Side reactions of various compounds present may alter the theoretical pM,, value. If the same interfering substance is always present, as is often the case in routine analyses in industry, it is possible to add fairly large amounts of the interfering substance to the reference solution used for the determination of corresponding wavelengths as well as t o the sample solution. The pM jump will then diminish, but nevertheless the sharpness of a color change may often be sufficiently high for the dichrotitrator. As a n example we may mention the complexometric titration of a met.al ion MI in the presence of another metal ion, MII. The conditional constant is then [cf. (IO)] where Alog K = log KYIY- log K3rIIy. If large amounts of MII are added, the conditional constant, K I C ~ will Y ~ , be practically independent of the amount of MII in the original sample solution. To keep KIIrYtsufficiently high, the choice of complexing agent has to be based on theoretical principles. The value of Alog K is important, and in complexometric titrations other titrants than EDTA may often be advantageous. The presence of MII may affect the choice of indicator; the colors of MIIn and MIrIn must differ sufficiently. General aspects of stepwise photometric titrations were recently discussed by Skrifvars and Ringbom (15).
CONCLUSIONS
The main aim of this paper has been to clarify the basic theory of the function of a dichrotitrator, since a good knowledge of this theory is indispensable for the successful use of the instrument. The theory presented has been checked by experiments, partly using various combinations of commercial photometers, partly using a titrator of simple construction built in our laboratory (barrier layer cells, interference filters, shutters, magnetic stirrer). The results were in agreement with theory, and even titrations based on reactions with equilibrium constants below l o 4 were performed without difficulty. However, the results and experimental details will be reported in a separate paper, where the potentialities of a dichrotitrator will be discussed, taking into consideration the fact that the zero current principle of the instrument makes it particularly appropriate for automatic applications. RECEIVED for review February 13, 1967. Accepted May 24, 1967. Work supported in part by Statens Teknologiska Kommission and Oy Neste Foundation in Finland. ~
(15) B. Skrifvars and A. Ringbom, Zbid., 36, 105 (1966).
Supportilng Electrolyte Effects in Nonaqueous Electrochemistry Coordinative Relaxation Reactions of Reduced Metal Acetylacetonates in Acetonitrile Royce W. Murray and L. Kenneth Hiller, Jr.’
Department of Chemistry, Unicersity of North Carolina, Chapel Hill, N . C. 27514 The reduction potentials of a number of metal acetylacetonates in acetonitrile solvent are shifted to more positive potentials by the addition of LiClO, to the tetraethylammonium perchlorate supporting electrolyte. Studies of the F e ( a ~ a c )case ~ show that this effect is caused by a coordinative relaxation reaction of the Fe(acac)s- reduction product in which an acetylacetonate ligand becomes transferred to the lithium ion. Cyclic voltammetric data demonstrate that reoxidation of Fe(a~ac)~-can be kinetically controlled by the reverse coordinative “unrelaxation” reaction. When n < 3 in Fe(acac), complexes, coordinative relaxation of the reduced complex can also occur by ligand exchange with the diffusing electrode reactant. Preliminary electrochemical data on other metal acetylacetonates are presented.
USEOF THE WORD inert to describe the supporting electrolyte employed in a nonaqueous electrochemical investigation requires an appropriate quantity of discretion. An electrochemical o r chemical perturbation can result from interaction of the supporting electrolyte with either the electrode reactant or product, and a supporting electrolyte innocuous in Present address, Procter and Gamble Co., Miami Valley Laboratory, Cincinnati, Ohio.
