Zinc Amalgam Electrode Reaction in Alkaline Media As Studied by Chronocoulometric and Voltammetric Techniques

The Mechanism of the Zinc(ll)-Zinc Amalgam Electrode Reaction in Alkaline Media As Studied by Chronocoulometric and Voltammetric Techniques

DeWitt A. PayneI and Alien J. Bard* Department o] Chemistry, The University of Texa~ at Austin, Austin, Texas 78712

ABSTRACT The reduction of zinc (II) and the oxidation of zinc amalgam was studied in 0.18-4.0M KOH solutions. The primary electrochemical technique employed was potential step chronocoulometry with data acquisition on a small digital computer. The kinetic parameters were obtained by fitting the experimental charge-time curves to the complete theoretical equation for a stepwise electron transfer mechanism. The sytem was also studied by d-c and a-c polarography and linear scan voltammetry. The results of this study were compared to those of previous workers and shown to be consistent with a mechanism based on stepwise electron transfer Zn(OH)42- ~ Zn(OH)~ + 2 OH- Zn (OH) 2 + e ~--- Zn (OH)=- Zn(OH)2- ~- Zn(OH) + OH- Zn(OH) ~u Hg -t- e ~=~Zn(Hg) -b OH-

One of the most significant features of the study of purpose programmable digital computers (20, 21), have electrochemical kinetics during the last 20 years has been very useful, particularly for experimental times been the evolution of theoretical and experimental in the sub-second region, in obtaining this data. The procedures which are useful in uncovering the differ- data obtained by these methods can be fitted to the ent stages in the complex series of processes which equations in their complete form, without the necessity comprise an electrode reaction. An investigation of the of approximations or linearizations sometimes required kinetics of an electrochemical reaction would ideally to make the analysis of data tractable. We report here lead to the elucidation of the nature of the various a study of the zinc(II)-zinc amalgam system using steps and a determination of their rate constants, the several electrochemical methods and digital data ac- identification of the intermediates and products, and quisition techniques. the determination of the adsorption isotherm for all A number of studies of the alkaline zinc electrode adsorbed species. Usually, because of experimental reaction have been made. A significant part of this and theoretical limitations, only part of the informa- effort has come from the space program's search for tion is accessible for a given system. Although charac- high energy-density primary and secondary batteries terization of intermediates is of prime importance, di- and the important role of silver/zinc and zinc/air rect observation of these may not be possible if their primary batteries in this connection. Although studies concentrations are too low or their lifetimes are too of the alkaline zinc electrode reaction often are con- short. However, analysis of the current-potential rela- cerned with reactions at the pure metal electrode, it is tionship obtained by several nonsteady-state methods common practice in batteries to amalgamate the zinc can yield further information on complex mechanisms plates. Hence, we deemed a study of the alkaline and faster processes. zinc (I) -zinc amalgam electrode reaction justified. Of particular interest in this work is the study of Moreover, the reaction at the amalgam electrode is electrode processes involving more than one electron easier to understand than the reaction at the pure metal transfer step (1). Vetter (2-4), Hurd (5), and Mohilner electrode, which may be complicated by the crystal- (6) have calculated the steady-state polarization lization process and more difficult surface preparation. curves for a set of two or more consecutive single elec- A number of workers (22-31) have studied the alka- tron transfer steps. Some reactions for which consecu- line zinc (II) -zinc amalgam electrode reaction with tive electron transfer mechanisms have been proposed somewhat different results. Gerischer (22, 23) deter- on the basis of steady state-measurements are TI(III)/ mined reaction orders of hydroxide, zinc, and zincate TI(I) (7) and quinone/hydroquinone (8). The theory by measuring the change of the charge transfer re- of consecutive electron transfer mechanisms for elec- sistance with concentration and expressed the exchange trochemical techniques involving potential steps, cur- current, io, as rent steps, and a-c polarography has also been given (9-15). io = 2FAk~176 ]~ ~176[1] The establishment of the mechanisms of an electrode This result led to the reaction mechanism in Eq. [2] reaction often requires acquiring large amounts of ac- and [3] curate experimental data and fitting this data to com- fast plicated theoretical equations. Digital data acquisi- Zn(OH)42- ~ Zn(OH)2 ~ 2 OH- [2] tion systems (16-21), especially those based on general Zn(OH)2 ~ 2e ~ Zn (Hg) ~ 2 OH- [3] * Electrochemical Society Active Member. 1 Present address: Tennessee Eastman Company, KingsDort, Ten- nessee 37660. Farr and Hampson (24) duplicated Gerischer's results Key words: potential step chronocoulometry, electrode reaction in ultrapure solutions by faradaic impedance measure- kinetics, polarography, digital data acquisition, consecutive electron transfer reactions. ments. Matsuda and Ayabe (25) studied the reduction

