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Cu(Hg) electrode reaction in acetate solutions
Journal of Electroanalytical Chemistry, 375 (1994) 175-183
175
Participation of dinuclear metal complexes in charge transfer at electrodes: The Cu( II) /Cu( Hg) electrode reaction in acetate solutions S. Fronaeus Inorganic Chemistry 1, Chemical Center, University of Lund, PO Box 124, S-221 00 Lund (Sweden)
(Received 24 September 1993; in revised form 23 February 1994)
Abstract The electrode reaction Cu(II)/Cu(Hg) in complex acetate (AC-) solutions has been studied at the equilibrium electrode potential by a cyclic current-step method. The data refer to an ionic strength of 1 M with sodium perchlorate as the supporting electrolyte and to a temperature of 25°C. Double-layer data were obtained from electrocapillary measurements. The kinetics indicates that the electron transfer Cu(II)/Cu(I) via the amalgam, which is the slowest step in the overall charge transfer, is substantially accelerated at increasing ligand concentrations within the range covered ([AC-] I 20 mM). The results obtained show that Cuz+, CuAc+, CuAc, and Cu,Ac; take part as oxidants. For ligand numbers Ti> 0.2, CuAc+ and Cu,Ac: are predominant. The rate enhancement can primarily be explained by the formation of an electron-mediating carboxylate bridge between Cu(I1) and the amalgam. Both C&AC: and the corresponding reductant, the mixed-valence complex Cu”Cu’Ac,, can form such bridges, which probably is the cause of the very strong electrocatalysis displayed by these dinuclear complexes.
1. Introduction
During the last decade there has been an increasing interest in dinuclear mixed-valence metal complexes, in particular their thermodynamic [l] and spectroscopic [2] properties. Reactivity studies have mostly dealt with intramolecular electron transfer and in some cases with homogeneous redox reactions [3]. However, no systematic investigation of the role of dinuclear complexes in heterogeneous electron transfer at electrodes seems to have been reported. We have previously studied the influence of complex formation and solvation on the electrode reactions of different metal ions. It was found that dinuclear complexes sometimes contribute considerably to the rate of charge transfer, even if their concentrations in the solution bulk are very low. Thus measurements on the Hg(II)/Hg electrode reaction in chloride + dimethyl sulfoxide (DMSO) solutions [4] indicate that, as well as the complexes HgCl?-’ (j = 0 ,4), Hg,C13+ also takes part as the oxi&ant in thi ‘charge transfer step HgtII)/HgG). Similarly, in the reaction Cu(I)/Cu(Hg) in DMSO solutions of chloride, at concentrations where CuCl; 0022-0728/94/$7.00 SSDZ 0022-0728(94)03411-U
and CuClg- are the main complexes in the solutions [5], the predominant oxidants are Cu+, Cu,Cl, and Cu,Cl; 161. An early investigation of the electrode reaction Cu(II>/Cu(Hg) in aqueous acetate solutions [7] seemed to indicate that the step Cu(II>/Cu(I) was rate determining over the whole ligand concentration range available. On this basis the result obtained was that the predominant oxidants in the charge transfer were CuAc+ and CuAci for [AC-] > 10 mM. The large contribution from CuAc; was unexpected and hard to explain. However, in a later study of the corresponding electrode reaction of the Cu(I1) glycollate system [8], it became clear that at higher ligand concentrations the step Cu(I)/Cu(Hg) has a considerable influence on the total charge transfer measured. This finding motivated the present reinvestigation of the copper acetate system, also including electrocapillary measurements. 2. Experimental 2.1. Chemicals
Cu(I1) perchlorate and liquid copper amalgam (0.1% by weight) were prepared as described earlier [7]. Per0 1994 - Elsevier Science S.A. All rights reserved
176
S.
Fronaeus/ CM(H)/Cu(Hg)
chloric acid, sodium perchlorate and sodium acetate were of analytical grade, and all solutions were made up using double-distilled water. 2.2. Experimental details The measurement cell has been described previously [9]. The surface area of a single amalgam drop, used as the polarizable electrode, was 0.034 cm*. All measurements were carried out at 25.0 + 0.2”C. The ionic strength of the solutions was 1.00 M with sodium perchlorate as the supporting electrolyte. The complex solutions were kept free from oxygen by flushing with pure nitrogen. The charge transfer resistance R,, was determined according to a cycling current-step method [lo], theoretically improved 1111,and by use of a modified technique [121. In the earlier investigation faradaic impedance measurements showed that the electrode reaction is controlled by charge transfer and diffusion only. This is also a necessary and sufficient condition for the applicability of the cyclic current-step method. The bridge used and the procedure for determining R,, has been described elsewhere [12]. However, in the present investigation the bridge was adjusted until the faradaic voltage response was compensated at a time 0.094 r after the beginning of each half-period (duration 7/2) [ll]. After renewal of the amalgam drop, an initial value of R,, was measured and the constancy of this value was checked over a period of about 1 min. This is an indication that a possible deviation from Coulomb symmetry of the square wave within this time interval was unimportant [lo]. Furthermore, R,, for some of the complex solutions had been obtained earlier from impedance measurements, and both polarization methods gave consistent values. The capillary electrometer and the other experimental equipment for the determination of 42 potentials and specific anion adsorbabilities were the same as used previously [ 121. Values of [H+] in all the complex solutions were obtained in separate emf measurements. 3. Electrode kinetics
where i, 1 and i,, are the exchange current densities of the steps Cu(I>/Cu(Hg) and Cu(II)/Cu(I) respectively. It is assumed that i, is calculated from R,, by using the expression R,, = RT/(2FAi,) where A denotes the area of the polarizable electrode. The system CU*++ AC- mainly consists of mononuclear complexes [131 at the low Cu(I1) concentrations used in the present study. However, at [Cu(II)] > 20 mM, the formation of dinuclear complexes is also noticeable. However, in the thermodynamic measurements there was no indication of formation of hydroxo complexes or complexes with HAc in the buffer solutions used. It is well known that hydrated Cu*+ exchanges water extremely rapidly in solution. Accordingly, its complexes with the hard base AC- with oxygen as the donor atom are certainly very labile and in mutual equilibrium during the measurements of R,,. The presence of an amalgam pool also ensures equilibrium between C&I) and Cu(1) in advance. Then the following reaction scheme can be proposed for the overall charge transfer: CuAcT-’ + e- (am) = Cu,Ac;-j
+ e-(am)
CuAcj’-j + e - ( am) e
CuAc J! e
-j
Cu”Cu’Ac3J -j Cu(am) +jAc-
(2)
(3)
(4)
The following final expressions (5) and (6) are obtained for i,,, of reactions (2) and (3) and i,,, of reaction (4) [4,71: i,,, = C( kj[cu2+]0~5(1+a~) + k:[Cu2+]05(3+~~~)[AC-]’ i
(5) i,,, =
~k~[C~2f]o’5a’[Ac-]’
(6)
i
o<“j’“;,“J
The
kj = Fk;pi”jp(ic’-9)
3.1. Expressions for the exchange current density The disproportionation reaction 2Cu(I) s Cu(I1) + Cu(Hg) must be taken into account in the system Cu(I1) + Cu(1) + Cu(Hg). If this reaction is slow compared with the charge transfer steps and [Cu(I)] < [Cu(II)I, the implication is that the two steps become consecutive at polarization, and the following equation can be deduced for the electrochemically determined overall exchange current density i, [8]: ii’ = OS( ici + ii:)
electrode reaction in acetate solutions
(1)
xexp[(j - 1 -“j)42F/R’] k;
=
(7)
Fkkgrp(l”‘K-“.‘“:.[Cu(am)] 1-o.5a;
Xexp[(j-a;)$,F/RT]
(8)
In expression (7) koj and aj denote the true rate constant and the anodic transfer coefficient of reaction (2), pj and P(i are the stability constants of CuAc;-j and CuAcf -j respectively, and K is the disproportion-
S. Fronaeus / CL&I) / Cu(Hg) electrode reaction in acetate solutions
177
ation constant of Cu+. The exponential factor is the Frumkin factor. Equation (7) is also applicable for k(i’ if $’ and the stability constants p; for Cu,Ac~-j and /37 for CU”CU’AC~-~ are used and j - 1 in the Frumkin factor is replaced by j - 3. An average value of the exponents for [Cu2’] appearing in the complete expression for i, can be obtained from the function cu= (ai0gi,/ai0g[cu2+])L,-l
(9)
For the single-electron steps two further quantities ‘Yi and Z2 can be defined by replacing i, by i,,, and i,,, in eqn. (9). From eqn. (5) it is easily found that i 0,2’y2 = ~(O.S(l
+ Lyj)kj[Cu2+]0.50+ni)
j +0.5(3 +$!)k;[C~~+]~‘~(~+“)[Ac-]j
(10) IogGkYM)
Finally, eqn. (1) yields Z/i,
= OS( EJi,,,
+ ‘Y2/io,,)
(11)
As the determination
of i, was carried out in the presence of a supporting electrolyte of constant and fairly high ionic strength, it can be assumed that variations in the activity coefficients and in the $Q potential are suppressed, so that true rate constants are obtained. Different polarization measurements (discussed in ref. 8) indicate that in acidic copper perchlorate solutions the disproportionation reaction is slow compared with the charge transfer steps. Evidence for the applicability of eqn. (1) to the glycollate (L-1 system was given by the fact that the slope of Z as a function of [L-l decreases considerably at higher [L-l. A similar decrease is found for the acetate system (Fig. 2 below) and leads to the same conclusion. However, if the disproportionation is much faster than the charge transfer steps, they become parallel and then i, = 0.5(io,, + i,,,). It is easy to verify that such an equation is not compatible with the variations in i, and E in the acetate system and with the fact that i,,, > 2i, at [AC-] = 0 [8]. 3.2. Measurements of i, and calculations As the exchange current density is fairly high in this system, it was necessary to keep the total Cu(I1) concentration cc” between 0.3 and 3 mM and the acetate concentration cAc at 20 mM or less to obtain measurable and reliable R,, values. In each measurement series coU was kept constant (0.66 mM) while cAc was varied by successive additions of perchloric acid. In separate emf measurements the dissociation constant of acetic acid was re-determined as pK, = 4.59 (cf. ref. 14). Then the free ligand con-
Fig. 1. Plots of (a) log i,, (b) log i,,, and (c) log i0,, as functions of log[Ac-] at c Cu = 0.66 mM. The curves were calculated from eqns. (l), (5) and (13) using the parameters in Table 1.
