92
TERRELL N. ANDERSEN AND HENRYEYRING
Vol. 67
ELECTRODE DEPOLARIZATION KLNETICS ON OPEN CIRCUIT’ BYTERRELL N. ANDERSEN AND HENRY EYRING Department of Chemistry, University of Utah, Salt Lake City, Utah Received M a y 31, 196R Platinum wire electrodes, in nitrogen-saturated, aqueous solutions containing Fe+3, Mn04-, Ce+*,Fe( CN)e-3, or CrzOl-e ions, were cathodically polarized to potentials a t or near that of a reversible hydrogen electrode. The polarizing circuit then was broken and the ensuing chemical oxidation of the electrode surface was studied kinetically by following the potential with respect to time. Three segments were observed in the open circuit potential-time depolarization curves. The first was a decay in less than 0.005 see. from the hydrogen overpotential to the reversible hydrogen potential. During the second segment, the chemisorbed hydrogen was diminished in concentration a t a rate equal to the limiting current of the oxidant. The rate of change of potential during the third segment was controlled by the rate at which oxidant accumulated a t the electrode and reductant was transported away from the electrode. A mathematical analysis was given which satisfactorily predicted the shape of the second and third segments. Between these latter portions of the curve, the potential was a mixed one, and the shape of the curve was not correlated with the concentrations of species present. However, this somewhat linear slope corresponded to a charging of the double layer (of constant capacity) a t a rate near that of the limiting current of the oxidant. The results indicated that the electrode, at the reversible hydrogen potential, had a hydrogen coverage of approximately one monolayer. Similar experiments were performed with a palladium electrode to study the importance of absorbed (or occluded) hydrogen. It was found in this case that the flux of absorbed hydrogen to the electrode surface was important throughout most of the depolarization, to potentials very close to the steady state.
Introduction If a hydrogen electrode is subjected to an oxidative environment, a t least two processes must take place before the potential attains a steady state. These are (1) the removal of chemisorbed hydrogen from the electrode surface and (2) the arrangement of a new double layer corresponding t o the potential of the oxidant or of the new environment. During such processes, potential-time curves exhibit inflections and currentpotential curves exhibit maxima, which indicate that more than one rate-controlling mechanism is important in establishing the new potentiaL2-” It is the object of this paper to study the kinetic processes taking place during the chemical oxidation of smooth platinum cathodes by following the potential change. Palladium cathodes also are studied in order to emphasize the importance of absorbed hydrogen, The oxidizing system chosen was nitrogen-saturated, dilute sulfuric or hydrochloric acid containing Mn04-, Ce+4, Crz07-2J or Fe(CN)6-3 ions. The hydrogen was supplied to the electrode by cathodic polarization, whereupon the polarizing circuit was broken and the electrode was allowed to depolarize on open circuit. For any electrode we may write, in general
(1) This is an essential portion of a thesis submitted to t h e Chemistry Department, University of Utah, i n partial fulfillment of the requirements tor a Ph.D. Degree. (2) J. K. Lee, R. N. Adams, and C. E. Bricker, Anal. Chim. Acta, 17, 321 (1957). (3) H. P. Agarwal and D. R. Sikka, Bull. India Sect. Electrochem. Soc., 6, 1, 11 (1957). (4) J. Giner. Z. Elektrochewa., 64,491 (1960). (5) T. C. Franklin and S. L. Cooke, Jr.. J . Electrochem. Soc., 107, 6,556 (1960). (6) A. L. Ferguson and M. B. Towns, Trans. Electrochem. Soc., 83, 271 (1943). (7) F. P. Bowden, Proc. Rov. SOC.(London), A125, 446 (1929). ( 8 ) J. A. V. Butler and G. Armstrong, ibid., A187,604 (1932). (9) A. Frumkin and E. E. Aikasyan, Dokl. Akad. Nauk SSSR, 100, 35 (1956). (10) M. Breiter, C. A. Knorr, and W. VolM, Z. Elektrochenz., 59, 681 (1956). (11) J. D. Pearson and J. A. V. Butler, Trans. Faraday Soc., 84, 1163 (1938).
