Analyst, September, 1973, Vol. 98, Pp. 635-646 635 Mass and Charge Transfer Kinetics and Coulometric Current Efficiencies Part X.* An Examination of the Tin(1V) - Tin(I1) - Tin(0) Systems at Platinum and Gold Electrodes? BY E. BISHOP AND P. H. HITCHCOCK: (Chemistry Department, University of Exeter, Stocker Road, Excter, EX4 4QD) Tin(I1) is more readily handled coulometrically than volumetrically, and the electrode processes are critically evaluated. Zero-current tin(1V) - tin(I1) potentials cannot be measured or derived from Lewartowicz plots, and charge- transfer kinetic parameters must therefore be referred to 0 V. Gold cathodes are deactivated towards reduction of hydrogen ion by specific adsorption of bromide ion, and give well separated waves for the reduction of tin(1V) to tin(I1) and to tin metal, with limiting currents proportional to the tin(1V) concentration in 3.0 M bromide @us 0.4 M perchloric or hydrobromic acid medium.Mass and charge transfer kinetic parameters are derived from the voltammograms. Platinum cathodes become filmed and theories of the nature of the film are reviewed in the light of new work, which shows that the film is difficult to remove and was not completely removed in earlier work. The generation of tin(I1) in bromide medium is superimposed on the film- suppressed hydrogen-ion wave. Chloride media are unsuitable. Kinetic parameters must be derived from anodic voltammograms of tin(II), which are uncomplicated in the bromide medium. At low bromide concentrations, the platinum anode is filmed with a species such as [SnBr,OHI2-, which blocks the reaction.The electrode mechanism is discussed. Charge-transfer para- meters vary with potential or current, but synthesised computer-plotted voltammograms give a good fit with experimental curves. From the kinetic parameters the current efficiency for tin(I1) generation is computed, and for 0-2 M tin(1V) the efficiency is better than 99.98 per cent. over the current density range 100 to 300 mA cm-2 but decreases rapidly outside this range. Sample concentrations must be chosen so as to maintain the intermediate current within range throughout the determination, and platinum cathodes must be filmed quickly, but not aged for too long. TIN(II) is a well known volumetric reductant, but is infrequently used because it reacts with atmospheric oxygen, is prone to hydrolysis and its reaction kinetics lead to induced reactions.These objections do not arise if the tin(I1) is electrogenerated in an oxygen-free medium. Although it is the third most popular reductant intermediate, the electrode processes are not straightforward and the applications are not numerous. After its first introduction by Bard and Lingane,l generation of tin(I1) has been used in determinations of platinum(1V) ,2 g ~ l d ( I I f ) , ~ copper(II),4 iodine,5-7 br0mine,~7' ceri~m(IV),~,~ vanadi~rn(V),~ selenium(IV)8-10 and tel- lurium(IV).lO Little is known of the kinetics and mechanism of the reaction at solid electrodes. An empirical investigation of the current efficiency in bromide medial showed a current efficiency loss of 0.3 per cent., and in chloride media7 of 7 per cent.Early work2-4 indicated that platinum or gold electrodes in acidic halide media were most suitable. Platinum cathodes became filmed,l,ll whereby hydrogen-ion reduction is suppressed, but other reductions, e.g., of tin(1V) and antimony(III), continue with little change. No such film has been reported for gold electrodes. The current efficiency for the generation of tin(I1) appears to be better in bromide than in chloride media. The contention that this effect occurs because bromide complexes tin(1V) more strongly than chloride and thus makes the reduction potential more positive is neither logical nor supported by the extremely meagre data.12 Chloride-free media * For Part IX of this series, see p.625. t Presented a t the International Symposium on Analytical Chemistry, Birmingham, 1969. Present address: Ever Ready Co. (G.B.) Ltd., Central Research Laboratories, St. Ann's Road, London, N15 3TJ. @ SAC and the authors.636 BISHOP AND HITCHCOCK: MASS AND CHARGE TRANSFER [Analyst, Vol. 98 have not been investigated, and specific adsorption of bromide ion is probably the relevant factor. Finally, it can be demonstrated from his own resultsll that Bard did not always succeed in removing the film from his electrodes in experiments claimed to have been made with “clean electrodes.” More and better quantitative information