Kinetic and Mechanistic Study of the Reduction of Copper(l1) in Lithium Nitrate Using Alternating Current Polarography Fred M. Hawkridge, Jr.,l and Henry H. Bauerz Department of Chemistry, University of Kentucky, Lexington, K y . 40506
A quasi-reversible electrode process was found for the reduction of Cu(ll) in LiNOI at high pH (ca. 5); Cu(0H)(H20)6t is considered to be the electroactive species. The reduction of Cu(ll) at low pH ( 5 c a . 1) was found to follow a mechanism involving a chemical reaction preceding charge transfer. Dehydration of the C U ( H ~ O ) ~ ~ + ion at the electrode surface is considered to be the preceding chemical reaction. Both reaction paths are followed at intermediate values of pH. Kinetic parameters are determined describing the reaction path over the range of pH studied. ALTERNATING CURRENT POLAROGRAPHY and modifications thereof (Le. phase-selective fundamental and second-harmonic ac polarography) are known to be sensitive and practical in their application to kinetic and mechanistic problems at the dropping mercury electrode (1-3). The recent theoretical treatment of McCord and Smith ( 4 , 5) and the earlier work of Smith (6) have shown how the kinetics and mechanisms of numerous systems can be determined. The phase angle and current amplitude are the experimental variables through which the parameters of an electrode process can be determined. In the present study, it has been found that the reduction of Cu(I1) at high pH follows a quasi-reversible path, controlled by the rate of charge transfer and by diffusion. At low pH, the electrode process involves (in addition to electron transfer and diffusion) a chemical reaction preceding charge transfer, following the scheme kl
Y
0 IC 2
+ ne-=
ka,u
R
(1)
The chemical reaction is postulated to be the partial or total dehydration of Cu(H20)e2+. It was noted in this investigation that the cation of the supporting electrolyte affected the rate of the overall electrode process over the range of pH studied, ?he rate increasing in the order Li > Na > K. This effect has not been previously reported for reduction at a positively charged electrode to the authors’ knowledge. The results given here indicate that this effect may be due to the influence of the cations on the rate of the preceding chemical reaction. 1 Present address, Department of Chemistry, Case Western Reserve University, Cleveland, Ohio 44106. 2 To whom correspondence should be addressed.
(1) B. Breyer and H. H. Bauer, “Alternating Current Polarography and Tensammetry” in “Chemical Analysis,” P. J. Elving and I. M. Kolthoff, Ed., Vol. 13, Wiley (Interscience), New York, N.Y., 1963. (2) T. G . McCord, Ph.D. Thesis, Northwestern University, Evanston, Ill., 1970. (3) D. E. Smith, “Advances in Electroanalytical Chemistry,” A. J. Bard, Ed., Vol. 1, Chapter 1, Dekker, New York, N.Y., 1965. (4) T. G . McCord and D. E. Smith, ANAL.CHEM.,41, 116 (1969). (5) T. G. McCord and D. E. Smith, J . Electroanal. Chem. Znterfacial Electrochem., 26, 61 (1970). (6) D. E. Smith, ANAL. CHEM., 35,602 (1963). 364
THEORY
Calculation of the series resistance (R,)and the doublelayer capacity (& --SA:/&
---\ ‘..----.-.-.----z.--*
c
0
Figure 3.
-.-.
4s’\,
*
.
m-.
-
I-
1 ” - 60 A .
I
I
- 40
I
I
I
E-E
I
0
-20 /2
I
I
I
I
20
I
40
(ve. S C E ) in Millivolts
‘[------I 5
Figure 4. Plot of cot
4 us. E
- Er+
-ec
0
0
Parameter values: Same as Figure 3, except f = 400 Hz
I
-40
I
I
1
-20
E-€
The nature of the preceding chemical reaction remained to be identified. Woodburn et a/. (25) postulated that a dissociation step precedes reduction of Cu(I1) particularly for the aquo complex; in a chronopotentiometric study, the product of for Cu(I1) in 0.2M Na2S04was shown to increase markedly with decreasing current density, indicative of a preceding chemical reaction (this effect was seen on a mercury pool but not on a platinum electrode). In explaining this effect, the work of Maki (26) was cited, which postulated that an electrode can be considered a ligand whose coordination power is strong enough to make dissociation of the (electrode/depolarizer) coordination compound rate-limiting. Shirai (27) noted that a dissociation of some type preceded reduction of Ni(I1). Gierst and Hurwitz (28) reported that the partial dehydration of the hexa-aquo (Ni(I1) ion is rate S. I. Woodburn, T. J. Cardwell, and R. J. Magee, Rec. Trau. Chim. Pays-Bas., 88, 1167 (1969). (26) N. Maki, “Polarography 1964, Proceedings of the Third International Conference-Southampton,” Macmillan, London, 1966, p 505. (27) H . Shirai, Nippon Kaguku Zasshi, 82, 339 (1961); CA, 55, 14127h. (28) L. Gierst and H. Hurwitz, 2.Elekrrochem., 64, 36 (1960). (25)
1
I
0
I
20
I
I
I
I
40
i2(vs.SCE) in Millivol?s
determining in the reduction of that ion. Von Sturm and Ressel (29) found the reduction of Zn(1I) reversible in dc polarography but irreversible in ac polarography ; a preceding chemical reaction, partial dehydration, was proposed which is affected by the ratio of the equivalent thickness of the diffuse double-layer to the thickness of the reaction layer. The results of the present study also indicate a rate-limiting dehydration step preceding charge transfer at low pH. It is difficult to envisage an alternative reaction with Cu(H20)e2+ as the reactant. Thus, we postulate ki
+ 2e-
Cu(Hz0)e2+J_ Cup2+ k2
kw,o
Cu(Hg)
(5)
where Cup2+represents a species which is probably partially dissociated and of the general form CU(H~O)B-,~+ with n = 1 to 6. The preceding chemical reaction is considered to be slow enough to be important compared to the rate of electron transfer and diffusion in the ac polarographic experiment. The mechanism postulated for the high pH case is a quasireversible path following the scheme (29) F. von Sturrn and M. Ressel, Microchem. J., 5, 5 3 (1961).
