Anal. Chem. 1995,67, 1125-1131
Voltammetry of Metals at Mercury Film Microelectrodes in the Absence and the Presence of Varying Concentrations of Supporting Electrolyte MalgOMta Ciszkowskat and Janet 0. Ostetyoung*
Department of Chemistry, North Carolina State Universiiy, Raleigh, North Carolina 27695-8204
The steady-state limiting current for reduction of monoand divalent metal cations to amalgam in solution without supporting electrolyte depends on both the charge of the cation and the charge of the associated anion. The ratio of limiting current in the absence of supporting electrolyte (il") to di&lsional current (id) was found to agree well with theoretical predictions (for reduction of M+, 2 and 3/2 for X-and X2-,respectively, and for M2+, 3 and 2 for Xand X2-,respectively). The reduction current of metal cation depends on the type and concentration of supporting electrolyte. The di&tsional current is reached at a lower electrolyte ratio when the cation of the electrolyte is divalent than when it is monovalent. In solutions without supporting electrolyte, the limiting current for reduction of a cation having a large negative reduction potential was found to increase in the presence of a cation reducing at a less negative potential. This phenomenon was observed for thallium ion with hydrogen ion and for lead ion with hydrogen ion. The increase of the current is due to the increased rate of transport of the more easily reduced cation at potentials where both reductions are transport-controlled. Microelectrodes allow voltammetry in highly resistive solutions, including solutions with no added supporting electrolyte.1,2 This possibility has triggered elaboration of the theory to describe the voltammetric response under steady-state conditions without electrolyte. The dependence of steady-state current at microelectrodes on the concentration of supporting electrolyte has been predicted for various The wave height of an electrode process that results in a neutral product is expected to depend on the charge of the reactant, the counterion charge (here, the charge of the anion that accompanies the metal cation), and the
type and concentration of the supporting ele~trolyte.~,~ Selected examples for the limiting value of current in the absence of electrolyte are presented in Table l.7The predictions listed have been verified experimentally for selected processes, including reduction of hydrogen iongand reduction and oxidation of a variety of Ru, Mo, Co, and Cu complexes.'j For a number of metal complexes, the difference between the theory and the experimental data is striking. No credible explanation for the observed phenomena has been given. A related case, for which the theory has not yet been worked out, is that of reduction involving a preceding chemical reaction. An example is the reduction of weak acid.1°The transport-limited current for reduction of a neutral weak acid depends on supporting electrolyte concentration according to the behavior expected for hydrogen ion, even though the free hydrogen ion is a minor component of the solution. Reduction of metal cations at mercury electrodes in solutions with no deliberately added supporting electrolyte was studied with classic polarography in the 1 9 3 0 ~ . ~Large ~ J ~ differences were observed between limiting currents in solutions without and with excess supporting electrolyte. The results in solutions without added supporting electrolyte were not reproducible, and the height of the wave decreased with time. This was probably due to the leakage of ions into the solution from the reference electrode. In this work we wished to make use of the special properties of mercury microelectrodesto extend the range of experimental evidence regarding transport by migration and diffusion in simple solutions of various ionic strength. Mercury film13-16 and mercury sphere microelectrode^^^-^^ have been applied to reduction of metal cations to amalgams. There is no report on reduction of metal cations at mercury microelectrodes in solutions without supporting electrolyte, although there are publications describing anodic stripping at mercury microelectrodes in media containing no deliberately
' Permanent address: Department of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland. (1) Utramicroelectrodes; Fleischmann, M., Pons, S., Rolison, D. R, Schmidt, P. P., Eds.; Datatech Systems Publishers: Morganton, NC, 1987. (2) Wightman. R M.; Wipf, D. 0. In Electroanalytical Chemisty; Bard, A J., Ed.; Marcel Dekker Inc.: New York, 1989. (3) Bond, A M.; Fleischmann, M.; Robinson, J. J. Electroanal. Chem. 1984, 172,11-25. (4) Amatore, C.; Fosset, B.; Bartelt, J.; Deakin, M. R.; Wightman, R M. J. Electroanal. Chem. 1988,256,255-268. (5) Baker, D. R; Verbrugge, M. W.; Newman, J. J Electroanal. Chem. 1991, 314,23-44. (6) Cooper, J. B.; Bond, A M.; Oldham, IC B.J. Electroanal. Chem. 1992,331, 877-895. (7) Oldham, K B.J Electroanal. Chem. 1992,337,91-126. (8) Myland, J. C.; Oldham, K B. J. Electroanal. Chem. 1993,347,49-91.
