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Cu+ electrode reaction at gold in concentrated aqueous Ca(ClO4)2 solutions
175
J. Electroanal. Chem., 292 (1990) 175-185 Elsevier Sequoia S.A., Lausanne
Kinetics ,of the Cu2+/Cu+ electrode reaction at gold in concentrated aqueous Ca( ClO,) 2 solutions Boiena
Stgpnik-hviptek
Department
of Chemistry, Pedagogical and Agricultural University, 08-110 Siedlce (Poland)
Jan Malyszko
*
Institute of Chemistry,
Pedagogical
University, 25-020 Kielce (Poland)
(Received 20 April 1990)
ABSTRACT The kinetics of the electrochemical reaction in the Cu(II)/Cu(I) system at gold have been investigated in highly concentrated aqueous Ca(ClO.,), solutions by means of the rotating disc electrode technique. On the basis of the kinetic data, the orders of the cathodic and anodic reactions with respect to water were determined, and a mechanism of the reaction is postulated. The rate constants obtained are also discussed in terms of Marcus’s theory.
INTRODUCTION
The mechanism of the electrochemical Cu*++ 2 e-*
deposition and dissolution of copper
Cu
(1)
at solid electrodes in aqueous non-completing solutions has been the object of numerous investigations which were reviewed by Bertocci and Turner [l]. It has been found by Mattson and Bockris [2] that the process considered occurs in the one-electron charge transfer steps: Cu*++ e-+ Cu++ e-*
Cu+
(2)
Cu
(3)
with the formation of soluble monovalent copper as an unstable intermediate. This mechanism was then confirmed by other workers, mainly using the rotating ring-disc electrode (RRDE) technique [3-51. Reaction (3) itself was also considered to
l
To whom correspondence should be addressed.
0022-0728/90/$03.50
0 1990 - Elsevier Sequoia S.A.
176
proceed via two steps [6-91. However, a different mechanism of process (1) was suggested by Kozin and co-workers [lO,ll]. Only a few publications, however, exist in the media mentioned concerning the kinetics of electron transfer step (2). It should be noted that the data published hitherto were obtained indirectly, based either on the analysis of Tafel curves [12-141 or on impedance data [15] for the overall reaction (1) occurring at the copper electrode. The aim of the present work was to determine the kinetic parameters of the Cu*+/Cu+ system in concentrated Ca(ClO,), solutions. It was known from our earlier investigation 1161 that Cu + ions are relatively stable with respect to the disproportionation reaction in such a medium. In particular, we were interested in the role of water as a solvent in this electrode reaction. Moreover, the investigations in highly concentrated electrolyte solutions seemed to us to be important because they fill the gap between the dilute aqueous solutions and molten salts. In previous work 1171 we have studied the electroreduction of Cu2+ on a foreign surface (gold) from aqueous perchlorate solutions using the RRDE technique. We have demonstrated that Cu+ ions were the only product formed under stationary conditions at low cathodic current densities. The deposition of metallic copper began after the equilibrium concentration of Cuf on the disc surface was exceeded, with respect to the disproportionation: 2 cu++
cu2++
cu
(4)
An analogous mechanism for the copper(I1) reduction was found at platinum electrodes in water + DMSO [18] and water + DMF mixtures 1191. This finding enabled us to determine the kinetics of the Cu2+/Cu+ system directly by the use of a rotating disc electrode (RDE). EXPERIMENTAL
Copper(I1) perchlorate and calcium perchlorate were obtained from the corresponding carbonates (POCh, p.a.) by neutralizing them with 60% HClO, (Merck, p.a.). The products obtained were then recrystallized from triply distilled water. Stock solutions of Ca(ClO,), were analysed by complexometric titration with EDTA. The solutions under study were acidified with HClO, (p.a., Merck). All solutions were deoxygenated by bubbling with pure argon for at least 30 min prior to the experiments. During measurements, this gas was passed over the solution. A home-made gold RDE (99.99% purity) with a geometric area of 0.196 cm2 was employed in voltammetric measurements. The electrode surface was polished mechanically to a mirror finish by a standard metallographic technique. After the mechanical pretreatment, it was degreased with acetone and rinsed with triply distilled water. Before each series of experiments, the disc was introduced into a solution containing 0.2 mol dme3 HClO,, and subsequently oxidized at + 1.6 V for 5 min and next reduced at -0.3 V, also for 5 min. Finally, the electrode was cycled several times between + 1.6 and - 0.3 V. The RDE was driven with a synchronous
177
motor supplied with a sinusoidal voltage by a Zopan PO 26 power generator. The rotation frequency was controlled by means of a Meratronic digital frequency meter. A three-compartment cell constructed of Pyrex glass contained the RDE in the main compartment. A spiral-shaped Pt counter electrode was placed in a compartment separated by a fritted glass disc. A saturated calomel electrode with NaCl solution, SCE(NaCl), was used as the reference electrode. This electrode was connected to the electrolytic cell through an intermediate vessel filled with the solution studied. RDE voltammetric experiments were done with a measuring system consisting of an EP 20 fast-rise potentiostat in combination with an EG 20 linear programmer, both produced by Elpan Laboratory Instruments. Voltammograms were recorded on a Riken Denshi F-3C X-Y recorder. Coulometric measurements were carried out with a Radelkis OH-404 coulometer. All experiments were carried out at 25 + 0.2OC. RESULTS
A series of experiments was made with solutions containing each 0.1 mol dmp3 Cu(ClO,), and 0.1 mol dmv3 HClO, and Ca(ClO,), at concentrations ranging from 0.9 to 3.9 mol dmW3. The relatively high concentration of copper(I1) salt in the solutions was needed to enhance the precision of the disc current measurements within the region of reaction (2). The solutions were acidified in order to prevent hydrolysis of Cu+ ions. The rate constants of the cathodic and anodic reactions in the Cu’+/Cu+ system were evaluated with the aid of different methods. Cathodic reduction of copper In an earlier investigation [17], we found that the voltammetric curves for the cathodic reduction of Cu2+ m . aqueous perchlorate solutions at the gold RDE are split into two waves. The first of them, being relatively small, corresponds to the generation of Cu + ions with 100% current efficiency, according to eqn. (2), as we proved using the RRDE technique. Similar splitting was also observed by Nekrasov and Berezina [3] as well as by Bruckenstein and Miller [20] in the case of copper(I1) reduction at the Pt electrode in acidic sulphate medium. The rate constants for the cathodic reaction Cu2++ e--, Cu+ were determined using a modified version of the method of Jahn and Vielstich [21], details of which have been described elsewhere [19,22]. The measurements were carried out within the wave considered. The disc current, I,, was measured point-by-point at a fixed potential and various rotation frequencies. The results of the measurements were plotted in coordinates l/1, vs. l/w ‘I2 in order to determine the activation currents by extrapolating to infinite angular velocity, w -+ 00. An example of the procedure employed is given in Fig. 1.