on the fundamentals of the reaction is needed before it can be regarded as viable and useful. EXPERIMENTAL General apparatus, reagents and procedures have been described and water has been defined earlier.13 All potentials are quoted versus the standard hydrogen electrode (S.H.E.) unless otherwise specified.REAGENTS- Tin(l1) chloride, 0-05 M solution in 2.0 M hydrochloric acid-A sample of granulated tin was dissolved in hydrochloric acid, and the solution was diluted as required with de-oxy- genated water and hydrochloric acid. The solution was stored under scrubbed nitrogen in the reservoir bottle of an automatic zero burette (Baird and Tatlock Ltd., B 41/0500), modified so as to exclude air from the system. The tin(I1) content was determined by iodate titration in the presence of excess of iodide with the aid of fresh starch solution as indicator. The titration was performed under nitrogen in a beaker fitted with a machined Perspex cover. The approximate acid concentration was determined by titration with standard sodium carbonate solution, with the aid of screened methyl orange as indicator. Tin(11) bromide, 0-05 M solution in 2.0 M hydrobromic acid-With the substitution of hydrobromic for hydrochloric acid, preparation, storage and standardisation were the same as for the previous solution.Tin(1V) chloride, 0.05 M solution in 2.0 M hydrochloric acid-Tin(1V) chloride was prepared by the action of cylinder chlorine on heated tin, and the product was re-distilled and dissolved in 2.0 M hydrochloric acid so as to give the required solution. The tin(1V) content was determined by reduction to tin(I1) with zinc amalgam, and the tin(I1) titrated under nitrogen with standardised potassium permanganate solution. Tin(1V) byomide, 0.05 M solation in 2.0 M hydrobromic acid-A sample of granulated tin was refluxed with hydrobromic acid until the reaction ceased.A slight excess of bromine was added, and the excess removed by prolonged boiling. The solution was then diluted so as to give the required composition and standardised in the same way as the tin(1V) chloride solution. ELECTRODE ACTIVATION- Gold-wire electrodes-These electrodes were activated by two methods : (a) the electrode was etched in fresh aqua regia at 60 “C for 15 s and thoroughly washed; (b) the electrode was etched as in method (a), then anodised in 0.1 M sulphuric acid at 100 mA cm-2 for 5 s so as to produce a red oxide film on the electrode, which was then reduced to gold black by cathodisation for 10 s at 100mAcm-2 in the same medium.The two treatments gave essentially the same results. Platinum electrodes-These electrodes were activated by either method 1 or method 2, described below, or by method 1 followed by method 2. The latter treatment involving both methods was found to be essential for filmed electrodes. (1) The electrode was immersed in fresh aqua regia at 60 “C for 2 minutes, washed, anodised in concentrated hydrochloric acid for 30 s at 100 mA cm-2, washed, cathodised in 0-1 M sulphuric acid at 100 mA cm-2 for 10 minutes, and finally washed. (2) Alternate anodisation and cathodisation at 100 to 300 mA cm-2 was carried out in %OM sulphuric acid for 2 to 5 minutes each. The cycle was repeated at least once more and the electrode washed.In all instances the electrode was held potentiostatically at 0.4 V for 5 minutes in the supporting electrolyte so as to remove adsorbed hydrogen. RESULTS AND DISCUSSION ZERO-CURRENT AND CONDITIONAL POTENTIALS I N BROMIDE MEDIA- It proved impossible to measure the zero-current potential of either a gold or a platinum electrode treated by any of the activation processes in a mixture of tin(1V) and tin(I1) inSeptember, 19731 KINETICS AND COULOMETRIC CURRENT EFFICIENCIES. PART x 637 any medium. Potentials drifted randomly at 3 mV min-l or above, and no two solutions or two electrodes gave potentials with satisfactory agreement. Evidently, the exchange current of the system is very low and it is possible that the electrodes become deactivated.This deactivation is not unexpected in view of similar findings in chloride media.l4,l5 Tafel and Lewartowicz plots are not helpful, which means that neither Ei nor E,, can be used as the reference potential in the derivation of charge-transfer parameters, and the conditional over-all rate constant, k , must therefore be referred to the zero point of the potential scale, that of the S.H.E., and will be annotated as kg (cathodic) and kz (anodic) in order to emphasise the distinction. Electrode potential versus S.H.E./V Fig. 1. Reduction of the supporting electrolyte a t a gold cathode: 1, 3.0 M sodium bromide, 0.38 M perchloric acid, fresh electrode, ramp speed -885 mV min-l; 2, same electrolyte, aged electrode, ramp speed -885 mV min-1; 3, same electrolyte, initially fresh electrode, manual plotting, duration 3.5 hours ; and 4, 0-38 M perchloric acid alone, fresh electrode, ramp speed -85 mV rnin-' CATHODIC VOLTAMMETRY AT GOLD ELECTRODES- It should be emphasised that earlier work was not carried out in entirely chloride-free media; solutions of tin chloride in bromide media were used.Media of 3 . 