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The kinetics of the zinc ion reduction at the dropping mercury electrode in dimethylformamide
THE
KINETICS OF THE ZINC ION REDUCTION THE DROPPING MERCURY ELECTRODE IN DIMETHYLFORMAMIDE J. S.
Department
of C‘hemical
DUNNETT*
and
D.
AT
GEAREY
tngineermg. University ol Manchester Institute PO Box 88, Manchester M60 1QD. England
of Science
and Technology,
electrochemical reduction of the 7inc ion to the amalgam has been studied in lithium perchlorate-dimcthylformamide solution. The true standard rate constant is 2.5 x 10d3 cm set-’ and the cathodic charge transfer coefficient is 066. Abstract--The
NOMENCLATURE
n,,,= diffusion n
,,I
/
=
E = E,, = I?., = p= ;=
id = R=
T=
: =
r(=
0 = li=
coefficient
of
electroactive
ion
in
the
electrode diffusion coeflicient of electroactivc ion in the: solution rlectrode potential standard electrode potential polarographic halfwavt: potential Faraday’s constant polarographic (I( mean diffusion limited current (Ilkovic equation) universal gas constant absolute temperature charge on rlectrnactive inn in solution cathodic transfer coefficient activation parameter in Faradaic impedance: diffusion parameter in Faradaic impedance.
ments were also made of the double layer capacity of the supporting electrolyte so that appropriate corrections could be applied to the measured rate constant. THEORY The results were interpreted by the impedance plane method of Sluyters-Rehbach and Sluyters[&61. However, in the present paper, the cathodic charge transfer coefficient, 2, corresponds to b in Ref. [S] and the cathodic current is taken to be positive, following Delahay[7]. Also r was dcrivcd by a modified procedure, as follows. A standard equation of polarography is[R]: exp -
ln(0/1
IRTRODUCTION Although the electrochemical reduction of zinc has solutions, there appear been much studied in aqueous to have been no studies of the kinetics in dimethylformamide (N,N-formdimethylamide). This solvent is technologically interesting on account of its aprotic nature, high relative permittivity. low viscosity and the wide potential range available[l]. It is now well established as a mt-dium hr chemical synthesis and there is an interest in developing electroplating baths based on itt2, 31. The study described here is intended as a contribution to the understanding of metal deposition reactions in dimethylformamide. A dropping mercury electrode was sclectcd to avoid complications from surface factors and trace impurities. The kinetic parameters were evaluated from the Faradaic impedance as measured with an UC bridge. The supporting electrolyte was lithium perchlorate as there is no evidence in the literature of inner layer adsorption at the electrode or of complex formation with the zinc ion in the solution. Measure* Present address: Battellr Geneva (‘arouge, GenBve, Switzerland.
Research
Centre,
1227
[(E,,
-
E,)zF/RTj
On substitution in the standard meter, &[4], it is found that: + exp -
[(E -
= \/‘&,+/D,,,. equation
(1)
for the para-
Ei)zF/RT]j = (E -
E&czF/RT
(2)
and r can be determined from the slope of the plot of this equation. In order to obtain the true standard rate constant, k,, from the apparent constant, k,,, the Frumkin corrcction for the diffuse layer potential was applied. This potential was calculated with the Gouy-Chapman ecluation[7] and the electrode charge was evaluated by integration of the double layer capacity curve. EXPERIMENTAL
DETAILS
MUfWidS
Dimethylformamide (BDH Co.) was distilled under reduced pressure in nitrogen after drying over molecular sieve, grade SA. The conductivity of the distillate, measured in an “in-line” cell was 3 x lo-” W ’cm- I. Lithium perchlorate was twice recrystallised from water; during the first rccrystallisation, the hot solution was treated with carbon. The crystals of trihydrate were decomposed to the monohydrate under vacuum at 85°C. The monohydrate was then decomposed at 135°C and the last traces of water were driven off at ?lU”C, leaving a fine white crystalline powder of the 907
90X
J. S. UCNNET
anhydrous salt in which chloride ion was less than 0+)5’>0 (siiver nitrate test[9]). Zinc perchlorate. prepared by mixing equivalent quantities of zinc oxide (A.R.) and perchloric acid (A.R.). was recrystallised from water and dried in a vacuum desiccator over phosphorus pentoxide. The solid was then dissolved in dimethylformamide. the solution was dried with molecular sieve SA and evaporated under vacuum until crystals formed. After filtering and further drying under vacuum, analysis of the colourless, deliquescent crystals with X-hydroxyqumoline showed Zn = 9.2”,, [cf Zn = 9.30 per cent forZn(ClO,), .6(CH,),NCHO]. Lithium chloride was recrystallised from water as the monohydrate. The bulk of the water was driven off at 80 C in a dry N2-HCl atmosphere. The last traces of water were then iemoved at 1ZO-C. Thallium chloride (BDH Co. 99 Der cent) was dried under vacuum at 15O’C. 1 ,Ol;,,, Thailium amalgam was prepared from thallium (BDH Co. 99.999 per cent) and triply distilled mercury. All sensitive materials were manipulated in a glove box purged with nitrogen and transfers to the electrochemical cell were also carried out under a blanket of nitrogen.