178
150
140
120
100
0.05
0
0.10
0.15 W-lfz/(s
rad-‘)1/2
Fig. 1. Plots of the reciprocal disk current, I;‘, against the reciprocal square root of the angular velocity, 0 -I/* 7 for the reduction of Cu*+ to Cu+ at an Au disc in a solution containing 0.1 mol dmm3 Cu(ClO,),, 1.9 mol dme3 Ca(ClO,), and 0.1 mol dmv3 HClO,. The numbers at the lines denote the disc potential in mV vs. SCE(NaCI).
Anodic oxidation of copper(I) In order to investigate the anodic reaction, Cu+ ions were produced in the solution by previous equilibration with a freshly prepared Cu deposit on a copper rod. After equilibrium of the reproportionation reaction Cu2++ Cu s 2 Cu+ had been achieved, the anodic voltammetric curves on the RDE were recorded by scanning the potential in the negative direction at a slow sweep rate (5 mV SK’) and constant rotation frequency. Finally, the copper rod was removed from the solution, and Cu+ ions were determined by coulometric titration with silver(I). Details are described elsewhere [16,23]. The concentrations of copper(I) in the solutions are given in Table 1. As reported in an earlier paper [23], distinct anodic waves with well-defined limiting currents were obtained. In order to evaluate the potential dependent rate constants, k,,, the voltammograms were analysed by applying the following relation derived by one of us [24]: I D,L nFAcr4 k,,
=
ZD.L -ID I,
ID,,
-
-I,
I,
In this equation, I,,, is the limiting disc current, n is the number of electrons, F is the Faraday constant and c,~ is the bulk concentration of the reduced form of the reactant. 1, denotes the hypothetical current at a reversible potential.
179 TABLE
1
Kinetic parameters of the Cu2+/Cu+ electrode reaction at gold in aqueous solutions each containing 0.1 mol dm- 3 NaClO, and 0.1 mol drne3 HClO,. (a) from anodic and (c) cathodic measurements. Concentration of Cu+ (in second column) is related to the anodic measurements Concentration of Ca(ClO,),/ mol dmm3
lo4 Concentration of Cu+/mol dmm3
0.9 1.4 1.9 2.4 2.9 3.4 3.9
2.2 2.7 3.3 4.4 5.5 8.1 11.0
E o ‘/mV
104k “/cm
VS.
SCE(NaC1) -70 -45 -16 23 54 103 154
s-’
(a)
(c)
2.7 2.3 3.9 6.4 3.4 3.0 6.1
2.6 3.2 3.3 3.3 2.2 3.1
0.56 0.54 0.51 0.47 0.51 0.53 0.46
0.38 0.40 0.43 0.44 0.51 0.36
In the case of a totally irreversible electrode process, eqn. (5) can be simplified to kx=&$
red
I
D,L
1, _I
(6)
D
Figure 2 shows a semi-logarithmic
analysis of some voltammograms.
0.1 0
100
200
300
400 E/mV
Fig. 2. Semi-logarithmic analysis of RDE oxidation curves in the Cu2+/Cu+ system for solutions containing 0.1 mol dmm3 Cu(ClO,), and 0.1 mol dme3 HClO, with Ca(ClO,), at different concentrations: (a) 0.9; (b) 1.9; (c) 2.9; (d) 3.9 mol dm-‘. The concentrations of Cu+ ions are given in Table 1. Rotation frequency 60 Hz.
180
10-2 7 In
E : ;
10-3
0 0 z Y 10-4
10-5
0
200
400 E/mV
electrode reaction. The lines are Fig. 3. Anodic (0) and cathodic (0) Tafel plots for the Cu2*/Cu+ labelled with the molar concentration of Ca(ClO,),. The bars indicate the formal potentials.
