Indian Journal of ChemistryVol. 16A. February 1978. pp. 123-125

Faradaic Rectification Polarographic Studies of Reduction ofZinc Ions in Indifferent Electrolytes

H. P. AGARWAL & (Miss) M. SAXENADepartment of Chemistry. Maulana Azad College of Technology. Bhopal 462007

Received 24 March 1977; accepted 15 July 1977

The faradaic rectification polarography and ac polarography at audio-frequencies have beenused to obtain kinetic parameters at the half-wave potential for the reduction of zinc ions at thedropping mercury electrode. The values of transfer coefficient and rate constants obtained inseveral indifferent electrolytes. are comparable to those corresponding to the second electroncharge transfer step of the reaction. The rate constants in the different supporttng electrolytesfollow the order: NOii>Br-> cr»CIO'> SO~-.

IN kinetic studies of fast electrode reactions, thefaradaic rectification method, discovered by Dossand Agarwap·2 appears to be full of promise3-s.

Barker", and Delahay and coworkersv" recognizedthe advantages of using very high frequencies in thedetermination of kinetic parameters of fast reactions.The merits of the method, when the sinusoidalvoltage was superimposed on a varying d.c. polarizingpotential, were investigated by Barker", which hetermed as low level faradaic rectification (LLFR)method or radio frequency polarography. Usingthis technique the kinetic parameters of some fastreactions were obtained and it was used for estima-tion of metal ion concentration as low as 1O-s to10-10 of a gram in 0·01 ml of the solution.

Recently Sluyters ei al.lO have extended themethod and have carried out a more systematicand theoretical study and renamed it as faradaicrectification polarography. In the recent paper byRe inmutht! the importance of second order methodsin the study of the kinetics of more complexelectrode reactions has been emphasized.

Faradaic rectification polarography has now beenapplied for the study of reduction of zinc ions indifferent supporting electrolytes at d.m.e. using analternating current at audio-frequency. The acpolarograms and faradaic rectification polarograms(which will be called FR polarograms) in the audio-frequency range have been used for determining thekinetic parameters in a few indifferent electrolytes.

Materials and MethodsAll the solutions were prepared in doubly distilled

water using AR (BDH/E. Merck) reagents. In thefirst instance solution of the supporting electrolytealone was taken into the cell and deaerated bypassing pure N2•

The circuit diagram used for ac polarography andFR polarography is shown in Fig. 1. The outputfrom an audio-oscillator (Philips model No. GM-2308/90) capable of giving frequencies from 10 Hzto 15 kHz was superimposed on a variable dcpotential obtained from a precision potentiometer(accuracy 2[1.V per division). The negative end of

p+

osIV

I(~

~~1T v

Fig. 1 - Circuit diagram used for ac polarography andFR-polarography

potentiometer was connected to d.m.e. The poolwas connected to the ground through a precisionresistance of 100 ohms. The alternating currentand the rectified current at varying de potentialswere measured at C, the junction of the pool andthe resistance. For ac measurements key K2 wasdisconnected and key K, was pressed so as toconnect C to the transistorized mixer preamplifier(Ahuja, type ASE/7MTR). The magnitude of theac output voltage from the amplifier was measuredon a solartron double beam oscilloscope (type CD1014'3, sensitivity 1 mV/cm). For the measurementof rectified direct current the key Kl was disconnect-ed and K2 was pressed so as to connect C to theinput of low pass filter F. The output from thefilter was connected to the de microvoltmeter (Philipsmodel GM 6020/90, sensitivity 1 [LV per division),so as to measure the rectified voltage. The residualde potential if any, was also measured by puttingoff ac. This was subtracted from the rectifiedpotential obtained at any frequency for a fixedvalue of interfacial potential which was always lessthan 10 mY.

The characteristics of the d.m.e. were: m = 0·64mg/sec; and t = 8·0 sec in distilled water in anopen circuit.

