8/3/2019 Teoria y Aplicacion de a Ciclica

1/5

m i n i m u m i n t h e T C vs . concentrat ionisotherm (21)-correctly describes th eda ta ob ta ined . However , i t seems un-l ikely that so many compounds wouldshow maxima or minima in ni trogen b utnone of them would d o so in Ar or CO,,while they do give positive and negativeresponses in these gases.One poss ible a l ternat ive explanationis that a concentrat ion gradient isestablished in the cell as a result ofthermal diffusion between the cell walland the hotter f ilament. This couldresult in a transfer cf thermal energyacross the gradient, the so-called D ufo ureffect (7). If so, it should be possibleto eliminate this effect by increasingth e tu1 bulence in the cell. Preliminaryinvest igation with such a cell indicatest h a t t h is is so .Th e lack of W peaks and th e low costof CO, suggest that it would be a bettercar rier gas than ni t iogen for prep arat ivework (and possibly even some analyticalwork) . Some workers hav e repor tedcollecting samples in CO, by freezing itto dry ice (9). Also, the wide variationin response values (positive andnegative) might be useful for quali ta t iveanalysis of pure compounds. Fu rth erwork w ith C Oz and oth er carrier gases oflow TC is planned.

ACKNOWLEDGMENTThe au thor s thank F loyd F r edr icksfor obtaining some of the da ta .

LITERATURE CITED(1 ) Bennett, L. A . , Vines, R. G., J .( 2 ) Bohemen. J.. Purnell, J. H., J . A p p l .Chem. P h y s . 23, 1587 (1955)., . . .Chem. 8 , 433 (1958). (3 ) Dal Piogare, S., Juvet , R. S. , Jr . ,Gas Liquid Chrom atography, p. 192,Interscience, N ew York, 1962;((4 ) Dreisbach, R. , compiler, PhysicalPro pert ies of Chemical Compou nds,3 Vols., American Chemical Society,Washington, D . C., 1955, 1959, 1961.(5) Hansen, R. S., Frost, R. R., Murphy,J . A. , J . P hys . Chem. 68 , 2028 (1964).( 6 ) Harvey, D., Norgan, G. O., inVapor Phase Chromatography-Lon-don, 1956, p. 74, D . H . Desty, ed.Academic Press, New York, 1957( 7 ) Hirschfelder, J. O., Curtiss, C. F.,Bird, R. B., Molecular Theory ofGases and Liquids, p. 522, Wiley,N ew York, 1954.(8) Hoffmann, E. G., A N A L . CHE%f.34 ,1216 (1962 ).(9 ) Hornstein, I. , Croae, P. , Ibid., 37,170 (1965).(10) Jamieson, C . R., J . Chromatog. 3,464. 494 11960): 4 . 420 11060): 8.

~~ , , -,i i i ( i 9 6 2 ) : i S , i 6 0 ( i964) .(11) Keppler, J. G., Dijkstra, G., Schols,J. A., i n Tapour Phase Chroma-tography-London, 1956, p. 222, D.

H. Desty, ed., Academic Press, NewYork, 1957.( 1 2 ) Keulemans, A . I . M., KFantes, A,,Rijnders, G. W . A., Anal. Chim. Acta16,29 (1957).(13 ) Littlewood, A. B. , Gas Chroma-tograp hy, pp. 329-33, ilcademicPress, he w Y ork, 1962.(14) Madison, J. J. , A X A L . C H E Y .30,1859 (1958).(15 ) hIessner, A . E. , Rosie, D. &I.,Argabright, P. A ., Ibid., 31, 230 (1959).(16) Panson, A. G., Adams, L. lI., .Gas Chromatog. 2 , 164 (1964).117) Pauschmann. H.. 2 . Anal. Chem.,203. 16 11964).(18) Purcell, J. E., E(19) Purnell, H., . Gas Chromatography,Chromatog.D. 286, Wilev. New York, 1962.

Xtre, L. S., . Gas3, 69 (1965).( 2 6 ) Rothman, A . J. , Bromlep, L. A , ,Ind. Ena. Chem. 47. 899 11955).(21) Schmiuch, L. J.,Dinerstein; R. A ,,(22) Smith, B. I)., Bowden, W . W.,(23) SDencer. H. M., . Am. Chem. SOC

A N A L .CHEM.32, 343 (1960).Ibid., 36, 82 (1964).