where iext is the external current, 2if is the sum of the currents for the faradaic processes a t the electrode, C d L is the differential capacitance of the double layer, q d L is the charge on the electrode side of the double layer, and E is the potential of the electrode compared to that of a reference electrode (using the GibbsStockholm sign convention). Zif may be expressed as a difference of the sums of the cathodic and anodic reactions, and is related exponentially to the p0tentia1.l~~’~ I n the event that mass transfer to or from the electrode is slow, equations may be set up for the conservation of mass of each species a t the interface. If both charge transfer and mass transfer are rate controlling, the system of differential equations describing the over-all process cannot be solved to give potential explicitly as a function of time. This results from the complex nature of the equations as well as from the lack of knowledge concerning the initial conditions, rate constants, and the diffusion mechanism of hydrogen in the metals. I n order to make simplifications in the analysis, an experimental analysis is first made to determine which processes predominate a t any given potential.
Experimental The cell consisted of a 600-ml. Pyrex electrolytic beaker tightly fitted with a rubber stopper,14 which held the various inlet tubes. 250 ml. of electrolyte (dilute HzS04 or HC1 with oxidant added) was chosen for each experiment; by using this volume the bulk concentration of any species would not change by m much as 1 % during a run. The electrolyte was vigorously stirred in all of the experiments (unless specified otherwise) by means of a magnetic stirring bar. The solution was kept Nz-saturated by bubbling 99.997% pure nitrogen through i t prior to each experiment. The indicator electrode consisted of 99.9% purity platinum (the palladium content was less than O.OlOj,), or palladium wire of 0.0406-em. diameter (B&S gage 26), with 10.2 cm. (12) S. Glasstone, K. J. Laidler, and H. Eyring, “The Theory of Rate Processes,” McGraw-Hill Book Co., New York, N. Y., 1941,p. 575. (13) P. Delahay, “New Instrumental Methods i n Electrochemistry,” Interscience Publishers, Inc., New York, N. P., 1954,p. 32. (14) The rubber stopper enclosing the top of the cell was presoaked in dilute base and acid solutions. Prior to and during the experiments neither the electrodes nor the electrolyte came in contact with the stopper The experiments were run within a few minutes after transferring the electrolyte t o the cell, with Nn vigorously bubbling through the solution in the meantime. Therefore it is considered t h a t t h e rubber stopper in no way affected the accuraay of the results within the ascribed precision.
Jan., 1963
ELECTRODE D E P O L A R I Z A T I O N KINETICS ON
immersed in the solution. The immersed portion of the electrode was in the shape of an inverted horseshoe with the two ends protruding out of the cell through ceramic tubes which insulated the wire from the rubber stopper. Therefore, the wire could be heated in the cell by passing current through it to clean its surface. A saturated calomel electrode was used as the reference halfcell and made contact with the electrolyte by means of a, KC1agar salt bridge drawn to a capillary a t its tip. The working electrode also consisted of platinum; it was enclosed in an inverted Pyrex tube which allowed oxygen gas produced during polarization to be evolved. A glass tube was contained in the stopper as an inlet for reagents; otherwise it was closed. The tubes and electrodes were positioned relative to one another SO that the salt bridge and working electrode were on opposite sides of the indicator electrode. The potential difference between the indicator and reference electrodes was recorded by means of an Offner Type P dynograph assembly with a Type 9405 cathode follower coupler inserted between the amplifier and electrode leads. The limit of precision of the instrument was A 5 mv. except at potentials positive of 6lDO mv. and negative of -150 mv. (0s. s.c.e.). A Model G Beckman pH meter was used to read steady-state potentials within l t 2 mv. A constant polarizing current was supplied by means of a d.c. battery connected in series with an ammeter and variable resistor. The electrolyte was prepared and purified following methode set forth by Boekris.16J6 The water was doubly-distilled from basic permanganate solution, chemically pure acid was added, and the resulting solution was pre-electrolyned. Electrolyte transference was made by means of Nz pressure or vacuum. The indicator electrode was flamed, placed in the cell, and heated to approximately 900’ for 1min. in a nitrogen atmosphere (by means of a powerstat), and then successively anodized and cathodized at 10 ma. for a few seconds. The latter treatment probably removed trace amounts of impurities, and may have produced a fresh coating of spongy platinum17 on the electrode. The electrolyte was introduced into the cell and nitrogen-saturated, after which analytical grade depolarizer, dissolved in solution, was added to the cell (along with product salt, if