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Acknowledgment. This work was supported by the United States Energy Research and Development Administration under Contract No. EY-76-S-02-0958. References and Notes (1) W. Schlenk and E. Bergmann, Berichfe,47, 473 (1914); Justus Liebbs Ann. Chem., 463, 134 (1928). (2) S. Bank and B. Bockrath, J . Am. Chem. Soc., 94, 6076 (1972). (3) D. E. Paul, D. Lipkin, and S. I. Weissman, J . Am. Chem. Soc., 78, 116 (1956). (4) S.Bank and B. Bockrath, J . Am. Chem. SOC.,93, 430 (1971). (5) G. Levin, C. Sutphen, and M. Szwarc, J. Am. Chem. So&., 94, 2652 (1972). (6) M. Szwarc, Acc. Chem. Res., 5, 169 (1972). (7) E. R. Minnich, L. D. Long, J. M. Ceraso, and J. L. Dye, J. Am. Chem. SOC.,95, 1061 (1973). (8) A. Rainis, R. Tung, and M. Szwarc, J . Am. Chem. SOC.,95, 659 (1973); A. Rainis and M. Szwarc, bid., 96, 3008 (1974). (9) C. J. Pedersen, J . Am. Chem. Soc., 89, 7017 (1967).
W. R. Fawcett and A. Lasia (10) J. L. Dye, M. T. Lok, F. J. Tehan, R. B. Coolen, N. Papadakis, J. M. Ceraso, and M. DeBacker, Ber. Bunsenges. Phys. Chem., 75, 659 (1971). (1 1) K. H. Wong, G. Konizer, and J. Smid, J . Am. Chem. Soc., 92, 666 (1970). (12) B. Dietrich, J. M. Lehn, and J. P. Sauvage, TefrahedronLett., 2885, 2889 (1969); J . Am. Chem. Soc., 92, 2916 (1970). (13) M. Szwarc in “Carbanions, Living Polymers, and Electron Transfer Processes”. Wiiev. New York. N.Y.. 1968. D 170. (14) J. L. Dye, M. T. Ldk, F. J. Tehan, J. M. Ceraso, and K. J. Voorhees, J . Org. Chem., 38, 1774 (1973). (15) R. R. Dewald and R. V. Tsina, J . Phys. Chem., 72, 4520 (1968). (16) N. Papadakis, R. B. Coolen, and J. L.-Dye, Anal. Chem., 47, 1644 (1975). (17) R. B. Coolen, N. Papadakis, J. Avery, C. G. Enke, and J. L. Dye, Anal. Chem., 47, 1649 (1975). 118) J. L. Dve and V. A. Nicelv. J . Chem. Educ.. 48, 443 (19711. (19j A. R a i k R. Tung, and M.-Szwarc, Proc. R . SOC.London, Ser. A , 339, 417 (1974). (20) R. M. Fuoss, J . Am. Chem. SOC.,80, 5059 (1958).
The Influence of Ion Pairing on the Electroreduction of Nitromesitylene in Aprotic Solvents. 2. Kinetic Aspects W. R. Fawcelt” and A. Lasiat Guelph-Waterloo Centre for Graduate Work in Chemistry (Guelph Campus), Department of Chemistry, University of Guelph, Gueiph, Ontario, Canada NIG 2W1 (Received September 8, 1977)
Double layer effects on the kinetics of electroreduction of nitromesitylene have been studied in dimethylformamide and acetonitrile solutions containing alkali metal and tetraalkylammonium perchlorate salts of varying concentration. The rate of the reaction was observed to depend on salt concentration, the nature of the base electrolyte cation, and the solvent. Analysis of these data revealed that the rate-limiting step was electron transfer followed by a rapid ion pairing reaction. As the ion pairing equilibrium shifts in the direction of more association, the equilibrium potential of the electrode moves positive of the standard potential and the rate of reaction decreases. Values of the standard rate constant, transfer coefficient, and apparent heat of activation are presented and discussed within the context of the polydimensional theory of electron transfer by Marcus, Levich, and Hush.