these respects in an aqueous medium may not remain so when employed in lower dielectric solvents. Understanding of the role played by the supporting electrolyte in the event of such interactions is necessary for a complete appreciation of the properties of the sample system. The general effects of complexing supporting electrolytes on metal ion electrode reactants are well known. The more subtle ion-pairing effects of noncoordinating salts in nonaqueous solutions are likewise well documented, and Schaap ( I ) has developed polarographic theory for the metal ion reactant ion-pairing with electrolyte anions. The possible effects of supporting electrolyte on the product of the electrode reaction, on the other hand, have received less investigative attention. Consider, for instance, reduction of a neutral reactant toward which the supporting electrolyte is inert. This negatively charged product may now interact with the cation of the supporting electrolyte in several ways. One is an ion-pairing reaction, which may be of a simple and relatively innocuous nature, or which could be of more consequence by stabilizing a product such as an organic radical against a further reaction which might otherwise immediately (1) W. B. Schaap, J. Am. Chem. Sor., 82,1837 (1960). VOL. 39, NO. 1 1 , SEPTEMBER 1967
1221
tend to ensue. Another mode of interaction is possible for metal coordination compound reduction products, as the supporting electrolyte cation may act as a scavenger for any ligand groups less strongly bound as a result of the reduction process. Coordination compound reduction products are also, of course, potential ligand acceptors from, rather than donors to, their electrode interfacial environment. Nonsolvent ligand sources could be the supporting electrolyte anion, o r t k incoming oxidized coordination compound reactant itself. Such ligand transfer reactions can constitute a dramatic perturbation of a coordination compound’s electrochemical behavior. Several examples of such processes will be illustrated in this report. Several reports dealing with organic compounds in nonaqueous media have noted changes in electrochemical behavior with alteration of the inert electrolyte employed. Philip et a / . ( 2 , 3) in studies of benzil reduction in dimethylformamide, have presented evidence that the effects of substitution of LiC104 electrolyte for tetrabutylammonium salts arise through strong association of lithium ion with the benzil dianion product. Peover and Davis (4, 5 ) compared lithium and tetraethylammonium electrolytes in quinone reduction and also found strong lithium-dianion product associations. Aylward et al. (6) report a similar effect of lithium on azobenzene reduction. Other reports, however, appear to have overlooked organic product-supporting electrolyte interactions as a possible source of effects observed. Study of the electrochemical and associated chemical reactions of metal coordination compounds has been a subject of recent active interest. The series of reports by Dessy et al. (7) furnishes examples of the investigative potential of electrochemical methods in this field. Achievement of adequate reactant stability and solubility for study will frequently require recourse to nonaqueous media. No information on possible supporting electrolyte effects in such studies of coordination compounds is a t present available in the literature. To the extent that the samples of interest are neutral complexes, attention to this problem will center on the behavior of the electron-transfer products. In experiments conducted on the acetylacetonate (acac-) complexes of Fe(III), Ni(II), Co(III), Co(II), Cu(II), Pd(II), and Cr(II1) in acetonitrile solvent, the present authors observed a pronounced variation of electrochemical behavior with the supporting electrolyte employed. In both cases in which the reduction of the neutral complexes proceeded to a n amalgam state and those in which it did not, a comparison of behavior in tetraethylammonium and lithium perchlorate electrolytes revealed, among other effects, substantial positive shifts of the reduction waves in the latter electrolyte. As these effects appeared to be consistent with strong postelectron-transfer interactions with lithium ion, parallel investigations were carried through with the objective of understanding and comparing the behavior of the acetylacetonate complexes in the apparently noninteracting tetraethylam(2) R. H. Philip, Jr., R. L. Flurry, and R. A. Day, Jr., J . Electrochem. SOC.,111, 328 (1964). (3) R . H. Philip, Jr., T. Layloff, and R. N. Adarns, Zbid.,p. 1189. (4) M. E. Peover and J. D. Davis, J . Electroanal. Chem., 6, 46 (1963). ( 5 ) M. E. Peover and J. D. Davis, “Polarography 1964” (Proc. 3rd Intern. Cong., Southampton), G. J. Hills, Ed., Vol. 11, Interscience, New York, 1966, p. 1003. (6) . , G. H. Avlward. J. L. Garnett. and J. H. Sharv. _ .Chem. Communs.. 1966, 137: (7) T. Psarras and R. E. Dessv. J . Am. Chem. Soc.. 88. 5132 (1966) and references therein. .
