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Depletion as a limiting factor for the polarographic currents observed in amalgam oxidation maxima
J Electroanal Chem, 146 (1983)201-206 Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands
201
Short communication D E P L E T I O N AS A LIMITING FACTOR FOR THE P O L A R O G R A P H I C C U R R E N T S O B S E R V E D IN A M A L G A M O X I D A T I O N M A X I M A
C1 B U E S S - H E R M A N and Ch. K I L L E N S Facult~ des Scwnces, Umversltb Ltbre de Bruxelles. 50, av F D Roosevelt, 1050 Brussels (Belgium) (Received 26th July 1982)
INTRODUCTION
It is well known (see for instance refs. 1-12) that polarographic maxima of the first kind are caused by a tangential superficial streaming directed towards the regions of highest interfacial tension. This movement affects the adjacent layers in both the aqueous and metallic phases and induces a convective regime, more or less stable, which is responsible for the abnormal increase of the faradaic current. More particularly, in the range of potentials negative with respect to the point of
0
Fig. 1. Schematic illustration of a depletion-controlled m a x i m u m of the first kind The dot density depicts the local amalgam concentration. 0022-0728/83/$03.00
© 1983 Elsevier Sequoia S.A.
202 zero charge (pzc), cathodic maxima are connected to the sliding from the bottom to the top of the mercury drop, while a reverse direction is observed with anodic maxima. In the case of amalgam oxidation, the supply of depolarizer is necessarily limited by the concentration of the amalgam and its flow rate. Since convection movements are most intense at the neck of the drop (which is precisely the region where fresh amalgam is constantly supplied), one may wonder whether the amphtude of the anodlc current could not become entirely controlled by the capillary flow, leaving most of the drop practically devoid of amalgam (Fig. 1). EXPERIMENTAL
Reagents The working electrode was a dropping Z n - H g amalgam electrode. The amalgam concentrations were settled by dissolving cleaned zinc pellets (Merck p.a) of known weight into a given volume of mercury, under nitrogen atmosphere. Their concentrations were checked by exhaustive selective chemical oxidation of a measured fraction of the amalgam, followed by polarographac determination of the amount of released Zn 2+ ions. The auxiliary electrode was also a Z n - H g amalgam of the same concentration. For some experiments, a pulsed-flow dropping electrode [13] giving periodically renewed and highly reproducible stationary drops was used as the working electrode. The growth of the drop was stopped after 4 s, by fast adjustment of the pressure prevailing inside the reservoir, with the help of an electromechanical valve. The constancy of the area was checked independently by measuring the capacity of the electrode by an ac method in the absence of faradaic processes. All solutions were prepared by dissolving analytical grade chemicals in freshly tridistilled water. Potentials are referred to the saturated calomel electrode (SCE). RESULTS AND DISCUSSION Screening experiments have shown that electrocapillary maxima are observed with several amalgams [ 14-16], provided that their concentration is kept sufficiently high (over about 5 m M ) . The present communication presents and discusses some particularities of the dropping zinc amalgam in contact with a KC1 1 M (or N H 3 / N H ~- M / M ) aqueous solution. In a system containing both Zn(Hg) and Zn 2÷ ions, a mixed polarographlc wave is observed (Fig. 2). The reduction process gives the usual diffusion-controlled wave while the reverse process presents a conspicuous, hortzontally truncated maximum, which subsists up to the pzc, thus exceeding a range of 500 mV. At more positive potentials, oxidation of the Zn amalgam appears to be essentially diffusion controlled. The existence of the maximum is revealed here by a constant limiting anodic
203
current exceeding the diffusion value, rather than by a peak. The fact that the flat part of the maximum corresponds to a state of nearly complete depletion of the drop is demonstrated by the following observations: (1) The instantaneous current is constant during most of the drop life and irrespective of the potential, if one excepts the short lapse of time required to restart the convection after the birth of each new drop. (2) If depletion is complete the current should agree with the value predicted by the Faraday law, 1.e. l = nFcdV/dt
where c is the amalgam concentration and d V / d t the mercury flow in dm 3 s-~. As expected, for constant capillary conditions, the current has been found to be closely proportional to the concentration in the range explored (from 6 × 10 -3 to 6 × 10 -2 M). Correlatively, the limiting current is proportional to the mercury height (Table 1), i.e. to the mercury flow, neglecting the second-order effect caused by the back pressure (heights were adjusted between 40 and 100 cm). By using a cell of adequate geometry, it has been possible to collect a sufficient number of depleted drops and to separate them from the solution. After selective oxidation the amount of Zn 2+ ions have been found to correspond to less than a few percent of the initial amalgam concentration.