centrations were calculated from values of [H+]. The i, values obtained are reported in Fig. 1. The following stability constants [13,14] were used for the Cu(II) complexes: log(&/M-‘)
= 1.67, log(p2/Me2)
log(p3/M-3)
= 3.06.
= 2.65
These constants were used to calculate the relationship CC”= [Cu2+] (1+ ~pi[AC-I’) j
and
[Cu2+] from
(
In order to determine the quantity E measurements
of
R,, were also carried out at varying values of cc” and
with [AC-] as a parameter. Values of cl! at cc” = 0.66 mM were obtained graphically according to eqn. (9) from the slopes of approximately rectilinear log i, vs. log[Cu2+] plots. The values are given in Fig. 2. It is evident Z increases with increasing [AC-] within the range investigated, but its value remains below 1.0. At [AC-] < 3 mM the experimental data can be represented fairly well by the equation ([Cu2+] and [AC-] in M) i,/mA
cme2 = 1.5 X 102[C~2+]0’65 + 2.4 x 105[Cu2+]o’70[Ac-]
(12) This is evident from Fig. 3. The value E = 0.7 obtained at low [AC-] indicates that i, = i,,, within this range of [AC-]. Then according to eqn. (1) we should have
S. Fronaeus / Cu(II) / Cu(Hg) electrode reaction in acetate solutions
178
TABLE 1. Values of the composite coefficients in eqns. (5) and (6) when i, 2 and io,I are expressed in mA cm-‘, and [Cuzf ] and [AC- I in M j 0 1 2 3
I
I
-3.5
I
-3.0
I
-2.5
I
-2.0
-I
log([Ad/M)
Fig. 2. Plots of Z (0) and Cu, (01 as functions of log [AC-I at cc. = 0.66 mM. The curves were calculated from eqns. (10) and (11).
Thus values of the coefficients zol B- lo2 and i, = 2i,,. k; (Table 1) and of the exponents OS(1 + ai> for j = 0 and j = 1 in eqn. (5) are obtained directly from eqn. (12). At higher ligand concentrations, where Z > 0.7, eqn. (12) is obviously not applicable. Further calculations imply an estimation of i,,, at higher [AC-]. To do this we need to use results from the investigation of the electrode reaction Cu(II)/Cu(Hg) in glycollate solutions [B]. In this system an expression similar to eqn. (12) and with the same value of 0.70 for the exponent 0.50 + a,) was found to be valid at [L-l < 5 mM. For
kj 75+5 (1.2+0.1)x105 12x106
k’! I
1O-2 k’j 2.5 + 0.5
9+1
electrode reactions where the second mononuclear complex also takes part in the charge transfer, it is generally found 1151that (Ye= (pi. Accordingly, for the glycollate system the maximum value of Z attained is ca. 0.70, and thus the quantity Eu, in eqn. (11) should also be ca. 0.70 at higher ligand concentrations, as there is no indication of formation of dinuclear complexes in this system [13]. Finally, if it is presumed that & and (Y: in eqn. (6) also have a value of 0.40 in both systems, i.e. Zu,= 0.20, it is feasible to calculate i,,, for the glycollate system from eqns. (1) and (11) and to determine values of the composite coefficients kb and k;. It is found that k;/k; = 20 f 8 M- ‘. The values of the stability constant pi in eqn. (7) are not known for the two Cu(1) systems, but they are probably approximately equal and small, as is the case for the corresponding Ag(I) systems [16]. However, the rate constant ky for the participation of CuL+ in the charge transfer step Cu(II)/Cu(I) is about 2.5 times larger than the corresponding rate constant for CuAc+. Also, it has been found that glycollate is a better electron mediator than acetate for some homogeneous redox reactions [17]. Thus it can be concluded that the rate constant k;’ in eqn. (8) also has a lower value for CuAc than for CuL. Consequently, in eqn. (6) for [AC-] < 2 x lo-’ M only the term with j = 0 is taken into account. Then eqn. (6) has the simple form (kb in Table 1) i,,, = kb[Cu2t]0.20
Fig. 3. Plots of lo&, - 1.5 X 102[Cu2+]0~65)[A~-I-’ as a function of log[Cu’+] at different low values of the parameter [AC-]: l 0.29 mM; n 0.87 mM; A 2.57 mM.
lo-”
(13)
At constant cc” there is a small decrease in i,,, with increasing [AC-] (Fig. l), as the stronger complex formation with Cu2+ makes [Cu(I)]/Cu(II)] decrease. Finally, using eqns. (0, (11) and (13), values of i,,, and ‘Y2 in the whole [AC-] range available can be calculated from the measurements of i, and Z. They are reported in Figs. 1 and 2. If another normal value of ct$ and a; is chosen (e.g. 0.50), both the coefficients kb and k; for glycollate become 1.48 f 0.02 times larger for the range 0.3 < [,f;“:h+&rnM < 0.6, b u t o f course this has no influence o,l values calculated from eqn. (13) with the
S. Fronaeus / Cu(II) / Cu(Hg) electrode reaction in acetate solutions
exponent ah/2 = 0.25. The effect on Cy, is very small; the maximum value attained decreases by 0.04. In the range 3 < [Ac-]/mM < 20 the complex CuAc, might take part detectably in reaction (2). However, as 5, attains a value of 1.25, it is evident that at least one dinuclear complex, Cu,AcP-i, contributes considerably to the charge transfer according to reaction (3). In the relevant terms of eqn. (5) the exponents 0.50 + a,) and 0.5(3 + al> can be expected to have the values 0.70 and 1.7 5 0.1, respectively. Then, if the terms with the coefficients k, and k, on the right-hand side of eqn. (5) are subtracted from i,,, and the remaining terms are divided by [CU~+]~~~[AC-]~,values of the quantity X= k, + k;[Cu’+]“[Ac-]‘-2
a = 1.0
I
179
I
’
A / /
:
/
1
‘f
s> ^
‘9
0
E.