Impedance measurements were made with a Wayne-Kerr B221 mark III transformer arm bridge. The UC signal to the bridge came from a Wayne--Kerr SI 21 oscillator and was adjusted so that the rn1.s voltage across the cell was 5 mV. The frequency was monitored with an Advance TC6 timer counter and the offbalance from the bridge was detected with a General Radio 1434 tuned detector. Lead impedances were measured, by the method recommended by the bridge manufacturer, and corrections were applied. The direct voltage bias was applied from a ten turn linear potentiometer connected in the neutral arm of the bridge and shunted by a 25 mF condenser to provide a negligible (IL’impedance. The direct voftage was measured with a “Vibret” pH meter. Tests showed that. in the range of impedances encountered in the present work, the errors in the minor component were generally less than 1 per cent. Direct current polarograms were recorded with a Cambridge X2P analyser. The three electrode electrochemical cell was mounted in an air thermostat at 25°C. In order to reduce frequency dispersion of the impedance of the mercury electrode, fine tipped, tapering capillaries were used[lO, 1 I]. The capillaries had outside diameters of about 0.2 mm at the orifice and diverged at I(tZO for 5 mm above It. A constriction further up the tube controlled the flow rate so that the natural period of the drops was about 10 sec. During measurements, the drop was dislodged before this period had elapsed with a magnetic hammer and the bridge was balanced shortly before dislodgement in order to avoid the efiects of the disturbance at this instant. A bistable
AND
D. GEAREY
timing circuit maintained balance times constant to within 0.1 per cent. Electrode areas were estimated from the weight of the drops. interpolated at the instant of balance and assuming that they were spherical. The counter electrode was a platinum gauze cylinder, diameter 20 mm, height 40 mm. The reference clectrode[l2] was Tl(Hg)l 01” QTlCl (solid)/LiCl (lO_’ mol I.- I) in lithium perchloratedimethylformaas in the main mide solution at the same concentration compartment of the cell to which it was connected through a bridge and fine porous frit. Such rererence electrodes proved sufficiently stable within the time scale of the experiments (up to 24 hr). but drifted over longer periods. In addition, there were significant differences between individual reference electrodes. RESLII.TS
Measurements were first made of the impedance of a 0.30mol l.- ’ solution of lithium perchlorate without electroactivc ion, to confirm that there was no disperand to check that sion of the capacity with frequency the effect of electrode imperfections was negligible. The capacity (Fig. 1) was the same at 636.6, 3183 and 12.370 Hz and the form of the curve is very similar to curves for sodium perchlorate and potassium hcxalluorophosphate in the same solvent[l3,14]. There was an anomalous increase in the solution resistance at the lowest frequency, equivalent to a conductance of 1,4fl-1 cm-’ shunting the double layer. Provided that the Faradaic admittance is 100 times this shunt, its effect can be neglected. Measurements were then made on a solution containing 0.45 mmol I.-’ zinc perchlorate in 0.21 mol l.- ’ lithium perchlorate dimethylformamide supporting showed that electrolyte. Direct current polarography the reduction of the zinc was “polarographically reversible”, ie, the slope of the E US log(& - i) plot was O-0287, close to the theoretical (0.0295) for a two elcctron transfer[8]. The diffusion coefficient of the 7inc
Fig. I. Double layer capacity of 0.30 mol l.- ’ lithium prrchlorate in dimethylformamide at 3183 Hz.
