Sept. 5, 1960
DOUBLELAYER.4ND
THE T H A L L I U M - h A L G A M
appear to be too low compared to ours, which is in agreement with Figurovskii’s result. Substituting ala, = 7.53 in eq. 17 we find x = 18 A. which can be considered as the width ( k c, dimension) of SrSO4 nuclei. This is about 3 times the c dimension of the unit cell 6.84 A. (paragraph c), It can be concluded, therefore, that a nucleus consists of 33 = 27 unit cells. By similar calculations La Mer arrives a t a for the size of Bas04 nuclei from value of 100
[CONTRIBUTION FROM
THE
ELECTRODE
4509
their experimental results. Nevertheless, in their calculation they use Hulett’s value (1500 erg. cm.-2) for the interfacial tension of Bas04 which we consider too high (cf. paragraph c and section 1). If we can assume that the c dimension of a Bas04 nucleus is also 3 times that of a unit cell, Le., 7.14 A.,31using LaMer’s value of 21.5 for the critical alao and a: calculated from the unit cell dimens i o n ~we , ~ obtain ~ from eq. 15 7 = 150 erg. cm.-2 for BaSOd/solution mean interfacial tension.
COATES CHEMICAL LABORATORY, LOUISIANASTATE UNIVERSITY, BATONROUGE,LOUISIANA]
Structure of the Double Layer and Electrode Processes. 11. Effect of the Nature of the Electrode and Application of the Thallium-Amalgam Electrode BY PAUL DELAHAY AND MARCOS KLEINERMAN~ RECEIVEDDECEMBER 22, 1959 The influence of the nature of the electrode in electrochemical kinetics in the absence of specific electrode effects is interpreted on the basis of a change in the double layer structure. This double layer effect, which can be quite significant, should also be considered in kinetic correlations for processes with specific electrode effects. Application is made of the dropping thallium-amalgam electrode (up to 31% T1) for which the point of zero charge can be shifted continuously by as much as -0.4 volt with respect t o this point for mercury. The following reductions are studied: bromate and iodate in alkaline solution, hexacyanochromate(II1) in cyanide medium, chromate in alkaline solution and tetracyano cadmium(I1) in cyanide medium. Shifts of the Tafel line for bromate and variations of the exchange current density for hexacyanochrornate(II1) are interpreted quantitatively. Chromate waves for the dropping thallium amalgam electrode in supporting electrolyte of low concentration exhibit a pronounced minimum which is quantitatively discussed. The maximum in the tetracyano cadmium(I1) waves is abscribed to a double layer effect in agreement with other investigators, and a quantitative study is attempted for the results obtained with the dropping mercury electrode.
Introduction this is one of the rare systematic studies of the inThe structure of the double layer a t an electrode- fluence of electrode material on double layer effects electrolyte interface affects the kinetics of electro- in correlation with kinetics. We began a study of the electrode effect by comchemical reactions occurring on this electrode for two reasons: (a) the concentrations of ionic re- parison of mercury and gallium electrodes but actants are not the same a t the reaction site as in the soon adopted the more versatile thallium amalgam bulk of the solution and (b) the effective difference electrode of varying composition. The point of of potential must be corrected for the difference of zero charge of the latter electrode can be shifted by potential across the diffuse double layer. These as much as - 0.4 volt in comparison with a mercury two fundamental effects were suggested by Frum- electrode as was shown by Frumkin and Gorodetzkin and investigated principally by him and his kaya.” This shift of the point of zero charge may school.2 Much interest has been shown recently result in a significant change in the difference of in such studies by other investigator^.^-^ (For potential across the diffuse double layer (Fig. 1) recent reviews of double layer effects in polarog- and a concomitant change in the kinetics of an raphy see ref. 8 and 9; also ref. 3.) In general, electrode reaction occurring on the amalgam. The interest has been focused on factors governed by thallium amalgam electrode has two advantages solution composition rather than on the effect of over the use of solid electrodes of different nature the electrode nature. Frumkin and co-workers in such studies: (a) the point of zero charge can did study the minimum in certain current-potential be changed continuously, and (b) spurious effects curves with electrodes of different metals1° but observed with solid electrodes (contamination, roughness, etc.) are minimized or eliminated by the (1) Predoctoral fellow, 1957-1959. (2) For a n extensive review, see for instance