(14)
are obtained. The same operation performed with eqn. (10) yields values of a similar quantity: Y = 0.7k2 + (a + 0.7) k;[ &“+I”[
Ac-]j-2
(15)
It is found that both X and Y increase with constant cc” and increasing [AC-], indicating that j > 2. The most probable value is j = 3, which corresponds to the cationic complex Cu,Ac:. Accordingly, X and Y for ccU = 0.66 mM, a = 0.9 and j = 3, have been plotted versus [CU~+]~.~[AC-] in Fig. 4. It is evident that both functions can be represented by straight lines, and the slopes yield consistent values of k’j. This finding confirms the value j = 3 and the high value of 0.5(3 + a;) anticipated. An upper limit of k, is obtained from the intercept of X on the ordinate axis. It is true that the intercept of Y seems to be approximately zero, but the random errors in Y are larger than those in X. A value a = 1.0 also gives straight lines, but in this case the intercept of Y is negative and so it seems that a = 0.9 yields the best fit with all the measurements. It is clear from Figs. 1 and 2 that the functions io,2, i,, (Y, and Z, calculated from eqns. (5), (1) plus (13), (10) and (11) with the constants listed in Table 1 reproduce the i, data very well and the Z data fairly well. The results obtained indicate that, in addition to hydrated Cu2+, the complexes CuAc+, CuAc, and Cu,Ac: take part as oxidants in the electron transfer step Cu(II)/Cu(I). Their relative contributions to i,,, as functions of the ligand number E have been calculated from eqn. (5) and are shown in Fig. 5. It is seen that at 7i > 0.2 the predominant contributions to i,,, come from CuAc+ and Cu, AC:. To see how the approximation of i,,, influences the results, calculations of the function X in eqn. (14) have been carried out using i,,, values obtained with k,/k, = 10 M-’ instead of zero, i.e. half the value valid for the glycollate system. With the same plot as in Fig. 4 a
I
I
I
4
8
12
[@f9
[AC-]10”
Fig. 4. Plots of Xc*) and Y(A) from eqns. (14) and (15) for a = 0.9 and j = 3 as functions of [CU~+]~~~[AC-]at ccU = 0.66 mM.
8(
a
% 4(
2(
Fig. 5. The relative contributions to io,z from the different Cu(II) oxidants at cc,, = 0.66 mM and varying ligand number E: (a) CL?+; (b) CuAc+; (c) CuAc,; (d) Cu,Ac, + . The curves have been calculated from eqn. (5).
S. Fronaeus / Cu(ll) /Cu(Hg)
180
electrode reaction in acetate solutions
TABLE 2. The interfacial tension y, components of charge and the potential dz in the electrode double layer at an electrode potential of - 4.5 mV vs. the fixed reference electrode Ag IAgCl(s) 10.1 M NaCl + 0.9 M NaClO, Electrolyte
q/pC
1.00 M NaClO, 1.00 M NaAc
13.0 15.0
cm-’
r/J
m-*
0.392 0.395
Fr+/pC
-q-‘/PC
cm-*
5.20 4.50
cm-*
- WmV
21 22
33 29
straight line is obtained which yields the same upper limit of k,, while k, decreases by only 10%. Thus the approximation that the use of eqn. (13) involves does not cause any uncertainty about the validity of the results. 4. The electrode double layer 4.1. Specific anion adsorption and C& potentials Electrocapillary measurements according to the method described earlier [12] were performed on pure mercury in contact with solutions of concentration c of sodium perchlorate or acetate. For the determination of the charge density q on mercury and the relative surface excess r+ of sodium ions, applied electrode potentials E in the range - 100 mV < E < 0 mV versus a fixed reference electrode (see Table 2) were used to measure the inter-facial tension y. For the determination of r+, solutions with c = 1.50 M were diluted stepwise and after each step E was increased until y had attained the value valid at c = 1.00 M and E = - 45 mV. The almost rectilinear curves in Fig. 6 give values of (aE/a log cl,,. The value of r+ was obtained from this quantity and q [12]. The potential #+ and the amounts qbo, or qiC- of specifically adsorbed anions were calculated in the usual way. [18]. The values obtained are given in Table 2. The q! values indicate that at the potential selected the specific adsorbability of AC- is approximately the same as that of Cloy. This potential corresponds to the equilibrium potential E” of the amalgam electrode in a complex solution with cc” = 0.66 mM and [AC-] = 6.5 mM. Furthermore, within the range [AC-] I 20 mM, E” varies from only - 41 mV to - 5 1 mV. Thus within this range the
logkm) Fig. 6. The mercury electrode potential E as function of log c for sodium perchlorate (0) and acetate (0) solutions at constant values of the interfacial tension y: o y = 0.392 J m-*; l y = 0.395 J m-*.
equation qiC-/ql = [AC-]/([ClO;l + [AC-]) should hold with q!_= q&,; + qiC- in the complex solutions. Now, as both (ClO;] + [AC-]) and E” are apbroximately constant, q!. should also be constant and qiCshould be proportional to [AC-]. The consequence is that, for an oxidant CuAcT-j or Cu,A&j that is specifically adsorbed via a carboxylate grou;, the number of ligands j also includes the acetate bridge to the electrode. Thus the contributions from &AC&, and cu, AcL to ia,, are proportional to -qic-[Cu2+lo.70 and -q~~-[Cu2+]1.6[Ac-]2. For the latter complex the formulation means that one ligand forms the carboxylate bridge to the electrode, whereas the other two ligands are not specifically adsorbed.
TABLE 3. The rate constants ky and ki” relating to the participation of CuAcT-j and Cu,Acz in the electrode reaction step Cu(II)/Cu(I), enthalpy changes AH: and entropy changes ASi” in the reactions CuAc;:i + AC-+ CUAC~-~ in aqueous solutions at 25°C
i
kpCuAc?-‘)/cm
0 1 2 3
(1.9 f 0.l) x 10-Z 5.8 go.5 I 200
s-l
3b 0.3 c
a From ref. 19. b From eqn. (7). ’ From eqn. (16).
AH; a/kJ mol-’
AS; a/J K-’ mol-’
4.4 1.7
51 30
and
S. Fronaeus / C&I)
/ Cu(Hg) electrode reaction in acetate solutions
4.2. The true rate constants k;
181
To obtain values of the true rate constants relating to reactions (21, it is necessary to make an assumption about the unknown stability constants p(i of Cu(I>. It is reasonable to use the values of the corresponding constants of the system Ag++ AC-, i.e. p’, = 2.5 M-l and pi = 1.5 Me2 [16]. It is true that this approximation should yield stability constants which are rather low because of the smaller radius of Cu+, but this fact cannot be of great importance for the conclusions that can be drawn from the ratios of the rate constants. It is evident from Table 2 that, for [AC-] < 20 mM, & = - 33 mV should be used in the calculations. Then, using the transfer coefficients at, = 0.30, czi = (Y*= 0.40, K-‘[Cu(am)] = lOA M [S] and the composite coefficients kj in Table 1, the rate constants k; have been calculated from eqn. (7) (Table 3).