1665

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process by d-c polarography and found that the mecha- Apparatus.--A single compartment electrolytic cell nism was the same as that of Gerischer, but that a was manufactured by Metrohm Ltd. (Model EA664) and 0.42 Behr et al. (26) and Morinaga (27) also obtained obtained from Brinkmann Instruments was used for results which were consistent with the above mecha- all experiments. The working electrode was either a nism. Stromberg and co-workers (28-31) obtained re- hanging mercury drop electrode (h.m.d.e.) or a drop- sults which were similar to those of Matsuda and ping mercury electrode (d.m.e.). The auxiliary or Ayabe (25) for the reduction process but found that counterelectrode was a piece of platinum wire im- the oxidation process did not fit the mechanism pro- mersed directly in the solution. The reference electrode posed from the study of the reduction reaction. They was a saturated calomel electrode (SCE) which was proposed that the reduction and the oxidation involved separated from the solution by a Luggin-Haber cap- two different, totally irreversible reactions, each in- illary. The tip of the capillary was placed as close as volving a single two-electron transfer step. Their possible to the working electrode to minimize uncom- mechanism for the oxidation reaction was pensated resistance. The hanging mercury drop electrode was manufactured by Metrohm Ltd. (Model Zn(Hg) + OH- -* Zn(OH) + + 2e [4] E-410). A fresh drop of 0.032 cm 2 theoretical area was Zn(OH) + + 3 OH---> Zn(OH)42- [5] used for each run. The capillary tip had to be cut off at intervals since the strong alkali solution attacked with ~r~ = 0.39 (for [3]) and 1 -- ao = 0.23 (for [4]). the glass, and eventually the tip would not hold a drop The measurements of Gerischer, Morinaga, and Farr of the proper size. Electrical contact to the drop was and Hampson showed that there was essentially no made by inserting a platinum wire into the reservoir dependence of the exchange current on hydroxide con- through the pumping nipple. centration, while the mechanism of Popova and Strom- The d.m.e, was constructed from a length of Sargent berg (31) would predict a fairly large variation of 6-12 second capillary. The mercury flow rate of the exchange current with hydroxide concentration. The d.m.e, was measured before each experiment since the mechanism we propose, based on the results shown capillary did not last long before the tip had to be cut below, involves consecutive one-electron transfer steps. off, changing the flow rate. Potential step chronocoulometry was performed Experimental with an instrument previously described (32) con- Chemicals.--Stock solutions of 4.0M KOH and 4.0M structed from Philbrick solid-state operational ampli- KF were prepared from "Baker Analyzed" Reagent fiers. A fraction of the voltage generated by the cur- grade KOH and KF obtained from the J. T. Baker rent follower could be fed back to the potentiostat for Chemical Company. The KOH solution was standard- resistance compensation; the stabilization scheme of ized by titrating a known amount of reagent grade Brown et al. (33) was used. A-C and d-c polarography potassium biphthalate using phenolphthalein as an were performed using a Princeton Applied Research end-point indicator. A stock solution of 0.05M.zinc (II) Corporation, Princeton, New Jersey, Model 170 electro- was made by dissolving "Baker Analyzed" ZnO in 50 chemical instrument. Data from potential step experi- ml of stock KOH solution. The Zn(II) solution was ments were taken using a PDP-12A computer system standardized by titrating with EDTA buffered to pH (Digital Equipment Corporation, Maynard, Massachu- 10. Purification of experimental solutions with acid setts). Data for potential sweep experiments at sweep washed activated charcoal (Barker's method) was rates below 300 mV/sec were recorded on a Moseley tried, but the results were the same with or without 2D-2 X-Y recorder. For sweep rates above 300 mV/sec, this step, so this procedure was not used regularly. a Tektronix Model 564 storage oscilloscope was used Solutions were prepared by pipeting a known amount with Type 2A3 (Y axis) and Type 2A63 (X-axis) plug- of KOH stock solution into a volumetric flask and ins. Permanent records of oscilloscope data were made then diluting with the stock KF solution, so that all with a Polaroid camera mounted on the oscilloscope solutions were at the same ionic strength. Zinc amal- using 3000 speed film. gam was prepared from 99.9% zinc wire and purified Initial and final potentials for potential step experi- mercury. The zinc wire was amalgamated by dipping ments and initial potentials for potential sweep ex- in mercuric chloride solution for a few seconds before periments were measured with a United Systems Cor- it was placed in the mercury to aid in more rapid poration Model 204 voltmeter to an accuracy of • inV. dissolution of the zinc. The amalgam was stored under Two of the relays in the relay register of the PDP-12 vacuum and removed from the storage vessel under computer were used to control the potentiostat and a blanket of prepurified helium. Under these condi- integrator. Timing of data acquisition was controlled tions, the concentration of zinc in the amalgam would by internal computer cycle counting; the time scale remain stable for more than a week. was calibrated by acquiring data from a function All experiments were carried out under a blanket generator (Wavetek Model 114). of nitrogen. Commercial water-pumped nitrogen was Data were taken at the same potentials and the same purified by first bubbling it through distilled water, time scales with and without zinc present. Different then through a solution of vanadous chloride stand- time scales were used at different potentials so that ing over saturated zinc amalgam, then passing over the charge measured with zinc was significantly larger copper strands heated to at least 350~ and finally than that without zinc, but at short enough times that through distilled water again. The copper strands had sufficient kinetic information was still present. The previously been exposed to oxygen at high tempera- quantity nFADI/2C/~ '/2, which is the slope of a Q vs. t'/2 ture and then been reduced by passage of hydrogen plot when the potential is stepped far enough so that gas at high temperature in order to assure an active the reaction rate is controlled by mass transfer, was surface. The water used in all experiments and in prep- evaluated for the reduction of zinc(II) by stepping aration of solutions was deionized water that had been from --1.0 to --1.TV and for the oxidation of zinc further purified by distillation from alkaline potassium amalgam by stepping from --1.7 to --1.0V and least permanganate in a Barnstead water still; its conductiv- squares analysis on the Q - t'/2 data. Three or four ity was less than 10 -7 (ohm-cm) -1. Potassium hydrox- steps were averaged for each potential using a fresh ide, potassium fluoride dihydrate, and zinc oxide were drop each time. reagent grade chemicals and were used without fur- The data acquisition system was checked by record- ther purification. Commercial mercury was washed in ing a current-time curve with a simple RC dummy 5% HNO8 with air bubbling for several days, then cell (R ---- 5 kohm, C ---- 1 ~J) for the potential stepped splashed at least twice through a 5% HNO3 scrubbing from 0 to +0.400V. The accuracy of measurement was tower. After drying, the mercury was distilled twice 1.2% or better. Further details about the apparatus, under vacuum. procedures, and calibrations are available (34).

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Theory These authors showed that the current during a step The best method of proving that a charge transfer to potential E is given by Eq. [16]. reaction consists of more than one electron transfer i(t) = FAC*oDo'/2 [nl~l(t) -{- n2~2(t)] [16] step is to demonstrate the existence of the intermedi- where ate products by some unambiguous technique (1). Consider the case ~l(t) = [(x-- ~2) exp (x-2t) (1 + eJl) (x+ + x-) 0 -t- n~e ~ Y E1 ~ [6] erfc (x-t ~/,) -- (x+ -- ~2) exp (x+St) erfc (x+tV,)] [17] Y -b n2e ~ R E2 ~ [7] At equilibrium, from the Nernst equations for [6] and ~s(t) ---- [exp (x+2t) [7] (1 + eh) (1 -b eJ0 (x- -- X+) erfc (x+t'/2) -- exp (x-St) erfc (X-t'/,)] [18] C~ "~+n, { n,n2F } : K = exp -- (Ei~ -- E2 ~ [8] CRnlCon2 RT X-----: [19] Hence, for a given total concentration of O and R, C*, 2 the maximum amount of Y is present when CR = Co. [ eJ2-~- e-Jl-~ e (j,-h) ] If E~o, is much greater than E~~ then solutions con- K ~--- ~1~2 [20] taining essentially only Y can be made. If E~ o' = E2 o', (1~- e j~) (1 -~ eJO then K : 1 and for n~ : n2 = 1, the maximum Cy is k~ . . ~i : ~te -a~Jl + e ~d') (i : 1,2) [21] given by Co : Cy : Cm As the quantity E1 o' -- E~ o" Di Y2 becomes more negative, the maximum amount of Y that can be present decreases rapidly. For example, Since we are interested here only in the case where for nl : n2 = 1, and Co : C~ : C*, if E1 ~ -- E2 ~ = E1 ~ <~ Es ~ and because E ~ Erl/2 = (Eri12,1 -~ --0.2V, then Cy ~ 0.03 C*, while if E~ ~ -- E2 ~ : Erl/s,2)/2, some simplifications can be made in these --0.4V, Cy~ (4 X 10-4) C *. equations, yielding However, depending upon the values of the rate constants for steps [6] and [7], the existence of stepwise ~1 (t) : [~2 exp (x-St) erfc (x-t '/2) electron transfer and transient formation of an inter- mediate, Y, can be deduced from electrochemical measurements [see Ref. (1) and general treatment of 2c ~-1 exp (x+st) erfc (x+t'/2)] [22] Albery and Hitchman (35) ]. ~1X2 Potential step chronocoulometry (33, 34) was chosen ~2(t) = [exp (x-~t) erfc (x_t~2) as the principal electrochemical investigative pro- (1 + eJO (;~ + X2) cedure in this research, because integration of the -- exp (x+St) erfc (x+t'/,)] [23] current signal removes most of the high-frequency noise from this signal. Moreover, the integrated signal The expression for Q (t) is obtained by integrating the always starts from zero and can always be adjusted above equations to obtain Eq. [24] and [25] to stay on a given scale, while in chronoamperometry initial double-layer charging current may be several orders of magnitude larger than the faradaic current f~l(t)dt -- (1 + eJ~) (~1 + ~2) ~_2 exp (x-2t) so that to obtain sufficient precision in the region of interest, the signal must be allowed to overdrive the 2X-t'A ) ~LI ( erfc (x-t ~/2) -t- ~ 1 Jr -- exp (x+2t) amplifiers of the measuring instrument. Chronocoulom- X+ 2 etry can also be used to obtain information about the double layer (36, 37). Although the theoretical equations for stepwise electron transfers in chronocoulom- erfc (x+t v2) +,------if-- 1 [24] etry have not been presented previously, they can be obtained quite easily by integration of the appropriate M~2 [ xl_2( exp (X_~) equations of chronoamperometry. f C~(t) ----- (l+eJ0(~l+X2) Potentiostatic current-time behavior for systems involving a quasi-reversible two-step charge transfer was first derived by Hung and Smith (10) for the erfc (x-tF~) + 2x-tv~~ 1 -- exp (x+2t) analytical solution for this case in a-e polarography. The partial differential equations and boundary conditions used by these authors in obtaining the follow- erfc (x+t~2) +- 2x+t'/"~'/~ 1)] [25] ing results are given in the Appendix. For the reaction given in Eq. [6] and [7] and following the notation of Since x+ is much greater than x-, the term in the Hung and Smith (10), let above equations in x+ can be neglected compared to il (t) the term in x-. Under these conditions, then ~(t) - [9] niFAC* oDo'A f~1 (t) dt : f~2(t) dt [26] Pt = 1 -- ai (i = 1,2) [10] and, defining Zr as in Eq. [27] D1 : Do~Dy ~ D2 : D~:~D~ [11] (n~ -k n2) FADo'/2C* o~I~2 Zc : [27] I1 = fortify az f2 = fY~fR c~2 [12] (1 + e j~) (~.1 -{- X2) then Erz/~..z:EI~ RT ln(fY)(D~ Zc ( 2x-t'/2 ) -- "t~l---'F- ~O Dy / [13] Q(t) : ~ exp (x-st) erfc (x_t~'2) -~ ~'/~ 1 [28] Erl/2,2"-E2 ~ RT ln( fR ) (Dye -- n2---F ~-Y DR / [14] For the case where R is initially present but not O and n~F the potential is stepped in the positive direction, the Ji = --~ (E -- Er~/~.t) (i = 1,2) [15] expression for Q (t) is the same as that in [28] except that Z~ is replaced by Z,