Kinetics
of the zinc ion
V
Fig. 2 Real component of the electrode admittance at 6366 (A). 3183 (B). 1592 (C), 6366 (D) and 318.3 Hz (E); W45 mmol I.- ’Zn’ + in LiCIO,-dtmethylformamide.
Fig. 3. lmagmary component of the electrode admittance at 6366 (A), 3183 (B), 1592 (C), 636,6 (D) and 318.3 Hz (E); 0.45 mmol I.- ’Zn’+ in LiClO,-dimethylformamide.
ion. calculated from the mean limiting current, was 3-5 x lO-‘cm’ set-‘. The ac impedance was measured over a range of potentials al five frequencies. The peaks in the impedance plane were close to a semicircle with centre on the real axis. showing that the charge transfer component of the Faradaic impedance is much greater than the diflilsional component. Figures 2 and 3 show the real and imaginary components of the electrode admittance. The shapes of all the real component curvcb are similar and the peak increases with frequency as the diffusion component lessens. At low frequencies. the spurious solution resistance increase, noted above. has a very small effect. In the imaginary component curves, peaks only occur at the lower frequencies; at high frequencies the curves are closely similar to the double layer capacity curve of the supporting electrolyte and it is concluded that there is no coupling between the double layer charging and the electrode reaction. The presence of the zinc ion does not alter the double layer and the treatments that take account of such interaction are not required[15]. 0 And (5 were calculated by successive approximations between all possible frequency pairs, using the Manchester University Atlas computer. The resulting values were plotted and the minimums were seen to be 23 R cm2 for t) at E = - I8 1 mV US the reference electrode and 100 R cm* set- f for 4. The large uncertainty 1n.a made It impossible to estimate an accurate value for the diffusion coefficient and instead that from the do. polarogram was used. On the other hand the preci-
sion in fI is suFTIcient for the calculation meters. CALCULATION
The tran&er cot$icient,
OF
KINETIC
of kinetic
para-
PARAMETERS
x
The half wave potential can be obtained neither from the (J --E plot because of the large errors nor from the dc polarogram on account of reference electrode variations. Instead, plots of equation (2) were drawn for a range of possible Et’s, Only when the correct E: was chosen were the anodic and cathodic parts coherent (qu Fig. 4). This occurred with E, = - 171 mV. Although the discontihuity is detectable with an error of only 1 mV, the slope is less sensitive so that the effect on r of an incorrect E+ is small. Hence r = 0.66.
The standard rate constant The apparent rate constant was calculated using Stromberg’s[16] value for the diffusion coefficient of zinc in mercu.ry (1.57 x lo-’ cm2 set- ‘). The values found at E. and at the potential where 0 is minimum were the same, 2.0 x IO-’ cm set- ‘. To apply the double layer correction, the position of E, on the rational potential scale must be established. Correlations between previous potidrographic[ l] and double layer studies[17] show that E+.for 7inc is at a rational potential of - 725 mV and It 10110~s that the rational potential of E,, is -734 mV. However, because of the reference electrode variations in the
J. S. DUNNETT AND D. GEARED
910
-ve-
E-EC,*_tve
Fig. 4. Plotsoflog :0/l + against E - E,. (equatlon - 171 (C). - I72 (D) and 011 each line mark
exp - [(zF/RT)(E - E;)]: (=y) 2) with E, = ~ 165 (A), - 170 (B), - 173 mV (E). The vertical arrows the point where E = E,.
present work, the potential scales for the double layer measurements for the supporting electrolyte and in the Lint containing solution do nut coincide. It is rrported that the double layer capacity is independent of concentration for sodium perchlorate in dimethylformamjde[ 161 and, if one assumes that the same is true for lithium perchlorate, points of reference can be estabIished where the capacities are the same in the solutions studied in the present work. Thus, in the zinc containing solution, the capacity at the zinc standard electrode potential is 7.4,pF crnm2 at 12 370 Hz; this capacity occurs at - 245 mV vs reference electrode in the pure lithium perchlorate solution and the charge on the electrode, determined by graphical integration of the capacity in Fig. 1, is 8.3 LLC cm-‘. Hence, taking the relative permittivity as 37.2[18], the diffuse layer potential is - 79 mV and the true standard rate constant is 2.5 x iOm3 cm set- ‘.