(9) Ciszkowska, M.; Stojek, Z.; Moms, S. E.; Osteryoung, J. G. Anal. Chem. 1992,64,2372-2377. (10) Stojek, Z.; Ciszkowska,M.; Osteryoung, J. G. Anal. Chem 1994,66,15071512. (11) slendyk, I. Collect. Czech. Chem. Commun. 1931,3,385-395. (12) Lingane, J. J.; Kolthoff, I. M. J. Am. Chem. SOC.1939,61,1045-1051. (13) Ciszkowska, M.; Stojek Z.J Electroanal. Chem. 1985,191,101-110. (14) Ciszkowska, M.; Penczek, M.; Stojek, Z. Electroanalysis 1990,2,203-207 (15) Dos Santos, M. M. C.; Goncalves, M. L. S. Electrochim. Acta 1992,37, 1413-1416. (16) Wojciechowski, M.; Balcerzak, J. Anal. Chim. Acta 1991,249,433-445. (17) Golas, J.; Galus, Z.; Osteryoung, J. G. Anal. Chem. 1987,59,389-392. (18) Galus, Z.; Golas, J.; Osteryoung, J. G. Electrochim. Acta 1987,32,669672. (19) Kounaves, S. P. Anal. Chem. 1992,64,2998-3003.
0003-2700/95/0367-1125$9.00/0 Q 1995 American Chemical Society
~
~~~~
Analytical Chemisrty, Vol. 67,No. 6, March 15, 1995 1125
Table 1. Normalized Steady-State Charge NeutrallzationCurrents, 4"lb, in the Absence of Supporting Electrolyte
if l i d ZMU
Zy6
predc
+1 +1
-1 -2 -3 -1 -2 -3 -1 -2 -3
2 3/2 4/3 3 2 5/3 4 5/2 2
+1 +2 $2 +2 +3 $3 +3
exptld 1.9,121.89 1.48 2.2.122.8F3 2.83 1.59,121.87
0 Charge of reactant (here, metal cation). * Charge of counterion ere, anion associated with metal cation). References 7 and 8. pReference numbers are given; results from this work undesignated.
added supporting e l e c t r ~ l y t e . ~Mercury ~ - ~ ~ film disk microelectrodes have some advantages over microdrops, since it is easier to calculate the theoretical reduction current due to well-defined surface area. The coefficient in the steady-state equation for spherical microelectrodes varies strongly with the shape of the sphere ~egment.2~Accordingly, we have chosen the silver amalgam-based mercury film electrode, which can be prepared with planar geometry and known t h i c k n e s ~ . ' ~ * ~ ~ A second objective was to extend the theoretical description of simple systems. As described above, Oldham has presented theoretical values for limiting cases with no ele~trolyte.~ Myland and Oldham have developed systematicallythe theory for the case where a reactant of charge z undergoes charge transfer of n electrons.8 Results are elaborated for a range of supporting electrolyte ratios and ranges of values of z and a, including both positive and negative values of each. However, the equations describing the dependence of limiting current on the concentration of supportingelectrolyte apply only to the case where all ions other than reactant and product are singly charged. We have extended this treatment to counterions and supporting electrolyte ions of arbitrary charge. Finally, we have extended the treatment to simultaneous reaction of two diflerent species. The aims of this paper, then, are to examine, under conditions of varying level of supporting electrolyte, several reduction processes that lead to formation of amalgams and to discuss these results in the framework of existing theory, which has been elaborated so as to treat multiply charged ions and multiple reactions. The specific objectives are to expand the body of experimental verikation of theoretical predictions, to provide experimental evidence for systems as yet not treated experimentally, and, finally, to explore the interaction of diffusion and migration under conditions where two ions are reduced simultaneously. EXPERIMENTAL SECTION
Electrochemical measurements were carried out with a threeelectrode system in a jacketed cell (25 "C) enclosed in an (20)De Vitre, R R; Tercier, M:L.; Tsacopoulos,M.; Buffie, J. Anal. Chim. Acta 1991,249,419-425. (21)Kounaves, S. P.;Deng, W. Anal. Chem. 1993,65,375-379. (22)Daniele, S.; Mazzocchin, G. A. A n d . Chim. Acta 1993,273,3-11. (23)Nyholm, L;Wikmark, G. Anal. Chim. Acta 1993,273,41-51. (24)Stojek, Z.;Osteryoung, J. G. Anal. Chem. 1989,61, 1305-1308. (25) Ciszkowska,M.; Donten, M.; Stojek, Z. Anal. Chem. 1994,66,4112-4115.