-'o]
05 E/V
400
~A Fig 2 Classical polarogram of a 6 × 10 -2 M amalgam electrode m the presence of Zn 2+ 3 × 10 -2 M in 1 M KCI
204 TABLE 1 Variation of the hmxtmg current, observed at - 0 . 7 0 V / S C E for the oxidation of the Z n - H g amalgam m N H 3 / N H 4 C 1 M / M , with the height of the amalgam reservoir Limiting current /1//ftA
Mercury height h /cm
Ratao
445 518 589
55.0 63.5 71.5
8.09 8 16 8 24
tl/h
Finally (in conformity with the preceding observations), the absolute value of the current which characterizes the truncated part of the maximum is in fair agreement with the Faraday law, with apparent values of n ranging from 1.93 to 1.95 instead of 2. (3) The most conclusive experiment (Fig. 3) is afforded by the pulsed-flow Zn amalgam electrode [13]. If the flow is kept constant (curve a) a constant current is observed. On the other hand (curve b), as soon as the flow is interrupted, the instantaneous current falls practically to zero, in accordance with the assumption that the extent of depletion is close to unity. For comparison, the current-time function which describes a purely-diffusion-controlled process is sketched by the broken line, which has been normalized with respect to the current and time coordinates corresponding to the flow interruption. The study of depletion-controlled currents leads to the conclusion that the
4
8
tls
/ / / / a '"
~..t
E: -0.7V
Fig. 3 The t - t curves (three successxve runs) obtained at a classical amalgam electrode (a) or at a pulse-flow electrode (b) (drop growth stopped after 4 s) The &ffuslon-controlled current which would be observed at the pulsed-flow electrode is gwen by the broken hne, normahzed with respect to the current after 4 s
205
established mechanism for the type of m a x i m u m discussed here (strong downwards electrocapillarity convection driven by the ohmic drop prevailing at the neck of the drop) is consonant with the fact that most of the amalgam is immediately oxidized as soon as it leaves the capillary lumen, without being able to subsist in appreciable amounts in the bulk of the drop. In some instances (small drop area, diluted amalgams, no suppressors) it is not too infrequent to record a limiting truncated current which is only slightly larger than the corresponding diffusion current (Fig. 4), the latter only being detected beyond the pzc. If not properly identified, this situation may have serious consequences in the exact determination of amalgam concentrations.
o
05
06 )
-E/V )
,0
Y ~uA Fig. 4. A n o d l c p o l a r i z a t i o n curve of a 1 4 × 10 - 2 M Cd a m a l g a m in 1 M KC1
A final observation is that the anodic chronopotentiometric transition curves observed under galvanostatic conditions at an expanding amalgam drop are either extremely long or reduce themselves to a mere inflexion, according to the ratio between the imposed current and the maximal current which can be sustained by the amalgam flow. This behaviour is in sharp contrast with the well-known Sand equation which is strictly valid for a diffusion-controlled process. In this respect, chronopotentiometry remains the best diagnostic tool in helping to assess whether or not a limiting current is controlled by diffusion or convection-assisted depletion. ACKNOWLEDGEMENTS
We are grateful to Prof. L. Gierst for help and advice and to Mr. P. Fifils, who contributed to the last stage of the experimental work.
206 REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
M. yon Stackelberg, H J. Antweller and L Kleselbach, Z. Elektochem, 44 (1938) 663. H J. Antweder, Z Elektrochem, 43 (1937) 596, 44 (1938) 719, 831, 888 M von Stackelberg, Z Elektrochem, 45 (1939) 466 M von Stackelberg, Fortschr. Chem Forsch, 2 (1951) 229, Proc. 1st Congress of Polarography, Prague, 1951, Vol. 1, p 359 A N Frumkln and B Bruns, Acta Physlcochlm U.R.S S., 1 (1934) 232 A N Frumkln and V G Levlch, Zh Flz Khlm, 19 (1945) 573, 21 (1947) 689, 953, 1335 B Bruns, A N Frumkm, S. Iofa, L Vanyukova and S Zolotarevskaya, Acta Physlcochlm U.R S S, 9 (1938) 359 M. von Stackelberg and R Doppelfeld m I.S Longmulr (Ed). Advances in Polarography, Pergamon Press, London, 1960, p 68 H Bauer in A.J Bard (Ed), Electroanalytlcal Chemistry, Vol. 8, Marcel Dekker, New York, 1974, p 169 S K. Rangarajan, J. Electroanal. Chem., 62 (1975) 21. B M Grafov and A N Frumkm, J Electroanal Chem, 75 (1977) 205 R. Guldelll, J Electroanal. Chem, 100 (1979) 711 R. Dlas, C1. Buess-Herman and L. Glerst, J Electroanal Chem, 130 (1981) 345 J Lmgane, J Am Chem. Soc., 61 (1939) 976 J Heyrovsk~,, Chem Llsty, 36 (1942) 267 J. KtSta and I Smoler, Collect Czech Chem Commun, 28 (1963) 2874
201
Short communication D E P L E T I O N AS A LIMITING FACTOR FOR THE P O L A R O G R A P H I C C U R R E N T S O B S E R V E D IN A M A L G A M O X I D A T I O N M A X I M A
C1 B U E S S - H E R M A N and Ch. K I L L E N S Facult~ des Scwnces, Umversltb Ltbre de Bruxelles. 50, av F D Roosevelt, 1050 Brussels (Belgium) (Received 26th July 1982)
INTRODUCTION
It is well known (see for instance refs. 1-12) that polarographic maxima of the first kind are caused by a tangential superficial streaming directed towards the regions of highest interfacial tension. This movement affects the adjacent layers in both the aqueous and metallic phases and induces a convective regime, more or less stable, which is responsible for the abnormal increase of the faradaic current. More particularly, in the range of potentials negative with respect to the point of
0
Fig. 1. Schematic illustration of a depletion-controlled m a x i m u m of the first kind The dot density depicts the local amalgam concentration. 0022-0728/83/$03.00
© 1983 Elsevier Sequoia S.A.