desired). The oxidizing agents used were KZCrz07, KMn04, Ce(SO&, Fez(S04)aor Fe(NOa)j, and KtFe(CN)6and the product solutions were CrK(SO&, MnSO4, Ce(NO& FeS04, and K4Fe(CN)e. The range of concentrations studied was 10-4 to 5 X M. The electrode then was cathodically polarized,18 the nitrogen was turned off, and the polarizing circuit was broken, allowing the indicator electrode to depolarize on open circuit. The nitrogen was turned off to prevent bubbles from impinging on the electrode or on the tip of the salt bridge during depolarization. The cleanliness of the electrode was ascertained by the overvoltage corresponding to a given current density and by the lengi,h of time necessary for the depolarization to take place. The electrode was considered “clean” in the above tests, as well as in actual experiments, when (1) good reproducibility was obtained in the repetition of experiments, and ( 2 ) when further purification of the solution or electrodes did not yield different results. Any data presented here were remeasured several times, and the relative precision was better than 15% unless otherwise stated. Except for the experiments in which the stirring rate was varied, the speed of the stirring bar was 670 i 25 r.p.m. The temperature was 25 1 in all experiments except when 5” was varied and thLe nitrogen pressure was approximately 0.85 atm. in each experiment. The time of depolarization in the absence of oxidant was 30 or more times that obtained in the presence of oxidant at its lowest concentration, so oxygen and other stray depolarizers were considered t o have negligible effect on the results. O
Experimental Results and Conclusions The typical shapes of the depolarization curves for platinum and for palladium are shown in Fig. 1, although the particular curves shown were obtained in Mn04-.19 In each case the polarization current was (16) A. M. Aazam, J. O’M. Bookris, E. E. Conway, and A. J. Rosenberg, Trans. Faraday Sac. 46, 918 (1960). (16) J. O’M. Bockris, “Modern Aspects of Electrochemistry,” Academic Press, New York, N. Y.,1954, p. 135. (17) r C Anson, Anal Chem., 33, 934 (1061). (18) It made no dlfferenre in the results whether polarization u a s begun before or after oxidant was added. (19) Any effects illustratpd in the case of a particular solution were abserved in any of the depolarizers unless speolfied otherwise.
OPEN CIRCUIT
93
L-
t, SEC (CURVES 2- 4). I 2 3 t, SEC.(CURVES I). Fig. 1.-Depolarization curves for Pt and Pd showing the effect of polarization time: curve 1, P t ; t p o l = 0.5 to 120 sec., curves 2 to 4,Pd; tpol = 5.5,11, and 30 sec., respectively. Solution: 0.45 M HzSOl containing 3.2 X M MnOl-.
o
greater than the limiting current of the oxidant, so liberation of hydrogen occurred. It can be seen t h d the depolarization curves each consist of three distinct segments, AB, BC, and CD, by which these segments shall be referred to throughout the remainder of this paper. The length of BC (in seconds) will hereafier be referred to as T or the transition time. Interpretation of the results along with experimental and theoretical justification is given below. Depolarization during AB.-When the battery circuit is opened, the hydrogen concentration on the platinum electrode immediately decreases to that coverage which can be supported by atmospheric pressure; any hydrogen more than this immediately leaves the electrode as gas, due to a pressure difference across the interface. Thus the potential rises from EA to E g , the reversible hydrogen potential, in less than 0.005 sec. Since hydrogen overvoltage decay has been studied extensively elsewhere20,21 segment AB was not studied kinetically here. In the case of palladium, (Pd-H), and/or (Pd-H)B are/is formed inside the metal at some concentration.22*23When the current ceases, the surface h ydrogen immediately is absorbed or evolved to the extent that the palladium surface and interior are approaching equilibrium with respect to hydrogen (although, of course, the surface hydrogen is being oxidized rapidly by the oxidant). If very little hydrogen is present in the metal, the potential EB will be positive with respect to the hydrogen potential, while if the interior is nearly saturated, the potential will lie near the hydrogen electrode potential. Depolarization during BC.-From B to C the onKy net change taking place a t the electrode-solution interface is the decrease of adsorbed hydrogen, due to its oxidation by depolarizer. The oxidant ions are reduced as rapidly as they reach the electrode surface, so their concentration at the interface, as well as that of the production, is not changing. The chemistry thus consists of a competition between (a) diffusion of absorbed hydrogen from the metal interior, and (b) mass transport of oxidant from the solution to the electrode surface. In the case of platinum there is very little ab(20) P C. Milner, J . Electrochem. SOC.,107, 343 (1960). (21) P. Ruetschi, zbzd., 106, 819 (1959). (22) S. Schuldiner, G. W. Castellan, and J. P. Hoare, J . Chem. Phys., 28, 16 (1958). (23) T. B. Flanagaii ana P. A. Lewis, J . Electrochem. Sac., 108, 437 (1961).