Introduction Although numerous studies of ion pairing equilibria involving electrochemically generated anion radicals have been made,l the influence of ion pairing on the mechanism and kinetics of the electrode reaction has not been investigated. Studies of the corresponding homogeneous electron transfer process between an anion radical paired with a cation and the parent molecule have shown that cation transferal accompanies electron transfer when the ion pair is of the “contact” type.3 On the other hand, the kinetics of anion radical formation have been studied for a series of organic molecules both homogeneously and heterogeneously under conditions for which ion pairing is assumed to be absenL4p5 Since the reaction may then be classified as a simple electron transfer process, these data werz examined with respect to the Marcus-Levich-Hush model for electron transfer kinetics.6-8 If the mechanism of the heterogeneous reaction which results in an ion pair is the same as the homogeneous mechanism, then one would expect the reaction rate to depend markedly on the nature of the cation in the electrolyte solution. The purpose of the present investigation was to study double layer effects on the rates of electroreduction of organic molecules in more detail, especially in systems +Onleave from the Department of Chemistry, University of Warsaw, Warsaw, Poland. 0022-3654/78/2082-1114$01.00/0
where ion pair formation is strong. As pointed out previously,2 nitromesitylene is a convenient choice for the reactant since the rate constant for anion radical formation falls in a range where precise data may be obtained by ac impedance technique^.^^^^ Investigation of the ion pairing equilibria in dimethylformamide (DMF) and acetonitrile (AN) between nitromesitylene anion radical and alkali metal cations revealed that contact ion pairs are formed with moderately high association constanta2 In the present paper, the results of a study of the kinetics and mechanism of the reduction of nitromesitylene in these systems are reported.
Experimental Section and Method of Data Analysis Heterogeneous rate data were obtained using a phase sensitive ac impedance technique similar to that described by Kojima and Bard.lo The basic apparatus consisted of a PAR Model 174A polarographic analyzer as potentiostat together with a precise oscillator (Hewlett-Packard Model 4204A) and phase sensitive lock-in amplifier (PAR Model 129A) interfaced to the potentiostat via the PAR ac interface (Model 174A/50). The dc potential of the working electrode with respect to a constant reference electrode was monitered with a digital multimeter. The ac current flowing between the working and counter electrodes was fed into the lock-in amplifier which provided dc output 0 1978 American Chemical
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The Journal of Physical Chemistry, Voi. 82, No. 10, 1978
Electroreduction of Nitromesitylene in Aprotic Solvents
voltages proportional to the in-phase and out-of-phase components of the current with respect to the ac voltage applied to the cell. The response time of the potentiostat was ascertained to be satisfactory for frequencies up to 1100 Hz by studying the performance of the system on a dummy cell consisting of a variable precision resistance and capacitor in series. Amplification of the current signal in the current processing amplifier of the potentiostat had to be restricted to the lower sensitivity range in order to avoid phase shift errors due to the inductive character of the large resistors involved in the higher sensitivity range of the PAR Model 174A. However, sufficient sensitivity without phase shift errors could be achieved when the ac signal was amplified in the lock-in amplifier. The magnitude of the superimposed ac potential (10 mV peakto-peak) was determined by replacing the working cell by a dummy cell consisting of a precise standard resistor and measuring the ac current using the lock-in amplifier; this operation also served to calibrate the lock-in amplifier with respect to phase shift. The cell contained four electrodes, a dropping mercury electrode as working electrode, a Pt counter electrode, and two reference electrodes. One of these was either AglAg+ in DMF or AglAgCl in AN as described previously;2 its function was to measure the potential of the working electrode on a convenient scale and it was not involved in the potentiostat circuit. The second reference electrode, a W wire, was immersed in the test solution and positioned in the cell close to the working electrode via a Luggin capillary. The purpose of the second reference electrode which was incorporated in the potentiostat circuit was to avoid large resistances in the working electrode-potentiostat-reference electrode feed-back loop. The behavior of the system with other conventional reference electrodes in the potentiostat circuit was both unstable and irreproducible. Current-potential data were obtained using very slow potential sweep rates, the current being determined at the end of drop life. The in- and out-of-phase components of the ac current were measured a t no less than five frequencies in the range 110-1050 Hz. The solution resistance and double layer capacitance were found by estiniating the ac admittance of the system in the potential range of interest by interpolation