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, i r J , I , (nl + n2) FADRV2C*RLlks Za = [29] (1 + e -J2) (~.1 -~- ~.2) Thus, for a two-step electron transfer reaction, the equation for Q(t) is identical in form to the expression for Q(t) for single-step charge transfer, Eq. [30] LOG,o(X_)

(36, 37) 0

Q(t) =-~ K( exp (L2t) erfc (Ltv,) "t- 2~t~"--'~-/=- 1) [30]

2 ko 2 k -- ~ (e -aJ -i- e~J) [31] D~'= nF j -- ~ (E -- E o') [32] Za -4

K = nFAko(C*oe -cd -- C*Re~,~) [33] LOGlo (Z) To use Eq. [28] or [29] to determine kinetic parameters and reaction mechanisms, one steps from a po- --6 tential where no appreciable current flows to one where a measurable cathodic or anodic current is obtained and measures the Q vs. t behavior. From this data K and k are determined. These values are determined at a number of potentials and then the loga- rithm of K and k are plotted vs. the potential. For a single-step charge transfer case, the plot of In K vs. E is a straight line with a slope equal to --anF/RT. The

plot of In ~ vs. E is a curve which has a minimum near i i i i i i I E ~ and asymptotically approaches straight lines for E 3 2 I o 1 --2 --3 greater than and less than E ~ The slope of the asymp- POTENTIAL (2.3RT/F volts/div.) tote for E less than E o' is --anF/RT, while for E greater Fig. 1. Log X- and log Z vs. E for case (ii). al "-- c~ -- 0.5, than E o', it is ~nF/RT. Erl/9.1 = --0.2V, Erl/2,2 = --I-0.2, k~ = 2.0, k% -- 0.02, nl "- In the case of a two-step charge transfer reaction, Z and x- can be determined from Q vs. t (or i vs. t) data n2 -- 1, D1 ','= -- D2 V= = 0.00316, fl -- f2 == 1.0, Co = CR = in the same manner as K and ~ in a one-step reaction. 2.03 x 10 -e moles/cm 3, A == 0.032 cm 2. However, the behavior of the plots of In Z and In x- vs. E can be more complex than in the one-step Case. i [ i i ] I I It is this difference in behavior that can sometimes allow one to demonstrate the existence of a two-step 0 mechanism. The behavior of In x- vs. E and in Z vs. E LOG,olX I can be illustrated by some examples: (i) If kOl and k% are very large, then the over-all rate of the reaction may be so fast that the reaction --2 appears to be Nernstian. In this case, it is not possible to calculate x- and Z and the reaction is indistinguishable from a one-step multi-electron transfer reaction (10). (ii) For k~ >> k~ when (RT/F) In (k%/kOl) < E < Erl/22, then 0 In Zc/OE = --(1 + a2)F/RT [see Fig. 1 (Zc,1) ] and in x- has a minimum near E = 0 (where LOGIo [Zl Erz/2.1 is taken as --0.2V, and E5/2.2 is +0.2V). When (RT/F) In (ko2/kol) < E < O, then O ln(x-)/OE = 6 --(1 -t- a2)F/RT [Fig. 1 (x-2)]- When 0 < E ~ Eq/2,2 8 ln(x-)/SE -- (1 -- a)F/RT [Fig.1 (x-.l)] and 0 In Za/OE = ~2F/RT [Fig. 1 (Za,1)]. When Eq/2,1 < E (RT/F) In (k%/kOl), then 0 In Zc/OE = --axF/RT [Pig. 1 (Zc,2)], 8 In Z/OE --(2 -- al)F/RT [Fig. 1 (Za,2)] and ~ In (X-)/OE : --azF/RT [Fig. 1 (X-,3)]. (iii) For ko2 >> ko,, the results are the mirror image of those for case (ii) above. i i i i i i i (iv) The results for ko2 -- k% are shown in Fig. 2. 3 2 1 O --1 --2 --3 Therefore, to determine whether a reaction is single POTENTIAL {2.3RT/F volts/div.] step or multi-step, not only must the over-all reaction Fig. 2. Log X- and log Z vs. E from case (iv). The conditions are be slow enough to be measurable, but also the rate the same as in Fig. 1 except k~ -- 0.02. must be slow enough to be measurable in the vicinity of aE = (2 --~I)F/RT and a In Zc/aE : --.IF/RT. Under Erl/2,1 -~- Erl/2,2 RT k~ E' ---- + In , [34] these conditions a In Za/aE -- a In Zc/aE -- 2F/RT and 2 F k~ the results cannot be distinguished from a single-step reaction with the same over-all rate and ~ : ~1/2. The Otherwise, the reaction is indistinguishable from a behavior of In (x-) is similarly indistinguishable. single-step reaction. For example, for k% >> k%, if the In order to assign values to both ~i and a2, both most positive potential at which measurements of Z cathodic and anodic plots of In Z and In x- vs. E must and x- can be made is less than E' in 38, then O In Za/ have linear segments whose slope is less than nIF/RT.