DlSCUSSlON
With results at five frequencies, it is possible to make an approximate statistical analysis of the precision. Standard deviations of the minimums of 0 and d were calculated to bc 1R cm* (k 1 per cent) and lOOR cm’ set- * (+ 100 per cent), respectively. Both deviations increase on either side of the minimums. It is clear that little useful information can be obtained from G. On the other hand. the deviation in B only caused an uncertainty of 5% in the rate constant. To this must be added the errors in the diffusion coeflicients, estimated to be about S”/, in each (amalgam and solution). Their combined effect on the rate constant is to cause an error of 5 per cent so that the overall error limit for the rate constant is + 10 per cent.
The only solvent in which the zinc reduction has been extensively studied is water. The rate constaut in lithium perchlorate zupporting electrolyte does not appear to have been measured but there are measurements in aqueous sodium perchlorate which show, nevertheless, considerable scatter[ 19, 201. A representative value[19] for the true standard rate constant is 2.2 X lo-” cm XX- 1, not greatly different from the constant in dimethylformamide. The agreement is probably fortuitous as the transfer coefficient is different and varies with the ionic strength and overpotential in aqueous solution. In comparing the two solvents, the rates of solvent exchange of dissolved ions, as measured by NMR, are interesting. Although these rates arc similar for scvcral ions[21], the activation energies and entropies are different. Similarly, if the solvation properties of an ion influence its electrode reaction, a direct comparison of rate constants is of little meaning. The results presented in this paper provide an insufficient base on which to speculate on the mechanism of the reduction in dimethylformamide. However, it can be concluded that the zinc reduction is a single step. two electron process with the following parameters: 2.5 + standard rate constant: (I) True _ 0.3 x 10~3cmsec~‘. (2) Cathodic charge transfer coefficient: 0.66. (3) Diffusion coefficient of the Zn’ ’ ion: 3.5 x IO-” cm2 set-I. Of these quantities only the diffusion coefficient has The value found. 3.4 x. previously been measured[22]. 10. (r cm’ set- *, is in good agreement with that reported here. Acltnowledgr/,?~,lt~We would Menzies, now at Loughborough advice.
like to thank Prolcssor I. A. University, for his help and
REFERENCES
I. M. Breant and G. Demange-GuPrin. Bull. Sot, Chi!?~. Fr. 2935 (I 969). 2. I. A. Menzies and B. S. White. Traris. 1~s~. Met. Fin. 45,
ISI (1967). 3 N. R Rharucha and J J Ward, Prnd. Firtishi,~/ (Tinrirv nati) 33, 64 ( 1969). and J. H. Sluyters, KM. Trau. 4. M. Sluyters-Rehbach Chim. 82, 535 (1963). 5. B. Timmer, M. Sluyters-Rehbach and J. H. Sluyters, J. elrcfroana/. Chrm. 14, 169 (1967). and J. H. Sluyters. Ekctromalyt. 6. M. Sluyters-Rehbach Chrm 4, I (1970) Dauhlr Lrryrr and Electl-adr Kii~ti~~. Inter7. P. D&hay, science, New York ( 1965). Polnrogrophy. Vol. I. 8. I. M. Kolthoff and J. J. Lingane, Tnterscience, New York (1952). Am~lWs, 5th edn. blse9. F. Fe&, Spa/ Tests in lnoryanrc vier, Amsterdam (1958). I 0. R. de Levie, J. rlecrrorrnof. Chem. 9, I I7 (1965). 11. G. C. Barker. Anal_vt. Chm. Acta IS. 1 I8 (1958). 12. J. N. Butler, .4du. Elccrroche,,1. clc~ctvn~~lwr??. EII~I~ 7, 77 (19701
Kinetics 13. Y. Doilido, R. V. lvanova and B. B. Damaskin. Elocrrokhiwiya 6, 3 (I 970). 14. R. Payne. J. phps. Chew. 71, 1548 (1967). 15. R. Parsons. Adl,. Elrcwochrm. rlrcr~~chrm. Er~gn~g7, 177 ( 1970). 16. A. H. Stromberg, Dokl. Acad. Nauk 85,-U I (1952). 17. V. D. Bezugli and L. A. Korshikov. Elrctrokhuni~u 1. 1472 (I 965); 3. 390 (1967). t8. D. S. Reid and C. A. Vincent. J. efr~ct~oortul. C/WNI. 18, 427 (1968).