A. N. Frumkin, 2. use of a dropping amalgam electrode with a conElekfrochem., 69, 807 (1955). tinuously renewed surface. (3) M. Breiter, M. Kieinerman and P. Delahay, THISJOURNAL, 80, The following reactions were studied: (a) re5111 (1958). A detailed bihliography is given. duction of bromate and iodate in alkaline solution (4) L. Gierst, “Cindtique d’approche e t reactions d’dectrodes iras examples of slow electrode processes without reversibles,” these d’agregation, University of Brussels, 1958. (5) I,. Gierst, article in “Transactions of the Symposium on Elecchemical complication: (b) the reduction of trode Processes, Philadelphia, M a y 1959,” E. Yeager, editor, John hexacyanochromate(II1) as an example of fast Wiley and Sons, Inc., New York, N. Y . , in course of publication. reaction; (c) the reduction of chromate ion in (6) R . Parsons, i b i d . . in course of publication. (7) W. H. Reinmuth, L. B. Rogers and L. E. I. Hummelstedt, THIS alkaline medium as an example of a process yieldJOURNAL, 81, 2947 (1959). ing current-potential curves with a minimum when (8) P. Delahay, article in “Advances in Polarography P. Zuman, amalgam electrodes of proper concentration are ”
editor, Interscience Publishing Co., S e w York, N. Y . , in cuurse of publication. (9) P. Delahay, article in “Proceedings of t h e Second International Congress of Polarography,” Pergamon, London, in course of publication.
(10) A. X. Frumkin, article in ref. 5: see alco ref. 2. (11) A. N. Frumkin and A. W. Gorodetzkaya Z p h y r i k . Chem., 1968, 461 (1928). We are indebted t u Dr. I-. Gierst for calling this investigation t o our attention.
-0.12
- 0.08
ol. no
-1.0
-1.2 POTENTIAL
-I 4 (VOLTS
VS.
-1.6 S.C.E.).
Fig. 1.-Difference of potential across the diffuse double layer (from the plane of closest approach to solution) as a function of electrode potential for the dropping mercury electrode and dropping thallivm amalgam electrodes (concentration in weight per cent) in 0.1 M NaCN a t 30”. Kate that the intersection of the curves for the 3.45 and l0.0!2 amalgams is due to experimental errors.
utilized (no minimum is observed with a mercury electrode) ; (d) the discharge of tetracyanocadmium(I1) as an electrode process with a preceding chemical reaction. Preliminary results on some of these reactions were summarized during discussion periods a t a recent symposium.12 Experimental Solutions.-Analytical grade reagents were used except for “electronic grade” (for masers possibly) potassium hexacyanochromate( 111). (The latter was purchased from City Chemical Corporation, S e w York, N. Y.) Traces of adsorbable impurities were removed from sodium cyanide by passing a stock solution over a column of activated charcoal according t o the procedure recommended by Parsons.6 The charcoal was purified by treatment with hydrochloric acid in a Soxhlet (no cartridge!) extrartor for two weeks and, subsequently, with distilled water (frequently renewed) for one week. Potassium chloride and sodium sulfate were calcinated at 500’ in a n electric oven for several hours to destroy organic matter. Amalgams.-A stock thallium amalgam was prepared by electrolysis of a saturated solution of thallous sulfate at a stirred mercury electrode. A platinum foil was used as anode. Qualitative tests on the salt indicated negligible concentrations of heavy metals other than thallium. The solution was kept saturated by repeated addition of solid thallous sulfate. h-o critical conditions were required for electrodeposition. The concentrated amalgam was kept at a potential of -0.7 v. (us. 5.c.e.) for several hours in a solution of 5Y0 sulfuric acid, which was renewed about every fifteen minutes, t o eliminate traces of metals less noble than thallium. Some thallium was lost in this operation, but this was not important since in all cases amalgams were analyzed for thallium before use. Three thallium amalgams of the following concentrations were prepared: 3.45 i~ 0.0570; 10.0 f 0.1% and 31%. The amalgam flowing from the capillary of the dropping electrode was analyzed as follows. Samples whose weight depended on the approximate thallium concentration were dissolved in 1: 1 nitric acid and the solutions sZowZy evaporated until dryness. The residue was digested hot with at least five successive portions of 10-15 ml. of water. Sodium sulfate and water were then added to make 250 ml. of 0.1 3f NanS04. After the precipitate had settled, 50 ml. of the solution were diluted to a final volume of 100 or 250 ml. with 0.1 Af Na2SOc. The final solution, which also contained Cl.000270 Triton X-100 as maximum suppressor, was ana-____ (12) P. DFlahay in discussion of the papers by A. N. Frumkin and I.. Gierst i n ref. 5 .