The potential dependence of the anodic and cathodic rate constants (in a logarithmic scale) is presented in Fig. 3 for various concentrations of the background electrolyte. It should be stressed that the Tafel curves obtained manifest an unconventional shape since the cathodic data correspond to measurements performed in the underpotential region. Extrapolation of the lines of Fig. 3 to the formal potentials of the Cu’+/Cu+ couple, E O’, furnished the formal rate constants, k”. The anodic, (T~, and cathodic transfer coefficients, (Ye, were calculated from the slopes of the appropriate lines. The kinetic parameters determined for the system investigated are collected in Table 1. Inspection of the kinetic parameters contained in Table 1 shows that the values of k” obtained from anodic and cathodic measurements differ, especially in the case of higher background electrolyte concentration. The discrepancy between these two sets of data may be explained partly as due to the long extrapolation of the experimental values of the constants k,, and k,, to the formal potentials. On the other hand, it should be noted that two different procedures were employed to determine the anodic and cathodic reaction rates. DISCUSSION
Only a small change in the formal rate constant of the Cu2+/Cu+ system with increasing concentration of the background electrolyte is observed. Similar be-
181
haviour was reported in the literature for other redox systems, e.g. Ti02+/Ti3+ [25], Cr3+/Cr2+ [26,27] and Eu3+/Eu2+ [28] in concentrated perchlorate solutions at the mercury electrode. The formal rate constants presented in this paper are generally in agreement with that obtained at a Pt electrode for 1 mol dmp3 NaClO, solution [18]. On the other hand, the k o values determined by us are over two orders of magnitude higher than that reported by Reid and David [15] for a metallic copper electrode in sulphuric acid solution. However, the former value was referred to the rest potential in the system studied. As follows from Table 1, the transfer coefficients are also virtually independent of the supporting electrolyte concentration. The sum (r, + OL,is close to 1, except for the solution of 3.9 mol dme3 Ca(ClO,),. We should stress that the kinetic parameters given in this paper are apparent values which may be influenced by the potential difference across the diffuse double layer, $J~, (Frumkin correction). Unfortunately, true values could not be calculated since the +2 potentials are not available for the electrolyte employed at the Au electrode. However, it is very probable that in such concentrated electrolytes the values of the e2 potential are rather low and their changes are negligible. It is known that Ca(ClO,), acts as a strong dehydrating reagent, and a gradual increase of its concentration causes a lowering of the water activity. Taking this into consideration, the orders of the electrode reaction studied with respect to water we determined from an analysis of rate constants on the water activity. The values of the water activity were interpolated from literature data [29]. We assumed that the contribution of Cu(ClO,), in lowering the water activity is approximately the same as that of Ca(ClO,),. The influence of HClO, was neglected. Figure 4 shows plots of the cathodic and anodic rate constants at a fixed potential against the logarithm of the water activity, a:, expressed in the molar concentration scale. The plots obtained are linear in a limited region, i.e. at a: + 1. The deviation from linearity observed for highly concentrated Ca(ClO,), solutions may be explained to some extent by ion-pair formation; however, the lack of appropriate data makes any quantitative estimations impossible. For a: + 1, the order of the cathodic reaction P= 0
log Ld/a
log &),
(7)
was found to be - 2.7. In a similar way, p determined for the anodic oxidation of copper(I) was 3.9. Thus one can accept that electrode reaction (2) is connected indirectly with the exchange of ca. three water molecules. This interpretation with respect to hydration is valid under the assumption that the activity of ions in the sense of the Debye and Htickel theory does not change significantly with a decrease in the water activity, and that the changes in the liquid junction potential are negligible, at least at relatively low electrolyte concentration. The latter assumption may be supported by the results of Andreu et al. [30] who estimated changes in the liquid junction potential originating from varying the concentration of NaClO, within the range 0.2-7 mol dmp3, to be less than 10 mV.
182
10-G
I
1
I
I
I
I
0.1
I,,
J 1
c
a, Fig. 4. Dependence of the anodic (0) and cathodic (0) rate constant at constant potential, E = 200 mV vs. SCE(NaCI), on the water activity expressed in a molar concentration scale.