1126 Analytical Chemistty, Vol. 67, No. 6, March 15, 1995
aluminum Faraday cage. Silver disk working electrodes of 15 pm in radius (Project Ltd., Warsaw, Poland) were used as substrates for mercury films. The mercury film thickness was 1 pm. Mercury was deposited at -0.5 V (vs SCE) from a solution of 5 mM HgOD in 0.1 M HClO4. The procedure for preparation of the silver-based mercury film microelectrode has been described in dek1il.2~ Before being used, the surface of the film was inspected with an inverted microscope (Leitz Wetzlar, Germany). The counter electrode was platinum. A platinum quasireference electrode was used, as described previously for similar experimental conditions,26to prevent leakage of ions into the cell. The potential of the Pt quasi-reference electrode depends on the composition of the solution, but the magnitude of the limiting current is the same as that obtained with a saturated calomel reference electrode (SCE). The double pulse chronocoulometry experiments were performed using SCE and an electrolyticbridge filled with pure water. Staircase voltammograms were obtained using a Model 273 potentiostat (EG&G PARC) connected with a Keithley Model 427 current amplifier and controlled by software via a PC 486 computer. Unless explicitly stated, staircase voltammetry parameters were as follows: step height (hE) 10 mV, frequency v) 1 Hz. Double pulse chronocoulometryexperimentswere performed using a Model 273 potentiostat (EG&G PARC) controlled by software via a PC 486 computer. The deposition of mercury on the Ag disk electrodewas performed with a Model 173 potentiostat connected with a Model 179 digital coulometer @G&G PARC) in a threeelectrode system with Pt wire counter electrode and SCE. All reagents were of reagent grade purity and were used as received. Chemicals used for experiments were TlNO3 (Alfa), TIT SO4 (Aldrich), Cd(N03)~(Fisher), CdSO4 (Aldrich), Pb(N03)2 Fisher), LiC104(Aldrich), C ~ ( N O S@isher), )~ HC104(Fluka), NaT EDTA (Fisher), Hg(C€&COO)2(Mallinckrodt), CKCOOH (Fisher), and CH3COONa (Fisher). Ultrapure water (Milli-Q, Millipore Corp.) was employed in preparations of solutions and all rinses. The conductivity of water was 0.055 pS/cm (18.2 MQ/cm resistivity). The background level of ions in solution without added supporting electrolyte, determined by the procedure described previously, 26 was close to 1 pM. The pH value of 0.1 mM Pb(N03)~solution without supporting electrolyte was 5.2.The concentration of hydrogen ion in this solutions was 6.3 yM. Solutions were deoxygenated before voltammetric scans and blanketed with a stream of water-saturated argon. The results are described in terms of the ratio of concentration of added electrolyte to total concentration of metal ions; this ratio is denoted y. The reproducibilityof all limiting current and charge measurements was very good, with relative standard deviations better than 2%and 3.5%for staircase voltammograms and double pulse chronocoulograms, respectively. RESULTS AND DISCUSSION
Under the conditions for these experiments, the diffusionlimited current is given byz7 id = 4nFDC9f(t)
(1)
where a is the number of electrons transferred, F is the Faraday ~
(26)Ciszkowska, M.;Osteryoung, J. G. /. Phys. Chem. 1994,98,3194-3201. (27)Sinru, L;Osteryoung, J. G.; O'Dea, J. J.; Osteryoung, R A. Anal. Chem. 1988,60,1135-1141.