(24) Stuve,~ K. ,n Gas Chromatography-1958, p. 178, I). H. Desty, ed. , Aca-demic Press, X e w Ynrk. l Q 5 .(25) lerzele, AI., J .(1964).Talanta 10, 937 (1963).(26) Williams, A. F., Murray, W. .,

RECEI VED or review April 7, 1965.Accepted July 22, 1965. Pre-ented atthe Pittsburgh Conference o n AnalyticalChemistry and Applied Spectroscopy,March 3, 1965.

Theory and Applica tion of Cyclic Voltammetryf m Measurement of Electrode Reaction KineticsRICHARD S. NICHOLSONChemistry Department, Michigan State University, East Lansing, Mich.b The theory of cyclic voltammetryhas been extended to include electrontransfer reactions which are describedby the electrochernical absolute rateequation. Results of theoretical calcu-lations made it possible to use cyclicvoltammetry to measure standard rateconstants for electron transfer. Thus,a system which appears reversibleat one frequency may b e made toexhibit kinetic behavior at higherfrequencies, as indicated by increasedseparation of cathodic and anodicpeak potentials. The standard rateconstant for electron transfer is de-termined from this peak potentialseparation and frequency. Themethod provides an extremely rapidand simple way to evaluate electrodekinetics. The reduction of cadmiumi s used as an illustration.

U R I N G RECENT years a number ofD methods have been developedf or the measur ement of electrode reac-t ion kinet ics . I n one sense, some of

these determine electrode reversibilityindirect ly by measur ing the apparents tandard rate constant for e lectrontransfer from only cathodic (or anodic)polarization. In a few cases bothcathodic and anodic polarization giveconsistent results ( I S ) . M any of therelaxation techniques developed for fastr eac t ions have the d i sadvantage tha tsmall ampli tude per turbatio ns are used,and consequently differences or changesin mechanisms are not eas ily detecte d.A method which overcomes this dis-advantage and a t the s ame t ime g ivesa direct e stim ate of reversibility iscyclic t r iangular wave voltammetry.Th us , th e presence of homogeneo usreact ions in the mechanism is readilydetected , and interpreta t ion of resultsusually is simple. il direct estimate ofelectrode reversibility is provided, be-cause the potentia ls at which oxidationand reduction occur are observeddirect ly. For example, a t low fre-quencies it may b e possible with a givensystem th at e lectrochemical equil ibriumalways is maintained a t the electrode

surface. Under these conditions theseparation of cathodic and anodic peakpotentia ls is about 6 0 / n mv. , and thereaction is reversible.Clearly for this case no kinetic in-formation about the electron transferreaction can be obtain ed. However , iffrequency is increased sufficiently, apoint may be reached at which thekinetic s of elec tron transfe r becomecomp etitive with the rate of po tentialchange . Unde r these conditions it m a ybe possible to stu dy th e kinetics of t heelectrode reaction, and th e separation ofpeak potentia ls should be a measureof the s ta ndard rate constan t for e lec-tron transfer. Thus , a t leas t in pr inci-ple , one can es t imate s tandard rateconstants simply by observing cyclicpolarograms on the oscilloscope, andthen increas ing the tr iangular wavefrequency until th e separation of peakpotentials becomes greater than 60/nmv. The s tandar d r a te cons tan t thenshoul d be a calculable functio n of fre-quency at this peak potentia l separat ion.Unfo r tunately , there is no a priori w ay

VOL. 37, NO. 1 1 , OCTOBER 1965 0 1351

8/3/2019 Teoria y Aplicacion de a Ciclica

2/5

0.4 n l

-0I , , , ,120 60 0 -60 -120

(E - E , , h mv.Figure 1 . Cyclic polarograms showingeffect of charge transfer coefficient, a