TERRELL X. ANDERBEN AKD HENRYEYRIIW
94
I
I
I
I
I
TI ME. Fig. 2.-Depolarization curves for Pt in 0.45M H2S04conequiv./l.: (1) taining the various oxidants a t 16 i: 1 X MnOd-; (2) Cet4; (3) Crz07-2; (4) Fe+3; (5) Fe(CN)e-*.
ti 5
e
2 I
d
I
- 0.2
I
I
I
I
I
0.6 I.o POTENTIAL (VOLTS vs. SCE 1.
0.2
Fig. 3.--Experimental determination of limiting currents in 0.45 1M HzS04containing 36 X N solutions of various oxidants: ( 0 )MnOe-; (0)Fe+3; (A)Fe(CN)s-3; ( A ) Ce+4. Geometric electrode area = 1.3 cm.2.
sorbed hydrogen, so (b) is the slowest step during r , while in the case of palladium there is an abundance of absorbed hydrogen, and both (a) and (b) are comparably slow. The supporting evidence for the preceding explanation of BC is plentiful. (a) Platinum.-(1) All of the oxidants studied gave similar type curves as shown in Fig. 2. The break
Vol. 67
potentials EB and Ec were independent of the type or concentration of oxidant studied, but depolarization was more rapid in more concentrated solutions of oxidant. (2) The break potentials, Eg and Ec, were independent of any variables in the experiment except the hydrogen ion concentration. Eg corresponded to the reversible-hydrogen electrode potential a t a hydrogen pressure of 1 atm. Ec increased with an increase of hydrogen ion concentration in a manner commensurate with a hydrogen electrode from pH 0 to 3; for pH greater than 3, concentration polarization of H + occurred and masked the bulk pH effect. EB varied with pH in the same manner as did Ec, but the precision of the potential reading was quite poor ( i:25 mv.) . (3) Limiting currents were obtained in solutions containing Fe+3, Cef4, Mn04-, and Fe(CN)6-3; Figure 3 shows the potential-current plots for each of equivthese oxidants a t a concentration of 36 X alents/l. in 0.45 M H2S04 solutions stirred a t 670 r.p.m. The points were obtained by applying a constant current and observing the steady-state potential to which the electrode relaxed within 1 sec. The limiting currents were found experimentally to be directly proportional to the oxidant concentration. It can be seen from Fig. 3 that the oxidants are being transported to the electrode a t their limiting currents a t all potentials positive of Ec. I n the case of Cr20,-2, the potential a t constant current slowly drifted toward negative values and did not reach a steady-state within 1 min., except for potentials more negative than -2250 mv. As many authors have stated24126a film is formed on platinum, upon reducing dichromate, which prevents further reduction of the dichromate but which supports reduction of H+. This explains the negative drift of potential with time: Crz0,-2 reduction sites are continuously poisoned, so the effective current density for dichromate reduction increases while the total current is being held constant. (4) The depolarization rate a t BC was independent of the product ion concentration in the bulk of the solution, from very low concentrations (none added) to 10-1 M . High concentrations to 10-1 M ) of reacted with Mn04- to form Mn02, and hence slowed down the depolarization rate by lowering the effective Mn04- concentration. ( 5 ) The depolarization rate mas independent of hydrogen ion concentration from pH 0.2 to 4, a t constant ionic strength (by the addition of &SO4 to the H804). (6) The rate was independent of K2S04concentration within the concentration region for which the activity coefficient of oxidant ions did not vary greatly. I n solutions of 0.1 N HC1 containing Cr207-2 and Fe+3, r was identical with that in dilute sulfuric acid solutions over the entire range of concentration of oxidant. The anion was not varied in the case of the other oxidants. (7) r decreased significantly with an increase in stirring rate throughout the complete stirring range. In the range 300-900 r.p.m., r decreased by 32-325% for every 100% increase in stirring rate. In non-stirred solutions there was present an additional arrest starting ( 2 4 ) Yu. Yu. Matutis and A. Yu. Mitskene, Lietuuos T S R Mokslu Akad. Darbar Ser. B , 1, 45 (1959). ( 2 5 ) H. Gerisoher and M. Kappel, 2. p h y s i k . Chern., 20, 83 (1959).