lyzed polarographically. X 0.1 31 Na?SOcsolution containing a known amount of thallous nitrate was used as a cotuparison standard. I t was ascertaimd that no thalliutn wiis lost in this procedure by analysis of mixtures of mercury with known amounts of thallium nitrate. Electrode Assembly.-An all-glass apparatus was used for the dropping thallium amalgam electrodes, except for a x r y short piece of rubber tubiug joining the amalgam rcservoir column to the polarographic capillary. Tygon tubing developed a brownish color in contact with the amalgam, and its use was avoided. The bottom of the amalgam reservoir was fitted with a ground glass plunger (no grease!) which allowed one to interrupt the flow of amalgam at will. This plunger, when properly ground, mas quite leak-free. The following procedure was used to fill the electrode assembly: the reservoir was evacuated and pule mercury was sucked into the capillary up t o a very small section of the connecting glass tube. The amalgam was then quickly vacuum-pumped into the reservoir from the top. The oxidation of the amalgam by air in the reservoir was prevented by making it the cathode of an electrolytic cell in 0.1 3’HpSOa, the anode being a piece of platinum foil. The cell voltage was adjusted to maintain a slow contiriuouq evolution of hydrogen. A polarographic H-cell was used as electrolysis vessel, the solution under study being in both arms of the cell. The amalgam electrode entered one arm while the other arm was connected to a saturated calomel electrode through a salt bridge. Thus, contamination of the solution in the electrolysis compartment by potassium chloride was avoided. For a.c. impedance measurements a third electrode, % . e . . a platinum cylinder of about 1.5 cm. diameter coaxial with the capillary of the dropping amalgam was inserted in the cell. Capillaries were not ground t o a conic tip for double layer and faradaic impedance measurements to avoid danger of plugging. It was realized that this resulted in frequency dispersion13 but this effect was quite minor in comparison with other sources of errors (uncertainty on points of zero charge, etc.). Capillary characteristics in polarographic studies were as follows. I n the reduction of chromate, nt = 1.23 mg. sec.-I, T = 5.7 sec. a t E = -1.10 v. ( v s . s.c.e.) for d.m.e.; m = 2.65, 7 = 3.15 a t E = -1.10 v. for 3.45% T1; m = 1.22, 7 = 6.3 a t E = -1.10 v. for 10% T1. For the tetracyano cadmium(I1) reduction, m = 1.23, 2.70, 1.13, 1.18 mg. sec.-land~= 5.4,3.1,6.1,6.8sec.atE= --~.~OV.(VS. s.c.e.) for the same sequence of electrodes and the 31% TI electrode. Densities of amalgam (needed in computation of the numerical coefficient in the Ilkovic equation): 13.5 (3.4570 T l ) , 13.3 (10.0% Tl), 12.9 (3170 Tl). Determination of Points of Zero Charge.-The drop time method was applied for thallium amalgams in 0.1 M NapSOc but the determination of the apex of the electrocapillary curves was quite uncertain. Points of zero charge were finally estimated from the shift of the tail electrocapillary curves with respect t o the curve of pure mercury. This procedure is open to question since a n increase in thallium concentration in the amalgam not only shifted the electrocapillary curve but also altered somewhat its shape. Results are compared in Table I with those Frumkin and Gorodetzkayall obtained by the inherently mole precise method of the Lippmann electrometer. Recording of Current-Potential Curves.--A Sargent polarograph model XXI was used, the pen- and-ink recorder of which had been replaced by a faster recorder (1.2 seconds full-scale deflection). Currents were measured a t the end of drop life. Bridge .-Alternating current measurements followed conventional practice.l32l4 The amplitude of the alternating bridge voltage never exceeded 5 mv. The bridge was balanced at the end of drop life. Exchange Current and Transfer Coefficient Measurements.-The following method was adopted t o avoid the preparation of the highly unstable potassium hexacyanochromate(I1). A polarogram*5 was taken of the 5 X Jf solution of potassium hexacyanochromate(II1) in 0.2 AT sodium cyanide and the half-wave potential was carefully (13) D. C. Grahame, THIS JOURNAL, 68, 301 (19413). (14) D. C . Grahame, i b i d , 11, 2975 (1949). (15) For polarographic studies, see D. N. H u m e and I h I Kolthriff, ibid , 6 5 , 1897 (1943).