iC. = 0 .5 ; CY = 0.7...... C. = 0 . 5 ; a = 0.3---

to mak e thi s correlation because effectsof co ncen tration polarization can betreated only by mathematical analysisof th e mass tra nsp ort processes. Suchan analysis is not available for thepresent case, and consequently applica-tions of th ese ideas using cyclic volta m-metry have been limited to simples tatements tha t a given sys tem appearsto be reversible or irreversible ( 7 , IO).I n th e stud y of electrode reactionmechanisms, it often is useful to be ableto obtain experimentally a rapid esti-ma te of electron transfer rates . Be-cause this appeared to be possible withcyclic voltamme try in the way jus tdescribed, we have attempted a theo-retical treatment of the problem whichincludes the effects of conc entrat ionpolarization. Our primary objectivewas to determine if cyclic voltammetrycould be used to provide rapid andreasonably accurate determinations ofstandard rate constants for electrontransfer. Thu s, the theoretical correla-tions between peak potentials, standardrate con stant , and rat e of potentialscan have been emphasized, althoughother correlations are possible. A seri-ou s limitation of this approach wouldresult if peak potential separationsdepended also on the charge transfercoefficient, C Y . This would require anindependen t measure of C Y , and make themeth od of little use in term s of t hestated objectives. However, throughproper selection of conditions, peakpotential separations become nearlyindependent of a .Becauqe there is neither theoreticalnor experimental ad van tage to consider-ing more tha n one cycle of th e appliedtriangular wave, theoretical calcula-tions havt been limited to this case.Consid eratioIL also ha s been restrictedto the case of an situ generation of thereduced form of t he couple under in-vestigation. This actually has two

advantages. First, it reduces by oneth e number of ind ependent variables inth e theoretical calculations. Second, ithas the exper imental advantage of notrequiring preparation of amalgams ofknown concentration for the study ofreductions at mercury electrodes.The method described can be appliedto systems in which homogeneouschemical reactions precede or followelectron transfer provided such reac-tions are either rapid or slow comparedto the s tandard rate constant for e lec-tron transfer. The cases in whichthese conditions are not met are easilydetec ted from th e form of t he experi-mental current-voltage curves ( 11) .Th e reduc tion of ca dmiu m is used asan illustration of the method developedhere. Application to other systems isin progress and will be reported else-where.

THEORYWe assume the following mechanism:

O + n e * R ITher e k , and ka are heterogeneous ratecons tants of th e electron transfer, andare assumed to be functions of potentialas expressed through the electrochem-ical absolute rate equation. The timedepend ence of electrode pote ntial is theform of an isosceles triang le. Syste m Iis assumed to be initially in equilibrium,Both 0 and R are to be soluble eitherin the electrode or solution phase.T o account for concentration polariza-tion, diffusion to a plane electrode isassumed to be th e only source of ma sstranspor t . Mathematical formulat ionof this problem follows

kfkb

aco a v o_ -a t - D O T a x

t 2 O , x = O

Undefined terms have their usualsignificance (11).With the electrochemical absoluterate equation, Equation 6 can be trans-formed to

Ther e E is the electrode potential; E ois the s tandard potentia l ; k , is thes tandar d r a te cons tan t at E = E O ;LY is the transfer coefficient; an d theremaining terms have their usualsignificance.The potentia l in Equation 7 f or thefirst scan (reduc tion) of th e triangula rwave takes th e form

(8)= E , - utand for th e second scan (oxidation)

E = E , + u t - 2uX (9)Here, E , is the initial equilibrium po ten-tial, v is d E / d t , and X is the period ofthe tr iangular wave.If Equa t ions 7 , 8, an d 9 are combinedth e result is

acoaxo - k , ( C o * / C ~ * ) - " [ S x ( t ) ] - * x(CO, = 0 -( C O * / ~ R * ) ~ A ( ~ ) ~ R ,) (10)

Th e f unc tion Sx( t) is defined ast < X

(11)2ax t >( t ) =where

a = nFv/RT (12)Equa t ion 10 is t he final form of bound-ary condition 6 .By applica tion of Laplac e transformmethods the above boundary valueproblem can be converted to t he follow-ing dimensionless linear integral equa-tion w ith v ariable coefficientsX(Y) [?(CO*/cR*)sd( ! /)"=

!4

T o m a k e E q u a t i on 13 dimensionless thefollowing substitutions and changes ofvariable were mad e:

Y = (Do/DR)"' (14)y = at (15)

(16)4 = y 4 s / l / * a D o (17)

x(y) = Do aco,/Co*l/?rao,

For large values of $ (large k , orsmall v ) Equa t ion 13 becomes independ-e n t of 4 and CY and reduces to th e1352 ANALYTICAL CHEMISTRY

8/3/2019 Teoria y Aplicacion de a Ciclica

3/5

(E - E,,h, rnvFigure 2. Cyclic polarograms showingeffect of charge transfer parameter, +

$ = 7.0; CY = 0.5. $ = 0.25; CY = 0.5..