bridge from Cu(I1) in the OHP to the amalgam electrode is probably the main cause of the high value of k;/k”,. This conclusion is supported by a previous comparison [20] of the rate-enhancing effects of different carboxylate ions on the charge transfer C&I)/ Cu(I). The sequence of these ions according to their effect (acetate < glygollate < glyoxylate) is the same as that found if the ligands are arranged according to their catalytic effect on certain homogeneous redox reactions [17]. In the latter case, it was proved that the carboxylate group functions as an electron-mediating bridge. The sequence found provides a strong support to the suggestion that carboxylato-bridged electron transfer is important in the present electrode reaction. The following equation is easily derived from the general theory for the kinetics of electrode reactions [18]:
5. Discussion
k” = (z)“(E)‘-”
The results obtained indicate that formation of the complex gives rise to a strong catalytic effect on the overall electrode reaction. This effect relates to a pronounced rate enhancement of the electron transfer step Cu(II)/Cu(I). The strong increase in the exchange current density +2 of this step at increasing [AC-] cannot to any extent be ascribed to the Frumkin effect as 4*, the potential of the OHP, should have a value of ca. -33 mV in the complex solutions. Thus the complex formation causes the Frumkin factor in eqn. (7) to decrease. Neither can the increase in i,,, be caused by hydroxo complexes, which are present in very low concentrations. Such an effect should be more pronounced for acetate than for glycollate solutions because, since pK, = 3.60 for HL, the pH values of the complex glycollate solutions were in general one unit lower than those of the corresponding acetate solutions. However, the values of i, give identical values of k,, whereas k, is larger for glycollate [81. It is evident from Table 3 that on formation of CuAc+ there is a large relative increase in the rate constant (ky/k”, = 3001, whereas the formation of CuAc, gives an additional relative increase that is much smaller (k”,/k; I 35). Table 3 also shows that the values of AH: and AS; for the first two complex formation steps of Cu(I1) are positive. However, they are so low that it is unlikely that there is a pronounced change in the inner-sphere geometry in any of the steps (cf. the Zn*++ AC- system [19]) such that the difference in hydration energy between Cu(I1) and Cu(1) would decrease and considerably reduce the activation energy of the electron transfer. Formation of an electron-mediating carboxylate
where k and k denote the chemical parts of the rate constants of the forward or cathodic and the backward or anodic charge transfers of a simple electrode reaction with the true rate constant k”. The question is whether th_e h&h value of ky/k”, depends upon a large laluz of k,/k,, i.e. ligand bridging at C&I), or of k,/k,, i.e. effective ligand bridging at Cu(1). The low stability constants estimated for the Cu++ AC- system should indicate a weak and essentially electrostatic bond. This implies that the interaction between Cu+ and a specifically adsorbed AC- should be even weaker and give a very low concentration of CuAc,,, compared with that of nap-a_dsorbed CuAc at the OHP. Thus a high value of k,/k, cannot be expected. However, for the system Cu*++ AC- the specifically adsorbed AC- should make the concentration of CuAc& _muc& higher than that of CuAcads, implying a high k,/k, by the electron-mediating bridge at the amalgam. The moderate value obtained for k”,/ky is an upper limit. For this reason the only possible conclusion is that the ligand-bridging conditions for CuAc, should be similar to those of CuAc+. The considerable participation of the dinuclear complex Cu,Acl as an oxidant in the electron transfer step Cu(II)/Cu(I) is very interesting. It has been reported that Cu(I1) acetate in aqueous acetic acid of high concentration is partly dimeric [21]. In a previous thermodynamic study [13] of the complex formation, measurements were performed within the concentration range 25-100 mM of Cu(II), and the stability constants p; and p’; of the complexes Cu2Ac3+ and Cu,Acz+ were also obtained: log@‘;/M-*) = 1.70 and 10g@;/M-~) = 3.04.
(16)
182
S. Fronaeus / Cu(II) / Cu(Hg) electrode reaction in acetate solutions
To arrive at a quantitative measure of the electrocatalysis by the formation of the oxidant Cu,Ac: it is desirable to try to calculate the rate constant k;” relating to reaction (3) from both eqn. (7) and eqn. (16). In both cases the calculations have to be based on some reasonable assumptions. The values @‘;/pi = 1.1 M-l and @J/3, = 2.4 M-l make the estimate p’;/& = 6 M- ’ plausible, giving p’; = 7 x lo3 Me4. A rough estimate of the stability constant p,* of Cu”Cu’Ac, is obtained if it is postulated that &J/p’; = pi/p,. This relationship yields PT = 4 X lo2 MP4. With the two stability constants estimated and (~‘j= 0.4 inserted in eqn. (7) the result is k 03”= 3 x lo5 cm s-l. In these calculations the Frumkin factor does not compensate for the increase in the concentrations of both the oxidant and the reductant in the pre-electrode state as a result of the specific adsorption of the complexes on the amalgam. This effect should give value of the rate constant that is too high. The theory of bridged electron transfer is not very well developed. However, it should be possible to arrive at fairly simple but plausible relationships for the participation of different complexes in an electrode reaction, where the same ligand bridge to the electrode can be formed. In the present system it can be assumed that a carboxylate bridge between Cu(I1) and Cu(Hg) decreases the chemical part of the Gibbs energy of activation of the electron transfer by an approximately constant value for the different complexes or increases the transition probability by a constant factor. Thus, in the calculations based on eqn. (161, it is assumed that formation of CuAc+ and Cu,Aci give rise @ ap2roxim$ely the same relative increase in k, i.e. k, = k, = elk,. As to the reductants CuAc and Cu”CurAc3 the catalytic effect of the latter complex on the backward reaction in eqn. (3) should be the same on the forward reaction, as a as that of Cu,Acz carboxylate bridge between C&I) a@ Cu(am) can still be formed and consequently pi = elk,. Finally, as has been discussed above, coordination of-AC_ @ Cu+ should have a slight catalytic effect, i.e. k, = c2k, with c2 =SLci. Then eqn. (16) with (Y= 0.4 gives the expressions k;” = elk; k” = C0.4C0.6ko 1120
(17) (18)
Inserting the known value of k;/k”, and selecting c2 = 1 yields c1 = 1.6 x lo6 and k;” = 3 X lo4 cm s-l, which should be maximum values. However, the latter calculations do not take into account that, on the formation of a dinuclear complex a decrease in inner-sphere hydration should take place, implying that the difference in hydration energy be-
tween oxidant and reductant probably decreases, making the rate constant of the electron transfer increase. It is also probable that the assumptions made can influence the two calculations in different ways. Nevertheless, the high values of k;” obtained in both estimations strongly support the conclusion that in this case both the oxidant and the reductant can establish an electron-mediating bridge to the electrode, and that this is the decisive cause of the fast electron transfer. The strong electrocatalytic effect indicated is comparable with the rate-enhancing effect of some mono- and dicarboxylates on certain homogeneous redox reactions [22,23]. Finally, one interesting question is why Cu,Acg+ does not take part detectably as oxidant, although its concentration in the bulk of the solution is certainly larger than that of Cu,Ac: at the values of [AC-] used and the Frumkin factor is more favourable. It is possible that the predominant structures of both these complexes in solution contain a cyclic group with two carboxylate bridges between the two Cu2+ ions. In this case Cu,Acz+ cannot form a carboxylate bridge to the amalgam by itself without breaking the cyclic structure. If the energy required for this process is larger than the energy of the bond between the amalgam and a coordinated carboxylate group, substantial bridging is inhibited. References 1 D.E. Richardson and H. Taube, Coord. Chem. Rev., 60 (1984) 107. 2 L. Dubicki, J. Ferguson, E.R. Krausz, P.A. Lay, M. Maeder, R.H. Magnuson and H. Taube, J. Am. Chem. Sot., 107 (1985) 2167. 3 U. Fiirholz and A. Haim, Inorg. Chem., 26 (1987) 3243. 4 S. Fronaeus and CL. Johansson, J. Electroanal. Chem., 125 (1981) 139. 5 S. Ahrland, P. Blauenstein, B. Tagesson and D. Tuhtar, Acta Chem. Stand., Ser. A, 34 (1980) 265. 6 S. Fronaeus and CL. Johansson, J. Electroanal. Chem., 112 (1980) 197. 7 S. Fronaeus, R. Johansson and C.-O. &tman, Chem. Ser., 1 (1971) 52. 8 S. Fronaeus and C.L. Johansson, J. Electroanal. Chem., 48 (1973) 195. 9 R. Johansson and C.-O. &tman, Acta Chem. Stand., 23 (1969) 2939. 10 M.D. Wijnen and W.M. Smit, Reel. Trav. Chim. Pays-Bas, 79 (1960) 22, 203. 11 P. Teppema, M. Sluyters-Rehbach and J.H. Sluyters, Reel. Trav. Chim. Pays-Bas, 85 (1966) 303. 12 S. Fronaeus and C.L. Johansson, J. Electroanal. Chem., 80 (1977) 283. 13 S. Fronaeus, Doctoral Dissertation, University of Lund, 1948. 14 A.E. Martell and R.M. Smith, Critical Stability Constants, Plenum Press, New York, 1977. 15 S. Fronaeus, Coord. Chem. Rev., 88 (1988) 203. 16 L.C. Sill&r and A.E. Martell, Stability Constants of Metal-Ion
S. Fronaeus / C&l)
/ Cu(Hg) electrode reaction in acetate solutions
Complexes, Special Publication 17, Chemical Society, London, 1964. 17 H. Taube and S. Gould, Act. Chem. Res., 2 (1969) 321. 18 P. Delahay, Double Layer and Electrode Kinetics, Interscience, New York, 1965, pp. 60, 164. 19 P. Gerding, Acta Chem. Stand., 21 (1967) 2015.
183
20 S. Fronaeus and C.L. Johansson, J. Electroanal. Chem., 60 (1975) 29. 21 J.K. Kochi and R.V. Subramanian, Inorg. Chem., 4 (1965) 1527. 22 H.J. Price and H. Taube, Inorg. Chem., 7 (1968) 1. 23 C. Hwang and A. Haim, Inorg. Chem., 9 (1970) 500.