of the zinc ion
911
19. N. S. Hush and J. Blackledge, J. riectrour~ul. Chou. 5, 420 ( I963 )_ 20. M. Siuyters-Rehbach, J. S. M. C. Breukel and J. H. Sluylcr\. J. rlr~~trorrrzul. Clwrn. 19, x5 (1968). 2I. T R. Stengle and C. H Langford. Coor.d. C’he171. Ru 2, 349 ( 1967). 22. G. H. Brown and R. Al Urfali. J. Am them. SOL. 80, 2 I I3
(195X).
KINETICS OF THE ZINC ION REDUCTION THE DROPPING MERCURY ELECTRODE IN DIMETHYLFORMAMIDE J. S.
Department
of C‘hemical
DUNNETT*
and
D.
AT
GEAREY
tngineermg. University ol Manchester Institute PO Box 88, Manchester M60 1QD. England
of Science
and Technology,
electrochemical reduction of the 7inc ion to the amalgam has been studied in lithium perchlorate-dimcthylformamide solution. The true standard rate constant is 2.5 x 10d3 cm set-’ and the cathodic charge transfer coefficient is 066. Abstract--The
NOMENCLATURE
n,,,= diffusion n
,,I
/
=
E = E,, = I?., = p= ;=
id = R=
T=
: =
r(=
0 = li=
coefficient
of
electroactive
ion
in
the
electrode diffusion coeflicient of electroactivc ion in the: solution rlectrode potential standard electrode potential polarographic halfwavt: potential Faraday’s constant polarographic (I( mean diffusion limited current (Ilkovic equation) universal gas constant absolute temperature charge on rlectrnactive inn in solution cathodic transfer coefficient activation parameter in Faradaic impedance: diffusion parameter in Faradaic impedance.
ments were also made of the double layer capacity of the supporting electrolyte so that appropriate corrections could be applied to the measured rate constant. THEORY The results were interpreted by the impedance plane method of Sluyters-Rehbach and Sluyters[&61. However, in the present paper, the cathodic charge transfer coefficient, 2, corresponds to b in Ref. [S] and the cathodic current is taken to be positive, following Delahay[7]. Also r was dcrivcd by a modified procedure, as follows. A standard equation of polarography is[R]: exp -
ln(0/1
IRTRODUCTION Although the electrochemical reduction of zinc has solutions, there appear been much studied in aqueous to have been no studies of the kinetics in dimethylformamide (N,N-formdimethylamide). This solvent is technologically interesting on account of its aprotic nature, high relative permittivity. low viscosity and the wide potential range available[l]. It is now well established as a mt-dium hr chemical synthesis and there is an interest in developing electroplating baths based on itt2, 31. The study described here is intended as a contribution to the understanding of metal deposition reactions in dimethylformamide. A dropping mercury electrode was sclectcd to avoid complications from surface factors and trace impurities. The kinetic parameters were evaluated from the Faradaic impedance as measured with an UC bridge. The supporting electrolyte was lithium perchlorate as there is no evidence in the literature of inner layer adsorption at the electrode or of complex formation with the zinc ion in the solution. Measure* Present address: Battellr Geneva (‘arouge, GenBve, Switzerland.