60

80100-6 ,

43 120-140-160-

corresponding equation for reversible(Nernstian) electron transfer (11).Likewise, as $ approaches zero, Equa-tion 13 approaches the case for total lyirreversible electron transfer (11). T h eint erm edi ate case, which is of int eresthere, is described completely by Equa-t ion 13.Solution of Integral Equation.E q u a t i o n 13 cannot be so lved an-a ly t ica lly . Al though a so lu t ion inth e form of an inf ini te ser ies can beobtained, ser ies solut ions for moreth an one-half cycle become hopeless lycompl ica ted . Th e on ly pr ac t ical ap-pr oach , the r e f or e , which f or thepr esen t case can be appl ied wi thoutloss of ge nerali ty, is numerical e valu a-t ion. We have used a method describedpreviously (1 ) . Several othe r methodsalso are possible, and apparently themethod used by DeTtries and VanDalen(6) involves less computational timefor comparable acculacy ( 5 ) .Solutions of Equ ati on 13 were inde-pendent of values of r (C , * /CR*) pro-vided r ( Co*/CE*) was greater than e6 5.This corresponds to the experimentalf ac t tha t if R is ab sm t ini tia l ly and th evoltage scan is begun a t potentialsanodic of th e pcllarographic wave,current-voltage curves are independen tof the exact initial potential selected,All calculations have been performedusing r (Co*/CR*)= e65.With this simplifiaation it was possi-ble to calculate numerically current-voltage curves. These curves dependedon three vaiiables, p, y, and A. It h asbeen shown previously that h affectsonly the anodic wave, and that therethe effect on anodic peak potentials isquite small ( 1 1 ) . This is particularlythe case when sw itching potentials closeto the cathodic peak are avoided[(Ex- El ,Jn> 90 mv.] . All calcula-tions reported here are based on a valueof (E x - = 141/n mv. Thus ,

--

I I I

calculated current-voltage curve s couldbe interpreted on the basis of only twovariables, \L a n d a.Results of Calculations. W h e n +becomes sufficiently large ( k , large,or v smal l ) , curr en t - vo ltage cur vescalculated from Equation 13 are inde-pen den t of th e kinetic para mete rs $ an dCY. For this case results are identicalto ones obtained previously where theelectron transfer was assumed to beSer ns t ian (11). Thi s limit occurs when$ > 7, which is in good agreement withcalculations of Mats uda and Ayabe (8).W h e n $ < 7 , the current-voltagecurves are dependent on both the valuesof + an d a . For sufficiently small $( k , very small or v very large) , he backreaction for electron transfer is unimpor-tant, and the processes for oxidationand reduction can be treated separatelyas th e totally irreversible case. Thu s,results calculated from Equation 13 fo r$ = 0.001 agree exactly with previouscalculations in which electron transferwas assumed to be totally irreversible( 1 1 ) . This also is in agreement withcalculations of M atsud a and Ayabe (8).For interm ediate values of $ (a regionsometimes referred to as quasi-reversi-ble), the form of th e current-voltagecurves depends markedly on the exactvalues of $ an d cy.The dependence -on CY is shown inFigure 1 where curves for two values ofCY and $ = 0.5 are compared. Gener-ally, the results are as expected, and CYaffects the sym metr y of th e curves intwo ways. For cy < 0 . 5 , the cathodicpeak is more rounded than the anodicpeak. This broadening also results ina lowering of peak height. Fo r cy > 0.5,th e converse holds.The second effect involves a slightdispla ceme nt of th e waves along thepotential axis. Fo r example, as CYdecreases, the cathod ic peak is displacedcathodically. At least for the data usedto construct Figure I , th e effect is slight.Lloreover, as the cathodic peak shiftscathodically with decreases of CY, th eanodic peak also shifts cathodically.There fore, in ter ms of differences of p eakpotentials, AEP, changes in CY t e n d t ocancel. Thu s, values of AEp for thepresent case are nearly independent ofcy in the range 0.3 < CY < 0.7. T heextent to which this holds depends onthe exact value of $. S a t u r a l l y , as $increases the approximation becomesincreasingly good. Thus, for $ = 0 .5(AEp ca . 105/n mv.) , there is about a5% variation of AEP fo r CY changingfrom 0.3 to 0.7. For $ < 0.5 th evariation is greater, and causes about a20% change of A E P fo r + = 0.1. How-ever, for this case the curves havedeviated considerably from the reversi-ble case (AEP a . 200/n mv. comparedwith 60 /n mv. for th e reversible case).The dependence on $ of theoreticalcurrent-voltage curves is shown in