0 ~ bromide in 0.4 M hydrobromic acid or 0.4 M perchloric acid were used in this work and both media gave identical results. These supporting electrolytes gave the cathodic curves shown in Fig. 1. Curve 1 was obtained with a freshly activated electrode. After recording the curve, the electrode was returned to its starting potential and the scan repeated without intervening reactivation. Repetition of this process caused the scan to more to move negative potentials.If the electrode was then left on opencircuit in the solution, it recovered some of its activity and gave a scan at less negative potentials than the previous scan. The degree of recovery depended on the rest period, but the initial activity as in curve 1 was restored only on reactivation by method (a). Curve 2 in Fig. 1 was obtained with an electrode that had been activated, used to record five consecutive scans and left on open circuit for 2 hours. Curve 3 represents essentially the quasi-equilibrium situation : each point was obtained by maintaining a constant current until the potential drift decreased to below 1 mV in 5 minutes. This curve took 3.5 hours to produce, whereas the automatic scans required 8 minutes at a ramp speed of 85 mV min-I.Redzcction of tin(W)-A portion of the solution of tin(1V) bromide in hydrobromic acid was added to the supporting electrolyte and the acidity of the solution brought back to its original value by the addition of sodium hydroxide solution. The curve in Fig. 2 was recorded and shows the reduction waves of tin(1V) to tin(II), of tin(I1) to tin metal and the beginning638 BISHOP AND HITCHCOCK: MASS AND CHARGE TRANSFER [Analyst, Vol. 98 of the hydrogen wave. The electrode cannot be regarded as being gold over the whole potential range scanned, because after the second wave it would be a tin electrode, and the hydrogen-ion wave would be correspondingly moved to a more negative potential. Curves 3 and 1 in Fig. P can be regarded as the extreme limits for hydrogen evolution at a gold electrode in this medium, and can be used to define the maximum and minimum current efficiencies for the generation of tin(I1) if hydrogen evolution is the only competitive reaction.This conclusion also assumes that the presence of tin species in the contact layer does not alter the double-layer structure sufficiently to affect hydrogen evolution, which appears to be so. Quantitative measurement of the limiting current showed it to be proportional to the tin(1V) concentration over the range lW4 to M, which would not be so if an appreciable amount of hydrogen were produced, as predicted by curve 1 in Fig. 1. The electrode is therefore deactivated towards hydrogen evolution, but the degree of deactivation is not measurable on account of the further reduction to tin metal.Hydrogen evolution in the supporting electrolyte alone is not straightforward: curve 4 in Fig. 1 shows the hydrogen wave at a fresh gold surface in 0.4 M perchloric acid in the absence of bromide, in contrast to curve 1. The difference arises from specific adsorption of bromide ion. BreiteP found that in perchloric acid, a bromide concentration of M was sufficient to give a monolayer of bromide on a platinum electrode, and this monolayer altered the shape of cyclic voltammo- grams. The change in shape of the hydrogen region became more pronounced as the bromide concentration increased. Strong adsorption of bromide ions on gold has been dem0n~trated.l~ Anodic oxidations in bromide media were not attempted with gold electrodes because of the possible complications of attack of the electrodes.I I I I I 0.0 -0.2 -0.4 -0.6 Electrode potential versus S. H. E ./V Fig. 2. Reduction of tin species in bromide media a t a gold Freshly activated electrode, 3.0 M sodium bromide + M tin(1V) bromide, ramp cathode. 