Table 2. Charge Types Treated Experimentally and Theoretically (Absolute Value of Charge)
m
2
k
a
m
2
k
a
1 1 1 1
1 1 2 2
1 2 1 2
1 1 1 1
2 2 2 2
1 1 2 2
1 2 1 2
1 1 1 1
a c
constant, C is the bulk concentration of electroactive species, r is the electrode radius, andf(t) is given by
\
151
I
- 51 -0.6
-0.8
+
f ( z ) = 1 0.71835t-1'2 (2) where t = a t / + and t = t&,where tp is the period of the staircase and k is the step number. For our conditions,f(t) does not exceed 1.031. The ratio of limiting current to diffusion-limited current, for b-electron reduction of fb-charged cation accompanied by a monovalent anion and in the presence of univalent supporting electrolyte, is given by il/id = b
+ 1+ 2y - 2[y(b + y)I1"
(3)
where y is the ratio of the concentrationof supporting electrolyte to that of the electroactive species. We have developed a more general equation for the case in which any of the four ions may have any charge, with the simplification which applies in the present case, that the reactant be a cation and the charge on the product be zero. Thus, consider the reaction of Mm+to form P, uncharged, in solution of the salts MzYmand CA (supporting electrolyte), which include the ions Yz-, Ck+,and A'-. The ratio y is the bulk concentration of cation Ck+divided by the bulk concentration of Mm+. The resulting current is given by -il/id = [(z
+ m)/zI(x" - 1) - [(k - m > / m I ~ ( x-- ~1) + [(a + m)/amlkrV
- 1) (4)
where x = expW3, and YL is the dimensionless potential corresponding to zero concentration of the reactant on the electrode surface, given as the solution to x(z+l) - kyx(l-R)/m + kyx(a+l)
/m=O
(5)
The extension of eq 3 to the result of eqs 4 and 5 is somewhat complicated algebraically but in principle follows directly from the treatment of ref 8. We have obtained solutions to this general equation for various choices of m,z, k, and a, and we present here experimental results and theoretical predictions for the eight cases enumerated in Table 2. The limiting current ratios for these cases are known, as presented in Table 1, but through eqs 4 and 5, we were able to calculate the dependence of the limiting current on the concentration of supporting electrolyte for arbitrary m,z, k , and a values. The use o f z = k = a = 1, and m = b in eqs 4 and 5 gives the result of eq 3. Reduction of Monovalent M e t a l Cation. Voltammograms for reduction of thallium cations obtained in solutions of thallium sulfate with various concentrations of supporting electrolyte (LiClOk) are presented in Figure 1. The wave height diminishes by a factor of approximately 1.5 with increase in concentrationof lithium perchlorate from 0 to 100 mM. This is as the theory
-1 .o
-1.2
- 1 . 4
E / V Figure I. Staircase voltammograms for reduction of 0.65 mM TlzSO4 at the silver-based mercury film microelectrode. Concentration of added supporting electrolyte, LiCIO4: (a) 0, (b) 0.1, (c) 1, and (d) 100 mM.
predicts for a monovalent cation accompanied by a divalent anion (cf. Table 1). It is not possible to work with a solution containing absolutely no ions other than those of the added electroactive salt, so the experimental ratio, for example 1.48 for 0.65 mM Tl&O4 solution, will always be slightly lower than the theoretical value. The situation may be improved by working with higher concentrations of the metal cation, but then problems with limited solubility of the metal in mercury ahd with hydrolysis may appear. The limiting currents of reduction waves obtained without and with excess supporting electrolyte (0.04 M LiC104) were plotted versus concentration of thallium ion. The resultant calibration plots are linear over the range 0.1 5 C/mM I 2 and can be expressed as i/nA = 16.19C/mM 0.067 (correlation coefficient, 0.999 83) and 11.35C/mM 0.111 (correlation coefficient, 0.999 go), respectively. The ratio of the slopes is 1.43, in comparison with the theoretical value of 1.5. When thallium sulfate is replaced with thallium nitrate, the case of monovalent cation accompanied by the monovalent anion, the calibration slopes over the same concentration range are i/nA = 21.49C/mM - 0.75 (correlation coefficient, 0.999 78) and 11.40C/mM - 0.029 (correlation coefficient, 0.999 92), without and with excess supporting electrolyte (0.04 M LiClOk), respectively. The ratio of the slopes is 1.89, in comparison with the theoretical value of 2.00. A similar value of ratio of limiting current in the absence of supportingelectrolyte to diffusional current, il"/ i d = 1.90, was obtained for reduction of Tic1 at a dropping mercury electrode in 1939.12 The comparison of the theoretical and experimental limiting values of ilo/id in solutions without added supporting electrolyte shows that experimentalvalues are slightly lower than theoretically predicted, 1.89 vs 2.0 and 1.43 vs 1.5 for " J O B and TlzSO4, respectively. This is because of some level of ions present in the solution without added supporting electrolyte, under our experimental conditions, 5 pM. If we calculate the theoretical values of il"/id, according to eq 3, or eqs 4 and 5 for the case of "0s and Tl~S04,taking into account the background concentration of 1:l supporting electrolyte of 5 pM (which for 1mM concentration of electroactive cation gives a y value of 0.005), we obtain the calculated values 1.87 and 1.38 versus experimental results 1.89 and 1.43, respectively. We can calculate the diffusion coefficient value from the slope of the calibration plot, taking into account the deviation from the
+
+
Analytical Chemistry, Vol. 67, No. 6,March 15, 1995
1127
2
.-V
I
1
a ~
1
b
//
1
\
-
.+
1
I
0 -4
-3
-2
0
-1
log
1
2
-0 3,7
-a
Figure 2. Dependence of normalized wave heights (wave height in the presence of excess of supporting electrolyte, 1) on concentration of supporting electrolyte ( y = C$&+) for 1 mM TIN03 ( 0 , and ~) 1 mM T l ~ S 0 4( 0 , O ) .Supporting electrolyte: (0,O) LiC104 and (A,IJ) Ca(N03)~.(-) Theoretical plots (from the top) for $1 M and MY, CA; MY, CAz; M2Y, CA; and MzY, CA2.