Figure 2 where curves for two values of+ a n d CY = 0.5 are compared. Thecurve for $ = 7 corresponds (withina b o u t 1%) to t he reversible case and isindependent of CY. As $ decreases twoeffects can be distinguished from Figure2. Both cathodic and anodic peaksare lowered, and both waves appeardra wn out-Le., they occur over awider potential range. Thu s, the ca-thodic, wave is shifted cathodically andthe anodic wave is shifted anodically.This naturally results in an increasedseparation of catho dic and anodic peakpotentials.The exact var iation of peak potentialswith $ is shown in Figure 3, and theda ta used t o const,ruct Figure 3 a re inTable I. I n F igur e 3 AE p x n (n isthe number of electrons) is plotted as alogarithmic function of $. D a t a f o rFigure 3 were obtained using CY = 0.5,but from the previous discussion thecurve of Figure 3 is nearly independentof CY. As mould be expected the curveapproaches linearity for small $ [seeEq ua tio n for peak po tentia l of irreversi-ble waves (II)]. In Ohis region A E pis markedly dependent on CY.

Table I. Variation of Peak PotentialSeparations with Kinetic Parameters forCyclic VoltammetryAEP X 7 ~ , *

$" mv.20 617 636543210 . 7 50 . 50 . 3 50 .2 5

646566687 284921051211410.1 212a See Equation 17.* F o r CY = 0.5.

VOL. 37 , NO. 1 1 , OCTOBER 1965 1353

8/3/2019 Teoria y Aplicacion de a Ciclica

4/5

It should be noted t ha t the theoret icalcurv es of Fig ure 2 could correspondeither to two different systems havingdiffe rent electron transfer rates-andobserved a t the same scan rate-or to the same system observed attwo different scan rates. Thi s isexactly the behavior anticipatedin th e discuss ion a t the beginning andprovid es th e basis of us ing cyclic voltam -metry to es t imate electron transferrates. Figure 3 gives quanti ta t ivelyth e relationship betm een pea k poten-tials, scan rate, and electron transferrate .To use Figure 3 in this way a scanrate is selected which gives an experi-menta l A E p in the useful range ofFigure 3. From the exper imental AEpx n, the corresponding value of Vl . isobtained f rom Figure 3. If scan rate isknown, k , can be calculated from Equa-tion 17 . A4ctually, o app ly Eq uation 17r igorously yo also must be known.However, except for th e unusual case ofvery large differences between DO a n dD E , he quant i ty ya is very near un ity,regardless of CY.=ilthough the useful working range ofFigure 3 is fair ly restr icted, this is nota serious limi tatio n, especially if roughestimates of k , are al l th at is required.This is so because the wide range ofscan rates normally available withcyclic volt amm etry allows simple experi-me nta l selection of an y AEp for meas-urements .The upp er l imit of ra te constants tha tcan be determined experimentally bythe above procedure is discussed in alater section.APPLICATION OF THEORY TO REDUCTION OFC A D M I U M

To evaluate the method descr ibedabove a model system is required forwhich the mechanism and kinetic pa-rameters are well kno nn. The extensiveinvestigations on cadmium, which havebeen made previously using a var iety oftechniques , appeared to m ake cadm iuma logical choice. Ho wev er, th e compila-t ion by T anaka and Tamamushi ofkinet ic data (14) shows a considerablevariation of bo th stan dard rat e con-stants and charge transfer coefficientsfor cadmium when determined byvarious workers. Nevertheless, cad-mium was considered the best modelsys tem available , and therefore i t wasused to test the theoretical calcula-tions.