I
1222
ANALYTICAL CHEMISTRY
monium perchlorate medium and the apparently strongly interacting lithium perchlorate medium. This report describes the several interactions which were found to occur in the Fe(acac)a complex system. Some aspects of the polarographic theory for product-supporting electrolyte interaction effects and the general polarographic features of some of the other metal acetylacetonates, which are undergoing continued study, are also presented. THEORETICAL The polarographic relations developed below will deal with labile interactions of the nonadsorbing, solution-soluble product of the reversible electron-transfer reaction ML,
+ ne
+
ML,-”
(1)
with the cation Cf of the supporting electrolyte C+A-. The particular interaction of present concern is a “theft” of ligand(s) from ML,-” by Ct (coordinative relaxation), which will produce a positive shift of the reduction potential of Reaction 1. An ion-pairing interaction between ML,-n and C+ also causes such a shift, and in order to identify useful polarographic criteria for distinguishing these interactions, theory for both will be outlined. Criteria auxiliary to those discussed will naturally arise in special chemical circumstances and with nonpolarographic methods. If the supporting electrolyte C+A- tends itself to ion-pair, calculation of the actual [C+]is a necessary preamble to use of the equations. It will be presumed, for simplicity, that [C+] is sufficiently well buffered by its reservoir of C+A- as to not be depleted at the electrode surface by interaction with ML,-”. Interactions of the supporting electrolyte with the electrode reactant ML, are presumed to be absent. Ion-Pairing. A solvent medium of sufficiently low polarity will induce ion-pairing of MLPwnwith C+ to a n extent eventually producing a neutral species:
ML,-,
((n
+ c+e {c+, ML,-~{I-~
- I)c+, M L ~ - ~ )+- C+ * (nC+, M L , - ~ ]
Denoting the overall formation constant for association of ML,-n with one cation as K1, with n cations as K,, etc., solving for the equilibrium concentration of ML,-n, and insertion of the resulting expression into the Nernst equation written for Reaction 1 (neglecting activity coefficients) leads to Edme
=
E”
0.059 + 0.059 7log k,k,- + __ log ( 1 + n
where k, and k, are the current-concentration proportionality constants for the reactant and (average) product, respectively. As expected, this general expression for product ion-pairing is similar in form to Equation 17 of Reference 1, which describes the analogous reactant-electrolyte ion-pairing. In the limiting case that the association is sufficiently strong to ‘produce predominantly the neutral [nC+, ML,-,] species, the Elf2value ( E at i = i d / 2 ) will vary with +0.059 log[C+]. Positive shifts in El/*thus result from increases in C+A- concentration or from a change to another anion B- which gives a smaller CiB- association constant and, thus, a t the same electrolyte concentration, a larger [C+].
Coordinative Relaxation. If the metal-ligand bond in ML,-" is labile and of lower strength than that in ML,, ligand dissociation may occur from ML,-" whereas it did not from ML,. The extent of such dissociation can be governed by the nature of the supporting electrolyte cation, C+. Consider the case in which the ligand is singly charged (L-) and after rapid dissociation exists predominantly as CL ([CL] >> [L-1). A sequence of dissociations may occur: MLp-"
+ C+ * MLp-il-" + CL (4)
MLp-q+1*-'-'
+ C+
i=*,
MLp-gq-"
+ CL
I n the sense that these reactions occur as a result of a change in the formula metal oxidation state from one having coordinative stability (ML,) t o one having a coordination state unfavored in its environment (ML,-"), this reaction type will be referred to here as a coordinative relaxation process. Denoting the overall equilibrium constants of the relaxations as K1, K?, .KO,solving for [ML,+], and insertion of this into the Nernst equation for Reaction 1 leads to the general expression for a kinetically labile relaxation: +
+