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Then al can be obtained from the slope of the cathodic lowed consisted of guessing initial values of K and plot and a2 can be obtained from the slope of the anodic and calculating values of Q for each t using [30], Qcalr plot. (Erl/2,1 -5 Erl/2,2)/2 can be determined from the These values are compared to the experimental ones, potential where Za = Zc Qexp, and the total variance, which is the sum of (Qexp - Qc,lc)~, determined. The values of K and k are nlErl/2,1 -5 n2Erl/2,2 RT C*o Ezafzc : -5 In changed until the variance has been minimized. Details ~%1 JI- T/'2 (nl -5 n2)F C*R of this procedure and the method for calculating [35] exp (y2) erfc (y) are discussed elsewhere (34). Pre- liminary chronocoulometric measurements showed Even here kol, k~ Erl/2,1, and Erl/2,2 cannot be assigned that neither reactant (zincate) or product (zinc in absolute values, since the value of Erl/2.2 -- Erl/2,1 is mercury) were adsorbed, so that the number of cou- not known. We can, however, measure k~" and k2' at lombs required to charge the double layer capacitance, (Erl/e.1 -5 Erl/2,2)/2. Qdl, was determined on a test solution lacking zinc (II) Fornl:n~= 1 with a pure mercury electrode; Qexp was then taken as kOl Qmeas - Qd], where Qmeas is the measured charge. This k1' -- [36] procedure assumes that Qdl is not affected significantly [ --alF / Erl/2,2 Erl/2,1 exp [ k by the presence of the small amounts of zinc in solution or mercury. ko2 The log ~ and log K values at various potentials and k2t various hydroxide concentrations determined by this [ (I -- a2)F -- Erl/2,1 procedure are given in Table I. These values were exp [ plotted vs. E and an and/~n were determined from the slopes of the linear parts of the cathodic and anodic [37] branches of the plots at constant hydroxide concentra- If we could measure the concentration of Y at equi- tion. The dependence on hydroxide ion concentration librium, we could then determine the value of Erl/2,2 was determined from plots of log K at constant poten- -- Erl/2,1. For purposes of calculation it is sufficient to tial vs. log [OH-]. The results are given in Table II. select a value of E2 -- E~ greater than 0.2V and use that The diffusion coefficients of zinc (II) and Zn (Hg) were to calculate k% and k~ from the observed kl' and k2'. determined by measuring K/~ when [E -- Erl/2[ was Using the values determined above for al, a2, Erl/2,1, large. For the reduction process, this gives the value Erl/2.2, nl, n2, k~ and k~ one can calculate Z and x- of nFAC*oDo '/2, while for the oxidation nFAC*RDR I/,. over the whole potential range and see if these values The effective surface area of the Kemula type Metrohm give a good fit in the nonlinear portions of the In Z and h.m.d.e, has been shown to be about 90% of the geo- In x- vs. E plots. If the fit is good, one can say with metrical area (42) yielding a value for our electrode confidence that the charge transfer is multi-step. of 0.0291 cm 2. With this value for A, C*o ---- 2.03 X 10 -8 Clearly, potential step techniques are particularly moles/cm 3 and Kr = 2.82 X 10 -5, we obtain a Do lj~ useful for distinguishing between single-step and = 2.47 X 10 -3 cm/secV2. Similarly, with Ka/k ---- 2.66 multi-step electron transfer. Hurd (5) has stated that X 10 -5 and Da '/~ ---- 3.98 • 10 -3 cm/sec'/, (43), the unequivocal proof of a two-step consecutive electron concentration of zinc in the amalgam, C*m was found transfer mechanism can only be obtained from steady- to be 1.19 mM. The potentials for the intersection of state polarization curves if the exchange currents of Ka and Kc and the concentrations of Zn(II) Zn(Hg), the two steps differ by a factor of 100 or more while and OH- can be used to calculate Eq/2 for the over-all still being less than the mass transfer limited current. reaction. A plot of Erl/2 vs. log [OH-] had a slope of Hence, if rate constants are about equal, concentration --0.118V and an intercept of --1.445V vs. SCE. ratios would have to be very large in order to achieve D-C polarography.--The zinc (II)/zinc amalgam sys- the necessary exchange currents. Large concentration tem in alkaline media exhibits a quasi-reversible ratios usually mean large concentrations, high currents, polarographic reduction wave. The treatment of the and problems from solution resistance. Potential step data follows the treatment of Meites and Israel (44) techniques allow examination of the current-potential and is similar to that of Matsuda and Ayabe (25). behavior over a wider range of potentials and larger From the Ilkovic equation and the values m = 1.07 rates than is possible with steady-state techniques mg/sec, t ---- 1.0 sec, i d = 7.64 /~A and C*o ---- 2.03 mM, since the effects of mass transfer can be accounted for we find a value of Do w ---- 2.53 • 10 -3 cm/sec ~/~, in good by proper application of potential step theory. agreement with the value obtained from the potential step experiment. To determine kinetic data, a plot of Results log[i/(id -- i)] VS. E according to the equation for a Potential step chronocoulometry.--Kinetic param- totally irreversible reaction (44) eters are usually determined by linearization of Eq. [30] by taking Q values only at times where kt ~/2 > 5, 0.059 1.349kotV, 0.0542 E = E ~ -5 log -- log . so that exp (k2t) erfc (kt'/,) is negligible compared to an Do '/2 an ~d -- i the other terms in this equation (36). A similar pro- [38] cedure is often followed in chronoamperometric experiments (38, 39) where current values at times corre- was made for values of E sufficiently negative as to sponding to ~t'/, < 0.1 are used. The difficulty of using make the reverse reaction slow enough to be negligi- these approximations in practice has been discussed ble. Results are given in Table II. [see, for example (40, 41)] and is based on the neces- A-C polarography.--Measurement of kinetic param- sity of knowing the value of ~, the parameter to be eters by a-c polarography involved phase-sensitive de- determined by the experiment, before the valid ap- tection of the current, so that the phase angle of the proximation zone is established. Moreover, the zone current as well as its magnitude was measured. From of the approximation may be located where perturba- this data the cotangent of the phase angle, 8, was deter- tions caused by double layer charging or convection mined and used to calculate k at different values of E are important. However, the best use of the data is (45) made by fitting the experimental results to the com- Cot (8) ----Ioo/Igoo ---- 1 + (2~) w/~ [39] plete theoretical Eq. [30] using a high speed digital computer, and this procedure was followed here. The kinetic parameters can be obtained from a plot of Because digital data acquisition was employed, the log X vs. E or directly from a plot of cot(0) vs. E by data were in a particularly convenient form for fur- measuring the potential and magnitude of the maxi- ther processing on the computer. The procedure fol- mum value of cot(0) (45)

Downloaded 19 Feb 2009 to 146.6.143.190. Redistribution subject to ECS license or copyright; see http://www.ecsdl.org/terms_use.jsp 1670 J. Electrochem. Soc.: ELECTROCHEMICAL SCIENCE AND TECHNOLOGY December 1972