123

INDIAN J. CHEM., VOL. 16A, FEBRUARY 1978

The use of fine capillary with longer drop timehelped in accurate measurement of voltages on theoscilloscope screen.

The FR-polarograms were obtained by plottingrectified current at varying dc potentials. The ionicstrength of the supporting electrolyte (I·ON and0·5N) was kept much higher than that of theelectro-active species (1-2 mM), so as to minimizethe effect of post separation and of frequencydispersion of the double layer".Results and Discussion

The general nature of the FR-polarograms obtainedin KCI supporting electrolyte in presence of thedepolarizer is shown in Fig. 2. For brevity sakethe FR-polarograms in other supporting electrolytesare not incorporated. It is interesting to note fromthe plots in Fig. 2 that in absence of the depolarizer(i.e. in supporting electrolyte alone) the faradaicrectified current is zero. In the presence of de-polarizer the FR-summit peak currents are obtainedand the respective summit peak potential correspondsto the half-wave potential of the depolarizer.

A comparison of the results of ac-polarography(Fig. 3) with that obtained by FR-polarographyreveals the following salient features:

(i) The width of ac-polarograms spread over almostin a range three times more as compared to FR-polaro-grams in the proximity of half-wave potential of theZn2+. (ii) The FR-polarographic method appears tobe more versatile as compared to that of ac polarogra-phy in qualitative and quantitative analysis of evensuch mixtures which contain electro-active specieswhose half-wave potential may differ even by lessthan 40 mY. This fact is particularly confirmed onanalysing mixture of nickel and zinc ions in l'ONKCP2.

It is interesting to note that the FR-summitpeak current varies linearly with [depolarizer], unlike

80

70 ,.\

\ .. .,60 ,...•.+ •..--.•..-.• looo.n

a~ 50~lZ 40!;!a:::>0)0

"Z~~ ,0•••~« ;0

OO~--~---L--~~--------~'8 '9 ro 1"1

d.c, POTENTIAL IN VOlTS

Fig. 2 - Ac polarograrns of 2 mM Zn2+ in 1·ON RCI atdifferent frequencies of ac

124

e 04 ~

:" ~a:a:::>u

0.2owu,

~uwa: 0.1

~soV"JCr.--~--9C.tOOV'"~OOV\0-- -0- -0 400 V>

~&OOV\

0.0 p---'---;-----'.qt., 1..00 !.O~ uO

rl c POTENTIAL IN VOLTS

Fig. 3 - FR polarograms of 2 mM Zn2+ in l'ON ReI atdifferent frequencies of ac

n&r-----------------~e~ Lz 0,5

....~ 0.4exa:::>u 0.3ow~ 0.2

~ i

a: O~(~-~--~--~--~--~o I 2 3 4 5CONCENTRATION :N '!n.M

Fig. 4 - Variation of FR-summit peak current with con-centration of the zinc ion in l'ON RCI

in ac-polarograms (Fig. 4). Thus the concentrationorder of IO-4M can easily be carried out. Underdetermination of the unknown species even up tosimilar conditions the FR-summit peak current isobtained even at much higher frequencies as com-pared to the ac-sumrnit peak current.

It has generally been observed that for quasi-reversible and irreversible reactions the FR-summitpeaks are obtained in the audio-frequency rangewhereas for fast reactions the FR-summit peaks areobtained even up to 100 kHz or above. The faradaicrectification theory has been applied for determiningthe kinetic parameters using the summit peak currentvalues at varying frequencies at the half-wave poten-tial (when C~Db = C~Dt). The faradaic rectificationequation under these conditions simplifies to

AE = nF V2 (2ex-I) .lco RT' A 4 k~

~JWD +1J{J)D k~ 2

X -' •.. (1)2 2 JWD 1 wD

2+jf 2+k02 •2a a

AGARWAL & SAXENA: FR POLAROGRAPHY AT AUDIO FREQUENCIES

1 JWDand when 0 -~ 1, Eq. (1) reduces toka 2

AE = :zF. V2 (21X-l) (2)II IX) RT A 4 ...