from values obtained at potentials where no faradaic current flowed or from measurements of the cell admittance in the potential range of interest in the absence of depolarizer. The behavior of the system with iR compensation was carefully scrutinized by comparing the faradaic admittances of the system with and without iR compensation. Identical results within experimental error were obtained for the faradaic component provided the compensation was such that effectively 100 of solution resistance was maintained. Thus, iR compensation involving an experimentally determined uncompensated fraction of solution resistance was employed. In this way, the experiments could be carried out with higher sensitivity but without any problems due to phase shift from the compensation circuit or instability. The experimentally determined solution resistance R, was found to be independent of frequency within experimental error. When ion pairing is absent, the anion radical formation reaction R + e e R-. (11 N
is a simple electron transfer. The faradaic admittance at the peak potential was analyzed by plotting the corresponding in- and out-of-phase components of the impedance against o-'l2 according to Randlesll where o = 2 r f
1115
and f is the frequency of the ac signal. This analysis served to demonstrate whether the reaction is indeed simple. When normal linear plots were obtained, the standard rate constant was found by two one-parameter fits. The first determined the proportionality constant b between the out-of-phase impedance Zoand u-lIz: zo= bw-'/2 (2) The second one-parameter fit determined the vertical shift, a, of the corresponding plot for the in-phase impedance 2, which is directly related to the standard rate constant
kea: 2, - bw -112 = a (3) The dependence of the forward rate constant on potential was determined on the basis of the analysis of de Levie and HusovskylZwhich permits one to calculate the sum of the rate constants for the forward and reverse reactions without making an assumption regarding the form of the function relating the individual rate constants and electrode potential. From this analysis 4
YI - Y o
-
+ (2wDg)1/2 e;
(2wD*)1/2
(4)
where YI and Yo are the in- an_d out-of-phase components of the faradaic admittance, k , and k,, the forward and reverse rate constants in reaction 1, and DAand DB, the diffusion coefficients for the reactant and product, respectively. Assuming that the diffusion coefficients for R and R-- are equalADA =-D&= DR) and using the Nernst equation to relate k , and he (he = L e k ) ,eq 4 may be written
(5) where 7 is the overpotgntial with respect to the standard potential. Values of In k, determined in the potential range -30 I 17 I 30 mV were plotted against 7 to obtain a second estimate of the standard rate constant he,, and a value of apparent transfer coefficient a. When ion pairing is present the overall reaction could take place by an ec mechanism, namely
The analysis of de Levie and Husovsky'2 has been extended to systems with a following chemical reaction by Moreira and de Levie.13 From their results, it can easily be shown that eq 4 and 5 will be applicable to systems in which the following chemical reaction can be regarded to be at equilibrium in both the ac a_nd d_csense. Physically, chis requirement corresponds to h, k, >> o where k, and k , are the forward and reverse rate constants for the chemical step, respectively. If the rate constant for ion pair formation is close to the diffusion limited value, as one might expect, then the conditions under which the chemical step can be regarded at equilibrium are indeed met for the frequency range used. In applying eq 5, the overpotential 7 is replaced by the potential difference, E The peak potential E, is related to the standard potential for reaction 1 by14
+
(7) where KM is the association equilibrium constant for reaction 6b and a ~the , cation activity. Procedures for estimating aMand KM were described in part lS2 Analysis of ac admittance data for the case that both reactions 6a
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TABLE I : A Summary of Kinetic Data for the Electroreduction of Nitromesitylene at Mercury in Dimethylformamdie (DMF) and Acetonitrile (AN) /
0.1 M TEAP in DMF 0.1 M KClO, in DMF
0.1 M NaClO, in DMF 0.1 M LiClO, in DMF 0 . 1 M T E A P i n AN
0.027 0.092 0.142 0.170 0.025
0.43 0.093 0.030 0.017 0.92
-
W. R. Fawcett and A. Lasia
\d
0.62
0.49 0.52
0.28
0.48 0.50 0.50
0 0 0.56
a Peak potential with respect t o standard potential. Transfer coefficient. Rate constant at peak potential. Apparent reaction order with respect to the cation.
the ac admittance data ma57 be analyzed by the method of de Levie and Husovskyl12 provided the cation concentration is much greater than that of the organic nitro compound in the bulk. In the present case, the nitromesitylene concentration was maintained constant at 5 X M and the cation concentration varied in the range 0.04-0.10 M. Procedures for purification of salts and solvents were described previously.2 All experiments were carried out in a controlled atmosphere chamber maintained a t 25.0 f 0.2 "C. Experiments at temperatures near 25 "C were carried out in a cell in which the working compartment was surrounded by a glass chamber through which a fluid maintained at the desired temperature was circulated.