Table I. Potential step chronocoulometry. Results Potential sweep voltammetry.--Kinetic parameters can be obtained from linear potential sweep voltam- (a) Reduction reaction; Steps from --1.00V vs. SCE to E; solution metry at a stationary electrode by observing the varia- contained 2.03 mM zine(II) and KOH; electrode was Hg drop tion of Ep or of Ep -- Ep/2 with scan rate, v (46). E Stand. dev. [OH-] (V vs. SCE) Log k Log K • 107 Kinetic parameters for the cathode reaction were obtained from experiments in a 1.0M KOH solution con- taining 2.03 mM zinc(II) at a mercury electrode while 0.18 --1.36 --0.5675 --5.4399 6.74

-- 1.38 -- 0.3189 -- 5.0049 9.12 those for the anodic reaction used a zinc amalgam elec- -- 1.40 + 0.0055 -- 4.6406 11.20 trode, [Zn] = 1.2 mM and 1.0M KOH (34). Kinetic -- 1.42 0.3193 -- 4.3096 25.20 -- 1.44 0.7863 -- 3.9789 25.60 parameters obtained from these measurements are -- 1.46 0.7729 -- 3.8012 5.14 shown in Table II. --1.48 1.0177 --3.5614 2.46 -- 1.50 1.2498 -- 3.3153 15.40 Discussion -- 1.62 1.4933 --3.1080 13.50 0.34 -- 1.40 -- 0.6829 -- 5.3471 12.76 The results obtained by the different electrochemical -- 1.42 -- 0.4776 -- 5.0082 38.00 --1.44 --0.1598 --4.6555 17.10 methods in Table II are in fair agreement with each -- 1.46 + 0.1881 -- 4.3466 7.64 other. These results show that the electrode reaction -- 1.48 0.4876 -- 4.0607 6.94 of zinc in alkaline media is not a simple quasi-reversi- -- 1.50 0.8026 -- 3.7670 7.84 -- 1.52 1.0215 -- 3.5505 14.40 ble two-electron transfer. First, the quantity an + Bn --1.54 1.2627 --3.3110 3.05 --1.56 1.4239 --3.1461 2.65 is much less than two, when ~ and ~ are calculated 0.96 -- 1.43 -- 0.5593 -- 5.8622 6.30 from the appropriate slopes measures well away from --1.45 --0.6991 --5.4614 9.96 -- 1.47 -- 0.4673 -- 5.0589 12.20 Erl/2. Second, the log K vs. E plots show definite curva-

-- 1.49 --0.1595 -- 4.7091 10.90 ture in the region near Erl/2. This curvature cannot --1.51 +0.1403 --4.3978 6.51 --1.53 0.4478 --4.1129 9.58 be due to double-layer effects, since the rate of change -- 1.55 0.7000 -- 3.8504 I0.00 of potential at the outer Helmholtz plane with elec- -- 1.57 0.9316 -- 3.6158 2.88 --1.59 1.1671 --3.3903 2.05 trode potential is nearly constant in the region of in- -- 1.61 1.3156 -- 3.2317 2.02 terest, which is far negative of the potential of zero 1.76 --1.46 --0.5434 --5.8832 8.95 -- 1.48 -- 0.6788 -- 5.4323 9.77 charge, and the solution has a high ionic strength. Nor -- 1.50 -- 0.4698 -- 5.0280 16.30 can it be explained by uncompensated resistance, since --1.52 --0.1748 --4.7138 16.20 -- 1.54 + 0.0987 -- 4.4254 13.40 the region of maximum curvature is in the region --1.56 0.3821 --4.1427 11.50 where K was less than 100 ~A, and the uncompensated -- 1.58 0.6573 -- 3.8857 19,80

-- 1.60 0.9402 -- 3.6369 14.50 resistance was less than 10 ohms, i.e., where the curva- -- 1.62 1.0412 -- 3,4839 7.25 ture was most pronounced, contributions from IR -- 1,64 1.2536 -- 3.3069 7.29 effects were at a minimum. These features correspond

(b) Oxidation reaction: Steps from --1.700V vs. SCE to E, solution quite closely to a consecutive electron transfer mecha- contained no zinc(II) and KOH, electrode was zinc amalgam with a nism, however, and the following mechanism appears [Zn] = 1.2 mM to fit the experimental data quite well [OH-] E Stand. dev. (M) (V vs. SCE) Log k Log K x 107 Zn(OH)42-~ Zn(OH)2 + 2 OH- [42] 0.18 --1.38 --0.2117 --5.8534 4.97 Zn(OH)2 + e ~=~ Zn (OH)2- [43] -- 1.36 -- 0.3641 -- 5.4843 10.20

-- 1.32 -- 0.4563 -- 5.1238 6.47 --1.28 --0,1335 --4.7542 6.79 Zn(OH)2- ~ Zn(OH) + OH- [44] -- 1.24 + 0.1061 -- 4.4880 4.80 -- 1.20 0.3460 -- 4.2348 3.65 Hg+ Zn(OH) + e~=~Zn(Hg) + OH- [45] --1.16 0.6573 --3.9680 16.3.0 -- 1.12 0.7993 -- 3.7641 2.42 -- 1.08 1.0502 -- 3.5123 10.40 Comparison of this model to the experimental results -- 1.04 1.5222 -- 3.0975 36.40 is simplified by using a modification of the notation 0.34 -- 1.42 -- 0.8242 -- 8.0244 10.60 --1.40 --0.8504 --5.6479 15.60 of Hung and Smith (10), with O representing Zn (OH)2; -- 1.36 -- 0.8181 -- 5.1592 27.90 YO, Zn(OH)2-; YR, Zn(OH); and R, Zn(Hg). With ]o --1.32 --0.1515 --4.7376 68.30 -- 1.28 -- 0.0120 -- 4.4963 10.30 = [OH-]2,]vo = 1.0, ]YR = [OH-l-l, and fR = [OH-], --1.24 +0.3497 --4.2217 3.85 the following equations hold for Erl/2.1 and Erl/2,2 -- 1.20 0.6166 -- 3.9595 3.45 --1.16 0.8588 --3.7272 3.88 --1,12 0.9097 --3.6416 8.35 RT Do RT ]o

-- 1.08 1,2846 -- 3.2853 2.79 Erl/2,1 : E1 o' + In + - In [46] 0.96 --1.47 --0.3670 --5.8545 2.77 2F Dro F fro -- 1.45 -- 0.5167 -- 5.5910 4.46

-- 1.41 -- 0.3864 -- 5.0590 4.33 -- 1.37 -- 0.0143 -- 4.6425 12.60 RT Do RT --1.33 +0.2119 --4.3768 5.53 Erl/2,1 = E1 ~ + -- ln-- -- ln[OH-] 2 [47] -- 1.29 0.4428 -- 4.1431 4.30 2F Dyo F -- 1.25 0.6871 -- 3.8975 2.67 --1.21 0.8744 --3.7023 3.59 RT DyR RT -- 1.17 1.0797 -- 3.4987 16.00 Erl/2,2 = E2 o' + In -- -- ln[OH-] 2 [48] -- 1.13 1.3468 -- 3.2434 2.64 2F DR F RT [E]max = Erl/2 + -~ ln(=/~) [40] At constant E -- Er]/2, the hydroxide dependence of ~, is proportional to ft and ~2 to f2, where $1 and f2 are given by Eq. [49] and [50] (2~D) '/" [cot(0)]max = 1 + ko[(~/~)-~ + (~/~)~] [41] fl -- fo~lfY0 ~1 = [OH-]-~176 [49] The results are shown in Table II. f2 = [OH-]-~ [50]

Table II. Summary of experimental results by different techniques

0 log Kc 0 log K~. Erl/9 DO1~~ . ~n kOclDol/2 kOa/DRll 2 (V VS. SCE) (cm/sec 1/2) 0 log [OH-] 0 log [OH-]

Potential step 0.82 0.34 0.17 0.30 -- 1.445 2.47 • 10 -a -- 1.85 + 0.83 D-C polarography 0.82 -- 0.33 -- --1.445 2.53 • 10 -s -- A-C polarography 0.83 -- 0.18 ..... Linear potential sweep voltammetry (a) (Ep vs. log v) 9.78 0.33 0.40 0.34 ....