An additional criterion becomes available in instances in which the kinetics of Reaction 4 (or its reverse) are slow and detectable by polarographic o r other methods. Ion-pairing associations ordinarily exhibit high rates, and observation of an electrochemical reversibility dependent on [C+] or added C L is evidence favoring the relaxation type process. Coordinative relaxation situations different from that considered above are, of course, quite possible. Elaboration of the reversible case to include multivalent ligands o r supporting electrolyte cations, simultaneous ion-pairing effects, and oxidation reactions (relaxations involving either gain or loss of ligands) is readily accomplished when called for in specific chemical circumstances. The above equations apply t o reversible (electrochemically and chemically) processes. The qualitative effects of product-electrolyte interactions on wave potentials will persist, however, in quasireversible systems both in the context of polarography and other methods (such as cyclic voltammetry and chronopotentiometry), and quantitative theoretical treatments are possible (though perhaps cumbersome). In the limit of a completely irreversible electron transfer, the electrolyte dependency of Ells of Equation 1 will vanish and special experimental approaches will be required to establish the existence of product interactions. EXPERIMENTAL
where [MLp-n]lol,l is the total concentration of all forms of the product complex. Inquiry into the means by which ion-pairing effects can be experimentally distinguished from those of coordinative relaxation is pertinent. Consider as a n example the case n = q = 1 and a n essentially completerelaxation t o ML,-l. Equation 5 then reduces to
where k,, k,, and k,l are the current-concentration proportionality constants for ML,-l, ML,, and CL, respectively. This expression is analogous to that for ion-pairing (Equation 3, n = 1) in that the reduction wave is positively shifted by 59 mV for each decade of increase in [C+]. I n the relaxation case, o n the other hand, the mutiplicity of diffusing products generates a dependency of the potential Ellz o n the ML, sample concentration. At i = i d / 2 ,the last term of Equation 6 reduces to +0.059 Iog(2/id), predicting a negative shift in E,/? with increasing sample concentration. The for a n ion-pairing situation is invariant with sample concentration. A further test for coordinative relaxation is possible if the compound C L is available. Addition of C L in concentration such that [CL] >> [ML,] modifies Equation 6 to become (providing complete relaxation still occurs):
The operational amplifier instrument was based on a Philbrick Researches Model K7-AlO manifold and conventional passive circuitry. The reference electrode potential was monitored with a DeFord (8) follower (K2-W and K2-P amplifiers). Polarograms were recorded o n a Sargent SR recorder; cyclic voltammograms and chronopotentiograms were recorded oscilloscopically (Tektronix Model 564). Triangular potential signals were obtained from a HewlettPackard Model 202A Function Generator. Spectral curves were recorded on a Cary Spectrophotometer. The cell solution was connected t o a n aqueous SCE reference electrode through a pair of glass frit junctions arranged to prevent water contamination of the cell solution. The bridge solution was acetonitrile, 0.1M tetraethylammonium perchlorate; saturated NaCl was employed in the SCE to minimize precipitation fouling on the junction. The potential of this modified SCE, t o which all potentials reported herein are referred, is +0.006 volt us. a conventional SCE. The working electrode was either a D M E o r a hanging mercury drop electrode of the design of Shain et al. (9). A P t wire electrode served as auxiliary. Tetraethylammonium perchlorate (TEAP) was prepared according to Kolthoff and Coetzee (IO),doubly recrystallized and dried in vacuo a t 60" C. Tetrabutylammonium perchlorate was purchased from Southwestern Analytical Supply; other perchlorates were obtained from G. F. Smith Co. Eastman Spectrograde acetonitrile proved satisfactory for use as received. Tetrabutylammonium acetylacetonate was prepared by the method of Posner, Smith, and Shriver (11) and stored under nitrogen. All experiments were run a t 25" C with freshly prepared solutions degassed with solvent-presaturated nitrogen. Degassing was completed prior to introduction of the mercury working electrodes t o avoid appearance (12) of a cathodic
(7)
(8) D. D. DeFord, Division of Analytical Chemistry, 133rd Meeting, ACS, San Francisco, April 1958. (9) J. W. Ross, R. D. DeMars, and I. Shain, ANAL.CHEM.,28,
This equation predicts a -59 mV relation between a [ML,]independent Elluand the concentration of added CL. The addition of C L should not affect Elly when only Reaction 2 occurs.
(10) I. M. Kolthoff and J. F. Coetzee, J. Am. Chem. SOC.,79, 870 (1957). (11) J. C. Posner, D. E. Smith, and D. F. Shriver, Northwestern University, Evanston, Ill., private communication, 1966. (12) P. Arthur and H. Lyons, ANAL.CHEM., 24, 1422 (1952).
0.059 log
id - i ~
i
1768 (1956).
