Potentiostatic determination of kinetic parameters of electrode reactions with generation of a reactant in situ

Talmta,

1964. Vol

11. pp

203 to 210

Pergmott

Praa

Ltd

POTENTIOSTATIC DETERMINATION OF KINETIC PARAMETERS OF ELECTRODE REACTIONS WITH GENERATION OF A REACTANT IN SITU Y. OKINAKA*, S. TOSHIMA and H. OKANIWA Department of Apphed Chemistry, Faculty of Engmeermg,

Tohoku Umverstty, Sendal, Japan (Received 19 June 1963. Accepted 25 September 1963)

Summary-It is shown that kmetic parameters of sample, fast electrode reactions of the type 0 + ne = R, where R IS soluble in the solution or in the mercury electrode, can be determined by the potenttostatic method with a solution initially containmg only the substance 0, the substance R being generated m situ during electrolysa, provtded that the electrode reacbon involves only a single rate-determmmg step. Current-tune curves are recorded with a fast response, electromc potentiostat and an oscdloscope upon applymg a potential step from the zero+aurent potenttal to various potentials on the ascending part of the current-potenttal curve The forward rate constant k, at a grven potenttal 1s calculated from the current at zero tnne found by extrapolation of the hnear portion of the plot of current agamst square root of time, while the backward rate constant k, is calculated mdirectly from the slope of the same straight line. Plottmg log k, and log k, agamst potential allows a simultaneous determination of the formal standard rate constant k, both cathodtc and anodtc transfer coef?Xents, the number of electrons mvolved in the rate-determining step and the formal standard potential of the system bem studied. This method IS considerably simpler than the well-known b- nscherVlelstich method, and it should be particularly advantageous when R is highly reactive or forms an amalgam which IS unstable m air. The upper limit of k. that can be determined by this method IS the same as that determinable by the Gertscher-Vielstsh method. The kinettc parameters found by the present method for the electrode reactions xinc ion-xmc amalgam in 1M potasstum tutrate, copper11 ioncopper amalgam in 1Mpotassium a&ate and cadmium ion-cadmium amalgam in 0*5M sodmm sulphate were in fair agreement with the values reported in the literature. INTRODUCTION THE potentiostatic

method developed by Gerischer and Vielstichlle is a well-established method for the determination of kinetic parameters of fast electrode reactions. In their method, current-time curves are recorded upon applying a potential step from the equilibrium potential of a given system containing initially both oxidised and reduced species at known concentrations, and the exchange current is calculated from the slope at the equilibrium potential of the plot of current at zero time against potential. The standard rate constant and the transfer coefficient are normally * Present address:

Bell Telephone Laboratories, Whippany, New Jersey, U.S A. 203

Y

204

OKINAKA, S. TOSHIMA and

H. OKANIWA

evaluated by determining the variation of exchange current wrth the concentratton of erther oxidised or reduced species. Thus, the Gerischer-Vielstich method suffers experimental complications when the reduced species m solutton or in amalgam is highly reactrve and SubJect to air oxrdatron. In the method descrrbed in this paper, krnetlc parameters are evaluated by analysing current-time curves obtained at only one concentratton of the oxidised species, the reduced species being absent before electrolysis. Metal ion-amalgam systems can thus be studied by the present method without using an amalgam electrode of accurately known concentration. As expected from theoretical considerations, errors involved in the determination of the backward rate constant are somewhat greater than those involved in the determination of the forward rate constant, particularly at potentials away from the standard potential. Nevertheless, the method should be of practical value, as is evidenced by the fact that the kmetic parameters determined by the proposed method for the few systems are in satisfactory agreement with the values reported in the literature. CURRENT-TIME

RELATIONSHIP

Consider the reduction of a substance 0 to another substance R in an electrode process involving n electrons at a stationary mercury electrode under the following conditions: (1) The reduction product R is soluble either in solution or in mercury. (2) The solution contains the substance 0 at a known concentration and the concentration of R is negligible before electrolysis. (3) Because the electrolysis time is very short and the thickness of the diffusion layer is very small in the present potentiostatic method, semi-infinite linear diffusion is the sole mode of mass transfer. (4) The electrode process involves only a single rate-determining step. (5) The electrode potential is maintained constant during electrolysis. The general equation for current-time curves obtained under these conditions is well-known and takes the forma i = nFAk,Ca exp (&&z(E)

(1)

6 = st”a

(2)

s = k,D, -112+ kbDR-ti4

(3)

where

and i is the current in A, F the Faraday, A the surface area of the electrode in cma, k, and kb the rate constants for the forward and backward reactions in cm . set-‘, C, the concentration of substance 0 in the bulk of the solution in moles. cm-, t the time in set, and Do and D, the diffusion coefficients of 0 and R in cm*. se@. For values of t smaller than 1, one can write exp(P)=l+P+g+...