175
Participation of dinuclear metal complexes in charge transfer at electrodes: The Cu( II) /Cu( Hg) electrode reaction in acetate solutions S. Fronaeus Inorganic Chemistry 1, Chemical Center, University of Lund, PO Box 124, S-221 00 Lund (Sweden)
(Received 24 September 1993; in revised form 23 February 1994)
Abstract The electrode reaction Cu(II)/Cu(Hg) in complex acetate (AC-) solutions has been studied at the equilibrium electrode potential by a cyclic current-step method. The data refer to an ionic strength of 1 M with sodium perchlorate as the supporting electrolyte and to a temperature of 25°C. Double-layer data were obtained from electrocapillary measurements. The kinetics indicates that the electron transfer Cu(II)/Cu(I) via the amalgam, which is the slowest step in the overall charge transfer, is substantially accelerated at increasing ligand concentrations within the range covered ([AC-] I 20 mM). The results obtained show that Cuz+, CuAc+, CuAc, and Cu,Ac; take part as oxidants. For ligand numbers Ti> 0.2, CuAc+ and Cu,Ac: are predominant. The rate enhancement can primarily be explained by the formation of an electron-mediating carboxylate bridge between Cu(I1) and the amalgam. Both C&AC: and the corresponding reductant, the mixed-valence complex Cu”Cu’Ac,, can form such bridges, which probably is the cause of the very strong electrocatalysis displayed by these dinuclear complexes.
1. Introduction
During the last decade there has been an increasing interest in dinuclear mixed-valence metal complexes, in particular their thermodynamic [l] and spectroscopic [2] properties. Reactivity studies have mostly dealt with intramolecular electron transfer and in some cases with homogeneous redox reactions [3]. However, no systematic investigation of the role of dinuclear complexes in heterogeneous electron transfer at electrodes seems to have been reported. We have previously studied the influence of complex formation and solvation on the electrode reactions of different metal ions. It was found that dinuclear complexes sometimes contribute considerably to the rate of charge transfer, even if their concentrations in the solution bulk are very low. Thus measurements on the Hg(II)/Hg electrode reaction in chloride + dimethyl sulfoxide (DMSO) solutions [4] indicate that, as well as the complexes HgCl?-’ (j = 0 ,4), Hg,C13+ also takes part as the oxi&ant in thi ‘charge transfer step HgtII)/HgG). Similarly, in the reaction Cu(I)/Cu(Hg) in DMSO solutions of chloride, at concentrations where CuCl; 0022-0728/94/$7.00 SSDZ 0022-0728(94)03411-U
and CuClg- are the main complexes in the solutions [5], the predominant oxidants are Cu+, Cu,Cl, and Cu,Cl; 161. An early investigation of the electrode reaction Cu(II>/Cu(Hg) in aqueous acetate solutions [7] seemed to indicate that the step Cu(II>/Cu(I) was rate determining over the whole ligand concentration range available. On this basis the result obtained was that the predominant oxidants in the charge transfer were CuAc+ and CuAci for [AC-] > 10 mM. The large contribution from CuAc; was unexpected and hard to explain. However, in a later study of the corresponding electrode reaction of the Cu(I1) glycollate system [8], it became clear that at higher ligand concentrations the step Cu(I)/Cu(Hg) has a considerable influence on the total charge transfer measured. This finding motivated the present reinvestigation of the copper acetate system, also including electrocapillary measurements. 2. Experimental 2.1. Chemicals
Cu(I1) perchlorate and liquid copper amalgam (0.1% by weight) were prepared as described earlier [7]. Per0 1994 - Elsevier Science S.A. All rights reserved
176
S.
Fronaeus/ CM(H)/Cu(Hg)
chloric acid, sodium perchlorate and sodium acetate were of analytical grade, and all solutions were made up using double-distilled water. 2.2. Experimental details The measurement cell has been described previously [9]. The surface area of a single amalgam drop, used as the polarizable electrode, was 0.034 cm*. All measurements were carried out at 25.0 + 0.2”C. The ionic strength of the solutions was 1.00 M with sodium perchlorate as the supporting electrolyte. The complex solutions were kept free from oxygen by flushing with pure nitrogen. The charge transfer resistance R,, was determined according to a cycling current-step method [lo], theoretically improved 1111,and by use of a modified technique [121. In the earlier investigation faradaic impedance measurements showed that the electrode reaction is controlled by charge transfer and diffusion only. This is also a necessary and sufficient condition for the applicability of the cyclic current-step method. The bridge used and the procedure for determining R,, has been described elsewhere [12]. However, in the present investigation the bridge was adjusted until the faradaic voltage response was compensated at a time 0.094 r after the beginning of each half-period (duration 7/2) [ll]. After renewal of the amalgam drop, an initial value of R,, was measured and the constancy of this value was checked over a period of about 1 min. This is an indication that a possible deviation from Coulomb symmetry of the square wave within this time interval was unimportant [lo]. Furthermore, R,, for some of the complex solutions had been obtained earlier from impedance measurements, and both polarization methods gave consistent values. The capillary electrometer and the other experimental equipment for the determination of 42 potentials and specific anion adsorbabilities were the same as used previously [ 121. Values of [H+] in all the complex solutions were obtained in separate emf measurements. 3. Electrode kinetics
where i, 1 and i,, are the exchange current densities of the steps Cu(I>/Cu(Hg) and Cu(II)/Cu(I) respectively. It is assumed that i, is calculated from R,, by using the expression R,, = RT/(2FAi,) where A denotes the area of the polarizable electrode. The system CU*++ AC- mainly consists of mononuclear complexes [131 at the low Cu(I1) concentrations used in the present study. However, at [Cu(II)] > 20 mM, the formation of dinuclear complexes is also noticeable. However, in the thermodynamic measurements there was no indication of formation of hydroxo complexes or complexes with HAc in the buffer solutions used. It is well known that hydrated Cu*+ exchanges water extremely rapidly in solution. Accordingly, its complexes with the hard base AC- with oxygen as the donor atom are certainly very labile and in mutual equilibrium during the measurements of R,,. The presence of an amalgam pool also ensures equilibrium between C&I) and Cu(1) in advance. Then the following reaction scheme can be proposed for the overall charge transfer: CuAcT-’ + e- (am) = Cu,Ac;-j
+ e-(am)
CuAcj’-j + e - ( am) e
CuAc J! e
-j
Cu”Cu’Ac3J -j Cu(am) +jAc-
(2)
(3)
(4)
The following final expressions (5) and (6) are obtained for i,,, of reactions (2) and (3) and i,,, of reaction (4) [4,71: i,,, = C( kj[cu2+]0~5(1+a~) + k:[Cu2+]05(3+~~~)[AC-]’ i
(5) i,,, =
~k~[C~2f]o’5a’[Ac-]’
(6)
i
o<“j’“;,“J
The
kj = Fk;pi”jp(ic’-9)
3.1. Expressions for the exchange current density The disproportionation reaction 2Cu(I) s Cu(I1) + Cu(Hg) must be taken into account in the system Cu(I1) + Cu(1) + Cu(Hg). If this reaction is slow compared with the charge transfer steps and [Cu(I)] < [Cu(II)I, the implication is that the two steps become consecutive at polarization, and the following equation can be deduced for the electrochemically determined overall exchange current density i, [8]: ii’ = OS( ici + ii:)
electrode reaction in acetate solutions
(1)
xexp[(j - 1 -“j)42F/R’] k;
=
(7)
Fkkgrp(l”‘K-“.‘“:.[Cu(am)] 1-o.5a;
Xexp[(j-a;)$,F/RT]
(8)
In expression (7) koj and aj denote the true rate constant and the anodic transfer coefficient of reaction (2), pj and P(i are the stability constants of CuAc;-j and CuAcf -j respectively, and K is the disproportion-
S. Fronaeus / CL&I) / Cu(Hg) electrode reaction in acetate solutions
177
ation constant of Cu+. The exponential factor is the Frumkin factor. Equation (7) is also applicable for k(i’ if $’ and the stability constants p; for Cu,Ac~-j and /37 for CU”CU’AC~-~ are used and j - 1 in the Frumkin factor is replaced by j - 3. An average value of the exponents for [Cu2’] appearing in the complete expression for i, can be obtained from the function cu= (ai0gi,/ai0g[cu2+])L,-l
(9)
For the single-electron steps two further quantities ‘Yi and Z2 can be defined by replacing i, by i,,, and i,,, in eqn. (9). From eqn. (5) it is easily found that i 0,2’y2 = ~(O.S(l
+ Lyj)kj[Cu2+]0.50+ni)
j +0.5(3 +$!)k;[C~~+]~‘~(~+“)[Ac-]j
(10) IogGkYM)
Finally, eqn. (1) yields Z/i,
= OS( EJi,,,
+ ‘Y2/io,,)
(11)
As the determination
of i, was carried out in the presence of a supporting electrolyte of constant and fairly high ionic strength, it can be assumed that variations in the activity coefficients and in the $Q potential are suppressed, so that true rate constants are obtained. Different polarization measurements (discussed in ref. 8) indicate that in acidic copper perchlorate solutions the disproportionation reaction is slow compared with the charge transfer steps. Evidence for the applicability of eqn. (1) to the glycollate (L-1 system was given by the fact that the slope of Z as a function of [L-l decreases considerably at higher [L-l. A similar decrease is found for the acetate system (Fig. 2 below) and leads to the same conclusion. However, if the disproportionation is much faster than the charge transfer steps, they become parallel and then i, = 0.5(io,, + i,,,). It is easy to verify that such an equation is not compatible with the variations in i, and E in the acetate system and with the fact that i,,, > 2i, at [AC-] = 0 [8]. 3.2. Measurements of i, and calculations As the exchange current density is fairly high in this system, it was necessary to keep the total Cu(I1) concentration cc” between 0.3 and 3 mM and the acetate concentration cAc at 20 mM or less to obtain measurable and reliable R,, values. In each measurement series coU was kept constant (0.66 mM) while cAc was varied by successive additions of perchloric acid. In separate emf measurements the dissociation constant of acetic acid was re-determined as pK, = 4.59 (cf. ref. 14). Then the free ligand con-
Fig. 1. Plots of (a) log i,, (b) log i,,, and (c) log i0,, as functions of log[Ac-] at c Cu = 0.66 mM. The curves were calculated from eqns. (l), (5) and (13) using the parameters in Table 1.