0.38 M perchloric acid + 0.25 x speed -85 mV min-l Kinetic $umzrneters-The reaction is obviously slow, and the reverse reaction can be neglected. Lewartowicz plots corrected for mass transfe1-1~ are shown in Fig. 3, and the change of slope at -0.195 V suggests that a two-step mechanism obtains. As EA is not measurable, the rate constants are referred to 0 V, and the parameters are shown in Table I. Advanced pattern theory analysis is limited in accuracy only by the experimental errors at such rates,l8 and shows that both kg and cc are potential dependent.CATHODIC VOLTAMMETRY AT PLATINUM ELECTRODES- The nature of a ‘ffilmed electrode”-Bard and Linganel found that tin(I1) was generated with greater efficiency at a used electrode than at a freshly activated electrode. They found that this effect was due to an invisible film on the electrode, which inhibited the reduction of hydrogen ions. Chemical strippingll of the film and spectroscopic analysis demonstrated the presence of tin, and it was concluded that the film was a hydrated tin oxide, the oxidation state of which depended on the conditions of formation. Bardll proposed that the initial reduction of hydrogen ions at a clean platinum electrode decreased the hydrogen-ion con- centration at the electrode surface to such an extent that hydrolysis of the tin compoundsSeptember, 19731 KINETICS AND COULOMETRIC CURRENT EFFICIENCIES.PART x 639 1 I I I -0.15 - 0.20 -0.25 Electrode potential versus S.H.E./V Fig. 3. Lewartowicz plots for reduction of tin(1V) a t a gold cathode in 3.0 M sodium bromide + 0.38 M perchloric acid. Freshly activated electrode, ramp speed -855 mV min-l. [ S nII] / 1 0 -3 [SnIv] 10 --3 Curve moll-1 mol 1-1 1 0.25 0.25 2 0.25 0-50 3 0.50 0.50 4 0.50 0-75 occurred and the colloidal product stuck to the electrode. Conceivably, at the instant of starting the current, the hydrogen-ion concentration could transiently decrease to such a degree before the diffusion layer is set up by mass transport; otherwise, the current would have to be virtually the limiting current for hydrogen-ion transport, which is very high and was not approached. The tin(1V) oxide is less soluble than tin(I1) oxide, but the kinetics of hydrolysis are suchlg that tin(I1) oxide would be precipitated first, which accords with Bard’s observation that tin( 11) had a greater suppressive effect on hydrogen-ion reduction than tin(1V).However, the rate of hydrolysis hardly seems to permit the formation of oxides in the millisecond or so that is required to set up the diffusion layer for hydrogen ions, and the currents were too low to offer a sustained decrease in hydrogen-ion concentration. Some sort of film, however unlikely the conditions seem to be, is certainly formed, but it is possible that it might be, contain, or cover tin metal.Moreover, the film is very difficult to remove. Treatment by method 2 was expected to be adequate20 but was not, neither was method 1 alone, but the combination of method 1 followed by method 2 was found to be entirely reliable. Soaking in aqua regia and nitric acid was the method of pre-treating electrodes used by Bard, and does not seem to have given a reproducible surface: voltammograms for the reduction of hydrogen ion at a “clean electrode” in 3 M sodium bromide - 0.4 M perchloric acid differ in two of his diagrams that were supposedly recorded under identical conditions. In Figs. 10 and 11 of his paper,ll the foot of the hydrogen-ion wave appears at -0.1 V veysus640 BISHOP AND HITCHCOCK: MASS AND CHARGE TRANSFER [Analyst, VOl.98 S.C.E. and there is no evidence of a limiting current at the highest current density, 2 mA cm-2, reached. Yet in Fig. 2 of the same paper, the hydrogen wave starts at -0.2 V veysus S.C.E. and reaches a limiting current at 2 mA cm-2. The conditions used.should give a limiting current density of 4000 mA cm-2 at a clean platinum electrode. Repetition of Bard’s work gave agreement with his Figs. 10 and 11. Results similar to his Fig. 2 were obtained if a filmed platinum electrode was not completely cleaned before use. Bard also reported chrono- potentiometric transition times for hydrogen ion of 400 to 1200 s at a “clean” electrode, but calculated a value of 2 x 105s. Convection disturbs chronopotentiograms of such duration, but generally lengthens transition times instead of shortening them, and the short transition times again suggest inadequate cleaning.TABLE I MASS AND CHARGE TRANSFER KINETIC PARAMETERS FOR THE TIN(IV) - TIN(II) SYSTEM OVER THE CONCENTRATION RANGE 10-4 TO 3 x 10-3 M Working elec- Medium trode k;/l cm-2 s-1 k0,/1 cm-2 s-1 a ,!I kmaSs/l cm-2 s-1 3.0 M NaBr + 0.4 M HClO, 3.0 M NaBr + 0.4 M HBr 3.0 M NaBr + 0.4 M HC10, Pt (0.28 to i Au 6.0) x 3.0 M NaBr + 0-4 M HBr 1.0 M NaBr + 0.4 M HClO, 0.33 M NaBr + 0.4 M HC10, Pt 5.4 x 0.33 M NaBr + 0.4 M HClO, 3.0 M NaBr + 4.0 M HC10, Pt 8.13 x Pt Pt 1-1 x lO-g* 1.0 x 10-lo* + 2.7~NaC10, (u) (3.1 t o (b) (1.3 to (OX) 10-5 7.3) X lo-* to 0-37 - - 0.30 (red) to 0.35 5.7 x - - 0.16 1.4 x - - 0.16 1.1 x - - 0.22 2.3 x * For current densities < 0-1 mA cm-a.