.

and for any values of t e&(t)=

l--2

I-&l+*.-\/;; (

)

*

Kmetr parameters

of

elcctrodc reacttons

205

When 5 is so small that the higher terms in the above expanston can be neglected, equation (1) can be written in the following form *

This equation predtcts that plotting current agamst PI* yields a straight line at sufficiently short times at potentials where the condition sP’* < 1 is fulfilled. The current at t = 0 found by extrapolation of this straight line 1s directly proportional to k,, while kb can be calculated from the slope of this line, provided that the diffusion coefficients are known. On the other hand, k, and k, are related to the standard rate constant k, and potential E by

S=

k, exp

k,=

1

k, exp

where a and @are the cathodic and anodlc transfer coefficients and a + /3 = 1, n, is the number of electrons involved in the rate-determining step, and E” 1s the formal standard potential. Thus, it is anticipated that plotting log k, and log k,, against E should yield two straight lines, and that tt should be possible to find k, and E” from the intersection of these straight lines. From the slopes of these hnes, it should be possible to evaluate separately a, B and n,. EXPERIMENTAL Reagents AU chemicals used were of the highest purtty avatlable commerctally, and they were used wtthout further purificatton. De-aeranon was carncd out by passing high1 pure tank mtrogen. Solutions of zmc, copper** and cadmium ION wcrc prepared by dtssolution o r zmc nitrate, coppc.r” mtratc and cadmium sulphata, mspacttvely. The conccntrattons were determined polarographtcally in suitable supporting electrolyte so1ut10tls. Apparatus Electroth: A dropping marcury elect&e wtth a drop tune of about 10 see was used as the workmg electrode, and current-tima curvas wcra rac~rded upon closing the circtut at a certain tune (8 to 9 sac) after the beginningof the drop formation. The tune when the cucuit was closed was measured with a stopwatch, and the switch for closing the ctrcuit was operated manually. Cutrenttime curvea were parfactly reproducible, indicating that the error resultmg from the manual operation of the switch was quita negligible as compared to that assocrated wtth the oscilloscopic rccordmg. Bacausc current-time curves were naaded only up to 10 msec after the ctrcuit was closed, the variation of surface area of the mercury drop during the ~rtiiig was also neghgbk. A saturated ahnnal electrode served as tha reference electrode, and rt was connectad with the drop ing &ctro& through a Lugght capillary. l-G counter electrode was a platinum foil, which was placed in the compartment scparatcd by a sinteredglassdisk. used in the present study was M ekctronic potenttostat constructed Potewostat: The -t&w wara and by the authors accmdmg to the circuit das@d and described by Shtmodaira, Matsuo, S source for 200 V d.c. described in their paper wasYaound to be Ebiko’ of this University. Tha vol unsuitabk for this type of work aza it was replaced by batteries to mimtnisa disturbancas resulting from LDcompJctcmcti6ution. Tha rim tima of the potentrostat was about 6 x lo-‘ sac, which is one o&r of magnituda longer than that (2.5 x lo-’ sot) of the potentiostat constructedby Ekctronischc Werkstfitte of Germany. For the systems studied in this work, however, this was not critical. A micro mlay switch was usai in tba aarly stages of this investigation. &cause this switch ganam@d

Y. OWEI~KA,S. TOSH~M

206

and H. O~CANWA

transrents m 0 8 msec, rt was later replaced by a sealed-m mercury swatch, whtch was found to gave excellent results. The preset potenttal was read exactly with a potentio~ter. Current-time curves were recorded with a Synchroscope Model SSSf 51 combmed with a high gam differentla~ preamplifier Model SFO2-DFH-A, both manufactured by Iwasakt Commumcatton Apparatus Co. Ltd. The cahbrated reststances used had a value of 10 to 50 Q, and the sensmvtty of the oscilloscope was always set at the maxtmum sensmvity of 1 mV. cm-t All experiments were camed out m a thermostat mamtamed at 25”. RESULTS