(b) (Ep -- Ep/s) 1.00 0.46 ......

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O 0.18M KOH I ! r O ~ I

-4 Fig. 3. Log Kc vs. E for reduction reaction. Comparison of ex- LOGIo(K) perimental data from potential-step chronocoulometry ([Zn(OH)42-] = 2.03 raM) with values calculated from consecutive-electron transfer theory.

/ , /A ,/6 , , , -.,o .,.,o -,.o POTENTIAL (volts vs. s.c.e.)

This means that for any given value of E -- Erl/2, the may show large distortions of the current because of hydroxide dependence will be small. In particular, spherical diffusion inside the drop. Since the theoreti- when kl is nearly equal to ~2, and the hydroxide con- cal curves in these figures were calculated with param- centration is about 1.0M, the hydroxide dependence of eters from the potential step experiment, the agreement log K and log ~ will be zero. Since the region where must be considered satisfactory. ~1 is equal to ~2 is also the region of curvature of the It is of interest to compare our results with those of log K vs. E plot, the apparent ~ measured in this previous studies (Table III). Gerischer (22, 23) and region will be between the values for the high and later Farr and Hampson (24) determined the exchange low slope linear regions; for the Zn (II)/Zn (Hg) reac- current io by measuring the charge transfer resistance tion an would be equal to about 1.0 in this region. (RT = RT/nFio) at the equilibrium potential of a solu- The measured values of the hydroxide dependence tion and thus determining the variation of io with of log K at constant potential yield the following val- reactant concentration. From io, one can determine a ues for ]1 and f2: fl ---- [OH-]-~ and ]2 = [OH-] +0as. and k o from the relation To obtain a quantitative comparison between model and results, we take al = 0.82, a2 ---- 0.66, kol -- 0.228, io = nFAk~ a [53] ko2 = 0.0209, and use these parameters to calculate The exchange current can also be determined from values for log K and log ~ from consecutive electron consecutive electron transfer theory, either from the transfer theory equation derived by Vetter (2-4) or from the treat- RT ment of Hung and Smith (10) Erl/2.1 -- -- 1.645 -- ~ ln[OH-] 2 [51] F

RT 2.C ~ I I I I Erl/2,2 -- --1.245 -- -- ln[OH-]2 [52] o 0.18 ~ KOH F D 0~4 M KOH • D 0.96 M KOH o ~ & o We find that the potential step data fits the theoretical 1,E (~ 1.76 i KOH O curves quite well (Fig. 3-6). In particular, in the plot LOC-Io { )Q of log Ka vs. E where the curvature is most pronounced, the fit is excellent. These same parameters can also be used to calculate O.C e e [~ e a-c and d-c polarograms using Hung and Smith's equations (10). In calculating polarograms, the Matsuda function (47) was used instead of exp (~2t) erfc (kt~/,), because a d.m.e, is used for polarography and planar -lC ,14o , -,'~o ' -&o diffusion no longer occurs. The fit between the theo- POTENTIAL (volts vs. s.c,e.) retical a-c polarographic data (cot 0 vs. E) and d-c Fig. 5. Log ~. vs. E for reduction reaction. Comparison of data polarographic data [log(i/id -- i) VS. El and the ex- from potential-step chronocoulometry with theoretical calculations. perimental results are shown in Fig. 7 and 8. The agreement between theory and experiment for a-c polarography is not too good, but Delmastro and Smith i i i i I I i I (48) pointed out that amalgam formation reactions

1.0

-4 E3 Q

O.5

LOGI0 (K) O 0.18 M KOH LOGIo (~) 1~4 M KOH -$ o D o.18 M KOH O [3 0.34M KOH o.96M KOH O z~

6 -o.5

I I I I I i I \ "~i 1.1 1.2 1,3 --1,4 POTENTIAL (volts vs.s.c.e.) i I i I I I ~ I -1.1 -I.2 -1.3 1.4 POTENTIAL (volts vs. see) Fig. 4. Log Ka vs. E for oxidation reaction. Comparison of data from potential-step chronocoulometry ([Zn(Hg)] = 1.2 raM) with Fig. 6. Log ;~ vs. E for oxidation reaction. Comparison of data theoretical calculations. from potential step chronocoulometry with theoretical calculations.

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50 I O I I I I I I I o 1.2 A 40 %,,

A 30 .~ o'~ ~ _ COT(0) 0.8

20 LOG10 (R T)

10 O 0.4

I I I 1.30 -1,40 -1.50 POTENTIAL (volts vs. s,c.e.)

Fig. 7. Comparison of Cot(g) vs. E data from a-c polarographic measurements with theoretical calculations. The solution contained I I I I I [Zn(OH)42-] ~- 2.03 mM and [OH-] --- 0.18M. The d.m.e, was -' -6 -5 -4 mercury with a drop time of 1 sec. ~ ---- 11,0 Hz. LOG10(Zn(Hg)) (moles/cm 3) Fig. 9. Log RT VS. log [Zn(Hg)] for different concentrations of I I i I Zn(OH)4 2-. Comparison of theoretical calculations with experimental data from Farr and Hampson (24). Squares, [Zn(OH)42-] 5.05 x 10 -6 moles/cm3; triangles, [Zn(OH)42-] ~ 6.8 x 10 -5 moles/craB; circles, [Zn(OH)42-] ~ 1.834 x 10 -4 moles/cm 8. Open symbols are data from this work, solid symbols are from Farr and Hampson.