(a) Low current region. (b) High current region. Layers of tin are both strongly held and difficult to remove. Bowles and Cranshaw21 investigated the formation of monolayers of tin on platinum black at 0.1 V in an acidic solution of tin-119. The tin produced a “good Mossbauer spectrum” and it was concluded that the tin was plated on to the platinum surface, and not adsorbed in the electrical double layer, which would not have given a “good Mossbauer spectrum.” The Mossbauer results indicated that the tin existed as a monolayer that closely resembled tin metal, despite the use of an electrode potential that was anodic to that required for the bulk deposition of tin metal. Such adsorption for cadmium(I1) and thallium(1) on platinum has been reported by Frumkh22 He concluded that chemisorption led to the formation of a surface compound or surface alloy.Such a layer cannot be considered to be a pure metal or a true alloy, so its chemical and physical properties cannot be predicted with certainty, and it is difficult to devise unequivocal tests of the theory. It seems possible that in some instances Bard removed the hydrous tin oxide from the electrodes but a layer of tin remained that partially blocked the platinum surface for hydrogen-ion reduction. Generation of tin(I1) at platinum electrodes-Fig. 4 shows voltammograms of the sup- porting electrolyte (curve 1) and of tin(1V) in 3.0 M bromide - 0.4 M perchloric acid. Curve 2 shows the suppressed hydrogen-ion wave followed by reduction of tin(1V) to tin(I1). The transition from hydrogen-ion reduction to tin(1V) reduction is not distinct, but appears to occur at about -0-08 V; the third wave in curve 2 is not hydrogen-ion reduction, but reduction of tin(I1) and tin(1V) to tin metal.Curve 4 shows that a higher tin(1V) concentration sup- presses the hydrogen-ion wave to the extent that it cannot be detected without increasing the sensitivity of the current axis of the X - Y recorder. Curve 5 is a reverse sweep recorded immediately after curve 2 ; the maximum at -0.305 V represents the oxidation of the tin metal film. The reduction curves of tin(1V) to tin(I1) are superimposed on the suppressed hydrogen-ion reduction wave, and lack a well defined limiting current region, so that any deductions made from them can be of only a qualitative nature. The height of the tin(1V)September, 19731 KINETICS AND COULOMETRIC CURRENT EFFICIENCIES.PART x 641 wave increases with increasing tin( IV) concentration, but there is no strict proportionality. An electrode covered with an aged film gave a smaller hydrogen-ion reduction wave than a freshly filmed electrode. In addition, an aged film suppressed the tin(1V) reduction wave, although no effect was observed on the height of the wave that represented the formation of tin metal. A supporting electrolyte that consisted of a 4.5 M solution of ammonium chloride in 0.2 M hydrochloric acid was examined. Tin( IV) chloride suppressed the hydrogen-ion wave, but the suppressed wave appeared as a maximum, as reported by Bard. Suppression of the hydrogen-ion wave was less in chloride medium than in bromide medium.The repro- ducibility of the voltammograms was poor and the charge-transfer process was slower in chloride media. Oxidation of tin(11) at platinum electrodes-Clearly, the cathodic voltammograms at platinum are useless for the determination of kinetic parameters, and so anodic voltammo- grams were obtained in the same medium. Again, no difference was found between hydro- bromic and perchloric acids in the 3 . 