AND DISCUSSION

Experiments were camed out for reductions of zinc ran in lkf potassium nitrate, copper” ion in 144 potassium nitrate and cadmium ion in 05N sodmm sulphate. Examples of i - tl’* plots are reproduced in Fig. 1. Good straight lines were obtained

FIG. l.-f’lots

of 1 - I”‘: (1) 5 mM Zn*+ m 1M KNOt at -0 986 V; (2) 2 mM Cus+ in 1M KNOI at +@034 V; (3) 2 mM Cd*+ in 0-5M NatSO, at -@581 V.

in ail cases at su~cientiy short times. The upper timit of f before which a linear . I - t1j2 is obtained greatly depends on k, of the system and also on potential. For example, in the vicinity of the standard potential and for the ease of IJ,, = Dn(=L))* we have s RSkJF8 &$Iequations (3), (5) and (6)]. If one prescribes the condition St”* S 0.2 for a linear i - P plot to be obtained, then one finds t I; IO-* set for a reaction with k il = 1O-s cm.setY and I 5. 10-a see for a reaction with k, = lb2 cm.se@. For faster reactions, current-time curves must be recorded at shorter times, At very short times (< 16-’ set), however, correctron for the capacity current becomes excessive and limits the maximum measurable value of k,. The dtscussion given by

Kmettc parameters of ekxxrode reactions

207

Delahap on this point for the Gerischer-Welstich method apphes directly to the present case, and it can easily be shown that in both methods k, much greater than O-2 cm.sec-l cannot be measured. In the experimental examples given in this paper, it was not necessary to measure current at times shorter than 6 x IO4 set and the capacity current was quite neghgible. -15

-‘“r-----l

-a96

-0a E. V w

-l-o0

-192

SCE

FIG.Z.-Plot of log k - E obtained with 5 mM Zn’+ in IM KNO ,’

006

004

002

0

E, v vs. SCE FIG. 3 -Plot of log k - E obtained with 2 mM CL+ III 1M KNOs

FIG.4.-Plot of log k - E obtained with 2 mIU Cd’+ m @5M Na$O,.

As is obvious from the theory, a knowledge of diffusion coefficients of both the oxidised and reduced species is required in order to calculate kb. The values of diffusion coefficients used in the calculation were as follows (D x 105cms.sec-*): ZnP+ in 1M KNO,, 0.666; Zn in mercury, 19; CuGI-in 1M KNO,, O-713’; Cu in mercury, l-06*; Cds+ in 0-W NatSO,, O-720; Cd in mercury, 2-07s. The values for which no literature reference is given were calculated from the average polarographic diffusion current by using the original Ilkovic equation. it is generally recognised that diffusion coefficients calculated in this manner are often in considerable error. For example, the D value of zinc ion calculated by using a modified Ilkovic equatron (the numerical constant in the second, cmection term being taken qua1 to 34) was qual to 0.562 x 1c)d cms.se.+ instead of O-666 x IO4 cm*.sec-l found by using the original Ilkovic quation. This difference, however, resulted in only a minor difference in kinetic parameters. For example, the values of k, for the zmc

Y. OK~NAKA, S. TOSHIMA and H. OKANI~A

208

system calculated with the above two D values were 3.6 x 1O-3 and 3.8 x lOA cm set-l, respectively. Plots of log k, and log k, against potential for the three systems studled are shown in Figs. 2, 3 and 4. The kinetic parameters found from these plots are summarlsed and compared m Table I with the values reported in the literature. In general, the TABLE1 -KrNEIX

PARAMETERS AND

FORMAL

STANDARD

POTENTIALS

OF

SOME MErAL

ION-AMALGAM

SYSTEMS

Temp., System

“C

Zn*-/Zn(Hg) In 1M KNO,

25

SCE

-lx@5

25 Cu*-/Cu(Hg) in 1M KNOS

25

25

cm set-’

3 8 x 1O-3

n,

a

B

2

035

056

ro 022

19 x IO-’