Jan., 1963
ELECTRODE DEPOLARIZATION KINETICSo r OPENCIRCUIT
a t EB and ending approximately 60 mv. positive of EB. This was due to hydrogen gas near the electrode being oxidized. (8) The depolarization rate in vigorously stirred solutions was independent of the polarization time from tpol = 0.5 sec. to 2 min. Longer times were not studied due to the greater relative importance of impurities which were slowly plated out during cathodiz''5t'ion. (9) The depolarization rate was essentially insensitive to the polarization potential unless hydrogen gas was liberated, in which case the slope of the entire depolarization curve was noticeably decreased. Since 7 for platinum is independent of polarization time, and Ec - EBis a constant, we can assume that roughly the same amount of hydrogen is oxidized in each depolarization during the transition time. From the limiting current data we may further say that this rate is constant [electroii/(cm.2 sec.)], and is proportional to l / r . From the above deductions, several results can be obtained which further strengthen the previous discussion. (10) An apparent activation energy may be found for the slow process during r by employing the Arrhenius rate equation
where E is the activation energy, T is the absolute temperature, R equals the gas constant, and A and Icl are constan ts. Theref ore
95
ferred to that for Fe+3, a t concentrations of 9 X lo-* M . Column 4 indicates the relative reaction rates, given by l / ~for , section BC of the curve. Column 5 shows the relative flux (compared to that for Fe+3)for the several oxidants. Since ilim = AnFmCoxoand we have no theoretical way of knowing to what power D enters into m, the ratio of nD is taken to be the ratio of the flux for the various depolarizers. This approximates m by D/6 where 6 is an effective diffusion layer which is nearly the same for each oxidant. Since several products could result from the reduction of MnOa-, three values for the corresponding flux are listed which represent n values of 3, 4, and 5 , respectively. 130th experimental methods (transition times and limiting currents) show the same relative reaction rates among the depolarizers as do the diffusion coefficients. Since
the rate of reaction during r , as given by the over-all amount of hydrogen oxidized per unit time, should be first order with respect to the bulk concentratio:n of oxidant. This is assuming A(CE) is constant (ais is AE) during 7 ,and is independent of Coxo. Therefore (Coxor)should be constant in the case of each depolarizer over differing concentrations. This is shown tlo be nearly so in Table 11. It is to be noted that C in eq. 4 and 5 is the total measured capacit,y of the electrode and includes the so-called pseudocapacity due to hydrogen atoms. TABLE I COMPARISON 06 REACTION RATESUSINGDIFFERENT METHODS OF CALCUL.4TION
The slope of the log ( l / r ) vs. (-.l/T) curve (for the M F e + 9 gave an activation energy of oxidant 8 X 4.94 kcal./mole with a standard deviation of 0.4% between the experimental points and the line. The viscosity of aqueous solutions changes slowly enough between 2 and 85' (the range in which the temperahre variation was carried out) that the increase in reaction rate may be assumed to apply only to the diflusion coefficients of the ions (or the slow surface processl if there is one which is rate determining). The low activation energy obtained is typical of diffusion, and in fact very closely agrees with the 2.6% per degree increase in the diffusion coefficients of the ions in excess electrolyte as given by Jander.26 (11) We can compare the relative rates of reaction, as well as the relative limiting currents of the various depolarizers, to their diffusion coefficients. This is done in Table I a t the same stirring rate and concentraM ) for each oxidant species. Column tion (9 X 2 shows the diffusion coefficients2' of the various ions in excess electrolyte (as the experiments here employed) a t 22'. These values were chosen from the data of Jander.26 It has been shown that D, for ions in excess electrolyte, is independent of concentration in the range to 10-L M,28so these values are considered applicable in all the work here reporteld. Column 3 shows the limiting currents for the various depolarizers, re(26) G. Jander, C . Blollm, and B. Griittner, Z. anoi'g. allgem. C h m . , 268, 205 (1949). (27) No value for Dee+ 4 in excess electrolyte could be found; 0.43 was approximated a8 D C ~ + ~ ( D F ~ ~ + /2).D F ,The + value agrees quite closely w i t h DThia, and is assumed t o be accurate to within 15%. (28) B. Gruttrier and G. Jander, Z. ~ ~ L O T allgem. Q. Chem., 266, 225 (1951).