0 ~ bromide medium. Fig. 5 shows anodic scans of the supporting electrolyte, with the bromine wave at 0.75 V, and the oxidation of tin(I1) with a single well defined limiting current region. The full pre-treatment process was used for activating the electrode, but the anodic scans were reproducible whether or not the elec- trode was pre-treated.Tafel and diffusion-corrected Lewartowicz plots are shown in Fig. 6, and the kinetic parameters derived are included in Table I. Pattern theory1* is highly precise in the context and gives parameter values in good agreement. Computer-plotted voltammo- grams23 prepared from the experimental values gave an exact fit with the experimental curves. I I 0.0 - 0.25 - 0-5 Electrode potential versus S.H.E./V Fig. 4. Reduction of tin(1V) a t a platinum cathode in 3.0 M sodium bromide + 0.4 M perchloric acid. Electrodes freshly activated by methods 1 and 2, ramp speed -85 mV min-l (+85 mV min-1 for curve 5). Curves: 1, background electrolyte alone; 2, 0.25 x M tin(1V) bromide; 3, 0.50 x M tin(1V) bromide; 4, 5.0 x M tin(1V) bromide; and 5, reverse scan of curve 2 Variations in hvdropen-ion and bromide-ion c I 1 0.8 0.6 0.Electrode potential versus S.H.E./V Fig. 5. Oxidation of tin(I1) a t a plati- num anode. Electrode activated by methods 1 and 2, ramp speed + 85 mV min-1. Curves: 1, 3-0 M sodium bromide + 0.4 M perchloric acid; and 2, as for curve 1 with the addition of 0.48 x M tin(I1) and 1.29 x M tin(1V) as bromides concentrations and ionic strength were examined. An elecirolyre that consisted of a 3.0 M solution of sodium bromidewin 4.0 M perchloric acid gave curves with the same shape as those in Fig. 5 ; the kinetic parameters are included in Table I. A decrease in bromide-ion concentration, while maintaining the ionic strength constant with sodium perchlorate, eventually produced a maximum (Fig.7)642 BISHOP AND HITCHCOCK: MASS AND CHARGE TRANSFER [AnaZyst, Vol. 98 I 1 I 0.6 0.5 0.4 Electrode potential versus S.H.E./V Fig. 6. Tafel and Lewartowicz plots for oxidation of tin(I1) at a platinum anode. Electrodes activated by methods 1 and 2, 3.0 M sodium bromide + 0.4 M perchloric acid, ramp speed +86 mV min-l. Curves: 1, Lewartowicz plot, 0.48 x 10-3 M tin(I1) + 1.29 x lW3 M tiri(1V); 2, Tafel plot of same scan; 3, Lewartowicz plot, 0-96 x M tin(I1) + 1.32 x M tin(1V); and 4, Lewartowicz plot, 0.96 x M tin (11) + 2.03 x M tin (IV) in place of the limiting current plateau of Fig. 5 . The same effect occurred when no sodium perchlorate was added; the kinetic parameters are given in Table I. The reverse scan in Fig. 7 also shows a maximum, absent in curve 1 in Fig.5 , but coincident with the maximum in the forward scan in Fig. 7. It is probable that at low bromide concentrations a layer of tin(1V) species, such as [SnBr5OHl2- or the dihydroxo complex, is formed on the surface of the electrode, so blocking the electrode surface and causing the current to decrease after the maximum in the anodic scan, and that this species is reduced on the reverse, cathodic, scan and gives the small maximum shown in Fig. 7 . KINETICS AND MECHANISM OF THE TIN(IV) - TIN(II) PROCESS- Only the reduction of tin(1V) at a gold cathode and the oxidation of tin(I1) at a platinum anode in bromide media give sufficiently well defined waves for the determination of kinetic parameters. Variations in the tin(I1) and tin(1V) concentrations showed that the cathodicSeptember, 19731 KINETICS AND COULOMETRIC CURRENT EFFICIENCIES.PART x 643 current is proportional to the tin(1V) concentration and independent of the tin(I1) concen- tration, and that the anodic current is proportional to the tin(I1) concentration and inde- pendent of the tin(1V) concentration. The reverse direction in either reaction is therefore without influence and the charge-transfer process is slow. The limiting currents were proportional to the stirring speed.13 All of these results accord with the over-all reaction SnIv + 2e + SnII taking place in a single two-electron step, or two consecutive one-electron steps. An alterna- tive mechanism would be an E.C.E. process in which the chemical step is the disproportionation of tin(II1).Vetter2* contends that two one-electron steps occur in reduction at mercury in chloride media, but there is no experimental evidence for this proposal and similar contentions concerning the thallium( 111) - thallium( I) 25 and quinone - hydroquinone26 systems have been ~hallenged.