2

0 43

0 53

4 5 x 10-l 4 5 x 10-z -0 587

3 6 x lo-’

Method This study A C. polarographys

3 5 x 10-s

25 20

Cd”/Cd(Hg)

k,,

E’, Vvs

This study A.C. polarography@ Faradarc tmpedanc@

2

029

0 62

Tha study

m 0 5M Na,SO, 25 25 20 20 20

0 38 25 26 42 45

Y x x x

10-l lo-* 10-a 10-a

0 25 0 17 0 22

A.C. polarography” A.C polarography” Voltage-stepls Faradax Impedan&’ Current-steplS

agreement between the values found by the present method and the hterature values was satisfactory, except that the k, value for the copper system was somewhat lower than the value found by other methods. In Figs. 2-4, It is noted that the pomts for log k, obtained at less negative potentials tended to deviate m the same dlrectlon m all three cases. The reason for this deviation 1s not obvious. At any rate, It 1s clear from equation (3) that errors involved m the determination of k, should be mimmum at potentials near the standard potential where Jc, and k, are of the same order of magmtude. It should also be noted that as the potential IS made more negative, the current-potential characteristics become steeper and this trend is more marked with faster reactlons. At such potentials the precision and stab&y of potential control of the potentiostat become critical. Also, because current becomes larger at more negative potentials, the effect of iR drop between the workmg electrode and the tip of the Luggin capillary becomes more serious at more negative potentials. For these reasons, satisfactory k, values could not be obtained at potentials much more negative than the standard potential. While the present method IS simpler than the Gerischer-Vielstich method from the experimental viewpoint, it is the disadvantage of this method that the accuracy m the determination of kb is less than that in the determination of k,. If it is desired that k, be determined with the same degree of accuracy as k, in a wider potential range and if the reduced species is s*&ciently stable, k, should be calculated from the anodic current at t = 0 measured with a system containing the reduced species alone, the oxidised species being generated in situ in this case. It also would be of interest to apply the principle of this method to totally irreversible reactions.

Kmetrc parameters of electrode reacttons Zusammenfassung-Es wtrd gezetgt, dau kmettsche Parameter emfather schneller Elektrodenreakttonen vom Typ 0 t IIC = R, wo R m der Losung oder n-t der quecksilbemen Elektrode loslich nt, mit der potenttostattschen Methode besttmmt werden konnen. Dte Losung enthalt dabet zuerst nur 0, R utrd UI SIIU be1 der Ekktrolyse erzeugt, vorausgesetzt, dau dte Elektrodenreaktton nur emen geschwmdtgkettsbesttmmenden Schrttt enthalt Strom-Zen-Kurven werden mtt emem schnell ansprechenden elektronischen Potenttostaten und emem Osztllographen regtstrtert. wobe~ das Potenttal sprunghaft vom Potential, bei dem kem Strom the&, auf ein Potential im anstetgenden Tell der Stromspannungskurve gellndert wtrd. Dii Konstante der Hmreaktton k, bei emem besttmmten Potential wird aus dem Strom zur Zett Null berechnet, den man durch Extrapolation des linearen Ansttegs des Stromes gegen die Quadratwurzel der Zeit findet. Dte Konstante der Ruckreaktron ks wird mdtrekt aus der Steteune derselben Geraden berechnet T&t man log k, und log k; g&n das Potential auf. so erhalt man eleichzettte dte formak Standard-Geschwmdtgkeitskdnstante k., katl&dtsche &td anodtsche Durchtrtttsfaktoren. dte am geschwmdtgkettsbesttmmenden Schritt beteiligte Anzahl von Elektronen und das formale Standardpotenttal des untenuchten Systems Dtese Methode 1st betrilchthch emfacher als dte bekannte Gertscher-Vtelstch-Methode und sollte besondere Vorteile bteten, wenn R sehr reakttonsfahtg 1st oder em mcht luhtbestiindtges Amalgam btldet Das groQte besttmmbare k, 1st fier gletch wie ba der GertscherVtelsttch-Methode. Dte nach der neuen Methode gefundenen kmettschen Parameter fur dte Reakttonen Zmkton-Zmkamalgam m lm KN03, Kupfer(II)-Ion-Kupferamalgam m lm KNO, und Cadmtumton-Cadmtumamalgam in 0,Sm Na,SO, stimmten mtt den m der Ltteratur angegebenen Werten befrtedtgend iiberem.