centrations were calculated from values of [H+]. The i, values obtained are reported in Fig. 1. The following stability constants [13,14] were used for the Cu(II) complexes: log(&/M-‘)
= 1.67, log(p2/Me2)
log(p3/M-3)
= 3.06.
= 2.65
These constants were used to calculate the relationship CC”= [Cu2+] (1+ ~pi[AC-I’) j
and
[Cu2+] from
(
In order to determine the quantity E measurements
of
R,, were also carried out at varying values of cc” and
with [AC-] as a parameter. Values of cl! at cc” = 0.66 mM were obtained graphically according to eqn. (9) from the slopes of approximately rectilinear log i, vs. log[Cu2+] plots. The values are given in Fig. 2. It is evident Z increases with increasing [AC-] within the range investigated, but its value remains below 1.0. At [AC-] < 3 mM the experimental data can be represented fairly well by the equation ([Cu2+] and [AC-] in M) i,/mA
cme2 = 1.5 X 102[C~2+]0’65 + 2.4 x 105[Cu2+]o’70[Ac-]
(12) This is evident from Fig. 3. The value E = 0.7 obtained at low [AC-] indicates that i, = i,,, within this range of [AC-]. Then according to eqn. (1) we should have
S. Fronaeus / Cu(II) / Cu(Hg) electrode reaction in acetate solutions
178
TABLE 1. Values of the composite coefficients in eqns. (5) and (6) when i, 2 and io,I are expressed in mA cm-‘, and [Cuzf ] and [AC- I in M j 0 1 2 3
I
I
-3.5
I
-3.0
I
-2.5
I
-2.0
-I
log([Ad/M)
Fig. 2. Plots of Z (0) and Cu, (01 as functions of log [AC-I at cc. = 0.66 mM. The curves were calculated from eqns. (10) and (11).
Thus values of the coefficients zol B- lo2 and i, = 2i,,. k; (Table 1) and of the exponents OS(1 + ai> for j = 0 and j = 1 in eqn. (5) are obtained directly from eqn. (12). At higher ligand concentrations, where Z > 0.7, eqn. (12) is obviously not applicable. Further calculations imply an estimation of i,,, at higher [AC-]. To do this we need to use results from the investigation of the electrode reaction Cu(II)/Cu(Hg) in glycollate solutions [B]. In this system an expression similar to eqn. (12) and with the same value of 0.70 for the exponent 0.50 + a,) was found to be valid at [L-l < 5 mM. For
kj 75+5 (1.2+0.1)x105 12x106
k’! I
1O-2 k’j 2.5 + 0.5
9+1
electrode reactions where the second mononuclear complex also takes part in the charge transfer, it is generally found 1151that (Ye= (pi. Accordingly, for the glycollate system the maximum value of Z attained is ca. 0.70, and thus the quantity Eu, in eqn. (11) should also be ca. 0.70 at higher ligand concentrations, as there is no indication of formation of dinuclear complexes in this system [13]. Finally, if it is presumed that & and (Y: in eqn. (6) also have a value of 0.40 in both systems, i.e. Zu,= 0.20, it is feasible to calculate i,,, for the glycollate system from eqns. (1) and (11) and to determine values of the composite coefficients kb and k;. It is found that k;/k; = 20 f 8 M- ‘. The values of the stability constant pi in eqn. (7) are not known for the two Cu(1) systems, but they are probably approximately equal and small, as is the case for the corresponding Ag(I) systems [16]. However, the rate constant ky for the participation of CuL+ in the charge transfer step Cu(II)/Cu(I) is about 2.5 times larger than the corresponding rate constant for CuAc+. Also, it has been found that glycollate is a better electron mediator than acetate for some homogeneous redox reactions [17]. Thus it can be concluded that the rate constant k;’ in eqn. (8) also has a lower value for CuAc than for CuL. Consequently, in eqn. (6) for [AC-] < 2 x lo-’ M only the term with j = 0 is taken into account. Then eqn. (6) has the simple form (kb in Table 1) i,,, = kb[Cu2t]0.20
Fig. 3. Plots of lo&, - 1.5 X 102[Cu2+]0~65)[A~-I-’ as a function of log[Cu’+] at different low values of the parameter [AC-]: l 0.29 mM; n 0.87 mM; A 2.57 mM.
lo-”
(13)
At constant cc” there is a small decrease in i,,, with increasing [AC-] (Fig. l), as the stronger complex formation with Cu2+ makes [Cu(I)]/Cu(II)] decrease. Finally, using eqns. (0, (11) and (13), values of i,,, and ‘Y2 in the whole [AC-] range available can be calculated from the measurements of i, and Z. They are reported in Figs. 1 and 2. If another normal value of ct$ and a; is chosen (e.g. 0.50), both the coefficients kb and k; for glycollate become 1.48 f 0.02 times larger for the range 0.3 < [,f;“:h+&rnM < 0.6, b u t o f course this has no influence o,l values calculated from eqn. (13) with the
S. Fronaeus / Cu(II) / Cu(Hg) electrode reaction in acetate solutions
exponent ah/2 = 0.25. The effect on Cy, is very small; the maximum value attained decreases by 0.04. In the range 3 < [Ac-]/mM < 20 the complex CuAc, might take part detectably in reaction (2). However, as 5, attains a value of 1.25, it is evident that at least one dinuclear complex, Cu,AcP-i, contributes considerably to the charge transfer according to reaction (3). In the relevant terms of eqn. (5) the exponents 0.50 + a,) and 0.5(3 + al> can be expected to have the values 0.70 and 1.7 5 0.1, respectively. Then, if the terms with the coefficients k, and k, on the right-hand side of eqn. (5) are subtracted from i,,, and the remaining terms are divided by [CU~+]~~~[AC-]~,values of the quantity X= k, + k;[Cu’+]“[Ac-]‘-2
a = 1.0
I
179
I
’
A / /
:
/
1
‘f
s> ^
‘9
0
E.