Taking into account the secondary hydration numbers of Cu*+ and Cu+, h cu(II) = 12 and hcucIj = 5 [16], respectively, the following mechanism, at least for moderately concentrated Ca(ClO,),, could be suggested: Cu(H,O);+
Cu(H2O)::
=
Cu(H,O)i+
+ e-+
+ 4 H,O
Cu(H,O);
+ 3 H,O
(fast)
(8) (9)
According to the theory of adiabatic electron transfer reactions at an electrode [31-331, the standard (formal) rate constant is related to the overall Gibbs energy barrier, AG * , by k” =A
exp(-AG#/RT)
(10)
The pre-exponential term A includes the transmission coefficient K, generally taken as equal to 1, and a frequency factor Z which is usually approximated by the kinetic expression for collisions of particles of mass m with the wall. Following this A = K( RT/2mN,m)“*
01)
where NA is Avogadro’s constant. From the point of view of the theory considered, the electrochemical Gibbs energy of activation is the sum of two terms: the work of solvent reorganization, X0, and the inner reorganization energy of the reacting particle, Xi: AGf=X/4=(h,+Xi)/4
(12)
183
hi depends on changes in the bond lengths and the bond angles. Equation (12) eventually has to be completed by work terms for the transport of the reactants to the reaction site. h, can easily be calculated on the basis of an extension of the Born model if the radius a of the reacting particle as well as the dielectric constants, optical E, and static es, are known. For a one-electron electrode process, X, is given as follows: h, = N,ei/8
ae,(l/a
- 1/2d)(l/e,
- l/c,)
(13)
where e, is the electron charge, ~a is the permittivity of vacuum, a is the radius of the reacting ion, while d is the distance from the ion to the electrode surface. The change in A, with increasing background electrolyte concentration is obvious, since cc0 and cS will vary. In our calculations, following the argument of Hale [32], the 1/2d term in eqn. (13) was neglected. One would expect that the reactant is located near the outer Helmholz plane and, consequently, the screening of the reactant by ions of the background electrolyte against its interaction with the image in the electrode should be effective. In the calculation of h, from eqn. (13) we used a = rcUoIj + 2r,, with the radius of the water molecule, r,, equal to 0.145 nm [34] and rcu~,l~= 0.079 nm [35]. Due to a paucity of data on the dielectric constants for concentrated Ca(ClO,), solutions, appropriate values for NaClO, were taken from the literature [36]. Here, we assumed that the values of z, and e, for Ca(ClO,), solutions approximate those for NaClO, solutions of twice as great molar concentration. This assumption may be supported indirectly by comparing the data on water activity in solutions of the both salts considered. From the standard rate constants, AG # and h values were calculated. Consequently, Xi was estimated from the difference X - X,. The number of coordinated water molecules in the first hydration sphere was assumed to be six, analogously to other divalent transition metal cations of the first row [37]. The results of calculations are listed in Table 2. This table includes also the data for the same reaction at a Pt electrode in 1 mol dm- 3 NaClO, solution estimated from our earlier investigation [18]. As follows from Table 2, the value of X, decreases markedly when going from 1 to 2 mol dmp3 Ca(ClO,), solution. On the other hand, the reorganization energy of
TABLE 2 Polarity parameter of solutions y = l/c, - l/r,, formal rate constants, activation and reorganization energies of the Cu*+/Cu+ reaction at platinum and gold electrodes Background electrolyte
Y
104k “/cm s-’
AG*/kJ
1 mol dmm3 NaClO, 1 mol drnm3 Ca(ClO,), 2 mol dme3 Ca(ClO,),
0.158 0.102 0.075
8.8 (Pt) = 2.6 (Au) 3.6 (Au)
38.4 41.4 40.6
a From ref. 18.
mol-’
X,/kJ 49 32 23
mol-’
A, /kJ mol-’ 105 134 139
184
the outer sphere is small compared with that of the inner sphere. Moreover, the Xi value does not change significantly under the same conditions. This leads to the conclusion that the relatively slow rate of the Cu*+/Cu+ reaction at a gold electrode may be explained in terms of changes occurring in the inner sphere. ACKNOWLEDGEMENTS
The authors thank Prof. Z. Galus of Warsaw University for helpful discussions during the work and kind advice for the preparation of the manuscript. Support of this work by a grant from Central Research Project CPBP 01.15 is acknowledged. REFERENCES
1 U. Bertocci and D.R. Turner in A.J. Bard (Ed.), Encyclopedia of Electrochemistry of the Elements, Vol. 2, Marcel Dekker, New York, 1974, p. 1. 2 E. Mattson and J. Q’M. Bockris, Trans. Faraday Sot., 55 (1959) 1586. 3 L.N. Nekrasov and N.P. Berezina, DoM. Akad. Nauk SSSR, 142 (1962) 855. 4 J. Jacq, B. Cavalier and 0. Bloch, Electrochim. Acta, 13 (1968) 1119. 5 L. Kiss and J. Farkas, Acta Chim. Acad. Sci. Hung., 66 (1970) 395. 6 G.W. TindaII and S. Bruckenstein, Anal. Chem., 40 (1968) 1051. 7 G.W. Tindall and S. Bruckenstein, Anal. Chem., 40 (1968) 1637. 8 Q.J.M. Slaiman and W.J. Lorenz, Electrochim. Acta, 19 (1974) 791. 9 Z.D. Stankovic, Electrochim. Acta, 28 (1983) 109. 10 L.F. Kozin, S.N. Nagibin and K.K. Lepesov, Ukr. Khim. Zh., 49 (1983) 1069. 11 L.F. Kozin and S.N. Nagibin, Ukr. Khim. Zh., 50 (1984) 854. 12 T. Hurlen, G. Ottesen and A. Staurset, Electrochim. Acta, 19 (1978) 39. 13 W. DaIla Barba and T. Hurlen, J. Electroanal. Chem., 91 (1978) 359. 14 B.D. Kumikov and T. Hurlen, J. Electroanal. Chem., 91 (1978) 367. 15 J.D. Reid and A.P. David, J. Electrochem. Sot., 134 (1987) 1390. 16 J. MaIyszko and L. Duda, Monatsh. Chem., 106 (1975) 633. 17 J. Malyszko and B. Stepnik-Swiatek, Pol. J. Chem., 55 (1981) 2535. 18 J. Malyszko and M. Scendo, J. Electroanal. Chem., 250 (1988) 61. 19 J. MaIyszko and M. Scendo, J. EIectroanaI. Chem., 269 (1989) 113. 20 S. Bruckenstein and B. Miller. Act. Chem. Res., 10 (177) 54. 21 D. Jahn and W. Vielstich, J. Electrochem. Sot., 109 (1962) 849. 22 J. Malyszko and D. Gierulska, Monatsh. Chem., 115 (1984) 1401. 23 B. Stepnik-Swiatek and J. Malyszko, Monatsh. Chem., 113 (1982) 715. 24 J. Malyszko, Chimia, 29 (1975) 166. 25 E. Malyszko and Z. Galus, Rocz. Chem., 46 (1972) 2291. 26 M. Zielinska-Ignaciuk and 2. Galus, J. Electroanal. Chem., 50 (1974) 41. 27 R. Andreu, M. Rueda, D. Gonzalez-Arjona and F. Sanchez, J. Electroanal. Chem., 175 (1984) 251. 28 J.J. Borodzinski, T. Jedral, P.K. Wrona and Z. Galus, Pol. J. Chem., 52 (1978) 2337. 29 I.E. Voznesenskaya and G.I. Mikulin in G.I. Mikulin (Ed.), Voprosy Fizicheskoi Khimii Rastvorov Elektrolitov, Khimiya, Leningrad, 1968, p. 361 (in Russian). 30 R. Andreu, M. Sluyters-Rehbach, A.G. Remijnse and J.H. Sluyters, J. Electroanal. Chem., 134 (1982) 101. 31 R.A. Marcus, Electrochim. Acta, 13 (1968) 995. 32 J.M. Hale in N.S. Hush (Ed.), Reactions of Molecules at Electrodes, Wiley-Interscience, New York, 1971, p. 229.