ANALYTICAL CHEMISTRY, VOL. 44, NO. 2, FEBRUARY 1972
367
5.0
4.0
v1
0
3.0
-z + z
w
2.0 3
V
1.0
0
-80
-60
-40
-20
0
E
20
- E:
40
60
80
100
IN MILLIVOLTS
'2
Figure 5. D c polarogram, experiment and theory
Figure 7.
Parameter values: Cum) = 1.00 mM, 1M LiN03,T = 298 "Cy t = 1.00 sec, A = 0.967 mm2, Do = 0.72 X lop5 cm sec-', D r = 1.06 X 10-6 cm se-', CY = 0.6, k,, = 0.048 cm sec-I, Ksq = 1.0, (A)kl = lP,(B)ki = 1200 Solid line: Theory Points: Experiment
Cu(OH)(H20)6+
3
Cu,*+
k?
kop.a
+ 2e- 17 Cu(Hg)
(6)
where Cuq2+represents a species analogous to the preceding chemical reaction case which, if different from Cupzf, differs so little that k., and CY are the same for both ions. The preceding chemical reaction in this case is considered rapid and
Effect of Keg on dc polarogram
Parameter values: Same as Figure 5 except k, A . Kq = 5.00 B. Kbq = 2.50 C. Kq = 1.00 D. Ksq = 0.75 E. Kq = 0.50
1000
therefore kinetically inoperative with respect to the rate of electron transfer and diffusion. The hexa-aquo Cu(I1) ion would have a greater degree of symmetry than the hydroxo complex and would be expected to be more stable with respect to partial or total dissociation of the hydrated water molecules. Thus, the hydroxo complex would be expected to penetrate to the reaction layer via dissociation more rapidly.
Figure 6. Ac polarograms, experiment and theory Parameter values: Same as in Figure 5 with AE = 10m V rams),f = 100 Hz 0 pH 5.75 pH1.00
EDC
368
=
ANALYTICAL CHEMISTRY, VOL. 44, NO. 2, FEBRUARY 1972
- REV E l l 2
IMILLIVOLTSI
e1
Figure 8. Effect of K., on ac polarograms Parameter values: Same as in Figure 7 with A E = 10 mV (r.m.s), f = 100 Hz
The values of Keq and kl for the preceding chemical reaction were determined by curve fitting the theoretical results to experiment from the theoretical treatment of McCord using his computer program (2). The values of k,, and a used in this treatment were initially taken from the values for the high pH limit; the resultant fit for the low pH situation is satisfactory, and this substantiates the assumption that the electroactive species are the same, or very similar. The results are shown in Figures 5 and 6; the values of K e gand kl result as 0.5 < Keq < 2.5 and 800 < kl < 1400. The diffusion coefficient was determined from the dc polarographic results and the electrode area from capillary characteristics. The effect of varying Keqis shown in Figures 7 and 8. The results in Figure 1 are inconclusive as to whether or not the Na and K systems reach a charge-transfer impedance equal to that of the Li system at high pH or whether they reach some other limiting value. The present interpretation of the mechanistic paths at low and high pH is consistent with the idea that a constant value equal to that of the Li system would be reached if it were experimentally possible to make measurements above pH 5.75 [the Cu(I1) precipitates above this pH and though some extension of the pH range would be possible by lowering the Cu(I1) concentration, it would not be enough to accomplish the above goal], Differences in the rate of reduction of Cu(1I) in the cations discussed would then be explainable in terms of their effect on the preceding chemical reaction in the diffuse double-layer. The exact nature of this effect is not clear but properties of the
cations such as their electronegativities (30) ( k . Li , greater than Na and Na greater than K) are in an order that would correlate with the presumed rates of dissociation of the hydrated Cu(I1) ion in that strongly electronegative ions would be more likely to interact with or distort the hydration sphere of a positive ion. CONCLUSIONS The decreased reversibility of the Cu(II)/Cu(Hg) system at low pH values is due to the presence of a rate-limiting reaction preceding reduction. This coupled reaction appears to be partial or total dehydration of the Cu(HzO)e*+species. At higher pH values, the species Cu(OH)(H?O),+ appears to be predominant in the bulk of solution, and there was no evidence of a rate-limiting reaction preceding reduction; presumably, the hydroxo species undergoes the dehydration more rapidly. The different apparent rate-constants for the reduction of Cu(I1) in electrolytes of Li, Na, and K at low pH may be due to the different influences of these cations on the ease of dehydration of C U ( H ~ O ) ~ ~ + . RECEIVED for Wiew June 24, 1971. Accepted August 309 1971. (30) F. A. Cotton and G. Wilkinson, ‘‘Advances in Inorganic Chemistry,” Interscience, New York, N.Y., 1967.
ANALYTICAL CHEMISTRY, VOL. 44, NO. 2, FEBRUARY 1972
369