DOUBLE LAYER
Sept. 5, 1960
AND THE
4311
THALLIUM-AMALGAM ELECTRODE
measured. The dropping (mercury or amalgam) electrode was kept a t the half-wave potential while the faradaic impedance was measured a t several frequencies. The chromium(III)_and (11) complexes thus had the same concentration M a t the electrode surface since their diffusion of 2.0 X coefficients should be nearly the same. The exchange current density 10 was calculated from the polarization resistance R, (series or parallel circuit) extrapolated to infinite frequency by
R a
-
RT 1 nFA Io
where A is the electrode area. This method of preparation of one reactant in situ under polarographic conditions is satisfactory when the standard cm. sec.-1 perhaps) rate constant is not too low ( > The effect of the curvature in the concentration profile near the electrode is then quite small. The transfer coefficient was determined from variations of 10 with the ratio of concentrations of chromium(I1) to chromium( 111) complexes a t the electrode surface. From the relation between exchange current density and standard varies rate constant one can show that log [~o/CC,,I,I,] , proportionality conlinearly with log [ CcF 12; (c) i t occurs a t polarographic current densities a t potentials a t which oxidation of thallium amalgam is negligible; (d) there is no specific adsorption of reactants a t the markedly negative potentials a t which this reaction occurs. Tafel lines in the absence of concentration polarization (foot of the wave) are plotted in Fig. 2. The change of overvoltage Aq a t constant current density with the difference of potential across the diffuse double layer, +H - 9 s from the Helmholtz plane to solution is (see eq. 3, ref. 3)
where a is the transfer coefficient, n a the number of electrons in the activation step and z the valence of bromate ion with its sign ( z = -1). Furthermore, one deduces from the slope of the Tafel line1*ana = 0.50. The values of +H - +S needed for application of eq. 2 were calculated from the point of zero charge and differential capacities for the electrolyte alone. In this case, the point of zero charge in the absence of specific adsorption must be used since bromate ion is not adsorbed in the range of potentials being covered ( = - 1.6 v. os. s.c.e.). The following values of the integral (16) This is varihtion of the classical method of determining a frnm a plot of log l a with the logarithm of one varying concentration. This modified method was reported by H. A. Laitinen, R. P. Tischer and D. K . Roe: see discussion section in ref. 5. See also ref. 6. (17) E. F. Orleman and I. M . Kolthoff, THISJOURNAL, 64, 1970 (1942). For double layer effects with the dropping mercury electrode see Gierst.6 (18) This procedure yields an apparent value una because the value of R determined in this fashion is affected by the variations of @H 98 over the interval of potential being considered. This point was already discussed.' The corrected value uf an, should be a little larger than 0.50 but the errnr ought to be quite small because of the narrow interval of potentials and the rather Bat QH - @a w s . E curve at -1.6 volts (us. s.c.e.). Corrected values of e n . can be obtained by the graphical method of Gierat.8
-
1.5
2.5
2
LOG I
I IN M I C R O A M R C M - e
)
Fig, 2.-Tafel lines for the reduction of 5 X l O F M hTaBrOnin 0.05 Jf NaOH and 0.1 M S a c 1 on mercury and thallium amalgam dropping electrodes of varying composition a t 30".