185 33 R.R. Dogonadze and A.M. Kuznetsov, Itogi Nauki, Elektrokhimiya 1967, VINITI, Moscow, 1969, p. 5 (in Russian). 34 H. Ekzanowska, Z. Galus and Z. Borkowska, J. Electroanal. Chem., 157 (1983) 251. 35 G.A. Krestov, Termodinamika Ionnikh Protsessov v Rastvorakh, Khimiya, Leningrad, 1984, p. 13 (in Russian). 36 H. Behret, F. Schmithals and J. Barthel, Z. Phys. Chem. N.F., 96 (1975) 73. 37 J. Burgess, Metal Ions in Solution, Ellis Hot-wood, Chichester, 1978, Ch. 5.3.5.
J. Electroanal. Chem., 292 (1990) 175-185 Elsevier Sequoia S.A., Lausanne
Kinetics ,of the Cu2+/Cu+ electrode reaction at gold in concentrated aqueous Ca( ClO,) 2 solutions Boiena
Stgpnik-hviptek
Department
of Chemistry, Pedagogical and Agricultural University, 08-110 Siedlce (Poland)
Jan Malyszko
*
Institute of Chemistry,
Pedagogical
University, 25-020 Kielce (Poland)
(Received 20 April 1990)
ABSTRACT The kinetics of the electrochemical reaction in the Cu(II)/Cu(I) system at gold have been investigated in highly concentrated aqueous Ca(ClO.,), solutions by means of the rotating disc electrode technique. On the basis of the kinetic data, the orders of the cathodic and anodic reactions with respect to water were determined, and a mechanism of the reaction is postulated. The rate constants obtained are also discussed in terms of Marcus’s theory.
INTRODUCTION
The mechanism of the electrochemical Cu*++ 2 e-*
deposition and dissolution of copper
Cu
(1)
at solid electrodes in aqueous non-completing solutions has been the object of numerous investigations which were reviewed by Bertocci and Turner [l]. It has been found by Mattson and Bockris [2] that the process considered occurs in the one-electron charge transfer steps: Cu*++ e-+ Cu++ e-*
Cu+
(2)
Cu
(3)
with the formation of soluble monovalent copper as an unstable intermediate. This mechanism was then confirmed by other workers, mainly using the rotating ring-disc electrode (RRDE) technique [3-51. Reaction (3) itself was also considered to
l
To whom correspondence should be addressed.
0022-0728/90/$03.50
0 1990 - Elsevier Sequoia S.A.