Depolarizer
Fe + 3 Mn04Ce +4 Fe(CP\')6+ C1-207-~
D
(;E*)
____ ilim ilirn(FeCS)
0.54 1.5 0.43 0.52 0.93
1.0 9.8 0.76 0.91 t .
1/r
ili,(calcd.) __ ilirn(F"e+8)(CdCd.)
I / r ( ~ e + ~ )
1.0 6.7 0.34 1.35 5.8
1.o 8.3,11.1,13.8 0.79 0.96 10.3
TABLE I1 DEPENDENCE OF T
CONCENTR.4TION 7Cc0x0
(equiv./l.)
x 104 36 24 16 10 6 2
(CO+)F~ +a
x 104 2.70 2.52 2.4 2.5 2.37 1.78
(nCor)cso,-*
x 104 2.70 2.76 2.72 2.8 2.82 2.6
(COT) +I
x
104
5.25 6.0 6.0 7.6 8.2
Although it has been established previously that the slow step, in the case of platinum, is the linear rate of oxidation of hydrogen, it is still necessary to explain the shape of the potential-time curve. Since the solution is nitrogen-saturated, the Xernst equation cannot be used to describe the electrode potential. Rather, the time dependence of the charge distribution along the coordinate vertical to the electrode surface, or of the electrode capacity, must be taken into account. Considering ey. I we have, therefore, during section BC of the platinum depolarization curve : Zif = -d(CE)/ dt. Consider the H a d s and protons to be essentially in equilibrium. The rate of oxidation of the reductant is negligible, and the reduction of the depolarizer proceeds
TERRELL N. ANDERSENAND HENRYEYRING
96 W 0
v)
0.1-
I
I
I
l
l
I
I1
-
0
.I .I5 .2 .25 TIME IN SECONDS.
0.5
.3
Fig. 4.--Experimental and calculated E us. E curves from t = 0 7 for Pt. Solutions 1.6 X lo-* M Mn04-: (1) calcd.; (2) exptl.; 18 X .&f Ce+4; (3) calcd.; (4) exptl.
to
It is interesting to calculate the amount of hydrogen oxidized during r . The amount of hydrogen will be reported as the number of surface platinum atoms covered assuming one hydrogen atom per surface platinum atom. Calculating the quantity of hydrogen as i l i m 7 , we obtained the results in Table 111. e is the fraction of surface platinum atoms covered with hydrogen. The results are consistent with one another (considering that the capacity oi the electrode might vary somewhat from one system to another). The results also agree wjt h other authors who have anodically oxidized platinum from the hydrogen equilibrium potential, and who have concluded that the metal is covered largely with atomic hydrogen.10~1'JO~37 To realize further the importance of occluded hydrogen (as compared to that of adsorbed and gaseous hydrogen) experiments were run with palladium similar to those for platinum.