Results The rate of electroreduction of nitromesitylene (NM) a t the peak potential was measured in tetraethylammonium perchlorate (TEAP) solutions in DMF and AN and in LiC104,NaC104, and KC104 solutions in DMF for electrolyte concentrations in the range 0.04-0.10 M. Experiments were not carried out with the alkali metal perchlorate systems in AN because of the limited solubility of the K+ salts and disproportionation reaction which follows electron transfer to NM in the Li+ and Na' systemsS2Data are also not reported for the CsC104 system in DMF since the reaction occurs in a potential region where the interfacial capacity changes markedly with potential due to specific adsorption of the Cs+ ion.16 The apparent rate constant was observed to increase with electrolyte concentration in the TEAP system, as one would expect on the basis of the simple double layer effect for a uncharged reactant being reduced a t a negatively charged electrode. At a given electrolyte concentration, the rate constant decreased with decrease in crystallographic radius of the base electrolyte cation, that is, with increase in the cation's tendency to form an ion pair with the resulting anion radical. At the same time, the rate of increase in NM reduction with electrolyte concentration decreased with decrease in cation crystallographic radius, reaching zero with the smallest cations considered, namely, Li+ and Na' (Table I and Figure 1). The traqsfer coefficient a determined from the dependence of In k, on electrode potential in a very small range near the peak potential is close to 0.5. Double layer effects were ignored in estimating a;however, they will have a negligible effect
.-.-----*--. N a*
-m
and 6b affect the observed current is much more complex but could be carried out the basis of a study of the frequency dependence of the admittance at a given electrode potential.13-15 If the reaction mechanism in the presence of ion pairing involves simultaneous electron and atom transfer R + M + f e --'. R - , ...M+ (8 1
Ll*
I
-2 4
-32 In cM
Figure 1. Dependence of the rate constantfor the electroreduction of nitromesitylene at the peak potential, k,,, on base electrolyte concentration cMfor various 1: 1 perchlorate salts in dimethylformamide. The nature of the cation is indicated adjacent to each set of data. I
1000
-
/:AA 500-
0 01
003 o-112
51i2
Figure 2. In-phase (Z,) and out-of-phase (Z,)components of the faradaic impedance for the electroreduction of nitromesitylene in dimethylformamide at a mercury electrode for typical reactant and electrolyte concentration with (0)and without (A)iR compensation as a function of w-"* where w = 2 n f , fbeing the frequency of the ac signal.
since the data were collected over a very small potential range at potentials very negative of the point of zero charge where the potential drop across the diffuse layer varies slowly with electrode potential. The role of the base electrolyte cation in the electrode reaction was first assessed on the basis of the frequency dependence of the faradaic impedance at the peak potential. Since normal Randles plots were obtained in the frequency range considered (Figure 2) it was assumed that if the ion pairing step followed electron transfer (reaction 6), it was essentially at equilibrium with respect to the ac perturbation. The cation role was further examined on the basis of the reaction order analysis developed by Vetter.17 Assuming the electron transfer step involves one electron and that it is first order in NM and xth order in M+, the dependeqce of the apparent rate constant at the peak potential, k, , on cation concentration and peak potential is given i y C#J~
The Journal of Physical Chemistry, Vol. 82, No. 10, 1978 1117
Electroreduction of Nitromesitylene in Aprotic Solvents -A
In k,, = In he,,
+ x In CM + ( a - x
) f -~afq ~
(9)
I
where cMis the concent,ration of univalent cations, and 7 = E, - E,,.18 Substituting eq 7 into eq 9, the order with respect to the cation is given by
(; ye;) :=
x
+ ( a - x ) f (aiYC' )
When the reaction occurs a t potentials considerably negative of the pzc, it is easily shown from the GouyChapman model for the diffuse layer, that f a+d/a In cM N 1 when CM is equal to the ionic strength. In the case of strong ion pairing K$M >> 1and eq 10 may be rewritten
(a
2
In k,,/a
In c M )= x
+ ( a - x) - a = 0
i
0.15
0 20
rl'
(11)
when changes in cation activity coefficient with ionic strength are neglected. Thus, when ion pairing is strong as in the cases of Li+ and Na', the increase in rate constant expected when double layer effects are reduced by increasing the ionic strength is offset by a corresponding decrease due to the shift in peak potential in the positive direction with respect to the equilibrium potential. As ion pairing becomes less strong, the term a[ln (1+ KMaM)]/a In cMapproaches zero and the reaction order with respect to the cation is given by
0.25
v,v
Figure 3. Dependence of the logarithm of the rate constant fPr the electroreduction of nitromesitylene at the peak potential, In k,, on overpotential corrected for the potential drop across the diffuse layer, 7 - $ d for various 0.1 M perchlorate salt solutions in dimethylformamide.
-2.
(a In k,,/a
In cM)2 or
(12)
This situation holds approxiEately for the TEAP systems in DMF and AN where (a In k,,/a In cM) = 0.62 and 0.56, respectively. Because of the double layer effect, the concentration of cations at the outer Helmoltz plane (oHp) changes very little with ionic strength a t far negative potentials. Thus, the above analysis confirms the role of ion pairing in the electrode reaction but does not clarify the cation's possible role in the electron transfer step. If the cation is involved in the rate-determining step (reaction 8), one would expect the standard rate constant to depend on cation nature. This follows from the fact that the cation will influence the nature of the potential energy surfaces describing the transition state. On the other hand, if it is not involved in the electron transfer step which is also the rate-controlling step (reaction 6), kinetic data obtained in the presence of various cations should fall on one Tafel plot indicating that the standard rate constant is independent of cation nature. Data obtained in 0.1 M solutions of TEAP, KC104, NaClO,, and LiC10, are presented in the form of a corrected Tafel plot in Figure 3. It is readily apparent that these data can be described by the equation 2
In h e , = In h e ,
+a
f ( ~ q~)
(13) The value of a determined by least squares is 0.63. The rate constant uncorrected for double layer effects at 7 = 0 (+d = -0.121 V in 0.1 M TEAP) is 0.79 cm s-l. Values of q5d were calculated from electrode charge density-potential data20 assuming no ionic specific adsorption and the Gouy-Chapman model for the potential drop across the diffuse layer. Thus, the above analysis clearly indicates that the electrode reaction in the presence of ion pairing involves a rate-controlling electron transfer step followed by a rapid ion pairing equilibrium which is sufficiently fast that it shows no noticeable influence on the ac admittance a t lower frequencies.