VOL. 39, NO. 1 1 , SEPTEMBER 1967
1223
Table I. Summary of Electrochemical Data for Fe(acach in 0.1M TEAP in Acetonitrile Eilz = -0.667 volt US. SCEa Polarography: id/mZ'3f"6c= 3.18 Zk 0.09' Id Chronopotentiometry: Ell4 = -0.67 volt us. SCE ir1'2/AC = 337 amp secl'*cm/mole (.i. 1.6%Ib f j / + b = 3.1 O.lc iPc/ACv1/2= 865 amp secl/Zcm/mole Cyclic voltammetry: volt1'2 (=k2.6%)d AEpeak 60-80 mV i,c/i,* = 0.98 (4~0.02) These values also obtained in 0.1M TEAP containing 9.7mM acetylacetone, 0.9mM tetramethylammonium chloride, or 0.1 water, and in 0.1M tetrabutylammonium perchlorate with or without lOmM tetrabutylammonium acetylacetonate. Range of transition time 7 = 0.03 to 0.5 second. Calculated D = 1.56 X cm2/sec. c Range of current reversal time t f = 0.05 to 0.3 second. Range of potential sweep rate v = 0.2 to 40 volts/second. ~
~
~
Table 11. Polarographic Data for Fe(acacIr in 0.1M TEAP in Acetonitrile for [LiC104]/[Fe(acac)s] > 1 [Fe(acac)d, -Eliz, volt slope, E us. mM [L~CIOIJ, mM L'S. SCE log[(id - i)/i2] 0.500 0 0.66 a 11.0 0.344 0.058 79.6 0,227 b 0.667 a 1.00 0 0.496 a 1.05 0.420 b 3.84 5.15 0.390 0,058 0.061 8.40 0.382 0.056 10.44 0.347 0.051 20.5 0.306 51.5 0.250 0.049 82.0 0.238 0.045 5.00 79.0 0.269 b 4 Plot curved. b Plot not made.
mercury-oxygen reaction product wave a t -0.1 volt us. SCE.
A diffusion-controlled impurity wave appeared a t -2.3 volts in initial experiments. Standard addition experiments indicated that this wave was not due to water, acrylonitrile, or acetic acid impurities. Alterations in experimental procedure and solvent source ultimately eliminated this wave. A small cathodic impurity wave appearing a t - 1.4 volts in polarographic experiments was not evident in cyclic potential studies. No other background waves were observed. RESULTS
F o r the most thorough understanding of the electrochemical behavior of a given neutral reactant in a nonaqueous solvent, it is desirable to conduct parallel electrochemical studies with several different supporting electrolytes. These electrolytes are chosen t o provide a spectrum of capabilities for interaction with the negatively charged reduction product. In this study of F e ( a ~ a c )and ~ other metal acetylacetonates in acetonitrile, the electrolytes most extensively employed have been tetraethylammonium perchlorate (TEAP) and mixtures of TEAP and LiC104. Fe(acac)a in 0.1M TEAP. The electrochemical behavior of F e ( a ~ a c )in ~ 0.1M TEAP is summarized in Table I. The single one-electron reduction wave observed is diffusion controlled by the conventional polarographic, chronopotentiometric ( i T l l z constant) and cyclic voltammetric (iPc/o1/* 1224
ANALYTICAL CHEMISTRY
I
H
G
F
E
D
C
B
A
POTENTIAL
Figure 1. Polarograms for 0.99mM Fe(acac), in 0.1M TEAP in acetonitrile for [LiCI041/[Fe(acac)3]< 1 Numbers above curves are m M added LiC104. Potential -0.70 volt us. SCE noted on potential allis for each curve. Markers on curves represent theoretical id for LiC104
constant) criteria. Diffusion-only behavior of the reduced complex is likewise indicated by the proximity of the chronopotentiometric current reversal ( t s , k b , ) and cyclic voltammetric (ipc/ip")data to the theoretical 3.00 and 1.00 values, respectively. Added water has no effect, indicating that the residual water in the solvent is of little consequence here. It is significant that added acetylacetonate also has no effect, as a significant degree of coordinative relaxation in this medium is thus excluded. The anodic mercury wave (13) observed when acetylacetonate is present is likewise not affected by the presence of Fe(acac)s. The cyclic voltammetric cathodic-anodic peak potential separation indicates a somewhat imperfect reversibility (AEp,,k > 59 mV). (Uncompensated resistance in the cell employed probably contributes some of the deviation in AE,,,k.) The reduction of F e ( a ~ a c )in~ 0.1M TEAP thus leads to a stable (on the electrochemical time scale) Fe(acac)lproduct complex in a relatively uncomplicated manner. Experiments at