EXPERIMENTALApparatus. T h e c i r c u i t was es-sen t ia l ly the s am e as desc r ibed pr evi -ously (10). All measurements werem a d e w i t h a three-electrode potentio-static circuit, using a single Philbrick>lode1 SK2-V operational amplifier(G . A. Philbrick Researches, Inc.Boston, Mass . ) . To improve rise-time

and increase current capabilities, aPhilbr ick Model K2-BJ boosteramplifier was used in series with thepotentio s tat . T he bandwid th of thepotentios tat was adjus ted for the solu-tion used to provide optimum rise-t ime and s tabil i ty. To do th i s theideas of Booman and Holbrook wereused ( I , 2 ) . A good qualit y commercialpotentios tat (e .g. , Wenking Potentio-s ta t , Br inkmann I ns t r uments , W es t -bur y , 3 .Y.) presumably could be usedin place of th e poten tios tat just de-scribed.Two different signal generators wereused, and both proved adequ ate . Onewas constructed from operation al ampli-fiers and has been described previously( 10 ) . The o the r was an Exac t Mode l255 function generator (Exact Elec-tronics, Inc. , Hillsboro, Ore.) , whichproved useful an d versatile.The detector was a Tektronix Model536 oscilloscope provided with a Po -laroid camera at tachment (TektronixT y p e C-12). The ver t ical input wasalways a T y p e D plug-in preamplifier.This could be operated in the differen-tial mode and p ermitted use of a f loatingload resistor in the poten tiostatic circuit(10). To measure scan rates for thefunction generator constructed fromoperational amplifiers, a T y p e T plug-inpreamplifier was used for the horizontalin pu t of the oscilloscope. W ith theExact function generator , scan ratescould be dialed directly with an ac-curacy of =t2% and this proved to bea considerable advantage over t he o thersignal generator. To measure peakpotential separations a T y p e H plug-inpreamplifier was used for the horizontalinp ut of t he oscilloscope. T he hori-zontal axis then was dr iven by the cel lpotential, and peak potential separationscould be measured with a n accuracy ofa b o u t 1 2 m v .Th e cell assembly has been describedpreviously (10) .Materials. Solutio ns were preparedf r om cadmium su l f a te ( Baker A. R.)and anhydr ou s sodium su l f a te ( BakerA . R.). Th e concent r a t ions wer e : cad-mium sulfate, ea. 2 x 10-4M1; sodiumsulfate, 1. 0 X , The exact cadmiumconcentrat ion was not determined.Xeasurements were made in a cons tan ttemper a tur e r oom a t ambien t t emper a -tures of 23 t o 25 C.

RESULTS AND DISCUSSIONBoth one-cycle and multi-cycle

(steady state) experiments were runand as would be expected the differ-ences between A E p for the two methodswere of t he orde r of e xperim ental erro r.Nevertheless, data reported here arefor one-cycle experiments to conform totheoretical calculations. Fo r all experi-ments an initial potential of -0.370volt us . S.C.E.was used, and the ampli-tud e of t he tr iangular wave alway s was300 mv.Results for reduction of 2 X 10-4Mcadmium in 1.022 sodium sulfate aresummarized in Table 11. To conver texperimentally determined values of +

Table II . Determination with CyclicVoltammetry of k, for Reduction ofCadmiumAEPv , x n, ke,volt/sec. mv. $ 5 cm./sec.

48.0 94 0.70 0 . 2 560.0 98 0.61 0.2590.0 108 0.48 0.24120, o 115 0.41 0.23a Determined from Figure 3; seeb 2 X 10-4M cadmium sulfate, 1.OMEquation 17.sodium sulfate.

to k,, the diffusion coefficients ofOkinaka (12) were used. A value of (ILequal to 0.25 also was used. Althou ghno effort was made to determine aaccurately, the value of 0.25 was esti-mated by compar ing with theory thesymm etry and shap e of cathodic andanodic waves for cadmium. Th e calcu-lated value of k , is fairly insensitive tovariations of a, s already mentioned.The values of k , in Table I1 agreereasonab ly &-ellwith some oth er workers(14) . The disagreement with others( 12 , 14) is no t entirely explained. Th eapparen t ra te constant does change somewith different supporting electrolytes.Fo r example, we find k , equal to about0 .6 cm./sec. in 2 M perchloric acid.The value in sulfuric acid is slightlyhigher. In addition, electrodes are sub-ject to a n aging ef fect noted by Delah ay( 3 , 4 ) . We also ob serve this decrease ofapparent ra te constants with t ime, butthe effect in our solutions is not as g reatas Delah ay found (about a facto r of tw ochange in k , for the first 20 minutesquiescence).Th e upper limit of rate constan ts tha tcan be determined by t he above methodappears to be set by a combination offactors . F irs t , in the measurementof peak potential separations, uncom-pensated ohmic potential losses are aserious source of error. Thus, for therapid scan rates required to s tudy fas telectrode reactions, peak curre nts be-come fairly large and even relativelysmall solution resistances can introduceserious error. Moreover, the effects ofuncompensated iR drop qualitativelyare very similar to kinetic effects (9).