-1.61
33
34 1/ T . ~ o ~ , ~ K - ~
Figure 4. Arrhenius plot of the rate constant for electroreduction of nitromesitylene at the peak potential with 0.05 M tetraethylammonium perchlorate as base electrolyte in dimethylformamide.
Kinetic data obtained at the peak potential using 0.05
M TEAP as base electrolyte are presented in Figure 4 for temperatures in the range 14-30.5 "C. From the slope of the Arrhenius plot, an approximate value for the apparent heat of activation is 17.4 kJ mol-l. This estimate ignores the probable change in overpotential at the peak potential with temperature and double layer effects; however, as is shown below, these corrections are not large. Comparison of the present result with those reported for other electrode reactionsz1reveals that it is rather low as one would expect for a fast electron transfer reaction.
Discussion T h e Reaction Mechanism. From the above data analysis it is clear that electron transfer reactions which are accompanied by ion pairing may proceed by different mechanisms in the homogeneous and heterogeneous modes. WeissmanZ2and S ~ w a r chave ~ ~ shown that the homogeneous process in systems where the anions radicals exist primarily as ion pairs is accompanied by simultaneous transfer of the cation in the ion pair. The systems studied involved anion radicals of aromatic hydrocarbons and ketones paired with alkali metal cations in ethereal solventa of low dielectric constant. As expected, they found large differences in the rate constants for exchange between an
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W.R. Fawcett and A. Lasia
The Journal of Physical Chemistry, Vol. 82, No. 10, 1978
unpaired anion radical and its parent molecule, and between a paired anion radical and its parent molecule. It has been customary to that ion pairing could be avoided in solvents of higher dielectric constant such as DMF by using tetraalkylammonium salts as electrolytes. The rate data thus obtained for the simple homogeneous process could then effectively be compared with those obtained heterogeneously. However, Krygowski et ala2' found strong ion pairing between nitrobenzene anion radical and tetraethylammonium cations in DMF. Thus, some of the kinetic data reported by AdamsZ5and Bardz6 for homogeneous electron transfer may not be those for the simple electron transfer process, especially when the anion radical involved is highly polar. The conclusion reached above that heterogeneous electron transfer does not involve simultaneous atom transfer in systems with strong ion pairing in the bulk is supported by the theoretical and experimental work of Hurwitzz8and Nurnberg.z9 Accordingly, under most experimental conditions, the electrical field in the double layer acts to decrease the extent of ion association at the reaction site. These authors showed that an exact analysis of the field dissociation effect requires estimation of the extent of dielectric saturation in the double layer. However, the field dissociation effect is generally expected to predominate over the effect of the lower dielectric constant in the region of the oHp which enhances ion association. Thus, the ion pairing reaction occurs after the anion radical formed a t the interface has diffused to a region in the diffuse double layer where the electric field is lower. It is obvious from the above considerations that comparison of rate data for homogeneous and heterogeneous electron transfer within the context of the Marcus-Levich-Hush theory6-8 should not be made for organic systems without determining the role of ion pairing. Ion pairing is undoubtedly an important factor contributing to the anomalous behavior of the nitrobenzenefnitrobenzene anion radical system with respect to the correlation between free energies of activation for the two modes of electron transfer presented by Kojima and Bard.5 The extent to which ion pairing affects the other systems considered is unknown. The Kinetic Parameters. The kinetic parameters obtained in the present study compare favorably with those reported earlier by Peover and P ~ w e l l They . ~ obtained an apparent rate constant of 0.28 cm s-l and transfer coefficient of 0.5 for 0.1 M tetra-n-butylammonium iodide as base electrolyte in DMF at 30 "C. The fact that the rate constant is lower than that observed here with TEAP a t 25 "C may be a reflection of some blocking of the electrode by the larger tetraalkylammonium cation, or of a change in the average potential at the reaction site with change in the size of the cation at the o H ~ . ~This O conclusion is supported by the results of Senda et al.31who found that the rate constants for the electroreduction of p-nitrotoluene and p-nitroaniline decreased with increase in tetraalkylammonium cation size. These workers reported a standard rate constant of 1.3 cm s-l for the electroreduction of NM in 0.5 M TEAP in DMF at 25 "C using the radio-frequency polarographic techniqueU3lConsidering the fact that they ignored the effects of ion pairing, this result is much higher than one would expect on the basis of the present study and that of Peover and P ~ w e l l . ~ From the data presented in Table I, the transfer coefficient estimated from the potential dependence of the rate constant near the peak potential is 0.50 independent of cation nature. As pointed out above, this result does