202 zero charge (pzc), cathodic maxima are connected to the sliding from the bottom to the top of the mercury drop, while a reverse direction is observed with anodic maxima. In the case of amalgam oxidation, the supply of depolarizer is necessarily limited by the concentration of the amalgam and its flow rate. Since convection movements are most intense at the neck of the drop (which is precisely the region where fresh amalgam is constantly supplied), one may wonder whether the amphtude of the anodlc current could not become entirely controlled by the capillary flow, leaving most of the drop practically devoid of amalgam (Fig. 1). EXPERIMENTAL
Reagents The working electrode was a dropping Z n - H g amalgam electrode. The amalgam concentrations were settled by dissolving cleaned zinc pellets (Merck p.a) of known weight into a given volume of mercury, under nitrogen atmosphere. Their concentrations were checked by exhaustive selective chemical oxidation of a measured fraction of the amalgam, followed by polarographac determination of the amount of released Zn 2+ ions. The auxiliary electrode was also a Z n - H g amalgam of the same concentration. For some experiments, a pulsed-flow dropping electrode [13] giving periodically renewed and highly reproducible stationary drops was used as the working electrode. The growth of the drop was stopped after 4 s, by fast adjustment of the pressure prevailing inside the reservoir, with the help of an electromechanical valve. The constancy of the area was checked independently by measuring the capacity of the electrode by an ac method in the absence of faradaic processes. All solutions were prepared by dissolving analytical grade chemicals in freshly tridistilled water. Potentials are referred to the saturated calomel electrode (SCE). RESULTS AND DISCUSSION Screening experiments have shown that electrocapillary maxima are observed with several amalgams [ 14-16], provided that their concentration is kept sufficiently high (over about 5 m M ) . The present communication presents and discusses some particularities of the dropping zinc amalgam in contact with a KC1 1 M (or N H 3 / N H ~- M / M ) aqueous solution. In a system containing both Zn(Hg) and Zn 2÷ ions, a mixed polarographlc wave is observed (Fig. 2). The reduction process gives the usual diffusion-controlled wave while the reverse process presents a conspicuous, hortzontally truncated maximum, which subsists up to the pzc, thus exceeding a range of 500 mV. At more positive potentials, oxidation of the Zn amalgam appears to be essentially diffusion controlled. The existence of the maximum is revealed here by a constant limiting anodic
203
current exceeding the diffusion value, rather than by a peak. The fact that the flat part of the maximum corresponds to a state of nearly complete depletion of the drop is demonstrated by the following observations: (1) The instantaneous current is constant during most of the drop life and irrespective of the potential, if one excepts the short lapse of time required to restart the convection after the birth of each new drop. (2) If depletion is complete the current should agree with the value predicted by the Faraday law, 1.e. l = nFcdV/dt
where c is the amalgam concentration and d V / d t the mercury flow in dm 3 s-~. As expected, for constant capillary conditions, the current has been found to be closely proportional to the concentration in the range explored (from 6 × 10 -3 to 6 × 10 -2 M). Correlatively, the limiting current is proportional to the mercury height (Table 1), i.e. to the mercury flow, neglecting the second-order effect caused by the back pressure (heights were adjusted between 40 and 100 cm). By using a cell of adequate geometry, it has been possible to collect a sufficient number of depleted drops and to separate them from the solution. After selective oxidation the amount of Zn 2+ ions have been found to correspond to less than a few percent of the initial amalgam concentration.