different electrolyte concentrations t o determine the extent (probably small) of R4N+,Fe(acac)3- ion pairing were not conducted. F e ( a c a ~ in ) ~TEAP-LiCI04 Electrolyte Mixtures. The magnitude of the F e ( a c a ~ )reduction ~ wave observed in LiCI0,0.1M TEAP electrolyte mixtures is unchanged from that observed in TEAP electrolyte alone. Under the conditions [LiC104]/[Fe(acac)3] = 0 to 1, and > 1, the polarographic Id = 3.16 .i. 0.09 and 3.10 =t0.08 and chronopotentiometric ir1/2/AC = 334 =k 2.8z and 337 f 1.9% constants, respectively, are in excellent agreement with the data of Table I. Substantial alterations in the F e ( a ~ a c reduction )~ potential d o occur, however. F o r 0 < [LiC104]/[Fe(acac)3] < 1, the wave becomes split into a more positive step and a step a t essentially unchanged potential, as shown in Figure 1. Both of these waves exhibit diffusion-controlled polarographic properties. For [LiClO,]/[Fe(a~ac)~] > 1, the more positive step has completely supplanted the original one (Curve I) and the single wave now observed is positively shifted as [LiC104] is further increased. These shifts are illustrated by the data of Table 11. Interaction of LiClO, with the F e ( a ~ a c elec)~ trode reactant is eliminated as a source of these effects by the lack of any change in the F e ( a c a ~ absorption )~ spectrum (see below) and also by the absence of the anodic mercury acetylacetonate wave which should occur ( I S ) if lithium ion were t o extract ligand from the complex. The potential shifts can (13) L. K. Hiller, Jr., R. W. Murray, J. R. Cockrell, and J. N. Burnett, Division of Analytical Chemistry, 152nd Meeting, ACS, New York, September 1966.
then be reasonably attributed to an interaction of lithium ion with the F e ( a ~ a c ) ~ -electron-transfer product. Preliminary evidence that the interaction is a coordinative relaxation of F e ( a ~ a c ) ~is- found in the negative shift of El,z at increased sample concentration (see Table 11, E1,2at 80mM LiClOJ. Before formulating a reaction for the relaxation process, some comment on the species expected from association of acetylacetonate with lithium ion should be made. When dissolved in acetonitrile, lithium acetylacetonate is present largely as the undissociated Li(acac) species. If a large excess of LiC104 is added to this solution, a second lithium ion becomes associated (13) with the acetylacetonate ligand: Li+
+ Li(acac) s Li?(acac)+
(8)
The association constant for this process is 1.1 X lo3. A further weak (Kip = 14) ion-pairing association of Li2(acac)+ with perchlorate ion will be neglected in the present discussion. It is accordingly expected that relaxation of an acetylacetonate ligand from Fe(acac)a- when [LiCI04]/[Fe(acac)3] < 1 should yield a Li(acac) relaxation product. Presuming relaxation of a single ligand, the overall electrochemical process under this condition would be Fe(acac), Fe(acac),-
+e
-
Fe(acac)l-
+ Li+ ~1F e ( a ~ a c )+~ Li(acac)
Figure 2. Plot of El/, data of Table I1 (1 mM F e ( a c a ~ ) ~against ) [Li +I [Li+] calcd from [LiC104] and [TEAP] using respective ion association constants 68.5 and 11.2 (15, 16); [Clod-] is essentially constant
(9)
We will first consider the data for the condition [LiCIOa]/ Fe(acac)J < 1 (Figure 1). Reaction 1 1 should not occur at all under this condition, owing to the deficiency of lithium ions. If the more positive step of the split waves of Figure 1 is assumed to correspond to reduction (Reaction 9) followed by rapid relaxation (Reaction lo), the magnitude of this step should be diffusion-controlled by the available lithium ions rather than by the iron complex. That this is, in fact, experimentally observed is shown by the reasonable agreement of the markers on the curves of Figure 1 with the actual step height. The markers represent a theoretical diffusion current for lithium calculated from the chronopotentiometrically-measured (14) D = 1.9 X lop5cmz/sec for lithium perchlorate in 0.1M TEAP-acetonitrile medium. This agreement simultaneously