not depend on a double layer correction since the oHp potential changes negligibly with electrode potential for the present experimental conditions according to the Gouy-Chapman theory.lg The value obtained from the dependence of the rate constant a t the peak potential on cation nature is much higher (0.63). In this case, errors in the estimation of 4d and 17 will have a large effect on the accuracy of the estimation. It is probable that for the higher electrolyte concentrations used in the present experiments, conditions are such that the simple GouyChapman model is no longer valid. Thus, the latter estimate of the transfer coefficient is not considered to be reliable. It is interesting to examine the kinetic parameters with respect to the polydimensional theories of electron transfer.6-8 The value of the standard rate constant determined from the data obtained for TEAP solutions in DMF is 6.4 f 0.9 cm s-l after correction for double layer effects. This parameter is related to the standard electrochemical free energy of activation AGd* by the equation
k,, = K Z , ~ - * G O ~ * / R T (14) where K is the transmission coefficient assumed to equal unity for an adiabatic process, and Z, = (RT/27rW1I2,the heterogeneous collision frequency, M being the molecular weight of the reactant. In the present case, 2, = 4.89 X lo3 cm s-l at 25 "C, and AG,: = 16.5 kJ mol-l. On the basis of the Marcus-Levich-Hush modeP8 and assuming double layer effects are given by Frumkin's theorylg
where X is the work of solvent reorganization. At the standard potential and after correction for the potential drop across the diffuse layer, AGa* = X/4; thus, the solvent reorganization energy in the present case is 66.0 kJ mol-l. By the same model, the transfer coefficient is
Accordingly, the transfer coefficient should increase from a value of 0.63 in 0.1 M TEAP to 0.75 in 0.1 M LiC104. The fact that no significant increase in cy was observed suggests that this particular aspect of the polymensional models is not correct. A similar conclusion was reached by Weaver and Anson50 on the basis of data for the electroreduction of chromium complexes obtained in aqueous solutions over a wide potential range. The work of solvent reorganization may be independently estimated on the basis of a simple extension of the Born Assuming that NM may be modeled as two contiguous spheres corresponding to the nitro group and the methyl-substituted benzene ring, and neglecting the volume effect,32A is given by
f2* _
R2
R14 f+1 fE2 ,
1
where No is Avogadro's number, e , the charge on an electron, eo, the permittivity of free space, and E , and ,e, the static and optical dielectric constants of the solvent, respectively. fl and fz are the dimensionless fractions of charge on the two spheres whose radii are r1 and r2,and R1 and R2 are the distances of the two spheres from their images in the electrode. On the basis of unpaired spin
Electroreduction of Nitromesitylene in Aprotic Solvents
densities measured by ESR spe~troscopy,3~ the fraction of the charge density in the anion radical on the nitro group, f,, is 0.61. Following Peover and P ~ w e l lit, ~is assumed that r1 = 2.75 and r2 = 3.5 A. Ignoring the imaging terms, the main contribution to A equals 82.1 kJ mol-’. If it is assumed that the dipole vector in NM is aligned in the electrode’s field and that the center of the closer sphere can approach the electrode to a distance of 5 A, then R1 = 22.5 A and R2 = 10 A. In this configuration, the imaging terms contribute -19.6 kJ mol-,, the final estimate of X being 62.5 k J mol-,. When NM is oriented against the electrode’s field (R, = 10 A, R2 = 22.5 A), h = 58.5 kJ mol-,; when it is parallel to the electrode (R, = Rz = 10 A), h = 50.0 kJ mol-l. All three estimates fall below the experimental value, the closest being that for the case that the molecule is oriented in the electrode’s field. Considering the assumptions which must be made in order to estimate A, it is really not possible to assess the role of imaging in determining the work of solvent reorganization. Kojima and Bard5 concluded that imaging effects are negligible (R, = Rz = m) on the basis of a comparison of free energies of activation for a series of electron transfer reactions studied both homogeneously and heterogeneously. This conclusion relies heavily on the assumptions made regarding the work terms. Their analysis was also based on the assumption that the reaction site is the oHp, the appropriate work term for a species with charge zi being ~ $ 4 As ~ .discussed below, this assumption ignores possible noncoincidence of the reaction plane and o H ~ , ~disO creteness-of-charge effects,34 and polarization energy.35 Dietz and P e ~ v e examined r~~ double layer effects for several simple radical anion formation reactions in DMF with n-tetrabutylammonium iodide as base electrolyte. As expected, the apparent rate constant for heterogeneous electron transfer increased with increase in electrolyte concentration. After carrying out the usual Frumkin correction, the corrected rate constants were found to increase somewhat with base electrolyte concentration. A similar trend is found with the present data obtained in TEAP solutions; after correction