-'o]
05 E/V
400
~A Fig 2 Classical polarogram of a 6 × 10 -2 M amalgam electrode m the presence of Zn 2+ 3 × 10 -2 M in 1 M KCI
204 TABLE 1 Variation of the hmxtmg current, observed at - 0 . 7 0 V / S C E for the oxidation of the Z n - H g amalgam m N H 3 / N H 4 C 1 M / M , with the height of the amalgam reservoir Limiting current /1//ftA
Mercury height h /cm
Ratao
445 518 589
55.0 63.5 71.5
8.09 8 16 8 24
tl/h
Finally (in conformity with the preceding observations), the absolute value of the current which characterizes the truncated part of the maximum is in fair agreement with the Faraday law, with apparent values of n ranging from 1.93 to 1.95 instead of 2. (3) The most conclusive experiment (Fig. 3) is afforded by the pulsed-flow Zn amalgam electrode [13]. If the flow is kept constant (curve a) a constant current is observed. On the other hand (curve b), as soon as the flow is interrupted, the instantaneous current falls practically to zero, in accordance with the assumption that the extent of depletion is close to unity. For comparison, the current-time function which describes a purely-diffusion-controlled process is sketched by the broken line, which has been normalized with respect to the current and time coordinates corresponding to the flow interruption. The study of depletion-controlled currents leads to the conclusion that the
4
8
tls
/ / / / a '"
~..t
E: -0.7V
Fig. 3 The t - t curves (three successxve runs) obtained at a classical amalgam electrode (a) or at a pulse-flow electrode (b) (drop growth stopped after 4 s) The &ffuslon-controlled current which would be observed at the pulsed-flow electrode is gwen by the broken hne, normahzed with respect to the current after 4 s
205
established mechanism for the type of m a x i m u m discussed here (strong downwards electrocapillarity convection driven by the ohmic drop prevailing at the neck of the drop) is consonant with the fact that most of the amalgam is immediately oxidized as soon as it leaves the capillary lumen, without being able to subsist in appreciable amounts in the bulk of the drop. In some instances (small drop area, diluted amalgams, no suppressors) it is not too infrequent to record a limiting truncated current which is only slightly larger than the corresponding diffusion current (Fig. 4), the latter only being detected beyond the pzc. If not properly identified, this situation may have serious consequences in the exact determination of amalgam concentrations.
o
05
06 )
-E/V )
,0
Y ~uA Fig. 4. A n o d l c p o l a r i z a t i o n curve of a 1 4 × 10 - 2 M Cd a m a l g a m in 1 M KC1
A final observation is that the anodic chronopotentiometric transition curves observed under galvanostatic conditions at an expanding amalgam drop are either extremely long or reduce themselves to a mere inflexion, according to the ratio between the imposed current and the maximal current which can be sustained by the amalgam flow. This behaviour is in sharp contrast with the well-known Sand equation which is strictly valid for a diffusion-controlled process. In this respect, chronopotentiometry remains the best diagnostic tool in helping to assess whether or not a limiting current is controlled by diffusion or convection-assisted depletion. ACKNOWLEDGEMENTS
We are grateful to Prof. L. Gierst for help and advice and to Mr. P. Fifils, who contributed to the last stage of the experimental work.
206 REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
M. yon Stackelberg, H J. Antweller and L Kleselbach, Z. Elektochem, 44 (1938) 663. H J. Antweder, Z Elektrochem, 43 (1937) 596, 44 (1938) 719, 831, 888 M von Stackelberg, Z Elektrochem, 45 (1939) 466 M von Stackelberg, Fortschr. Chem Forsch, 2 (1951) 229, Proc. 1st Congress of Polarography, Prague, 1951, Vol. 1, p 359 A N Frumkln and B Bruns, Acta Physlcochlm U.R.S S., 1 (1934) 232 A N Frumkln and V G Levlch, Zh Flz Khlm, 19 (1945) 573, 21 (1947) 689, 953, 1335 B Bruns, A N Frumkm, S. Iofa, L Vanyukova and S Zolotarevskaya, Acta Physlcochlm U.R S S, 9 (1938) 359 M. von Stackelberg and R Doppelfeld m I.S Longmulr (Ed). Advances in Polarography, Pergamon Press, London, 1960, p 68 H Bauer in A.J Bard (Ed), Electroanalytlcal Chemistry, Vol. 8, Marcel Dekker, New York, 1974, p 169 S K. Rangarajan, J. Electroanal. Chem., 62 (1975) 21. B M Grafov and A N Frumkm, J Electroanal Chem, 75 (1977) 205 R. Guldelll, J Electroanal. Chem, 100 (1979) 711 R. Dlas, C1. Buess-Herman and L. Glerst, J Electroanal Chem, 130 (1981) 345 J Lmgane, J Am Chem. Soc., 61 (1939) 976 J Heyrovsk~,, Chem Llsty, 36 (1942) 267 J. KtSta and I Smoler, Collect Czech Chem Commun, 28 (1963) 2874