steady state in the limiting current value described by eq 2, f ( z ) = 1.031. The diffusion coefficient of Tl+ in 0.04 M LiC104obtained from the slope of current versus concentration is 1.97 x m O 3 solution) and 1.96 x cm2s-l (TIfiO, solution). These values are close to the value D = 1.86 x cm2s-l determined for Tl+in 0.1 M KN03.28 The diffusion coefficient depends on ionic strength (aqueous solutions, 25 "C) through the relationz9 D = D o ( l - 0.5115C,"2/2)
(6)
where D and Do are the diffusion coefficients of ion in the presence and in the absence of supporting electrolyte, respectively, and C, is the concentration (in M) of 1:l electrolyte. For 0.04 M LiC104 solution, the ratio of D/Do is 0.95. The diffusion coefficientvalues corrected for the influence of supporting electrolyte,Do, are 2.06 x and 2.07 x cm2 ss1 for TIN03 and TlzS04 solutions, respectively. These values agree very well with the value Do = 2.10 x 10-5 cm2 s-1 for Tl+at idmite dil~tion.~O The diffusion coefficient also depends on the viscosity of solution,
D =kT/6qR
(3
where k is the Boltzmann constant, Tis the temperature, 7 is the absolute viscosity, and R is the hydrodynamic radius of the diffusing particle. However, for the concentrationsof supporting electrolyte we used, the changes in viscosity are negligible, and no changes in diffusion coefficient value were Figure 2 presents plots of normalized wave heights, i l l i d , where il is the wave height for a given y value and i d is the wave height obtained in the solution containing excess supporting electrolyte. It is clear that thallium cation accompanied by a monovalent anion (NO3-) behaves differently from the situation where the anion is divalent (S042-). The corresponding ratios of the wave heights without and with excess supporting electrolyte are close to 2.0 and 1.5, respectively. When the one-to-one (LiC104) supporting electrolyte is replaced by the one-to-two electrolyte (Ca(NOs)Z), the limiting ratio, ilo/id,does not change, but the diffusionalvalue of the wave height is reached at smaller electrolyte concentration (28) Biondi, C.;Bellugi, L. J. Electrounal.Chem. 1970,27, 431-445. (29) Bockris, J. 0.; Reddy, A. IC N. Modern Electrochemistm Plenum: New York, 1970; Vol 1. (30)Heyrovsky, J.; Kuta, J. PnncifilesofPolurogruphy; Academic Press: New York, 1966.
1128 Analytical Chemistry, Vol. 67, No. 6, March 15, 1995
-1.1
-0.9
-1.3
E / V Figure 3. Staircase voltammograms for reduction of 0.9 mM CdS04 at the silver-based mercury film microelectrode. Concentration of added supporting electrolyte, LiCIO4: (a) 0, (b) 0.1, (c) 0.7, (d) 3, and (e) 100 mM.