176
proceed via two steps [6-91. However, a different mechanism of process (1) was suggested by Kozin and co-workers [lO,ll]. Only a few publications, however, exist in the media mentioned concerning the kinetics of electron transfer step (2). It should be noted that the data published hitherto were obtained indirectly, based either on the analysis of Tafel curves [12-141 or on impedance data [15] for the overall reaction (1) occurring at the copper electrode. The aim of the present work was to determine the kinetic parameters of the Cu*+/Cu+ system in concentrated Ca(ClO,), solutions. It was known from our earlier investigation 1161 that Cu + ions are relatively stable with respect to the disproportionation reaction in such a medium. In particular, we were interested in the role of water as a solvent in this electrode reaction. Moreover, the investigations in highly concentrated electrolyte solutions seemed to us to be important because they fill the gap between the dilute aqueous solutions and molten salts. In previous work 1171 we have studied the electroreduction of Cu2+ on a foreign surface (gold) from aqueous perchlorate solutions using the RRDE technique. We have demonstrated that Cu+ ions were the only product formed under stationary conditions at low cathodic current densities. The deposition of metallic copper began after the equilibrium concentration of Cuf on the disc surface was exceeded, with respect to the disproportionation: 2 cu++
cu2++
cu
(4)
An analogous mechanism for the copper(I1) reduction was found at platinum electrodes in water + DMSO [18] and water + DMF mixtures 1191. This finding enabled us to determine the kinetics of the Cu2+/Cu+ system directly by the use of a rotating disc electrode (RDE). EXPERIMENTAL
Copper(I1) perchlorate and calcium perchlorate were obtained from the corresponding carbonates (POCh, p.a.) by neutralizing them with 60% HClO, (Merck, p.a.). The products obtained were then recrystallized from triply distilled water. Stock solutions of Ca(ClO,), were analysed by complexometric titration with EDTA. The solutions under study were acidified with HClO, (p.a., Merck). All solutions were deoxygenated by bubbling with pure argon for at least 30 min prior to the experiments. During measurements, this gas was passed over the solution. A home-made gold RDE (99.99% purity) with a geometric area of 0.196 cm2 was employed in voltammetric measurements. The electrode surface was polished mechanically to a mirror finish by a standard metallographic technique. After the mechanical pretreatment, it was degreased with acetone and rinsed with triply distilled water. Before each series of experiments, the disc was introduced into a solution containing 0.2 mol dme3 HClO,, and subsequently oxidized at + 1.6 V for 5 min and next reduced at -0.3 V, also for 5 min. Finally, the electrode was cycled several times between + 1.6 and - 0.3 V. The RDE was driven with a synchronous
177
motor supplied with a sinusoidal voltage by a Zopan PO 26 power generator. The rotation frequency was controlled by means of a Meratronic digital frequency meter. A three-compartment cell constructed of Pyrex glass contained the RDE in the main compartment. A spiral-shaped Pt counter electrode was placed in a compartment separated by a fritted glass disc. A saturated calomel electrode with NaCl solution, SCE(NaCl), was used as the reference electrode. This electrode was connected to the electrolytic cell through an intermediate vessel filled with the solution studied. RDE voltammetric experiments were done with a measuring system consisting of an EP 20 fast-rise potentiostat in combination with an EG 20 linear programmer, both produced by Elpan Laboratory Instruments. Voltammograms were recorded on a Riken Denshi F-3C X-Y recorder. Coulometric measurements were carried out with a Radelkis OH-404 coulometer. All experiments were carried out at 25 + 0.2OC. RESULTS
A series of experiments was made with solutions containing each 0.1 mol dmp3 Cu(ClO,), and 0.1 mol dmv3 HClO, and Ca(ClO,), at concentrations ranging from 0.9 to 3.9 mol dmW3. The relatively high concentration of copper(I1) salt in the solutions was needed to enhance the precision of the disc current measurements within the region of reaction (2). The solutions were acidified in order to prevent hydrolysis of Cu+ ions. The rate constants of the cathodic and anodic reactions in the Cu’+/Cu+ system were evaluated with the aid of different methods. Cathodic reduction of copper In an earlier investigation [17], we found that the voltammetric curves for the cathodic reduction of Cu2+ m . aqueous perchlorate solutions at the gold RDE are split into two waves. The first of them, being relatively small, corresponds to the generation of Cu + ions with 100% current efficiency, according to eqn. (2), as we proved using the RRDE technique. Similar splitting was also observed by Nekrasov and Berezina [3] as well as by Bruckenstein and Miller [20] in the case of copper(I1) reduction at the Pt electrode in acidic sulphate medium. The rate constants for the cathodic reaction Cu2++ e--, Cu+ were determined using a modified version of the method of Jahn and Vielstich [21], details of which have been described elsewhere [19,22]. The measurements were carried out within the wave considered. The disc current, I,, was measured point-by-point at a fixed potential and various rotation frequencies. The results of the measurements were plotted in coordinates l/1, vs. l/w ‘I2 in order to determine the activation currents by extrapolating to infinite angular velocity, w -+ 00. An example of the procedure employed is given in Fig. 1.
178
150
140
120
100
0.05
0
0.10
0.15 W-lfz/(s
rad-‘)1/2
Fig. 1. Plots of the reciprocal disk current, I;‘, against the reciprocal square root of the angular velocity, 0 -I/* 7 for the reduction of Cu*+ to Cu+ at an Au disc in a solution containing 0.1 mol dmm3 Cu(ClO,),, 1.9 mol dme3 Ca(ClO,), and 0.1 mol dmv3 HClO,. The numbers at the lines denote the disc potential in mV vs. SCE(NaCI).
Anodic oxidation of copper(I) In order to investigate the anodic reaction, Cu+ ions were produced in the solution by previous equilibration with a freshly prepared Cu deposit on a copper rod. After equilibrium of the reproportionation reaction Cu2++ Cu s 2 Cu+ had been achieved, the anodic voltammetric curves on the RDE were recorded by scanning the potential in the negative direction at a slow sweep rate (5 mV SK’) and constant rotation frequency. Finally, the copper rod was removed from the solution, and Cu+ ions were determined by coulometric titration with silver(I). Details are described elsewhere [16,23]. The concentrations of copper(I) in the solutions are given in Table 1. As reported in an earlier paper [23], distinct anodic waves with well-defined limiting currents were obtained. In order to evaluate the potential dependent rate constants, k,,, the voltammograms were analysed by applying the following relation derived by one of us [24]: I D,L nFAcr4 k,,
=
ZD.L -ID I,
ID,,
-
-I,
I,
In this equation, I,,, is the limiting disc current, n is the number of electrons, F is the Faraday constant and c,~ is the bulk concentration of the reduced form of the reactant. 1, denotes the hypothetical current at a reversible potential.