This is amply i l lus trated by Figure 3where the dashed curve is a plo t of da tacalculated previously for the effect ofiR losses on cyclic voltammetry (9).Th e definition of the horizo ntal axis ($)of Figure 3 for this case should be (9) :+ = l / ( n F / R T ) n F AX

( T ~ D O ) ~ C ~ * R ,18)Th us, the variation of peak poten tialseparation w ith scan rate is quite similarfor the two cases.The effect of ohmic potential lossescan be minimized in three mays. Firs t ,

1354 e ANALYTICAL CHEMISTRY

8/3/2019 Teoria y Aplicacion de a Ciclica

5/5

relatively conce nt-rated electrolyte s ofhigh conductivity can be used to reducethe tot al cell resistance. Second, witha three-electrode potentiostat place-me nt of t he Lugg-in capillary probe inclose proximity with the working elec-trode serves to compensate for a ma-jor ity of th e tota l cell resistance [seeI iooman and Holbrook for the exactrelat, ionship (2)1. Thir d, re lat ively lowconcentrations of dectroactive mater ialcan be used to keep total cell currentssmall. Thi s latte r approach is limited,however , by charging cur rent . Thu s , a thigh scan rates charging cur rent maybecome an ap preciable fraction of t hetotal cell cuirent, especially when lo^concentrations of electroactive mat'erialare used.For th e cadmium system investigatedhere a concentration of 2 t o 5 X 10-4Jlappeared to be optimum for low cel lcurrents without excessive chargingcurrent contr ibutions . hIas i mum peakcu rre nt s n-ere of t he ord er of 0.2-0.3 m a.Total solution resistance (ea. 20 ohms)

measured by peak potential shifts onmoLing the Luggin probe more than10 radii from the working electrodeagreed with values calculated from theconduc tivity of th e solution (2). B ycareful placement of the Luggin probethe uncompensated resistance was esti-ma ted to be 3 to 4 ohms (2) , so t h a tmaximum ohmic potential losses wereof t he o rder of 1 m v.The upper l imit of r a te cons tan tsmeasurable with cyclic voltammetrytherefore depends on several factors.The most im por tant of these is probab lyconduc tivity of th e solution und erinvestigation . W ith electrolytes of rea-sonably high conductivi ty, i t should bepossible to measure rate constants aslarge as 1 to 5 cm./sec.

LITERATURE CITED(1 ) Booman, G. L., Holbrook, W. B.,( 2 ) Zbid., 35, 1793 (1963).13) Delahav, P., Trachtenberg, I. , J . Am .

ANAL.C H E M . 7, 795 (1963).Chem. S i . '80, 094 (1958).-

(4) Delahay, P., J . Chim. Pkys . 54,369 (1957 .(5) DeVries, W . T., Free University,Amsterdom. The Xetherlands. orivate-communication, 1965.Electroanal. Chem. 8, 366 (1964).Zbid., 5 , 17 (1963).chem. 59. 494 11955).

(6) DeVries, W. ., VanDalen, E., J .( 7 ) Galus, Z. , Lee, H. Y., Adams, R. N.,(8 ) hlatsuda, H., Ayabe, Y., 2. Elektro-(9) Nicholbon, R . S.,' NAL.CHEM.37,(10 ) Nicholson, R. S. , Shain, I., Ibid.,667 (1965).

p. 190.(11) Zbid., 36, 06 (1964).(12 ) Okinaka, Y., Talanta 11, 203 (1964).(13) Selis. S. >I.. J . Phus. Chem. 68.~ 2538 (1964). '(14) Tanaka, X., amamushi, R., Electro-RECEIVED or review June 28, 1965.Accepted August 3, 1965. Presented inpart at the Division of Analytical Chem-istry, 150th XTeeting ACS, Atlantic City,N . J. , Septemb er 1965. Work supportedin part by the United States Army Re-search Office-Durham under Co ntra ctN o . DA-31-12PARO-LL308. Other sup-port was received from the National Sci-ence Foundation under Grant KO. GP -3830.

chem. -4cta 9,96 3 (1964).