Research
Centre,
1227
[(E,,
-
E,)zF/RTj
On substitution in the standard meter, &[4], it is found that: + exp -
[(E -
= \/‘&,+/D,,,. equation
(1)
for the para-
Ei)zF/RT]j = (E -
E&czF/RT
(2)
and r can be determined from the slope of the plot of this equation. In order to obtain the true standard rate constant, k,, from the apparent constant, k,,, the Frumkin corrcction for the diffuse layer potential was applied. This potential was calculated with the Gouy-Chapman ecluation[7] and the electrode charge was evaluated by integration of the double layer capacity curve. EXPERIMENTAL
DETAILS
MUfWidS
Dimethylformamide (BDH Co.) was distilled under reduced pressure in nitrogen after drying over molecular sieve, grade SA. The conductivity of the distillate, measured in an “in-line” cell was 3 x lo-” W ’cm- I. Lithium perchlorate was twice recrystallised from water; during the first rccrystallisation, the hot solution was treated with carbon. The crystals of trihydrate were decomposed to the monohydrate under vacuum at 85°C. The monohydrate was then decomposed at 135°C and the last traces of water were driven off at ?lU”C, leaving a fine white crystalline powder of the 907
90X
J. S. UCNNET
anhydrous salt in which chloride ion was less than 0+)5’>0 (siiver nitrate test[9]). Zinc perchlorate. prepared by mixing equivalent quantities of zinc oxide (A.R.) and perchloric acid (A.R.). was recrystallised from water and dried in a vacuum desiccator over phosphorus pentoxide. The solid was then dissolved in dimethylformamide. the solution was dried with molecular sieve SA and evaporated under vacuum until crystals formed. After filtering and further drying under vacuum, analysis of the colourless, deliquescent crystals with X-hydroxyqumoline showed Zn = 9.2”,, [cf Zn = 9.30 per cent forZn(ClO,), .6(CH,),NCHO]. Lithium chloride was recrystallised from water as the monohydrate. The bulk of the water was driven off at 80 C in a dry N2-HCl atmosphere. The last traces of water were then iemoved at 1ZO-C. Thallium chloride (BDH Co. 99 Der cent) was dried under vacuum at 15O’C. 1 ,Ol;,,, Thailium amalgam was prepared from thallium (BDH Co. 99.999 per cent) and triply distilled mercury. All sensitive materials were manipulated in a glove box purged with nitrogen and transfers to the electrochemical cell were also carried out under a blanket of nitrogen.
Impedance measurements were made with a Wayne-Kerr B221 mark III transformer arm bridge. The UC signal to the bridge came from a Wayne--Kerr SI 21 oscillator and was adjusted so that the rn1.s voltage across the cell was 5 mV. The frequency was monitored with an Advance TC6 timer counter and the offbalance from the bridge was detected with a General Radio 1434 tuned detector. Lead impedances were measured, by the method recommended by the bridge manufacturer, and corrections were applied. The direct voltage bias was applied from a ten turn linear potentiometer connected in the neutral arm of the bridge and shunted by a 25 mF condenser to provide a negligible (IL’impedance. The direct voftage was measured with a “Vibret” pH meter. Tests showed that. in the range of impedances encountered in the present work, the errors in the minor component were generally less than 1 per cent. Direct current polarograms were recorded with a Cambridge X2P analyser. The three electrode electrochemical cell was mounted in an air thermostat at 25°C. In order to reduce frequency dispersion of the impedance of the mercury electrode, fine tipped, tapering capillaries were used[lO, 1 I]. The capillaries had outside diameters of about 0.2 mm at the orifice and diverged at I(tZO for 5 mm above It. A constriction further up the tube controlled the flow rate so that the natural period of the drops was about 10 sec. During measurements, the drop was dislodged before this period had elapsed with a magnetic hammer and the bridge was balanced shortly before dislodgement in order to avoid the efiects of the disturbance at this instant. A bistable
AND
D. GEAREY