~’-~O Vetter used two criteria for distinguishing two consecutive one-electron steps from a single two-electron step : first, extrapolations of the mass transfer corrected Tafel plots to zero overpotential do not give the same exchange current, and second, the sum of a + /3 is not unity. For a single two-electron step, the exchange currents are identical and cc + ,L? is unity. However, potential-dependent adsorption2’ can so alter the electrode surface that these criteria are unreliable ; moreover, the potential difference between anodic and cathodic scans for such a slow system is great enough to produce other changes in the electrode surface.For tin, Vetter’s first criterion cannot be applied because the zero-current potential is not measurable, and the second criterion cannot be used in isolation because cc and ,8 are very susceptible to changes in adsorption on the electrode surface. The changes in slope of the Lewartowicz plots in Fig. 3 are in some agreement with Hurd’s predictions31 on successive steps, but are more likely to indicate a change in specific adsorption. The available evidence is insufficient to support a definite conclusion. 0.9 0-7 0.5 0.3 Electrode potential versus S. H . E./V Fig. 7. Oxidation of tin(I1) at a platinum anode in dilute bromide medium.Anode freshly activated by methods 1 and 2, 0.33 M sodium bromide + 0.4 M perchloric acid + 2.7 M sodium perchlorate. Curves: 1, iorward scan at + S S mV min-l; and 2, immediately following reverse scan at -85 mV min-1 Chemical studies of homogeneous reaction k i n e t i c ~ ~ ~ , ~ ~ show that the tin system accom- modates itself to the mechanism of the other reactant, and is a one-electron system for “one-electron reactants” such as cerium(IV), iron(III), chromium(V1) or manganese(VII), but a two-electron system for “two-electron reactants” such as hydrogen peroxide, iodine, bromine, thallium(II1) or mercury(I1). This property, however, is not of much help in the heterogeneous electrode process.644 BISHOP AND HITCHCOCK: MASS AND CHARGE TRANSFER [Analyst, Vol.98 TABLE I1 KINETIC PARAMETERS FOR BACKGROUND REACTIONS System k ~ / l @ -k ffH)mol-(2 aH)cm-2 s-1 a Freshly activated gold electrode, reduction of 0.4 M per- Gold electrode, manual plot, reduction of 3.0 M sodium chloric acid .. .. .. .. .. .. 1.93 x 10-1l 0.208 bromide + 0.4 M perchloric acid . . .. .. 2-24 x 0.13 Freshly activated platinum electrode, oxj dati on of 3.0 M sodium bromide + 0.4 M perchloric acid . . .. (mass transfer controlled, E: = 1.065 V) APPLICATION OF EXPERIMENTALLY DETERMINED KINETIC PARAMETERS IN COMPUTER CALCU- Parameters for the background reactions were derived by the curve-fitting process,13 pattern theory not having been fully developed for backgrounds at the time.34 The results, which were later confirmed by pattern theory, are shown in Table 11.The computer in use at the time did not have the capacity for an ecological matrix of k , cc and Ewe, and so LATIONS- 1 I 1 0.0 - 0.25 - 0.50 Electrode potential versus S.H.E./V Fig. 8. Computed voltammograms, reduction of tin(1V) a t gold cathode in 3.0 M sodium bromide + 0.4 M perchloric acid. [SnIv] = 2-5 x 10-4 M, [SnIIJ = 0. Curves A1 and A2, k H = 2.237 X 10-l1, aH = 0.133; B1 and B2, AH = 5.11 x 10-13, aH = 0.11; A1 and B1, Roc = 5.1 x lo-@, a = 0.435; A2 and B2, Roc = 34' x a = 0.348. A, Experimental pointsSeptember, 19731 KINETICS AND COULOMETRIC CURRENT EFFICIENCIES. PART x 645 two voltammetric curves were plotted by using low and high current values for k and a for the tin(1V) - tin(I1) system, and the experimental points are shown superimposed on the computer plots in Fig.8. The effect of superimposition of hydrogen-ion reduction on the generation current efficiency for tin(I1) is shown in Fig. 9, again with two plots for low and high current values of the charge-transfer parameters being used.The results are in fair agreement with the experimental values of Bard and Lingane,l who claimed a current efficiency of 99.7 -+ 0-2 per cent. for current densities ranging from 10 to 84 mA cm-2. The computed efficiency loss is 120 to 500 p.p.m. in the same range. The computed current efficiency shows a sharp decrease at current densities below 5 mA cm-2, again confirming the earlier observa- ti0n.l It is likely that the background parameters used in the current efficiency computation underestimate the loss.but the commtation does show the maximum efficiencv that can be attained and the range of current ldensities that are available. J Fig. 9. Computed current efficiency curves for the generation of tin(I1) at a gold cathode. Parameters as given for curves A1 and A2 in Fig. 8; [SnIVJ = 0.2 M CONCLUSIONS Values of the mass and charge transfer kinetic parameters for the tin(1V) - tin(1I) and background systems have been determined within the limits of reproducibility of the voltam- mograms. Current efficiencies computed on this basis are in agreement