA,+ -2l"s-) is referred to as the. surface charge. The surface charge will be positive or negative depending on whether an excess of silver or sulfide ions is present. By the establishment of a siirface charge, the electrochemical double layer is hitilt up a t the interface because an equivalent counter charge must be present in the solution phase adjacent t o the solid surface. A surface charge of potential determining ions will have a significance only if the concentration of these ions in solution is small cornpared to that of the indifferent electrolyte. Only under this condition will the contribution of the potential determining ions toward the counter charge in thc solution phase be negligible. This condition was met by working at high ionic strengths. Equation 22 neglects any contribution to the surface charge by free clect,rons in the solid. Rets silver sulfide is known to be an electronic as well as an ionic conductor.2" The role of free electrons in t8hissystem may be explained as follows.21 These electxons will have t o come from somewhere since neutral substances are the starting materials (e.g., AgNOa, NaHS, HZO,etc.). Free electrons may be generat,ed by some disproportionation reaction as, for cxa tnple S" .+ s- + e(231 Thn 8--ion is certainly not stable in the solution. It might exist in {,hesolid Rg28 but in the technique used, the influence of an electron plus a S- ion is indistinguishable from that of n S- ion, At the silver sulfide elect,rode where t?lectrons can be supplied from the silver, the situation might be different, but as long as the electrode behaves according t,o the Nernst equation, the actual mechanism is not, of importance in this study. By integrating equations 21 or 22 the change of interfacial free energy with silver ion activity in solution may be obtained. From equation 21 it follows that the interfacial free energy will be a niaximum a t pAg 10, the zero-point-of-charge, and will decrease above and below this point. However, since the absolute value of the interfacial free energy at the zero-point-of-charge is not known only changes in interfacial free energy with respect t o the zero-point-of-charge can be determined. In Fig. 5 the difference in interfacial free energy at, the silver sulfide-solution iiitmfacc txrsus pAg for vnri(20) M . 13. Hebb, ,I. Ckcnh. P h n ~ .20, , 185 (1962). (21) This silggestioii was inltde by l j r . -1. Th.(i. OveIl,n.k, Illiivnrsity or Utrecht, Nrtlierlaiids, tu the u u t h u w .
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PA& "2. 5.-CIiunges in mrface tension of the solution-silver sulfi e interface due to the adsorption of otential deter-
mining ions. Indifferent electrolytes: sodPum acetate at pH 4.64; sodium metaborate at pH 9.19.
ous ionic strengths is plotted. This figure has been obtained by graphical integration of Fig. 4. Differential Capacity and the Electrical Double Layer.-The electrical double layer a t the silver sulfide-solution interface, for the conditions investigated, is visualized to consist of a surface charge due to an excess of silver or sulfide ions at the solid surface and a counter charge contributed by nonspecifically adsorbed ions in the adjacent solution. Sodium acetate and sodium metaborate have been shown to act as indifferent electrolytes and depending on the pAg value of the solution an excess or a deficiency of sodium, metahorate and acetatte ions will contribute toward the counter charge. Neither H + nor OH- ions showed any specific affinity for the silver sulfide interface; of course, the concentration of these ions was always kept below molar. The behavior of these ions is of great interest to the flotation chemist since pH regulat,ion has always played an important role in effecting good mineral separations. The slope of the surface charge (@) versus potential (or pAg) curves measures the differential capacit y (Cr,) of the electrical double layer. Since all the potential jumps except that at the silver sulfidesolution boundary are kept constant, any change in p A g or cell e.m.f. ( E ) will also measure the change in potential difference across this interface. For the conditions maintained in this investigation, the differential capacity is defined, therefore, by the relation (:%I
(g)
p'8 (!o!l8Lfll\t Cxc'epL P l \ g + , ( p H - )
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Vol, 61
accord with the model of a diffuse double layer in the vicinity of the zero-point-of-charge at low ionic strengths. This minimum is, however, not a marked as in the case of m e r ~ u r y . ~The failure of the curve a t 5 X lo-* N to reach a minimum near pAg 10 is, however, puzzling. It might be that the, data are not smooth enough to show this minimum. The capacity curves approach a plateau a t about 15 p farads per cm.2 for negative polarization. This is in good agreement with the qualitative behavior predicted by the theory of Stern and Grahame' and with the quantitative results obtained with silver iodidea and mercury.7 The adsorption isotherms plotted in Fig. 4 show that all the curves coincide a t high pAg regardless of ionic strength. Thus it would appear that the properties of the double layer on silver sulfide under the conditions investigated, become independent of ionic strength for moderately high negative polarization. This same behavior was observed with silver iodide where it was found by Mackor that the surface charge a t negative polarization approaches a limiting value of -4 p coulombs per cm.*.
Conclusions 4
0
10 12 14 10 PA& Fig. 6.-Differential capacity of the double layer on silvcr sulfide 8.9 a function of p A g . Indifferent electrolytes: sodium acetate at pH 4.84; aodium metaborah at pH 8.19. 8
curve lies outside the field of thermodynamics and depends on the choice of the particular ph sical model to represent the electrochemical double ayer. I n Fig. 0 the differential capacity of the double layer on silver sulfide is plotted as a function of pAg for five different ionic strengths. These curves were determined by measuring the slopes of the curves in Fig. 4. Since the adsor tion isotherms are quite steep below pAg 8, a sma 1 change in the way the adsorption isotherm is drawn will have a profound effect on the slope and the capacity in this region. The most striking feature of the capacity curves is the steep rise of capacity to the left of the zeropoint-of-charge (pAg 10). This is more marked than the measurements made by Mackors on silver iodide and even more so than with mercury in contact with aqueous solutions of sodium fluoride.' The drop in the capacity in the pAg range of 7 to 6 and the minimum indicated between pAg 5 and 6 may or may not be real due to difficulties in establishing the very steep portions of the adsorption isotherms. Grahame' haa observed a similar behavior for solutions of several electrolytes in contact with mercury. The minimum in the capacity curve for ionic strength 2 X lo-* N occurs near pAg 10 and is in
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This electrochemical investigation of the silver sulfide-solution system established the silver and sulfide ions as potential determining ions in the p H range 5 to 9. Sodium acetate and sodium metaborate were used to determine the ionic stren th of the solution and were shown to behave as indi erent electrolytes. Within the pH range 5 to 9 hydroxyl and hydrogen ions showed no specific affinity for the silver sulfide surface. The zero-point-of-charge for silver sulfide was found to lie a t pAg 10; above this pAg, an excess negative charge; and below this pAg an excess positive charge is found a t the surface. This surface charge is a function of pAg and ionic strength. Estimations of the differential capacity from the adsorption isotherms indicate that the structure of the double layer is in qualitative agreement with the models set up by St,ernand Grahame. The capacity reaches a plateau in the region of moderately high negative polarization, I n general, the capacity curves agree well with those obtained by Qrahame for mercury and by Mackor for silver iodide except that a much steeper rise in the capacity curve on positive polarization was observed. Acknowledgments.-The authors are grateful to the Atomic Energy Commission for financial support in conducting this investigation. To Dr. J. Th. 0.Overbeek the authors extend thanks for the valuable advice given and interest shown in this investigation. The authors also wish to express their appreciation to Dr. A. M. Gaudin and Dr. Carl Wagner for helpful discussions.
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