R&sum&-On montre que les parametres cmettques des reacttons aux electrodes, stmpks, raptdes et du type 0 + ne * R, oft R est soluble darts la solutton ou darts l’&ctrode, peuvent Ctre dCtetmm& par une methode potenttostatique sur une solutton qui ne conttent irnttalement que 0, la substance R &ant fabriquee in sttu pendant l’tkctrolyse Cette m&hode tmphque qu’une seule reaction d&ermine la ntesse de Les courbes courant-temps sont enregtstrees la r&action a I’tlectrode a I’atde dun potenttostat Clectromque a rCponse raptde et d’un osc~lloscope, en apphquant un saut de potenttel allant du potentiel B courant nul ~usqu'A divers potenttels de la partre ascendante de ia courbe mtensttbpotenttel. La constante de vttesse duacte k, P un potenttel don& est calcuke a parttr du courant au n I CW 2 d&emunC par extrapolatton de la partte hn6atre de la COUI I U!nt-ractne cat&e du temps, tandts que la constante de vttease tnvcrse k, cst calculk mdtrectement P patter de la pente de la m&me droite. SI l’on trace log k, et log k, en fonctton du potenttel, on peut d&ermmer en mime temps la constante de vttesse globale k,, les deux &tents de transfer6 cathodtque et anodtque, Ie nombre d’tkctrons mts en Jeu au tours de la r&action qut dCtermme la vitease, et le potenttel normal du systtme. Cette mtthode est beaucoup plus simpk que la m&hode bien connue de Genscher-Vtelsttch. et devratt Etre parttcuhdrement avantageuse dans le cas ou R est t&s rtacttf ou fonne un amalgame mstable B Pair. La plus forte valeur de k, que I’on ptusae dttemuner par cette mtthode eat la m&me que celie que l’on determine par la rn&hode de Genacher-Vtelsttch Les param&es cmCttques trouvts par cette m&hode pour Ies reactions a I’&ctrode: ion rinc-atnalgame de zmc dans du nitrate de potassuun 1 M, ion ctnvre(II)-amalgame de cu~vre dans du nitrate de potassmm 1 M et ion cadmtum-amalgame de cadmium dans du sulfate de sodium 0.5 M sont en bon accord avec Ies valeurs indtqu&s dans la htt&ature. l

209

210

Y. OKINAKA, S.

TOSHIMA and

H

OKANIWA

REFERENCES I H Gerlscher and W Vlelstlch, Z phys. Chem (frunk/iurr), 1955, 3, 16. * W Vlelsttch and H. Gerlscher, rbrn, 1955,4, IO. a P Deiahay, New Instrumental Methods in EIectrochemrsfry Interscience Pubhshers, New York, N.Y , 1954 ’ S Shmlodalra, H. Matsuo, G Sugawara and E. Ebiko, J Sot Metals Japan, 1962, 26, 100 5 P Delahay, m Advances m Electrochemistry and Elecrrochemlcal Engrneerrng edited by P Delahay lntersclence Pubhshers, New York, N Y., 1961. Vol. 1, p 254 a A. G Stromberg, Doklady Akad Nauk. S S S R , 1952, 85,831, Chem. Abs , 1953. 47, 51 ’ L Meltes, Polarographrc Techniques InterscIence Pubhshers, New York, N Y., 1955 B N. H Furman and W. C. Cooper, J. Amer. Chem. Sot., 1950,72,5667 ’ T Kambara and T. Ishil, Rev. Polarography. 1961, 9, 30 lo J. E B Randles and K. W. Somerton, Trans. Faraday Sac , 1952,48,951 ” H H. Bauer and P. J. Elving, Analyf. Chem., 1958,30, 341 I* H H Bauer. D. L. Smith and P J Elvmg, J. Amer. Chem Sot , 1960,82, 2094 ‘I W. Vlelstlch and P. Delahay, ibid, 1957, 79, 1814. ” H Gerlscher, Z. Uektrochem., 1953, SI, 605 I5 T Berzms and P. Delahay, J Amer. Chem. Sot., 1955, 77, 6448.