Pola ro graphy of Lead(II) in Aqueous Hyd rof uoricAcid (1 to 12M) with a Dropping-MercuryElectrodle of TeflonHELEN P. RAAENAnalytical Chemistry Division, Oak Ridge Nat ional Laboratory, Oak Ridge, Tenn.

b The polarographic behavior ofPb+2 (-0.03 to 0.8rnM) in aqueousHF (1.00 to 12.00M) was studied witha D.M.E. of Teflon. The polarograph-ically usable potential span for 12.00MHF is about +0.4 to -1.0 volt vs .S.C.E.; for 1 .OOM HF, the limit extendsto about - .2 volts. Within this spanonly one polarographic wave for Pbt2exists; it is for the polarographicallyreversible 2-electron-change reductionPb+* -+ PbO. The E l l 2 values de-termined are -0.:380 for 1.00M HF)fa -0.370 (for 141.00M HF) h 0.003volt vs. S.C.E.; the values are notaffected by change in Pb+2 concen-tration. The wave is of excellentform and is usable for both quali-tative and qirantitcitive purposes. Therelation of j d , andl also of ($/dt)maz,to Pb+2 concentration is linear; plotsof these variables pass through theorigin. With increase in HF concen-tration from 1.00 to 12.00M, nochange occurs in the number of leadwaves, shape of the wave, polaro-graphic reversibility of the reduction,or n ; the i d deceases slightly; andthe El/* becomes about 10 mv. morepositive.

HE D R O P P I N G - N E R C U R Y electrode ofT ef lon (DuPont) has been described(8), nd i ts operat ion in noncorrodingmedia was invest igated (9, 10 ) . Areview w as given (8) of th e polarography-done before th e D. 3I .E. of Teflon wasdeveloped -of substances in liquid hy-drofluoric acid and in aqueous acidfluoride media.The polarography of lead in acidf luor ide media has been s tudied to al im ited es ten t . W es t , Dean , and Br eda( 21 ) obtained a well-defined wave forlead in 0 . 5 X N a2 F2 [qic]-O.Ol% gela tinsolu tion s of p H 1.1 to 2 .75 tha t con-tained con siderable amo unt s of nitr icacid added to dissolve the lead fluorideprecipitate; the solutions therefore con-tained lead ni trate and s l ightly dis-sociated hydrofluoric acid. Th e polarog-rap hy of lead, a s PbF2, n l iquid hydro-fluoric acid w as inv estig ated briefly byClifford (2). Mesar ic and Hume ( 7 )used polarography to s tud y lead fluor idecomplexes and their solubil i t ies ; thesolut ions they s tudied were 1mJf inP b + * , u p t o 0.7M in F-, a n d of 2 Mionic s trength adjus ted by addingKaC104. W i th a D.M.E. of Teflon,Headr idge and associates s tudied the

polarographic behavior of the ions of anum ber of elements, including lead, in0.1X NH4F-O. lM HF ( 4 ) and polaro-graphical ly determined molybdenum inniobium-base alloys using 0 . 5 X HF-0.5M H2S04 as sup por t ing medium (5 ) .W i t h t h e D.M.E.of Te flon, the polaro-graphic characteristics of P b + 2 inaqueou s hydrofluoric acid solutions ha venow been s tudied in some detai l . Th edata given herein are the f ir s t polaro-graphic data repor ted for Pb+2 inaqu eou s solution s of reasonab ly high HFconcent ra t ion and tha t conta in no o the radd ed constituents-e.g. , a salt to con-tr ibute ionic s trength or a maximumsuppressor.

EXPERIMENTALR e a g e n t s . S t a n d a r d Solutions ofP b + 2 n Aqueous HF. A q u a n t i t y ofl ead f luor ide , FbFz , (B & X purifiedg r a d e ) c a lc u l a te d t o g i ve 1 m X s ol u-t i o n w a s a d d e d t o a n a q u e o u s s o lu t i o nof HF (1.00, 4.00, 8.00, o r 1 2 . 0 0 M ) .Af te r maximu m dis so lu tion the so lu-tion was filtered to remove undissolvedPbF2. The Pb+* concent ra t ion of th efiltered solution was determined by aseparate analysis in which HF wasremoved f rom tes t por t ions by fuming

VOL. 37 , NO. 1 1 , OCTOBER 1 9 6 5 1355