(value of y ). The solid lines in Figure 2 are the theoretical plots based on eqs 4 and 5. The experimental results agree with theoretical predictions very well. Reduction of Divalent Metal Cation. Typical voltammetric waves for reduction of Cd(II) in solutions of cadmium sulfate with varying concentration of supporting electrolyte are presented in Figure 3. When the concentration of lithium perchlorate is increased from 0 to 100 mM, the wave height decreases to onehalf the value without electrolyte. This agrees with the theory for reduction of divalent cation, accompanied by divalent anion, to uncharged product.718The wave height increases linearly with increase in cadmium sulfate concentration, 0.1 5 C/mM 5 2, which can be described as i/nA = 14.57C/mM - 0.43 (correlation coefficient, 0.999 85), and 7.81C/mM - 0.037 (correlation coefficient, 0.999 95), without and with excess supporting electrolyte (0.05 M LiC104),respectively. The ratio of the two slopes is 1.87, which is close to the theoretical one, 2.00. A similar result has been obtained for reduction of Cu(II) in concentrated solution of CuSO4 with no added supporting electrolyte.31 The ratio of il/& = 1.59 in the absence and in the presence of supporting electrolyte for the reduction of Cd(II) in solutions of CdS04 has been obtained at a mercury drop electrode.lZ The lower value obtained in the polarographic experiment is probably due to the background level of electrolyte or leakage of electrolyte into the solution through the salt bridge. When cadmium sulfate was replaced by cadmium nitrate, the case of divalent cation accompanied by monovalent anion, the dependencies of the wave height versus concentration of cadmium ion were determined as i/nA = 22.5C/mM 0.287 (correlation coefficient, 0.999 83) and 7.95ClmM - 0.1085 (correlation coefficient, 0.999 92), without and with excess supporting electrolyte (0.05 M UC104), respectively. In this case, the ratio of the two slopes is 2.83, close to the theoretical value of 3.00. A similar result has been obtained in anodic stripping experiments at the mercury microelectrode. The ratio of the anodic stripping peak height in the absence of electrolyte to the peak height in presence of supporting electrolyte, ipm/i$, for CdClz and F'b(NO& was close to 3:LZ3The much lower ratio of il/id = 2.20 has been obtained for reduction of PbClz at the mercury drop electrode.lZ The diffusion coefficient of Cd2+ in 0.05 M Ec104 was determined, according to eq 1,from the corresponding slopes as
+
(31) Pillay, B.; N e w " , J. J. Electrochem.SOC.1993,140, 414-420.
3 .
3
..D \
'0 .e
2. \
-
2
. A
1 .
1
I
-4
-3
-2
-1
log
0
1
I
2
-4
-3
a
Figure 4. Dependence of normalized wave heights (wave height in the presence of excess of supporting electrolyte, 1) on concentration of supporting electrolyte (y = C$&+) for 1 mM Cd(NO& ( 0 , ~ ) and 1 mM CdS04 (0,O). Supporting electrolyte: (0,O) LiClO4 and (a,U)Ca(NO&. (-) Theoretical plots (from the top) for $2 M and MY2, CA; MY2, CA2; MY, CA; MY, CA2.
6.86 x (Cd(N03)~solution) and 6.74 x cm2s-l (CdSO4 solution). These values are very close to the value D = 6.90 x cm2 s-l reported for Cd2+in 0.1 M KNO3?* For 0.05 M LiC104solution, according to eq 6, the ratio of diffusion coefficients with and without supporting electrolyte, D/Do, is 0.94. The diffusion coefficient values, Do,corrected for the influence of supporting electrolyte are 7.30 x and 7.17 x cm2 s-l for Cd(NO3)z and CdSO4 solutions, respectively. These values agree very well with the value Do= 7.20 x cm2s-l for Cd2+ at infinite dilution.30 The dependence of the wave height for reduction of Cd2+on the electrolyte ratio, y , is illustrated quantitatively in Figure 4. The experimental data were obtained for various charges of counterion (anion) and ions of supporting electrolyte. The solid lines in Figure 4 are theoretical, calculated according to eqs 4 and 5. The agreement of experimental data with the theoretical prediction is very good for all cases. For the case of Cd(NO3)z in Ca(NO3)z electrolyte, the limiting values are the same as for the one-to-one electrolyte, but the diffusioncontrolled value is reached at lower electrolyte ratio ( y ) , and at each electrolyte ratio the effect of migration is less pronounced. The same phenomenon is observed, mutatis mutandis, for CdSO4 in solutions of LiC104. The il/id ratio does not depend on the concentration of the electroactive metal cation. This is illustrated in Figure 5 for the reduction of lead cation. The dependence of wave height on y is the same for three concentrations of lead nitrate and agrees well with theory for divalent cation accompanied by monovalent anion (solid lime in Figure 5). The wave height increases linearly with increase in lead nitrate concentration, 0.1 5 C/mM I 1.5, which can be described as i/nA = 26.11C/mM - 0.60 (correlation coefficient, 0.999 83) and 9.28ClmM 0.01 (correlation coefficient, 0.999 91), without and with excess supporting electrolyte (0.05 M LiC104), respectively. The ratio of the two slopes is 2.81, which is close to the theoretical value of 3.00. The diffusion coefficient of Pb2+,calculated according to eq 1from the slope of the calibration plot in 0.05 M LCIO4, is 8.01 cm2 s-l. This value is close to the value 8.28 x cm2 s-l obtained in 0.1 M KN03?8 Simultaneous Reduction of Two Cations. Reduction of Hydrogen Ion in the Presence of Thallium Cation. The limiting current for reduction of hydrogen ion in solution without s u p
+
-2
0
-1
log
1
2
a
Figure 5. Dependence of normalized wave heights (wave height in the presence of excess of supporting electrolyte, 1) on concentration of supporting electrolyte (y = C$Qv+)for Pb(N03)~of concentration (A) 0.5, (0)1, and (0)2 mM. Supporting electrolyte, LiC104. (-) Theoretical line (eq 3).