Hampson (24), we calculate an RT which is larger than their values by a factor of 3.5. This difference may be LOG10 attributed to differences in the conditions of measure- i/(i d i) ment in the two studies; for example, the ionic strength of Farr and Hampson's solutions was 3.0M, while in the 0 -- present work, it was 4.0M. They used NaOH and NaC104 while KOH and KF were used in the present work, and the solutions used by Farr and Hampson were purified by circulation over activated charcoal for at least 28 days. However, when the RT values calculated from potential step data are divided by 3.5, the values at different Zn(Hg) and OH- concentra- 1 tions agree fairly well with those of Farr and Hampson (Fig. 9). Matsuda and Ayabe (25) studied the reduction process by d-c polarography. Using the treatment for quasi- reversible polarographic waves they obtained the results shown in Table III, which agree very well with ours for the reduction process. -2 I I I I -1.30 -1.40 -1.50 Stromberg and Popova (29-31) studied both the oxidation and reduction reactions by d-c polarography POTENTIAL (volts vs. s.c.e.) with a dropping zinc amalgam electrode used to study Fig. 8. Comparison of log il(i~ -- i) vs. E data from d-c polarog- the oxidation reaction. Their results do not agree very ruphy with theoretical calculations. Conditions same as in Fig. 7. well with the results of the present work for the oxidation reaction, although the agreement is fairly good for the reduction reaction (Table III). However, their ).1).2 results still lead to the conclusion that one hydroxide io = 2FAC* oDo ~/= (1 + eJ,) (~1 + X2) is involved in the oxidation reaction rate limiting step, since the oxidation rate shows a dependence on the first ~1),2 power of the hydroxide concentration. This observation -- 2FAC*RDR v= [54] (1 2 I- e-J~) (;L1 Jr ~2) led Stromberg and Popova to conclude that the oxidation reaction was a two-electron reaction which oc- Using the kinetic parameters obtained from potential curred by a completely different path than that of the step measurements to calculate io and RT and compar- reduction reaction (Eq. [4] and [5]). However, if they ing these results with the data in Fig. 2 of Farr and were correct, then a plot of log K vs. E for any one

Table III. Comparison of our results to previous studies

O log /Ce log K= aTI, ~Sn log koe log ko= Era/= log [OH-] 8 log [OH-]

Present work 0,82 0.34 -- :~.37 --2.92 -- 1.445 -- 1,85 + 0.83 Farr and Hampson (24) 1.00 1.00 -- 3.00 ~ -- Matsuda and Ayabe (25) 0.84 -- --3.3 -- --1.444 --1"-.82 Papaya and Stromberg (31) 0.78 0.46 --3.43 --3.70 --1.434 --2.3 + 1,4

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hydroxide concentration should be linear over the aCy i2 (t) i, (t) Dy [9A] whole potential range (except for curvature due to Ox n2FA nlFA double layer effects and distortion due to uncompensated resistance); this is not the case. Moreover, this OCa --i2(t) DR ---- [10A] mechanism does not predict the negligible variation Ox n2FA of the exchange current with hydroxide concentration at equilibrium which several other researchers have il(t) _ Cox=0 exp ~--~lnlF [E(t) -- El~ t reported (22-24, 26, 27). The consecutive electron nIFAks.1 L RT transfer mechanism explains all the observed features. Recently Despic and co-workers (49) demonstrated --CYz=0exp { (1-al)nlF } that the Cd(II)/Cd(Hg) system in H2SO4 solutions, RT [E(t) -- El ~ [IIA] long thought to represent a mechanism involving a simple two-electron charge transfer step, probably i2(t) -- CYz=o exp ~--02~2F } occurs by a two-step single electron exchange mecha- n~FAks.2 [. ~ [E (t) -- E2 ~ nism. The findings here on the Zn(II)/Zn (Hg) system parallel these results and suggest that other electrode reaction mechanisms previously thought to involve -- CRx=o exp { (1- RTa2) n2F [E(t) -- E2 o] } [12A] multiple electron transfer steps bear reinvestigation. REFERENCES Acknowledgment 1. A. Bewick and H. R. Thirsk, in "Modern Aspects of The support of the National Science Foundation Electrochemistry," Vol. 5, p. 291ff, J. O'M. Bockris (NSF GP 6688X) and Delco-Remy Corporation (under and B. E. Conway, Editors, Butterworths, Wash- AF 33(615)-3487) is gratefully acknowledged. The ington (1969). PDP-12A computer was acquired under a grant from 2. K. J. Vetter, Z. Natur]orsch., 70, 328 (1952). the National Science Foundation (GP 10360). 3. K. J. Vetter, ibid., 8a, 823 (1953). 4. K. J. Vetter, "Electrochemical Kinetics," p. 149ff, Manuscript submitted April 21, 1972; revised manu- Academic Press, New York (1967). script received June 1, 1972. 5. R. M. Hurd, This Journal, 109, 327 (1962). 6. D. M. Mohilner, J. Phys. Chem., 68, 623 (1964). Any discussion of this paper will appear in a Discus- 7. K. J. Vetter and G. Thiemke, Z. Elektrochem., 64, sion Section to be published in the June 1973 JOURNAL. 805 (1960). 8. K. J. Vetter, ibi~d., 56, 797 (1952). LIST OF SYMBOLS 9. J. M. Hale, J. Electroanal. Chem., 8, 181 (1964). 1O. H. L. Hung and D. E. Smith, ibid., 11, 237 and 425 A electrode area (1966). C*j bulk concentration of jth species 11. J. Plonski, This Journal, 116, 1688 (1969). Dj diffusion coefficient of jth species 12. T. Berzins and P. Delahay, J. Am. Chem. Soc., 75, fJ activity coefficient of jth species 5716 (1953). Eo! formal redox potential of ith step (i ---- 13. M. Smutek, Coll. Czech. Chem. Comm., 18, 171 1,2) (1953). Erl/2A reversible half-wave potentials of ith 14. J. Cizek and K. Holub, ibid., 31, 689 (1966). steps 15. J. G. Mason, J. ElectroanaL Chem., 11, 462 (1966). n! number of electrons transferred in ith 16. E. R. Brown, D. E. Smith, and D. D. DeFord, Anal. charge transfer step Chem., 38, 1130 (1966). ai charge transfer coefficient for ith steps 17. G. Lauer and R. A. Osteryoung, ibid., 38, 1137 ;h = 1--al (1966). koi standard heterogeneous rate constants for 18. G. L. Booman, ibid., 38, 1144 (1966). ith step 19. M. W. Breiter, This Journal, 112, 845 (1965). F Faraday's constant 20. G. Lauer, R. Abel, and F. C. Anson, Anal. Chem., R ideal gas constant 39, 765 (1967). T absolute temperature 21. G. Lauer and R. A. Osteryoung, ibid., 40, 30A t time (1968). 22. H. Gerischer, Z. Physik. Chem. (Leipzig), 262, 302 J, 4, x, ~, K derived parameters, see Eq. [15]- [21] (1953). Za, Zc derived parameter, see Eq. [27] and [29] 23. H. Gerischer, Anal. Chem., 31, 33 (1959). Q(t) charge 24. J. P. G. Farr and N. A. Hampson, J. Electroanal. i(t) current Chem., 18, 407 (1968). 25. H. Matsuda and Y. Ayabe, Z. Elektrochem., 63, APPENDIX 1164 (1959). 26. B. Behr, J. Dojlido, and J. Malyszko, Roezniki The equations and boundary conditions for the solu- Chem., 36, 725 (1962). tion of the current-time behavior for a quasi-reversi- 27. K. Morinaga, J. Chem. Soc. Japan, 79, 204 (1958). ble two-step charge transfer are as follows (1O) 28. A. G. Stromberg and L. F. Trushina, Elektrok- himiya, 2, 1363 (1966). 0Co 02Co = Do- [1A] 29. A. G. Stromberg and L. N. Popova, Isv. Tomsk Ot Ox2 Politekhn. Inst., 167, 91 (1967). 30. A. G. Stromberg and L. N. Popova, Elektrokhimiya, 8Cy 02Cy 4, 39 (1968). = Dy [2A] 31. A. G. Stromberg and L. N. Popova, ibid., 4, 1147 Ot Ox2 (I968). 32. F. C. Anson and I:). A. Payne, J. Electroanal. Chem., OCR 02CR 13, 35 (1967). : DR ~ [3A] Ot Ox2 33. E. R. Brown, D. E. Smith, and G. L. Booman, Anal. Fort :0, anyx Chem., 40, 1141 (1968). 34. D. A. Payne, Ph.D. dissertation, The University of Co : C*o [4A] Texas at Austin (1970). C~ : Cr = O [5A] 35. J. Albery and M. Hitchman, "Ring-Disc Elec- For t > 0, x -* trodes," pp. 38-41, Oxford University Press Co ~ C*o [6A] (1971). 36. J. H. Christie, G. Lauer, and R. A. Osteryoung, J. CR "~ C:~ ~ 0 [7A] ElectroanaL Chem., 7, 60 (1964). For t > 0, x -- 0 37. J. H. Christie, G. Lauer, R. A. Osteryoung, and F. C. ~Co il (t) Anson, Anal. Chem., 35, 1979 (1963). Do : [8A] 38. H. Gerischer and W. Vielstich, Z. Physik. Chem. ax nlFA (Frankfurt), 3, 16 (1955).