capacity a t -1.6 v. (vs. s.c.e.) were used: 18:O microfarads cm.-2 (d.m.e.), 19.9 (3.45% Tl), 21.3 (10.0% T1) and 25 (31% Tl). Experimental and calculated values of A7 are listed in Table I1 for the points of zero charge of Table I. Points of zero charge determined in this TABLE I POINTS OF ZERO CHARGE FOR THALLIUM AMALGAMS IN 0.1 i\f h-aoSOa E",
T1 concentration,
79
O
volts vs. s.c.e.
0 3.35 3.45 10.0 10.35 31 33.9 Ref. 11. This work.
DATAFOR
THE
T1 concn.,
%
0 3.45 10.0
-0.45
-
.69" .57b - .68b - .76" - .8jb - .88"
TABLEI1 REDUCTION OF BROMATE (FIG.2) VOLTS (vs. S.C.E.)
-1.6
-
A(+A +d, mv.
A7 calcd.,
A7 exp.,
V.
mv.
mv.
-0.113
..
..
..
8 2
18
Ob
4n
-
- 45.5
AT
.lo5 .111 .lo4 ,109 .lo3
5
20 8 9 31 10 23 41 .lo5 8 18 Upper values calculated by using points of zero charge of Frumkin and Gorodetzkaya; lower values from points of zero charge determined in this work. Smaller than experimental errors. 9 4
work seem to give better agreement than the values of Frumkin and Gorodetzkaya but even so Aq
4512
P.\UL DELAH,\Y .\ND LfARCOS
KLEINERMAN
Vol. 82
fer coefficient was 0.67 for the d.m.e. and 0.73 for the 31% TI electrode. Since the apparent exchange current density is proportional3 to exp [(an- z ) F ( 4 ~ &)/RT]( z valence of hexacyanochromate(II1); n = l ) , the foregoing results indicate that 4~ - 4s hardly varied for the different electrodes. !Vow, C$H - d~s is the solution of (see eq. 5, ref. 3 )
-
25-
where Ki is the integral capacity of the Helmholtz double layer, E , the potential a t the point of zero charge, E the dielectric constant (assumed to 20 be constant in the double layer) and C i the conl i LL centration of ion i and valence z i . The plus and n minus signs correspond to E ? E,, respectively. I t follows from eq. 3 that 1 4 ~ decreases with : E - E,/ for a given K i . In this case, however, -0.75 -I - 1.25 - I 50 the decrease of ] E - E,l a t a given E is almost compensated by an increase in Ki (see differential P O T E N T I A L ( V.vs. S . C . E . ) capacity-potential curves of Fig. 3) a t the potentials Fig. 3.-Differeritial capacity for mercury and thallium ( = -1.4 v. VS. s.c.e.) a t which the reduction of amalgam dropping electrodes in 0 2 AI YaCX a t 30’. hexacyanochromate(II1) was studied (Fig. 1).?n Further, some specific adsorption of cyanide may calculated is markedly too low for the 31y0 T1 have complicated matters. This example shows the amalgam. The shift of Tafel line is in the right danger of rash conclusions about the effect of shifts direction and in semi-quantitative agreement with in the point of zero charge on electrode kinetics. theory. Shifts being quite small, there is no doubt Reduction of Chromate in Alkaline Solution.that experimental errors account in part for dis- Large double layer effects are observed for the crepancies. Uncertainty on the integral capacity, reduction of chromate in alkaline solution (see particularly for the 31% T1 electrode, is an other eq. 2 ; z = - 2 ) on the dropping mercury electrode source of error. as was shown by G i e r ~ t . ~ A marked shift of the Reduction of Iodate in Alkaline Solution.