timing circuit maintained balance times constant to within 0.1 per cent. Electrode areas were estimated from the weight of the drops. interpolated at the instant of balance and assuming that they were spherical. The counter electrode was a platinum gauze cylinder, diameter 20 mm, height 40 mm. The reference clectrode[l2] was Tl(Hg)l 01” QTlCl (solid)/LiCl (lO_’ mol I.- I) in lithium perchloratedimethylformaas in the main mide solution at the same concentration compartment of the cell to which it was connected through a bridge and fine porous frit. Such rererence electrodes proved sufficiently stable within the time scale of the experiments (up to 24 hr). but drifted over longer periods. In addition, there were significant differences between individual reference electrodes. RESLII.TS
Measurements were first made of the impedance of a 0.30mol l.- ’ solution of lithium perchlorate without electroactivc ion, to confirm that there was no disperand to check that sion of the capacity with frequency the effect of electrode imperfections was negligible. The capacity (Fig. 1) was the same at 636.6, 3183 and 12.370 Hz and the form of the curve is very similar to curves for sodium perchlorate and potassium hcxalluorophosphate in the same solvent[l3,14]. There was an anomalous increase in the solution resistance at the lowest frequency, equivalent to a conductance of 1,4fl-1 cm-’ shunting the double layer. Provided that the Faradaic admittance is 100 times this shunt, its effect can be neglected. Measurements were then made on a solution containing 0.45 mmol I.-’ zinc perchlorate in 0.21 mol l.- ’ lithium perchlorate dimethylformamide supporting showed that electrolyte. Direct current polarography the reduction of the zinc was “polarographically reversible”, ie, the slope of the E US log(& - i) plot was O-0287, close to the theoretical (0.0295) for a two elcctron transfer[8]. The diffusion coefficient of the 7inc
Fig. I. Double layer capacity of 0.30 mol l.- ’ lithium prrchlorate in dimethylformamide at 3183 Hz.
Kinetics
of the zinc ion
V
Fig. 2 Real component of the electrode admittance at 6366 (A). 3183 (B). 1592 (C), 6366 (D) and 318.3 Hz (E); W45 mmol I.- ’Zn’ + in LiCIO,-dtmethylformamide.
Fig. 3. lmagmary component of the electrode admittance at 6366 (A), 3183 (B), 1592 (C), 636,6 (D) and 318.3 Hz (E); 0.45 mmol I.- ’Zn’+ in LiClO,-dimethylformamide.
ion. calculated from the mean limiting current, was 3-5 x lO-‘cm’ set-‘. The ac impedance was measured over a range of potentials al five frequencies. The peaks in the impedance plane were close to a semicircle with centre on the real axis. showing that the charge transfer component of the Faradaic impedance is much greater than the diflilsional component. Figures 2 and 3 show the real and imaginary components of the electrode admittance. The shapes of all the real component curvcb are similar and the peak increases with frequency as the diffusion component lessens. At low frequencies. the spurious solution resistance increase, noted above. has a very small effect. In the imaginary component curves, peaks only occur at the lower frequencies; at high frequencies the curves are closely similar to the double layer capacity curve of the supporting electrolyte and it is concluded that there is no coupling between the double layer charging and the electrode reaction. The presence of the zinc ion does not alter the double layer and the treatments that take account of such interaction are not required[15]. 0 And (5 were calculated by successive approximations between all possible frequency pairs, using the Manchester University Atlas computer. The resulting values were plotted and the minimums were seen to be 23 R cm2 for t) at E = - I8 1 mV US the reference electrode and 100 R cm* set- f for 4. The large uncertainty 1n.a made It impossible to estimate an accurate value for the diffusion coefficient and instead that from the do. polarogram was used. On the other hand the preci-
sion in fI is suFTIcient for the calculation meters. CALCULATION
The tran&er cot$icient,
OF
KINETIC
of kinetic
para-
PARAMETERS
x
The half wave potential can be obtained neither from the (J --E plot because of the large errors nor from the dc polarogram on account of reference electrode variations. Instead, plots of equation (2) were drawn for a range of possible Et’s, Only when the correct E: was chosen were the anodic and cathodic parts coherent (qu Fig. 4). This occurred with E, = - 171 mV. Although the discontihuity is detectable with an error of only 1 mV, the slope is less sensitive so that the effect on r of an incorrect E+ is small. Hence r = 0.66.