justifies the assumption of the Fe(acac)z species as the other relaxation product of Reaction 10. After exhaustion of the LiClOl surface concentration in the first step, the balance of the diffusing Fe(acac)~ is reduced without any ensuing relaxation (Reaction 9 only) to produce a total current diffusion-controlled by Fe(acac),, as noted above. For the condition [LiC104]/Fe(acac)3] 1 (Figure 1, Curve I), sufficient lithium ions are available to allow all of the Fe(acach to react by the Reaction 9, 10 sequence, and the more negative wave, for the simple Reaction 9 is n o longer apparent. Turning now to the condition [LiC104]/[Fe(acac)3] > 1, if the reaction sequence 9,11 is rapid and the [LiC104]sufficiently high to drive Reaction 11 to completion, the single polarographic wave for F e ( a ~ a c )should ~ be described by the appropriate modification of Equation 6:
This relation is applicable only to data at the higher [LiC104] in Table 11, owing to its requirement that the surface concentration of [LiC104Jnot be appreciably depleted by Reaction 11. Also, its applicability to these data will actually be in semi-quantitative fashion only, owing to the imperfect reversibility of Reaction 9 observed above in TEAP electrolyte and a chemical irreversibility of Reaction 11 (discussed below) observable at faster experimental times. Examining the data with these restrictions in mind, the polarographic waves are found to exhibit a slope asymmetry consistent with the form of the last term of Equation 12. Plots of Eagainst that term are linear although their slopes, given in Table 11, are somewhat lower than the theoretical 59 mV value. The correct dependency of EI,Zon sample concentration has been noted above. A plot of E1/2against dissociated [Li+] for the four highest [LiC104] is given in Figure 2 ; the experimental 136-mV slope is slightly larger than the expected 119 mV value. These comparisons, while far from quantitatively precise, are reasonably consistent with Equation 12 and provide some support for the assertion of Reaction 11 as the predominant mode of coordinative relaxation of Fe(acac)sin these excess [LiC104]media. The solutions of Figure 1 were also examined with cyclic voltammetry and chronopotentiometry. With both methods, the pre-wave caused by LiC104 diffusion is again evident, but its quantitative evaluation is difficult, A double wave also appears on the anodic cycle of cyclic voltammograms and current-reversal chronopotentiograms. The ratio of time of cathodic current application to the total reverse chronopotentiometric transition time (includes both anodic waves) is t , / ~= 3.1 =t 0.1, indicating diffusion-only behavior of the reduction product. Representative cyclic voltammograms are shown in Figure 3. These data demonstrate that Reaction 10 can be reversed under these conditions. The first (more negative) anodic wave of Figure 3 is the reoxidation of the Fe(acac),- unreacted in Reaction 10 in the cathodic cycle;
(14) L. K. Hiller, Jr., Ph.D. Thesis, University of North Carolina, Chapel Hill, N. C., 1966.
(15) S. Minc, and L. Werblan, Electrochim. Acta, 7,257 (1962). (16) C. W. Davies, “Ion Association,” Butterworths, London, 1962.
(10)
When [LiClOr]/[Fe(a~ac)~] >> 1, on the other hand, Reaction 10 becomes followed by Reaction 8 to yield an overall electrochemical sequence of Reaction 9 followed by the reaction
+
F e ( a c a ~ ) ~ - 2Li+
~t Fe(acac)z
+ Li2(acac)+
(11)
VOL. 39, NO. 1 1 , SEPTEMBER 1967
1225
‘a 4
0.4
0
-0.8
0
-0.8
c ‘
c’ 0 U
0.4
0
-08 0.4
4
E
‘c
Figure 4. Cyclic voltamrnograms of 1.00mM Fe(acac)t in 0.1M TEAP in acetonitrile with excess LiCIOa
0 1,
E, SCE (VOLTS)
2
E ks. SCE (VOLTS)
Figure 3. Cyclic voltammograms for 0.99mM Fe(acac), in 0.1M TEAP in acetonitrile Area of HMDE = 0.0350 em2. Curve A : OmM LiCIOa, 0.145 V/sec; [Curve B: 0.48mM and 0.546 V/sec; Curve C: 0.70mM and 0.136 Vhec
Curve a: lOmM LiClOa and 0.15 V/sec; curve b: lOmM and 2.9 V/sec; curve c: 80mM and 0.15 V/sec; curve d : 80 mM and 2.9 V/sec. Area of HMDE = 0.036 cmz.