(14)
are obtained. The same operation performed with eqn. (10) yields values of a similar quantity: Y = 0.7k2 + (a + 0.7) k;[ &“+I”[
Ac-]j-2
(15)
It is found that both X and Y increase with constant cc” and increasing [AC-], indicating that j > 2. The most probable value is j = 3, which corresponds to the cationic complex Cu,Ac:. Accordingly, X and Y for ccU = 0.66 mM, a = 0.9 and j = 3, have been plotted versus [CU~+]~.~[AC-] in Fig. 4. It is evident that both functions can be represented by straight lines, and the slopes yield consistent values of k’j. This finding confirms the value j = 3 and the high value of 0.5(3 + a;) anticipated. An upper limit of k, is obtained from the intercept of X on the ordinate axis. It is true that the intercept of Y seems to be approximately zero, but the random errors in Y are larger than those in X. A value a = 1.0 also gives straight lines, but in this case the intercept of Y is negative and so it seems that a = 0.9 yields the best fit with all the measurements. It is clear from Figs. 1 and 2 that the functions io,2, i,, (Y, and Z, calculated from eqns. (5), (1) plus (13), (10) and (11) with the constants listed in Table 1 reproduce the i, data very well and the Z data fairly well. The results obtained indicate that, in addition to hydrated Cu2+, the complexes CuAc+, CuAc, and Cu,Ac: take part as oxidants in the electron transfer step Cu(II)/Cu(I). Their relative contributions to i,,, as functions of the ligand number E have been calculated from eqn. (5) and are shown in Fig. 5. It is seen that at 7i > 0.2 the predominant contributions to i,,, come from CuAc+ and Cu, AC:. To see how the approximation of i,,, influences the results, calculations of the function X in eqn. (14) have been carried out using i,,, values obtained with k,/k, = 10 M-’ instead of zero, i.e. half the value valid for the glycollate system. With the same plot as in Fig. 4 a
I
I
I
4
8
12
[@f9
[AC-]10”
Fig. 4. Plots of Xc*) and Y(A) from eqns. (14) and (15) for a = 0.9 and j = 3 as functions of [CU~+]~~~[AC-]at ccU = 0.66 mM.
8(
a
% 4(
2(
Fig. 5. The relative contributions to io,z from the different Cu(II) oxidants at cc,, = 0.66 mM and varying ligand number E: (a) CL?+; (b) CuAc+; (c) CuAc,; (d) Cu,Ac, + . The curves have been calculated from eqn. (5).
S. Fronaeus / Cu(ll) /Cu(Hg)
180
electrode reaction in acetate solutions
TABLE 2. The interfacial tension y, components of charge and the potential dz in the electrode double layer at an electrode potential of - 4.5 mV vs. the fixed reference electrode Ag IAgCl(s) 10.1 M NaCl + 0.9 M NaClO, Electrolyte
q/pC
1.00 M NaClO, 1.00 M NaAc
13.0 15.0
cm-’
r/J
m-*
0.392 0.395
Fr+/pC
-q-‘/PC
cm-*
5.20 4.50
cm-*
- WmV
21 22
33 29
straight line is obtained which yields the same upper limit of k,, while k, decreases by only 10%. Thus the approximation that the use of eqn. (13) involves does not cause any uncertainty about the validity of the results. 4. The electrode double layer 4.1. Specific anion adsorption and C& potentials Electrocapillary measurements according to the method described earlier [12] were performed on pure mercury in contact with solutions of concentration c of sodium perchlorate or acetate. For the determination of the charge density q on mercury and the relative surface excess r+ of sodium ions, applied electrode potentials E in the range - 100 mV < E < 0 mV versus a fixed reference electrode (see Table 2) were used to measure the inter-facial tension y. For the determination of r+, solutions with c = 1.50 M were diluted stepwise and after each step E was increased until y had attained the value valid at c = 1.00 M and E = - 45 mV. The almost rectilinear curves in Fig. 6 give values of (aE/a log cl,,. The value of r+ was obtained from this quantity and q [12]. The potential #+ and the amounts qbo, or qiC- of specifically adsorbed anions were calculated in the usual way. [18]. The values obtained are given in Table 2. The q! values indicate that at the potential selected the specific adsorbability of AC- is approximately the same as that of Cloy. This potential corresponds to the equilibrium potential E” of the amalgam electrode in a complex solution with cc” = 0.66 mM and [AC-] = 6.5 mM. Furthermore, within the range [AC-] I 20 mM, E” varies from only - 41 mV to - 5 1 mV. Thus within this range the
logkm) Fig. 6. The mercury electrode potential E as function of log c for sodium perchlorate (0) and acetate (0) solutions at constant values of the interfacial tension y: o y = 0.392 J m-*; l y = 0.395 J m-*.
equation qiC-/ql = [AC-]/([ClO;l + [AC-]) should hold with q!_= q&,; + qiC- in the complex solutions. Now, as both (ClO;] + [AC-]) and E” are apbroximately constant, q!. should also be constant and qiCshould be proportional to [AC-]. The consequence is that, for an oxidant CuAcT-j or Cu,A&j that is specifically adsorbed via a carboxylate grou;, the number of ligands j also includes the acetate bridge to the electrode. Thus the contributions from &AC&, and cu, AcL to ia,, are proportional to -qic-[Cu2+lo.70 and -q~~-[Cu2+]1.6[Ac-]2. For the latter complex the formulation means that one ligand forms the carboxylate bridge to the electrode, whereas the other two ligands are not specifically adsorbed.
TABLE 3. The rate constants ky and ki” relating to the participation of CuAcT-j and Cu,Acz in the electrode reaction step Cu(II)/Cu(I), enthalpy changes AH: and entropy changes ASi” in the reactions CuAc;:i + AC-+ CUAC~-~ in aqueous solutions at 25°C
i
kpCuAc?-‘)/cm
0 1 2 3
(1.9 f 0.l) x 10-Z 5.8 go.5 I 200
s-l
3b 0.3 c
a From ref. 19. b From eqn. (7). ’ From eqn. (16).
AH; a/kJ mol-’
AS; a/J K-’ mol-’
4.4 1.7
51 30
and
S. Fronaeus / C&I)
/ Cu(Hg) electrode reaction in acetate solutions
4.2. The true rate constants k;
181
To obtain values of the true rate constants relating to reactions (21, it is necessary to make an assumption about the unknown stability constants p(i of Cu(I>. It is reasonable to use the values of the corresponding constants of the system Ag++ AC-, i.e. p’, = 2.5 M-l and pi = 1.5 Me2 [16]. It is true that this approximation should yield stability constants which are rather low because of the smaller radius of Cu+, but this fact cannot be of great importance for the conclusions that can be drawn from the ratios of the rate constants. It is evident from Table 2 that, for [AC-] < 20 mM, & = - 33 mV should be used in the calculations. Then, using the transfer coefficients at, = 0.30, czi = (Y*= 0.40, K-‘[Cu(am)] = lOA M [S] and the composite coefficients kj in Table 1, the rate constants k; have been calculated from eqn. (7) (Table 3).