The standard rate constant The apparent rate constant was calculated using Stromberg’s[16] value for the diffusion coefficient of zinc in mercu.ry (1.57 x lo-’ cm2 set- ‘). The values found at E. and at the potential where 0 is minimum were the same, 2.0 x IO-’ cm set- ‘. To apply the double layer correction, the position of E, on the rational potential scale must be established. Correlations between previous potidrographic[ l] and double layer studies[17] show that E+.for 7inc is at a rational potential of - 725 mV and It 10110~s that the rational potential of E,, is -734 mV. However, because of the reference electrode variations in the
J. S. DUNNETT AND D. GEARED
910
-ve-
E-EC,*_tve
Fig. 4. Plotsoflog :0/l + against E - E,. (equatlon - 171 (C). - I72 (D) and 011 each line mark
exp - [(zF/RT)(E - E;)]: (=y) 2) with E, = ~ 165 (A), - 170 (B), - 173 mV (E). The vertical arrows the point where E = E,.
present work, the potential scales for the double layer measurements for the supporting electrolyte and in the Lint containing solution do nut coincide. It is rrported that the double layer capacity is independent of concentration for sodium perchlorate in dimethylformamjde[ 161 and, if one assumes that the same is true for lithium perchlorate, points of reference can be estabIished where the capacities are the same in the solutions studied in the present work. Thus, in the zinc containing solution, the capacity at the zinc standard electrode potential is 7.4,pF crnm2 at 12 370 Hz; this capacity occurs at - 245 mV vs reference electrode in the pure lithium perchlorate solution and the charge on the electrode, determined by graphical integration of the capacity in Fig. 1, is 8.3 LLC cm-‘. Hence, taking the relative permittivity as 37.2[18], the diffuse layer potential is - 79 mV and the true standard rate constant is 2.5 x iOm3 cm set- ‘.
DlSCUSSlON
With results at five frequencies, it is possible to make an approximate statistical analysis of the precision. Standard deviations of the minimums of 0 and d were calculated to bc 1R cm* (k 1 per cent) and lOOR cm’ set- * (+ 100 per cent), respectively. Both deviations increase on either side of the minimums. It is clear that little useful information can be obtained from G. On the other hand. the deviation in B only caused an uncertainty of 5% in the rate constant. To this must be added the errors in the diffusion coeflicients, estimated to be about S”/, in each (amalgam and solution). Their combined effect on the rate constant is to cause an error of 5 per cent so that the overall error limit for the rate constant is + 10 per cent.
The only solvent in which the zinc reduction has been extensively studied is water. The rate constaut in lithium perchlorate zupporting electrolyte does not appear to have been measured but there are measurements in aqueous sodium perchlorate which show, nevertheless, considerable scatter[ 19, 201. A representative value[19] for the true standard rate constant is 2.2 X lo-” cm XX- 1, not greatly different from the constant in dimethylformamide. The agreement is probably fortuitous as the transfer coefficient is different and varies with the ionic strength and overpotential in aqueous solution. In comparing the two solvents, the rates of solvent exchange of dissolved ions, as measured by NMR, are interesting. Although these rates arc similar for scvcral ions[21], the activation energies and entropies are different. Similarly, if the solvation properties of an ion influence its electrode reaction, a direct comparison of rate constants is of little meaning. The results presented in this paper provide an insufficient base on which to speculate on the mechanism of the reduction in dimethylformamide. However, it can be concluded that the zinc reduction is a single step. two electron process with the following parameters: 2.5 + standard rate constant: (I) True _ 0.3 x 10~3cmsec~‘. (2) Cathodic charge transfer coefficient: 0.66. (3) Diffusion coefficient of the Zn’ ’ ion: 3.5 x IO-” cm2 set-I. Of these quantities only the diffusion coefficient has The value found. 3.4 x. previously been measured[22]. 10. (r cm’ set- *, is in good agreement with that reported here. Acltnowledgr/,?~,lt~We would Menzies, now at Loughborough advice.
like to thank Prolcssor I. A. University, for his help and
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