when ~ JWD ~ 1 then Eq. (1) can be written ass; 2

AE = ~~.V2 (21X-l) _1 JWDII IX) A 0 ••• (3)

RT 4 u; 2In Eqs (1-3) MIX) is the rectified potential at the

half-wave potential of the depolarizer at varyingfrequencies of ac; VA is the ac potential at the ele-ctrode solution interface, IXis the transfer coefficient,W = 2nf (f being the frequency of ac); D is thediffusion coefficient; k~ is the rate constant; n isthe number of electrons involved in the chargetransfer reaction; and F, Rand T have their usualsignificance.

For applying the above formulation for deter-mining the kinetic parameters, it is necessary toobtain the values of interfacial ac potential (V A)and the rectified potential (IlEIX»)' To determineVA, the ac potential (20 mV) initially superimposedon de potential (in ac polarography) was dividedby the magnitude of ac summit peak current of thecorresponding frequency, so as to obtain the totalimpedance in the d.m.e. circuit. From the totalimpedance thus obtained, the resistance due topotentiometer, resistance in the output of the audio-oscillator and the resistance (100 ohms) in theexternal circuit of d.m.e. were subtracted andthe remainder corresponded to the impedance of thed.m.e. interface. This impedance on being multipliedwith summit peak current enables the determinationof VA independent of the solution resistance and thedifference in phase in between the alternating currentand alternating voltage of the cell. The methodhowever has a limited application. It is notapplicable in those cases where ac polarograms arenot obtained (in very slow reactions i.e. kg<10-4

cm/sec). In such cases the impedance measurementshave got to be made using low frequency impedancebridge. The rectified potential was obtained bymultiplying the rectified summit peak current withthe impedance across the electrode solution interface.

2 -The plot between lllilX)/V A vs VW was obtainedfor the frequency range from 25 Hz to 600 Hz.At high frequencies (>,200 Hz) the llElX)fV~ tendsto be constant and USll1g Eq. (2), the value of IX,can be calculated. From the slope of the curveat frequencies <200 Hz, the value of kg can bedetermined using Eq. (3) provided the value ofdiffusion coefficient (D) is known. The values of Din different supporting electrolytes were experi-~entally determined using McBain-Dowson porousdiaphragm cell and applying King-Cathard equa-tion13•

The values of kinetic parameters obtained indifferent supporting electrolytes, given in Table 1,show that the values of (X in KCl, KN03 and KBr

TABLE 1 - KINETIC PARAMETERSOF ZnH IN DIFFERENTELECTROLYTESAT d.m.e, AT 25°C

(Concentration of the zinc ion in KNOa was 1·0 mM and inthe rest of the electrolytes it was 2·0 mM)

Supporting D (cm!{sec IX k~electrolyte xl06) (cathodic) (em.see

xl0!)

1·0N KCl 804- 0·52 2·51·0N KNOa 7·8 0·52 2·8l'ON KBr 6·7 0·525 2·60·5N K2S04 4·8 0·535 2·2l'ON NaClO4 4·6 0·53 2·4

are of the order of 0·52 whereas in K2S04 andNaCl04 it is in vicinity of 0·53. It is interestingto note that the rate constant in sulphate is thelowest whereas in bromide and nitrate media it ishigh as generally quoted in literature= for thereaction at d.m.e. interface. The values of kineticparameters in different supporting electrolytes followthe order: KNOa>KBr>KCl>NaCl04>K2S04•

The values of kinetic parameters as given inTable 1 are found to be of the order of 10-2,

similar to those reported by Van Der Pol et at.15for the second electron charge transfer step. Thisshows the second electron charge transfer processis in control of the overall reaction.

AcknowledgementThe authors wish to thank Dr B. L. Mehrotra,

Principal, for necessary facilities and the UGC, NewDelhi, for the award of a junior research fellowshipto one of them (M.S.).

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national symposium on industrial electrochemistry(SAEST, Indiana), Dec. 1976, 13-24.

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