bridge from Cu(I1) in the OHP to the amalgam electrode is probably the main cause of the high value of k;/k”,. This conclusion is supported by a previous comparison [20] of the rate-enhancing effects of different carboxylate ions on the charge transfer C&I)/ Cu(I). The sequence of these ions according to their effect (acetate < glygollate < glyoxylate) is the same as that found if the ligands are arranged according to their catalytic effect on certain homogeneous redox reactions [17]. In the latter case, it was proved that the carboxylate group functions as an electron-mediating bridge. The sequence found provides a strong support to the suggestion that carboxylato-bridged electron transfer is important in the present electrode reaction. The following equation is easily derived from the general theory for the kinetics of electrode reactions [18]:
5. Discussion
k” = (z)“(E)‘-”
The results obtained indicate that formation of the complex gives rise to a strong catalytic effect on the overall electrode reaction. This effect relates to a pronounced rate enhancement of the electron transfer step Cu(II)/Cu(I). The strong increase in the exchange current density +2 of this step at increasing [AC-] cannot to any extent be ascribed to the Frumkin effect as 4*, the potential of the OHP, should have a value of ca. -33 mV in the complex solutions. Thus the complex formation causes the Frumkin factor in eqn. (7) to decrease. Neither can the increase in i,,, be caused by hydroxo complexes, which are present in very low concentrations. Such an effect should be more pronounced for acetate than for glycollate solutions because, since pK, = 3.60 for HL, the pH values of the complex glycollate solutions were in general one unit lower than those of the corresponding acetate solutions. However, the values of i, give identical values of k,, whereas k, is larger for glycollate [81. It is evident from Table 3 that on formation of CuAc+ there is a large relative increase in the rate constant (ky/k”, = 3001, whereas the formation of CuAc, gives an additional relative increase that is much smaller (k”,/k; I 35). Table 3 also shows that the values of AH: and AS; for the first two complex formation steps of Cu(I1) are positive. However, they are so low that it is unlikely that there is a pronounced change in the inner-sphere geometry in any of the steps (cf. the Zn*++ AC- system [19]) such that the difference in hydration energy between Cu(I1) and Cu(1) would decrease and considerably reduce the activation energy of the electron transfer. Formation of an electron-mediating carboxylate
where k and k denote the chemical parts of the rate constants of the forward or cathodic and the backward or anodic charge transfers of a simple electrode reaction with the true rate constant k”. The question is whether th_e h&h value of ky/k”, depends upon a large laluz of k,/k,, i.e. ligand bridging at C&I), or of k,/k,, i.e. effective ligand bridging at Cu(1). The low stability constants estimated for the Cu++ AC- system should indicate a weak and essentially electrostatic bond. This implies that the interaction between Cu+ and a specifically adsorbed AC- should be even weaker and give a very low concentration of CuAc,,, compared with that of nap-a_dsorbed CuAc at the OHP. Thus a high value of k,/k, cannot be expected. However, for the system Cu*++ AC- the specifically adsorbed AC- should make the concentration of CuAc& _muc& higher than that of CuAcads, implying a high k,/k, by the electron-mediating bridge at the amalgam. The moderate value obtained for k”,/ky is an upper limit. For this reason the only possible conclusion is that the ligand-bridging conditions for CuAc, should be similar to those of CuAc+. The considerable participation of the dinuclear complex Cu,Acl as an oxidant in the electron transfer step Cu(II)/Cu(I) is very interesting. It has been reported that Cu(I1) acetate in aqueous acetic acid of high concentration is partly dimeric [21]. In a previous thermodynamic study [13] of the complex formation, measurements were performed within the concentration range 25-100 mM of Cu(II), and the stability constants p; and p’; of the complexes Cu2Ac3+ and Cu,Acz+ were also obtained: log@‘;/M-*) = 1.70 and 10g@;/M-~) = 3.04.
(16)
182
S. Fronaeus / Cu(II) / Cu(Hg) electrode reaction in acetate solutions
To arrive at a quantitative measure of the electrocatalysis by the formation of the oxidant Cu,Ac: it is desirable to try to calculate the rate constant k;” relating to reaction (3) from both eqn. (7) and eqn. (16). In both cases the calculations have to be based on some reasonable assumptions. The values @‘;/pi = 1.1 M-l and @J/3, = 2.4 M-l make the estimate p’;/& = 6 M- ’ plausible, giving p’; = 7 x lo3 Me4. A rough estimate of the stability constant p,* of Cu”Cu’Ac, is obtained if it is postulated that &J/p’; = pi/p,. This relationship yields PT = 4 X lo2 MP4. With the two stability constants estimated and (~‘j= 0.4 inserted in eqn. (7) the result is k 03”= 3 x lo5 cm s-l. In these calculations the Frumkin factor does not compensate for the increase in the concentrations of both the oxidant and the reductant in the pre-electrode state as a result of the specific adsorption of the complexes on the amalgam. This effect should give value of the rate constant that is too high. The theory of bridged electron transfer is not very well developed. However, it should be possible to arrive at fairly simple but plausible relationships for the participation of different complexes in an electrode reaction, where the same ligand bridge to the electrode can be formed. In the present system it can be assumed that a carboxylate bridge between Cu(I1) and Cu(Hg) decreases the chemical part of the Gibbs energy of activation of the electron transfer by an approximately constant value for the different complexes or increases the transition probability by a constant factor. Thus, in the calculations based on eqn. (161, it is assumed that formation of CuAc+ and Cu,Aci give rise @ ap2roxim$ely the same relative increase in k, i.e. k, = k, = elk,. As to the reductants CuAc and Cu”CurAc3 the catalytic effect of the latter complex on the backward reaction in eqn. (3) should be the same on the forward reaction, as a as that of Cu,Acz carboxylate bridge between C&I) a@ Cu(am) can still be formed and consequently pi = elk,. Finally, as has been discussed above, coordination of-AC_ @ Cu+ should have a slight catalytic effect, i.e. k, = c2k, with c2 =SLci. Then eqn. (16) with (Y= 0.4 gives the expressions k;” = elk; k” = C0.4C0.6ko 1120
(17) (18)
Inserting the known value of k;/k”, and selecting c2 = 1 yields c1 = 1.6 x lo6 and k;” = 3 X lo4 cm s-l, which should be maximum values. However, the latter calculations do not take into account that, on the formation of a dinuclear complex a decrease in inner-sphere hydration should take place, implying that the difference in hydration energy be-
tween oxidant and reductant probably decreases, making the rate constant of the electron transfer increase. It is also probable that the assumptions made can influence the two calculations in different ways. Nevertheless, the high values of k;” obtained in both estimations strongly support the conclusion that in this case both the oxidant and the reductant can establish an electron-mediating bridge to the electrode, and that this is the decisive cause of the fast electron transfer. The strong electrocatalytic effect indicated is comparable with the rate-enhancing effect of some mono- and dicarboxylates on certain homogeneous redox reactions [22,23]. Finally, one interesting question is why Cu,Acg+ does not take part detectably as oxidant, although its concentration in the bulk of the solution is certainly larger than that of Cu,Ac: at the values of [AC-] used and the Frumkin factor is more favourable. It is possible that the predominant structures of both these complexes in solution contain a cyclic group with two carboxylate bridges between the two Cu2+ ions. In this case Cu,Acz+ cannot form a carboxylate bridge to the amalgam by itself without breaking the cyclic structure. If the energy required for this process is larger than the energy of the bond between the amalgam and a coordinated carboxylate group, substantial bridging is inhibited. References 1 D.E. Richardson and H. Taube, Coord. Chem. Rev., 60 (1984) 107. 2 L. Dubicki, J. Ferguson, E.R. Krausz, P.A. Lay, M. Maeder, R.H. Magnuson and H. Taube, J. Am. Chem. Sot., 107 (1985) 2167. 3 U. Fiirholz and A. Haim, Inorg. Chem., 26 (1987) 3243. 4 S. Fronaeus and CL. Johansson, J. Electroanal. Chem., 125 (1981) 139. 5 S. Ahrland, P. Blauenstein, B. Tagesson and D. Tuhtar, Acta Chem. Stand., Ser. A, 34 (1980) 265. 6 S. Fronaeus and CL. Johansson, J. Electroanal. Chem., 112 (1980) 197. 7 S. Fronaeus, R. Johansson and C.-O. &tman, Chem. Ser., 1 (1971) 52. 8 S. Fronaeus and C.L. Johansson, J. Electroanal. Chem., 48 (1973) 195. 9 R. Johansson and C.-O. &tman, Acta Chem. Stand., 23 (1969) 2939. 10 M.D. Wijnen and W.M. Smit, Reel. Trav. Chim. Pays-Bas, 79 (1960) 22, 203. 11 P. Teppema, M. Sluyters-Rehbach and J.H. Sluyters, Reel. Trav. Chim. Pays-Bas, 85 (1966) 303. 12 S. Fronaeus and C.L. Johansson, J. Electroanal. Chem., 80 (1977) 283. 13 S. Fronaeus, Doctoral Dissertation, University of Lund, 1948. 14 A.E. Martell and R.M. Smith, Critical Stability Constants, Plenum Press, New York, 1977. 15 S. Fronaeus, Coord. Chem. Rev., 88 (1988) 203. 16 L.C. Sill&r and A.E. Martell, Stability Constants of Metal-Ion
S. Fronaeus / C&l)
/ Cu(Hg) electrode reaction in acetate solutions
Complexes, Special Publication 17, Chemical Society, London, 1964. 17 H. Taube and S. Gould, Act. Chem. Res., 2 (1969) 321. 18 P. Delahay, Double Layer and Electrode Kinetics, Interscience, New York, 1965, pp. 60, 164. 19 P. Gerding, Acta Chem. Stand., 21 (1967) 2015.
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20 S. Fronaeus and C.L. Johansson, J. Electroanal. Chem., 60 (1975) 29. 21 J.K. Kochi and R.V. Subramanian, Inorg. Chem., 4 (1965) 1527. 22 H.J. Price and H. Taube, Inorg. Chem., 7 (1968) 1. 23 C. Hwang and A. Haim, Inorg. Chem., 9 (1970) 500.