with earlier work,l but show that in order to attain a current efficiency loss of about 100 p.p.m., the current density for reduction of tin must be maintained between 100 and 300 mA cm-2 for a 0.2 M solution of tin(1V) bromide in 3.0 M sodium bromide plus 0.4 M hydrobromic or perchloric acid.This conclusion means that the sample size and concentration must be such, and the generation current density must be so chosen, that the intermediate current density never falls below 100 mA cm-2 at the beginning of the determination or exceeds 300 mA cm-2 at the end. This constraint may necessitate very short increments at high currents in approaching the end-point. This procedure is now p0ssible.~5 The essential factor for platinum cathodes is to form the film as fast as possible, to maintain it throughout the determination, but not to allow it to age so much that the reduction of tin(1V) is affected. A special cleaning process is essential for the removal of the films.The behaviour of gold electrodes in bromide media is ascribed to specific adsorption of bromide ions, although this conclusion is not amenable to absolute proof. Platinum646 BISHOP AND HITCHCOCK electrodes in tin halide solutions do acquire a film, which is attributed by some workers1 to hydrous tin oxides and others22 to alloy-like compounds of platinum and tin metal, and in the present work the evidence favours a film of tin metal covered with a partially hydrolysed tin halide. The significant point is that the films do form and do block or partially block certain electrode reactions while permitting other electrode reactions to proceed with little or no inter- ference. This effect does increase the generation current efficiency of tin(II), but severely complicates any fundamental investigation of mechanisms.Similarly, the specific adsorption of bromide on gold electrodes hinders mechanistic investigation. We are deeply grateful to Imperial Chemical Industries Limited for the provision of research funds over a period of 3 years. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. REFERENCES Bard, A. J., and Lingane, J. J., Analytica Chim. Acta, 1959, 20, 463. Bard, A. J., Analyt. Chem., 1960, 32, 623. Bard, A. J., and Lingane, J. J., Analytica Chim. Acta, 1959, 20, 581. Lingane, J. J., Ibid., 1959, 21, 227. Sakurai, H., Kogyo Kagaku Zasshi, 1961, 64, 2121. Suzuki, S., Ibid., 1961, 64, 2112.Takahashi, T., and Sakurai, H., Talanta, 1962, 9, 74. Tso, T.-C., Li, H. L., and Sun, C. C., Hua Hsueh Hsueh Pao, 1964, 30, 301. Agasyan, L. B., Nikolaeva, E. R., Agasyan, P. K., and Lebedeva, 2. M., Izv. Vjjssh. Ucheb. Zaved. Bard, A. J., J . Electroanalyt. Chem., 1962, 3, 117. Sill&, L. G., and Martell, A. E., “Stability Constants of Metal - Ion Complexes.” Special Pub- lication No. 17, Chemical Society, London, 1964. Bishop, E., and Hitchcock, P. H., Analyst, 1973, 98, 553. Forbes, G. S., and Bartlett, E. P., J . Amer. Chem. SOC., 1914, 36, 2030; 1915, 37, 1201. Huey, C. S., and Tartar, H. V., Ibid., 1934, 56, 2585. Breiter, W. M., Electrochim. Acta, 1963, 8, 925. Bode, D. D., Andersen, T. N., and Eyring, H., J . Phys. Chem., 1967, 71, 792. Bishop, E., Analyst, 1972, 97, 761. GuBron, J., Bull. SOC. Chim. Fr., 1934, 1, 561. Bishop, E., and Hitchcock, P. H., Analyst, 1973, 98, 625. Bowles, B. J., and Cranshaw, T. E., Phys. Lett., 1967, 17, 258. Frumkin, A., in Yeager, E., Editor, “Transactions of the Symposium on Electrode Processes, Bishop, E., Chemia Analit., 1972, 17, 511. Vetter, K. J., “Electrochemical Kinetics,” New York, Academic Press, 1967, p. 481. Vetter, K. J., and Thiemke, G., Z . Elektrochem., 1960, 64, 805. Vetter, K. J., Ibid., 1952, 56, 797. James, S. D., Electrochim. Acta, 1967, 12, 939. Loshkarev, M. A., and Tomilov, B. I., Russ. J . Phys. Chern., 1960, 34, 836. Tomilov, B. I., and Loshkarev, M. A., Ibid., 1962, 36, 1027. Hurd, R. M., J . Electrochem. SOC., 1962, 109, 327. Higginson, W. C. E., Leigh, R. T., and Nightingale, R., J . Chem. Soc., 1962, 436. Welton, E. M. A., and Higginson, W. C. E., Ibid., 1965, 5890. Bishop, E., Analyst, 1972, 97, 772. Wright, D. T., and Bishop, E., Proc. SOC. Analyt. Chem., 1973, 10, in the press. , , , K’o Hsueh T’ung Pao, 1964, 163. --- Khim. Khim. Tekhnol., 1967, 10, 1316. 1959,” John Wiley & Sons Inc., New York, 1960, p. 1. 9 , Ibid., 1962, 36, 66. -- NOTE-References 13, 18, 20, 23 and 34 are to Parts VII, 111, IX, I and IV, respectively, of this series. Received January 24th, 1973 Accepted March 27th, 1973