at the constant rate, ilim, throughout 7. Then, neglecting absorbed or gaseous hydrogen, we have (5) Since no explicit expression for C as a function of E was available, an experimentally determined capacity mas used. The C-E curve was graphically integrated to obtain q as a function of E. Then using the relationship q = qinit E was found as a function of t. The capacitance-potential curve was taken from the paper of Breiter'O as determined and confirmed by several a ~ t h o r s ~ for ~ * smooth ~ ~ - ~ platinum ~ in HzS04 solutions. In converting Breiter's data (8, the surface coverage) to q, it was assumed that there was present one hydrogen atom for each surface platinum atom a t a e value of 1. The value of 1.5 X l O I 5 surface platinum atoms per cm.2 of electrode was useda4and the true area of the present electrode was taken as twice its apparent area. Potential-time curves, as calculated and as obtained experimentally, are shown in Fig. 4 for two of the systems studied. It can be seen that the agreement in shape as well as slope of the calculated and experimental curves is very good. Since the roughness factor of the electrode surface was only estimated, the agreement of the slopes is not too important except that they agree to approximately 30%. The important agreement is the general linear curve with its slight inflection. The two slight maxima which occur on either side of the inflection also occur as maxima in polarography, and have been interpreted in the case of electrolytic oxidation of hydrogen electrodes as absorbed, as well as adsorbed, hydrogen in the p l a t i n ~ m . That ~ ~ ~ ~the amount of absorbed hydrogen is very small is evidenced by the short lived nature of the second arrest, as well as by the independence of the depolarization time on the polarization time. This is confirmed by other techniques which measure hydrogen in platinum.36 (29) E. Wicke and E. Weblus, 0.Elektrochem., 56, 169 (1952). (30) A. Euolcen and B. Weblua, ibid., 85, 114 (1951). (81) P. Dolin and B. Ershler, Acta Physicochim. URSS,13, 747 (1940). (32) P. Dolin, B. ErshIer, and A. Frumkin, %bid., I S , 779 (1940). (33) 111. Rreiter, H.Kammermaier, and C. A. Knorr, Z. EZektrochem., 60, 37 (1956). (34) H.A. Laitinen and C. G. Enke, J . Blectrochem. Soc., 107,773 (1960). (35) A. Frumkin and E. E. Aikrtsyan, Dokl. Akud. NuuB SSSSR. 100, 35 (1955) (36) D.P.Smith, "Hydrogen in Metals,' Univ. of Chicago Press, Chicago, Illinois, 1958.
Vol. 67
TABLE I11 SURFACE COVERAGE O F PLATINUM ELECTRODE Oxidant iiim, ma. 7. 8 0 C .
36 X lo-' iM Fe+3 16 X 10-4MFe+a 18 X lo-* M Cef4 18 X lo-* AI Fe(CN)6-3 5 x lo-' M
4.05 1.8 1.52 1.3 5.42
0.073 .15 .32
.I4 .092
0
0.49 .43 .73 .40 * 80
(b) Palladium.-A palladium electrode gave results which were very different from those of platinum in two respects: (1) a t a given polarization time or current (with other variables also being fixed), the depolarization time was very many times longer; and ( 2 ) in stirred solutions, the depolarization time for palladium was very sensitive to the time and current of polariz a t i o n i . e . , to the amount of hydrogen discharged at the surface. (1) and ( 2 ) above are exemplified in Fig. 2, which shows the depolarization curve for plat>i num and palladium in 0.45 M HaSOl containing 3.2 X M R/In04-. Palladium shows the same type of dependence on stirring rate and oxidant concentration as platinum. Depolarization during CD.-When the rate of supply of internal hydrogen has become slow enough (due to the diminution of its source), and the surface concentration is sparse enough that oxidant can accumulate at thd electrode surface, the potential rises sharply (C in Fig. 2 ) . At this stage of the depolarization, reactions (i) and (ii) become important in determining the potential. The reason that the depolarization during part CD (as well as BC) for palladium is slower than that for platinum is also due to absorbed hydrogen; this may be shown by slowing down the rate of transport of oxidant to the surface, If this is done (by suddenly decreasing the rate of stirring of the solution) the depolarization curve changes direction and the potential becomes negative again. When the transport rate of oxidant is decreased, the hydrogen concentration on the electrode actually increases since the diffusion rate of absorbed hydrogen to the surface overtakes the rate of transport of oxidant. When Mn04- or Cef4 was used as the depolarizer, the depolarization curve leveled out much more slowly than in the case of the other oxidants (see Fig. 2 and 3). This was due to the formation of platinum (or pel(b7) B. Ershlor, Acta Physzcochim., 7 , 327 (1937).