for both ion pairing and double layer effects, the apparent standard rate constant assuming cy = 0.5 increases from 5.2 cm s-l in 0.04 M TEAP to 7.5 cm s-l in 0.1 M TEAP. This result can be partially attributed to errors in the Gouy-Chapman model. In solvents of lower dielectric constant such as DMF and AN, the error is expected to increase with increase in cM,the true value of 14dl being less than that calculated from Gouy-Chapman theory.37 On the basis of a study of double layer structure for the Hg/AN i n t e r f a ~ ethis , ~ ~ error is expected to be larger in the case of tetraalkylammonium salts. Corrected standard rate constants for data obtained in 0.1 M salt solutions vary from 3.9 cm s-l for LiC104 to 7.5 cm s-l for TEAP. This change could be attributed to a change in the thickness of the inner part of the double layer with solvated cation size,30the potential a t the reaction site becoming less negative for a given reactant and product as the thickness of the inner layer increases. However, one would also expect to see a corresponding increase in the apparent transfer c o e f f i ~ i e n t .Since ~ ~ kinetic data in the presence of different cations cannot be obtained at the same potential by the present technique, it is rather difficult to assess the importance of this effect. Another factor which complicates analysis of double layer effects for the present system is the possibility that the charge distribution in the reactant and product may be significantly altered in the high field at the electrode/solution interface. Fawcett and Gardner35showed that, if a dipolar molecule such as NM reacts in the inner
The Journal of Physical Chemistry, Vol. 82, No. 10, 1978
1119
layer where the dielectric constant is significantly less than that in the bulk of the solution, the polarization energy constitutes a significant fraction of the work terms for the reactant and product. Because of the size of NM and probable variation in dielectric constant with distance from the electrode, the magnitude of the polarization energy is very difficult to estimate. However, if the reactant is oriented in the electrode’s field, the polarization contribution to the work terms would result in an increase in the apparent standard rate constant calculated on the basis of Frumkin’s model with increase in charge on the electrode. Thus, the polarization effect could partially account for the increase in standard rate constant which accompanies the negative shift in the accessible potential range with cation nature. Unfortunately, the polarization and cation size effects cannot be separated on the basis of the present data, since kinetic data could not be obtained over a wide potential range in the presence of one cation. This problem could be somewhat elucidated in future work, by studying the reaction a t various metals in the same electrolyte solution, under conditions where the electrode charge density varies significantly with metal nature at constant electrode p ~ t e n t i a l . ~ ~ Disregarding details of double layer structure and polarization effects and considering only the size of NM with respect to the ions and solvent molecules which make up the double layer, it is apparently that the simple Frumkin model grossly oversimplifies electrostatic effects on the kinetics of the heterogeneous electron transfer reaction in the present case. Even if the charge center of the product anion radical is located on the oHp, the spatial distribution of charge in the product is not insignificant with respect to the normally assumed potential variation in the double layer. In light of the above considerations, it is probably true that double layer effects are underestimated when the Frumkin model is used. This, in turn, implies that the estimates of the free energy of activation made here and e l ~ e w h e r eare ~ , ~high. ~ This point requires further investigation before reliable comparisons between homogeneous and heterogeneous rate data can be made. It is interesting to compare the kinetic parameters obtained in the two solvents with TEAP as base electrolyte. After correction for ion pairing and double layer effects, the standard rate constant in AN is 11.6 f 1.4 cm s-l, that is, almost twice that obtained in DMF. The corresponding value of the standard free energy of activation is 15.0 kJ mol-l. If the work terms have been correctly estimated, the lower value of AGeo* in AN must be attributed to a correspondingly lower energy of solvent reorganization. Assuming the reactant has approximately the same position and orientation in the double layer in the two solvents, the observed difference can be related to differences in the dielectric properties of the two solvents (eq 17). However, the static dielectric constants are approximately equal, the optical dielectric constant of DMF being 13% higher than that of AN.40 Thus, the reorganization energy estimated on the basis of eq 17 is higher in AN. The fact that the opposite is observed experimentally could be attributed to failure of any one of the assumptions stated above. If the reaction site is indeed at the oHp, then the use of the dielectric constant of the pure solvent for cB may constitute a serious error in the estimation of However, it does not seem probable that differences in dielectric saturation in the two solvents could account for the increase in X when the solvent is changed from AN to DMF. Saveant and found that the standard rate constant for electroreduction of tert-nitrobutane is larger in DMF than AN. They at-