this is followed in the second anodic wave by reoxidation of Fe(acac)3- formed by coordinative “unrelaxation” (reversal) of Reaction 10. Application of cyclic voltammetry to solutions where [LiC104]/[Fe(acac)3] >> 1 reveals a n irreversibility of the relaxation Reaction 11 which was not obvious a t the lower [LiCI04] or with the slower polarographic method. Figure 4 shows than a n increase in [LiC104] shifts the cathodic wave positively, as before, but also a t constant scan rate increases both the AEpeakand the peak current ratio ipaJipc (becomes > 1) of the main cathodic-anodic couple. The latter two effects, and a negative potential shift of the cathodic wave, are produced by an increase in the potential scan rate a t constant [LiCI04]. An appreciably slowed tailing-off of the anodic member also appears as it becomes attenuated. The first (more negative) anodic wave in the curves of Figure 4 corresponds t o the reoxidation of F e ( a ~ a c ) ~ - .Since during the diffusion-controlled cathodic wave (recall chronopotentiometric i7 * I * above) this species has completely relaxed (Reaction l l ) , it is necessary in the subsequent anodic wave for it to be retrieved from Reaction 11 by a n unrelaxation process. The qualitative behavior of this anodic wave, relative to its cathodic counterpart, is in agreement with that expected for a reversible charge transfer process (Reaction 9) coupled with a n incompletely reversible chemical reaction (Reaction l l ) , as discussed by Nicholson and Shain (17). Thus, under fast time conditions and high lithium concentrations, the reverse of Reaction 11, in contrast to its very rapid forward rate, can become rate-controlling and prevents complete regeneration of the Fe(acac)3- species for reoxidation in the anodic wave. Quantitative study of the kinetic behavior is complicated by the second-order nature of the unrelaxation reaction under these conditions. (17) R. S. Nicholson and I. Shain, ANAL.CHEM., 36, 706 (1964).
1226
ANALYTICAL CHEMISTRY
WAVE LENGTH (my)
Figure 5. Spectra of Fe(C104)s-Liz(acac)+mixtures in acetonitrile Fe(C104)3.6Hz0]= 0.25mM. For curves a-A, [acac]/[Fe] 0.53, 1.05,1.58,2.11,2.64,3.16,3.69,respectively
=
0,
I n concert with the kinetic suppression of the Fe(acac)3reoxidation wave, Figure 4 shows that a n additional anodic wave emerges a t more positive potentials. This new process is expected, from its obvious coupling with the main cathodicanodic waves, t o involve either the Fe(acac)2 or Li2(acac)+ remaining after the incomplete unrelaxation of Reaction 11. It is known that the Li,(acac)+ species gives rise to a n anodic mercury wave at essentially the same potential (13), but this possibility becomes eliminated by the observation that cyclic voltammograms of the solutions of Figure 4 on a Pt working electrode have a n essentially unchanged appearance. The new anodic wave is then attributed t o the direct oxidation of Fe(acac)2: Fe(acac):!
-
Fe(acac)2+
+e
(13)
(Confirmation of the potential for this reaction will be shown later.) The formulation of Reaction 13 to account for the new anodic process simultaneously raises two questions: the absence of the anodic reaction expected for Li2(acac)+ at the mercury drop electrode, and of any cathodic wave for the reduction of Fe(acac)?+ formed by Reaction 13. These two difficulties annihilate themselves when combined, however. Fe(acac)?+
+ Li,(acac)+ F! Fe(acac), + 2LiT
(14)
This reaction is expected to occur with a large K e a ,and as its reactants are present at identical concentrations a t the electrode interface, it can proceed to stoichiometric completion to regenerate the original solution species. Reaction 14 is a second type of coordinative relaxation in the iron acetylacetonate system; in this case, the coordinative relaxation involves acceptance of a ligand by the electron-transfer product from its environment. The above interpretation of the curves of Figure 4 is consistent with the following experimental observations: Reaction 14 is not expected to be completely irreversible, and the potential for Reaction 13 is accordingly shifted in a n anodic direction a t higher [LiC104]. Also, addition of Li(acac) to the solution [forms Li2(acac)+] enhances the “unrelaxation” of Reaction 11, depressing the ratio ipc/ipa (although not to unity) and decreasing its dependency on scan rate. F o r example, for 80mM LiC104, 0.48mM Fe(acac)~,and u = 1.0 V/sec, addition of 5mM Li(acac) changes the i p c / i p aratio from 2.1 to 1.6. In this experiment, the anodic-cathodic mercury
n
2
0.8