a C
3
i
\
c,
c
a, L L
J
u
-1 -0.3
-0.6
-0.5
-1.2
-1.5
E / V Figure 6. Staircase voltammograms obtained at the silver-based mercury film microelectrode in (a) 0.01 mM HCIO4, no supporting electrolyte; (b) (a) 0.1 mM TIN03; and (c) (b) 10 mM LiC104. E vs SCE.
+
+
porting electrolyte can be increased in the presence of another electroactivecation with a less negative reduction potential. This is illustrated in Figure 6. Curve a presents the reduction wave of 0.01 mM hydrogen ion (HClOJ at the mercury microelectrode in a solution without added supporting electrolyte. After addition of thallium ion "03) at concentration 0.1 mM, there are two well-defined waves for reduction of thallium and hydrogen cations, as shown in curve b. The wave for reduction of hydrogen ion is amplilied by the concurrent reduction of thallium ion. Addition of supporting electrolyte, LiC104, at concentration 10 mM (100 fold excess compared to llNO3) diminishes the heights of both waves, as shown in curve c. The values of limiting currents for both cations are presented in Table 3. The limiting current for reduction of "l+ without supporting electrolyte is twice the current obtained with excess electrolyte. In the presence of 0.01 mM HC104, the limiting current for reduction of Tl+is 1.51 and 1.72 times higher than the diffusional current for 0.1 and 0.5 mM Tl+, respectively. This agrees with the theory, according to eq 3, since HC104 in this potential range serves as an unreactive, univalent supporting electrolyte. The predicted values of the ratio il/id for y = 0.1 and 0.02 are 1.54 and 1.75, respectively. The reduction wave of hydrogen ion obeys the theory when Tl+is absent; iIo/id is close to the predicted value of 2.00, as shown in Table 3. In the presence of thallium ion, this wave is 2.67 and Analytical Chemistry, Vol. 67,No. 6,March 15, 1995
1129
~~~~~~
Table 3. Llmitlng Currents for Reduction of TI+ and H+
cation
CJmM
ida/nA
ilob/nA
ilc/nA
TI+
0.1 0.01 0.5 0.01
1.10 0.70 5.25 0.71
2.18 1.38 10.40 1.40
1.66 1.87d 9.03 2.72e
H+d
TI+ H+e
1.51 2.67 1.72 3.83
~
Table 4. Charges for Reduction of TI+ and H+ and Oxidation of TI from Mercury Fllm in Solutions wlthout and with Supporting Electrolytea
without
+
Q(I+ H+)b/nC
Diffusion-limited current in 10 mM LiClOI. Limitin current without other electrolyte. Limiting current with both #No3 and HClOl present. 0.1 mM flNO3. e 0.5 mM qNO3.
Q(I+)c/nC Q(H+)d/nC
with
ERI/EO
Em/Eo
E~ilEo
Em/Eo
196.4 135.4 61.0
95.4
99.1 65.2 33.9
64.8
Double pulse chronocoulometry,E R = ~ -1.65 V, Em = -1.1 V, EO = -0.3 V (vs SCE); t~ = 50 s, to = 100 s. From the reduction charge. From the oxidation charge. Q(I+ H+) - &(Tl+). (I
+
\
a,
m
J
-50
zoo}
B
i
I 1S I 000t
- 50
50
1 0 0
1 5 0
1
Time / s Figure 7. Double pulse chronocoulograms obtained at the silverbased mercury film microelectrode in solution with no supporting electrolyte (A) and with 10 mM LiClO4 (B). (0)0.01 mM HC104; (-,A) 0.01 mM HC104,O.l mM TINO3. tR = 50 S, ERI= (O,-) -1.65 V, ERZ = (A) -1.1 V; = 100 s, Eo = -0.3 V (VS SCE).