Jan., 1963
ELECTRODE DEPOLdRIZhTION KINETICS ON
ladium) 0xide,~J8 which took place before the steady state could be attained. The depolarization rate during CD depended on the concentration of oxidant and stirring rate qualitatively in the same manner as did l / ~ .In order to evaluate the idea that, mass transport was the slow step a model was set up and compared with the experimental results with platinum. The Fe+2-Fe+'L system was considered, since oxides were absent, and the oxidationrzduction reaction was assumed to be in equilibrium. Because of the geometry of the cell, the approximation was made that there was a diffusilon layer of thickness 6 around the electrode, beyond which the stirring of the solution kept the depolarizer concentration constantthe bulk concentration. Between the electrode surface and 6, a diffusion which obeyed Fick's law was assumed to be the only mode of mass transport. This model is very approximate since the immobile layer would vary in thickness from one part of the electrode to the other because of the motion of the liquid. During the transition time, 7,Fe+3does not accumulate a t the electrode, so the initial condition is b C ~ . , t ~ / bt = 0. Therefore, from Fick' ssecond law, i>CFet3/dX = constant wherd IC is the radial distance out from the surface of the wire. Linear diffusion, rather than cylindrical diffusion, is sufficient here since the diffusion layer, 6, is small compared to the radius of the wire. We shall assume, for calculation purposes, that C F ~ + * is constant and equals C0Fef2throughout CD, although the concentration of Fe+2 near the electrode is larger than its value in bulk and decreases with time. From the initial and boundary conditions Cpeta was obtained as a function of time using a Fourier series for the product solution, to Fick's second law. Since the series converged very slowly, a Burroughs 205 Datatron was used to obtain numerical results to the resulting equation
The computer was set t o calculate values for the eeries a t a given t until two successive values differed by less than lo%, a t which time the computer increased t and calculated the next series. The experimental values were compared with the calculated ones by converting the experimental poand comparing the result with tential to CFnt3/CoFe+3, the calculated ratio. The theoretical results are shown in Fig. 5a for different values of the parameter 6, and the experimental curve, for C'FetJ = 1.6 X M and C'Fetl = 3.2 X M (in 0.45 M H2S04)isshown in Fig. 5b. Since there is no way of knowing a t which (38) I. M. Kolthoff and N. Tanaka, Anal. Chem., '26, 632 (1954).
0
0.2
C)PEN
0.4
CIRCUIT
06
97
T I ME.
TIME IN SECONDS.
Fig. 5a (left).-Calculated values of C/Co: (@) = 0.001 cm.; (A) = 0.002 cm.; (0) = 0.005 cm.; ( A ) = 0.01 cm. Fig. 5b
(right): C/Co taken from experimental decay curve.
potential the oxidation-reduction couple becomes irate controlling, there is no way to choose t = 0 for the experimental curve. Therefore the upper half of the curves were compared to determine an optimum 6; this can be seen to be approximately 0.0015 em. The theoretical and experimental curves agree well from ED down to C/CQvalues near 0.25, which is below the sharp bend in the depolarization curve (between C and D). Below this value the calculated C/CO drjops much faster than the experimental one. This ie because the Nernst equation no longer applies. The potential can change no faster than the double layer can be charged and this rate is a t least as slow as the limiting current. Considering a constant double layer capacity of approximately 20 pf./cm.2, the dE/dt curve can never attain the steep asymptotic slope which the diffusion equation predicts. Some hydrogen probably is present during part of this potential climb. Neglecting the Concentration polarization of Fe+2 would tend to make the curve less steep also. I t is interesting to note that the limiting current obtained in this work resulted in a calculated value for 6 of 0.0011 em. (Cm = ADC0n5/6). This calculation also uses the diffusion layer concept which must be considered only approximate. Acknowledgments.-The authors wish to expyess appreciation for financial support of this work to the U. S. Army Ordnance under OOR Project Number 1889, Contract No. DA-04-495-ORD-959, to the U.S. Atomic Energy Commission under Contract KO. AT(11-1)-1144, and T. N. A. wishes to express appreciation to the NLttional Science Foundation for a Cooperative Fellowship. They also wish to thank Mr. Edwin Dallin, Department of Chemicad Engineering, for coding the computer for the diffusion problem.