-chromate wave was observed with thallium amalDouble layer effects in kinetics can be conveniently gam electrodes of increasing thallium concentration, studied for the reduction of iodate in alkaline solu- and waves exhibited a minimum a t low supporting tion (@H> 12), and indeed relatively large shifts electrolyte concentrations (Fig. 4). Minima were were observed with thallium amalgam electrodes particularly pronounced for the 3.45% T1 amalgam. of varying composition. Thus, in the reduction of Yo minimum was observed for mercury. M NaI03 in 5 x M NaOH and 0.1 5 X These minima recall those studied by Frumkin X NaC1, A7 = 12 and 41 mv. with respect to the and his schoo12,10and others for a number of anions. dropping mercury electrode for the 3.45 and 1 0 . O ~ o According to Frumkin’s views, the decrease in T1 electrodes. Quantitative interpretation was too current is due to a decrease in concentration of uncertain because of specific adsorption of the re- chromate ions a t the reaction site because of action product, iodide, on the thallium amalgam electrostatic repulsion ; and the increase of current (especially for the 10% TI electrode) in the range of beyond the minimum is observed because the inpotentials in which iodate reduction was studied crease of the rate constant for charge transfer, ( = - 1.05 v. B S . s.c.e.). as the potential becomes more negative, more than Reduction of Hexacyanochromate (111).-The ap- compensates the decrease in chromate concentraparent exchange current density for the couple tion a t the reaction site. The chromate concentraCr(CN)6-3 e = Cr(CN)6-4 strongly depends tion C* in the plane of closest approach (identified on double layer effects because of the highly nega- with the reaction site) is (see eq. 2, ref. 3) tive charge of the ions and the very negative standC* = C. exp[--zF(dH - ds)/RTI (4) ard potential for this couple ( = -1.4 v. vs. s.c.e.). Kandles and Somerton19indeed reported a marked where C, is the concentration outside the diffuse effect of supporting electrolyte concentration on layer and z = -2. One has C* < C, for +H the standard rate constant, and preliminary quan- 4s < 0, ,i.e. for E < E,, E, being the point of zero titative results on this double layer effect were charge. A decrease in current is observed proobtained in this Laboratory.12 Unexpectedly, vided that the rate constant for charge transfer is NaCN at not too large for potentials a t which C* < C,. The the exchange current density in 0.2 30 hardly varied for mercury and thallium-amal- difference between the 3.45 and log;’, T1 amalgams amp.cm.-* for the gam electrodes: 3.9 X (20) Figure 1 pertains to the tetracyanocadmium(I1) study in 0.1 M d.m.e., 3.45 and 10% TI electrodes and 4.8 X whereas hexacyanochromate(II1) was studied in 0.2 M N a C N . amp. for the 31% T1 electrode. The trans- NaCN Values of 4~ - 08 are of course slightly different for these two con0
a a a u
+
(19) J. E. B. Randles and K . W. Somerton, Trans. Faraday Soc , 48, 957 (1952).
-
centrations but the (@= 4 ~ ) ’ sare nearly the same at - 1 . 4 vults uersus s.c.e. for the two solutions.
DOUBLE LAYERAND
Sept. 5 , 1960
THE
THALLIUM-AMALGAM ELECTRODE
4513
-2.5
-3.5 ~.
D I F F E R E N C E ACROS: D O U B L E L A Y E R (VOLTS).
POTENTIAL DIFFUSE
Fig. 5.-Plot of log [ I / ( l d - I ) ](line A ) and log k (line B ) against +H - +s for the reduction of chromate a t -1.10 v. (us. s.c.e.) on the 3.45% TI electrode (Fig. 4). POTENTIAL
(VOLTS
vs. 9.C.E.)
Fig. 4.-Tracings of current-potential curves for the reduction of lo-' M Na?CrOc in XaOH of varying molar concentration on thallium amalgam dropping electrodes a t 30". Upper curve for 10.070TI amalgam and 0.01 M S a O H ; the others for 3.45% TI and a varying molar concentration of NaOH. Curves are corrected for the residual current.
is now understood. Thus, E , is more negative for the 10% T1 amalgam than the 3.45y0 T1 amalgam, and ( 4 ~ 4s)3.45