3.83 times higher (for 0.1 and 0.5 mM Tl+, respectively) than the diffusioncontrolled wave. The sum of limiting currents of reduction of thallium and hydrogen cations in the solution without supporting electrolyte is 1.96 and 1.97 times higher (for 0.1 and 0.5 mM Ti+,respectively) than the sum of the diffusioncontrolled currents. One may hypothesize that the reduction of hydrogen ion increases the flux of thallium ion and thus contributes to the increase in the height of the reduction wave for hydrogen. A similar situation has been observed for reduction of potassium cation in the presence of thallium cation at the dropping mercury electrode in solution without supporting electrolyte.12 This phenomenon was called “current exaltation” and was explained in terms of increased transport of both thallium and potassium cations. To check this, the amount of thallium reduced into the mercury phase in the presence of hydrogen ion was determined by double pulse chronocoulometry experiments. Figure 7 presents double potential pulse chronocoulograms obtained in the solution of two cations, 0.01 mM H+ (from HClOk) and 0.1 mM TI+ (from TINOS) with no electrolyte present (A) and with 10 mM LiC104 as supporting electrolyte (E%). The first potential pulse was the reduction pulse, and two different potentials were applied as reduction potentials, the potential on the plateau of the reduction wave of thallium cation (-1.1 V) and the potential on the plateau of the reduction wave of hydrogen ion (-1.65 V). The second potential pulse was the oxidation pulse, and the potential of -0.3 V (enough positive for the oxidation of thallium from the mercury film)was applied. The values of the charges 1130 Analytical Chemistry, Vol. 67, No. 6, March 15, 1995
for reduction and oxidation of both cations are presented in Table 4. If the reduction process takes place at the potential of the plateau of the wave of thallium ion reduction, the ratio of the charge of reduction of thallium ion in the solution without supporting electrolyte (only in the presence of hydrogen ion) to the charge in the presence of excess supporting electrolyte is 1.47. This value agrees very well with the ratio of il/id = 1.51 obtained for the reduction of thallium cation under the same conditions. If the reduction step takes place at the potential of the plateau of the reduction wave of hydrogen ion, the charge of the reduction of both cations, Tl+ and H+, in the solution with no supporting electrolyte is 1.98 times higher than that in the solution with excess supporting electrolyte. This agrees very well with the value of il/id = 1.96 obtained from voltammetric experiments under the same conditions. Thus the charge ratios on the forward steps agree well with the corresponding current ratios. In contrast, the charge ratios on the reverse steps are quite different. The charge required to oxidize thallium metal from the amalgam is 1.42 times greater when it is deposited at the potential of hydrogen ion reduction compared to the deposition at the potential of thallium ion reduction. By inference, the limiting current for reduction of thallium ion is 1.42 times greater on the limiting current plateau for reduction of thallium and hydrogen ions than on the plateau for reduction of thallium ion only. Additionally, the charge of oxidation of thallium from mercury after reduction at potentials on the hydrogen ion plateau without electrolyte is twice the charge obtained in the solution with excess supporting electrolyte. Thus, at the potential of the plateau for reduction of hydrogen ion, thallium cation behaves as in a solution without any other cations. This shows clearly that the increased height of the reduction wave of hydrogen cation in the limiting current region after addition of thallium cation is due to the additional transport of thallium cations. Consider the limiting case of reduction of M+ and N+ in a solution of MY and NY,for which the diffusion coefficients of M+ and N+ are the same. Clearly this problem is formally equivalent to that of reduction of a single cation of the same total concentration. That is, the limiting current on the second plateau should behave according to eqs 4 and 5. In the present case, the cations are H+ and Ti+,so the diffusion coefficients are quite different. A simple treatment based on the approach leading to eq 3 gives the result for unequal diffusion coefficients of (&iw/idM
f
Ckf&/idN
= 2(cL f
ci)
(8)
where CMand CNare the bulk concentrations of Tl+ and H+, respectively. As this relation must be valid for arbitrw choice
~~
Table 5. Limiting Currents for Reduction of W2+and H+
cation
CJmM
ida/nA
ilob/nA
ilc/nA
il/id
Pb2+
0.1
H+
0.01
1.11 0.73
3.26 1.41
2.49 2.23
2.24 3.05
Diffusion-limited current in 10 mM LiC104. Limitin current without other electrolyte. Limiting current with both #NOS and HClO4 present.
Table 6. Charges for Reduction of Pb2+and H+ and Oxidation of Pb from Mercury Film In Solutions without and with Supporting Electrolyte.
without Q(Pb2+
+ H+)b/nC
Q (Pb2+)