179 TABLE
1
Kinetic parameters of the Cu2+/Cu+ electrode reaction at gold in aqueous solutions each containing 0.1 mol dm- 3 NaClO, and 0.1 mol drne3 HClO,. (a) from anodic and (c) cathodic measurements. Concentration of Cu+ (in second column) is related to the anodic measurements Concentration of Ca(ClO,),/ mol dmm3
lo4 Concentration of Cu+/mol dmm3
0.9 1.4 1.9 2.4 2.9 3.4 3.9
2.2 2.7 3.3 4.4 5.5 8.1 11.0
E o ‘/mV
104k “/cm
VS.
SCE(NaC1) -70 -45 -16 23 54 103 154
s-’
(a)
(c)
2.7 2.3 3.9 6.4 3.4 3.0 6.1
2.6 3.2 3.3 3.3 2.2 3.1
0.56 0.54 0.51 0.47 0.51 0.53 0.46
0.38 0.40 0.43 0.44 0.51 0.36
In the case of a totally irreversible electrode process, eqn. (5) can be simplified to kx=&$
red
I
D,L
1, _I
(6)
D
Figure 2 shows a semi-logarithmic
analysis of some voltammograms.
0.1 0
100
200
300
400 E/mV
Fig. 2. Semi-logarithmic analysis of RDE oxidation curves in the Cu2+/Cu+ system for solutions containing 0.1 mol dmm3 Cu(ClO,), and 0.1 mol dme3 HClO, with Ca(ClO,), at different concentrations: (a) 0.9; (b) 1.9; (c) 2.9; (d) 3.9 mol dm-‘. The concentrations of Cu+ ions are given in Table 1. Rotation frequency 60 Hz.
180
10-2 7 In
E : ;
10-3
0 0 z Y 10-4
10-5
0
200
400 E/mV
electrode reaction. The lines are Fig. 3. Anodic (0) and cathodic (0) Tafel plots for the Cu2*/Cu+ labelled with the molar concentration of Ca(ClO,),. The bars indicate the formal potentials.
The potential dependence of the anodic and cathodic rate constants (in a logarithmic scale) is presented in Fig. 3 for various concentrations of the background electrolyte. It should be stressed that the Tafel curves obtained manifest an unconventional shape since the cathodic data correspond to measurements performed in the underpotential region. Extrapolation of the lines of Fig. 3 to the formal potentials of the Cu’+/Cu+ couple, E O’, furnished the formal rate constants, k”. The anodic, (T~, and cathodic transfer coefficients, (Ye, were calculated from the slopes of the appropriate lines. The kinetic parameters determined for the system investigated are collected in Table 1. Inspection of the kinetic parameters contained in Table 1 shows that the values of k” obtained from anodic and cathodic measurements differ, especially in the case of higher background electrolyte concentration. The discrepancy between these two sets of data may be explained partly as due to the long extrapolation of the experimental values of the constants k,, and k,, to the formal potentials. On the other hand, it should be noted that two different procedures were employed to determine the anodic and cathodic reaction rates. DISCUSSION
Only a small change in the formal rate constant of the Cu2+/Cu+ system with increasing concentration of the background electrolyte is observed. Similar be-
181
haviour was reported in the literature for other redox systems, e.g. Ti02+/Ti3+ [25], Cr3+/Cr2+ [26,27] and Eu3+/Eu2+ [28] in concentrated perchlorate solutions at the mercury electrode. The formal rate constants presented in this paper are generally in agreement with that obtained at a Pt electrode for 1 mol dmp3 NaClO, solution [18]. On the other hand, the k o values determined by us are over two orders of magnitude higher than that reported by Reid and David [15] for a metallic copper electrode in sulphuric acid solution. However, the former value was referred to the rest potential in the system studied. As follows from Table 1, the transfer coefficients are also virtually independent of the supporting electrolyte concentration. The sum (r, + OL,is close to 1, except for the solution of 3.9 mol dme3 Ca(ClO,),. We should stress that the kinetic parameters given in this paper are apparent values which may be influenced by the potential difference across the diffuse double layer, $J~, (Frumkin correction). Unfortunately, true values could not be calculated since the +2 potentials are not available for the electrolyte employed at the Au electrode. However, it is very probable that in such concentrated electrolytes the values of the e2 potential are rather low and their changes are negligible. It is known that Ca(ClO,), acts as a strong dehydrating reagent, and a gradual increase of its concentration causes a lowering of the water activity. Taking this into consideration, the orders of the electrode reaction studied with respect to water we determined from an analysis of rate constants on the water activity. The values of the water activity were interpolated from literature data [29]. We assumed that the contribution of Cu(ClO,), in lowering the water activity is approximately the same as that of Ca(ClO,),. The influence of HClO, was neglected. Figure 4 shows plots of the cathodic and anodic rate constants at a fixed potential against the logarithm of the water activity, a:, expressed in the molar concentration scale. The plots obtained are linear in a limited region, i.e. at a: + 1. The deviation from linearity observed for highly concentrated Ca(ClO,), solutions may be explained to some extent by ion-pair formation; however, the lack of appropriate data makes any quantitative estimations impossible. For a: + 1, the order of the cathodic reaction P= 0
log Ld/a
log &),
(7)
was found to be - 2.7. In a similar way, p determined for the anodic oxidation of copper(I) was 3.9. Thus one can accept that electrode reaction (2) is connected indirectly with the exchange of ca. three water molecules. This interpretation with respect to hydration is valid under the assumption that the activity of ions in the sense of the Debye and Htickel theory does not change significantly with a decrease in the water activity, and that the changes in the liquid junction potential are negligible, at least at relatively low electrolyte concentration. The latter assumption may be supported by the results of Andreu et al. [30] who estimated changes in the liquid junction potential originating from varying the concentration of NaClO, within the range 0.2-7 mol dmp3, to be less than 10 mV.