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39. H. Gerischer and W. Vielstich, ibid., 4, 10 (1955). 45. D. E. Smith in "Electroanalytical Chemistry," Vol. 40. K. B. Oldham and R. A. Osteryoung, J. Electroanal. 1, p. 26ff, A. J. Bard, Editor, Marcel Dekker, New Chem., U, 397 (1966). York (1966). 41. J. Osteryoung and R. A. Osteryoung, Electrochim. Acta, 16, 525 (1971). 46. R. S. Nicholson and I. Shain, Anal. Chem., 36, 766 42. Katsumi Kanzaki Niki, Ph.D. dissertation, pp. 16 (1964). and 80, The University of Texas at Austin 47. H. Matsuda, Z. Elektrochem., 59, 494 (1955). (1966). 48. J. R. Delmastro and D. E. Smith, Anal. Chem., 38, 43. A. G. Stromberg and E. A. Zakharova, Elektrok- himiya, 1, 1036 (1965). 169 (1966). 44. L. Meites and Y. Israel, J. Am. Chem. Soc., 83, 4903 49. A. R. Despic', D. R. Jovanovic', and S. P. Bingulac, (1961). Electrochim. Acta, 15, 459 (1970).

The Kinetics of the p-Toluquinhydrone Electrode F. Kornfeil* Electronics Technology and Devices Laboratory, United States Army Electronics Command, Fort Monmouth, New Jersey 07703

ABSTRACT The reaction mechanism of the redox system p-toluquinone/toluhydroquinone (toluquinhydrone electrode) on smooth platinum was elucidated with the aid of the electrochemical reaction order method. It was found that in the pH range 0.1-3.2 the reaction proceeds according to the scheme Q % H + ~=~ HQ +, HQ + + e- ~ HQ, HQ -~ H + ~ H2Q +, H2Q + + e- ~=~ H2Q. This mechanism is identical with the Helle sequence determined by Vetter for the benzoquinone electrode. The relatively fast rate of the charge-transfer steps, however, necessitated measurements of the electrode polarization in the nonsteady state. A method is described to determine the individual exchange current densities in moderately fast consecutive charge-transfer reactions.

The reaction mechanism of the redox couple p- Kodak "practical grade" reagents. The toluquinone benzoquinone/hydroquinone (quinhydrone electrode) was purified by sublimation under atmospheric pres- was first elucidated by Vetter (1) who interpreted the sure and the sublimate collected as canary-yellow steady-state overpotential on smooth platinum with needles (mp 68.0~ The toluhydroquinone, however, the aid of the electrochemical reaction order method. required repeated recrystallization from benzene and He showed that, in the over-all electrode reaction had to be subsequently twice sublimed in vacuo before H2Q ~:~ Q -}- 2H + -}- 2e-, the electrons are exchanged snow-white crystals could be obtained (mp 126.5~ in two different charge-transfer steps. Hale and Par- All other reagents used in the electrolyte solutions sons (2), using the Koutecky method on dropping were of C.P. quality and were used without further mercury, and Eggins and Chambers (3), employing purification. Triply distilled water served as the cyclic voltammetry on polished platinum electrodes, solvent. The toluquinone and toluhydroquinone con- arrived at essentially similar conclusions in more centrations varied from 10 -2 to 10 -4 molar. recent studies of the reduction of benzoquinone and Because of the known vulnerability of aqueous other p-quinones. The consecutive charge-transfer solutions of toluquinhydrone to photodecomposition (7) mechanism is, however, challenged by Loshkarev and the toluquinone and toluhydroquinone were dissolved Tomilov who account for their experimental results in the electrolyte immediately before the start of each obtained on Pt (4, 5) and other metals (6) by postu- experiment. No decomposition could be detected within lating that both electrons are transferred simultane- a 6-hr period, provided that the solutions were kept ously in a single charge-transfer step. free of dissolved oxygen. Purified argon was, therefore, The present paper describes an investigation of the bubbled through the electrolyte at the start of each kinetics of the redox system methyl-p-benzoquinone/ series and also, intermittently, between individual methyl-hydroquinone (toluquinhydrone electrode). measurements within a series of determinations of the The aim of this study has been (i) to clarify the situa- overpotential. This procedure insured sufficient sta- tion with respect to the reaction mechanism and (it) bility during the 2-3 hr normally required for estab- to ascertain what effect, if any, the addition of the lishing the anodic and cathodic current density- CH~-group to the benzene ring may have on the potential relation at a given concentration. kinetic parameters of the quinhydrone electrode Reierence electrodes.--The values of all electrode reaction. potentials are referred to the SHE and were measured Experimental Procedure against a Ag/AgC1/KCI(1M) electrode (co = 40.2387 All measurements of the overpotential were made V). Highly stable reference electrodes were prepared at the same constant temperature (25 ~ • 0.5~ in by the electrolytic formation of AgC1 on thermally solutions of equal ionic strength ~/2zcjnj: ---- 1.0. The reduced spheres (r ~ 0.2 cm) of Ag20 (8) attached to excess of supporting electrolyte accomplished, as usual, small Pt spirals. The scatter of potential differences the suppression of the ~-potential to negligible values, among these electrodes never exceeded 0.05 inV. minimal tranference numbers tj, and the virtual con- Electrolysis celI.--A Pyrex cell as shown in Fig. 1 stancy of the activity coefficients of all reacting species was used in all the polarization measurements described Sj, thereby making the substitution of cj for aj possible. in this paper. The working electrode, a smooth Pt wire Electrolyte solutions.--Both the toluquinone and the (r ,~ 0.25 mm), was sealed into a glass tube leaving toluhydroquinone used were obtained from Eastman 2.55 cm exposed to the electrolyte solution, and was located along the axis of a cylindrical Pt counter- * Electrochemical Society Active Member. Key words: toluquinhydrone electrode, reaction mechanism, ex- electrode through which a small hole had been drilled change current densities, electrochemical reaction order. to accommodate the Haber-Luggin capillary of the

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