182
10-G
I
1
I
I
I
I
0.1
I,,
J 1
c
a, Fig. 4. Dependence of the anodic (0) and cathodic (0) rate constant at constant potential, E = 200 mV vs. SCE(NaCI), on the water activity expressed in a molar concentration scale.
Taking into account the secondary hydration numbers of Cu*+ and Cu+, h cu(II) = 12 and hcucIj = 5 [16], respectively, the following mechanism, at least for moderately concentrated Ca(ClO,),, could be suggested: Cu(H,O);+
Cu(H2O)::
=
Cu(H,O)i+
+ e-+
+ 4 H,O
Cu(H,O);
+ 3 H,O
(fast)
(8) (9)
According to the theory of adiabatic electron transfer reactions at an electrode [31-331, the standard (formal) rate constant is related to the overall Gibbs energy barrier, AG * , by k” =A
exp(-AG#/RT)
(10)
The pre-exponential term A includes the transmission coefficient K, generally taken as equal to 1, and a frequency factor Z which is usually approximated by the kinetic expression for collisions of particles of mass m with the wall. Following this A = K( RT/2mN,m)“*
01)
where NA is Avogadro’s constant. From the point of view of the theory considered, the electrochemical Gibbs energy of activation is the sum of two terms: the work of solvent reorganization, X0, and the inner reorganization energy of the reacting particle, Xi: AGf=X/4=(h,+Xi)/4
(12)
183
hi depends on changes in the bond lengths and the bond angles. Equation (12) eventually has to be completed by work terms for the transport of the reactants to the reaction site. h, can easily be calculated on the basis of an extension of the Born model if the radius a of the reacting particle as well as the dielectric constants, optical E, and static es, are known. For a one-electron electrode process, X, is given as follows: h, = N,ei/8
ae,(l/a
- 1/2d)(l/e,
- l/c,)
(13)
where e, is the electron charge, ~a is the permittivity of vacuum, a is the radius of the reacting ion, while d is the distance from the ion to the electrode surface. The change in A, with increasing background electrolyte concentration is obvious, since cc0 and cS will vary. In our calculations, following the argument of Hale [32], the 1/2d term in eqn. (13) was neglected. One would expect that the reactant is located near the outer Helmholz plane and, consequently, the screening of the reactant by ions of the background electrolyte against its interaction with the image in the electrode should be effective. In the calculation of h, from eqn. (13) we used a = rcUoIj + 2r,, with the radius of the water molecule, r,, equal to 0.145 nm [34] and rcu~,l~= 0.079 nm [35]. Due to a paucity of data on the dielectric constants for concentrated Ca(ClO,), solutions, appropriate values for NaClO, were taken from the literature [36]. Here, we assumed that the values of z, and e, for Ca(ClO,), solutions approximate those for NaClO, solutions of twice as great molar concentration. This assumption may be supported indirectly by comparing the data on water activity in solutions of the both salts considered. From the standard rate constants, AG # and h values were calculated. Consequently, Xi was estimated from the difference X - X,. The number of coordinated water molecules in the first hydration sphere was assumed to be six, analogously to other divalent transition metal cations of the first row [37]. The results of calculations are listed in Table 2. This table includes also the data for the same reaction at a Pt electrode in 1 mol dm- 3 NaClO, solution estimated from our earlier investigation [18]. As follows from Table 2, the value of X, decreases markedly when going from 1 to 2 mol dmp3 Ca(ClO,), solution. On the other hand, the reorganization energy of
TABLE 2 Polarity parameter of solutions y = l/c, - l/r,, formal rate constants, activation and reorganization energies of the Cu*+/Cu+ reaction at platinum and gold electrodes Background electrolyte
Y
104k “/cm s-’
AG*/kJ
1 mol dmm3 NaClO, 1 mol drnm3 Ca(ClO,), 2 mol dme3 Ca(ClO,),
0.158 0.102 0.075
8.8 (Pt) = 2.6 (Au) 3.6 (Au)
38.4 41.4 40.6
a From ref. 18.
mol-’
X,/kJ 49 32 23
mol-’
A, /kJ mol-’ 105 134 139
184
the outer sphere is small compared with that of the inner sphere. Moreover, the Xi value does not change significantly under the same conditions. This leads to the conclusion that the relatively slow rate of the Cu*+/Cu+ reaction at a gold electrode may be explained in terms of changes occurring in the inner sphere. ACKNOWLEDGEMENTS
The authors thank Prof. Z. Galus of Warsaw University for helpful discussions during the work and kind advice for the preparation of the manuscript. Support of this work by a grant from Central Research Project CPBP 01.15 is acknowledged. REFERENCES
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