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tributed their observation to stronger solvation of the anion radical in AN. It could well be that specific solvating properties of the solvent are more important in determining h than nonspecific properties such as the dielectric constant.43 However, considering the fact that the electron density in the anion radical of tert-nitrobutane is located on the nitro group: ion association is expected to be strong. Furthermore, since ion pairing is stronger in AN,2 the relative lowering of the rate constant at the half-wave potential with respect to the standard rate constant will be greater in this solvent. In summary, ion pairing and double layer effects must be carefully analyzed before any meaningful comparison of kinetic parameters is attempted. The Heat of Actiuation. According to the modified version of transition state theory used above, the relationship between the rate constant at the peak potential and the standard free energy of activation 4Go*is44345
W. R. Fawcett and A. Lasia
and AHo = 3.6 kJ mol-'. The corresponding value of a ( q / T ) / a ( l / T ) at CM = 0.05 M (UM 0.029 M) is -0.019 V. At large negative potentials, the potential drop across the diffuse layer is given by
4 -2RT d= In (-uM/Oe,'/2T''2) F where UM is the charge density on the electrode and 13, a temperature independent constant. The necessary temperature derivative is
(25) It is easily shown from the appropriate double layer data20 that the first term in eq 25 is negligible with respect to the other two. Thus, in DMF solutions when IuMI is large, a(4d/T)/a(~/T)is 0.010 V. In k , = In ( ~ 2 ,-)AG,*/RT- In T * The real heat of activation according to eq 21 is 17.6 kJ a m d - 17 - $ o m ) (18) mol-l. It follows that Ma* is approximately equal to the standard electrochemical free energy of activation AG,,' where y*is the activity coefficient of the activated complex estimated on the basis of the polydimensional theories.68 at the reaction site and 4om,the inner potential of the metal This suggests that the preexponental factor assumed in electrode at the standard potential. The activity coefficient eq 14 is realistic and that the reaction is indeed a simple y* can be regarded as a parameter accounting for elecadiabatic electron transfer according to the criteria of the trostatic contributions ignored in the Frumkin model, polydimensional theories.6-8 namely, discreteness-of-charge and dipolar effects, and Very few data exist in the literature for the heat of effects associated with possible non coincidence of the activation of similar reactions. Adams et alZ5reported an reaction and outer Helmholtz planes;46 its possible deapparent heat of activation of 14.6 kJ mol-l for the pendence on temperature will be neglected in the following electroreduction of nitrobenzene. Although this result was analysis. Assuming the transfer coefficient a is also innot corrected for ion pairing and double layer effects, AH: dependent of temperature, the slope of the Arrhenius plot is smaller than that for NM as one would expect. Since at the peak potential is the electron density in the nitrobenzene anion radical is more uniformly distributed, both the solvent reorganization energy and heat of activation are smaller. Dietz and P e ~ v e reported r~~ Arrhenius parameters for the electroreduction of substituted stilbenes some of which were where AH: is the ideal heat of a ~ t i v a t i o n .Since ~ ~ the variation in q50m cannot be determined e ~ p e r i m e n t a l l y , ~ t ~ ~sterically hindered. Although the apparent heats of activation fall in the range expected, the preexpontential the real heat of activation AH: with consideration of factors were much lower than normal in the presence of double layer effects is steric hinderance. These authors concluded that entropy effects or nonadiabaticity play an important role in the latter case. In conclusion, determination of the heat of activation In the present case should be employed more frequently in the analysis of kinetic parameters for simple heterogeneous electron transfer processes. Estimates of the work of solvent reorganization and intrinsic transfer coefficient from data at a single temperature rely heavily on double layer corrections. Some of the uncertainty connected with carrying out these corrections could be removed if the The variation in cpd and 7 with temperature may be appropriate Arrhenius parameters are also determined. estimated from the Gouy-Chapmanlg and DenisonAcknowledgment. The research was supported by a Ramsey models,47respectively. From eq 7 and neglecting grant from the National Research Council of Canada. the dependence of UM on temperature References and Notes 2
+
where AHo is the standard enthalpy for the ion association process. According to the theory of Denison and RamseP7
( a,;)
AH" = AG" i +
where AGO is the corresponding standard free energy of association. Using tabulated data for the dielectric constant of DMF in the temperature range -60 to 100 0C,48149 (a In €$/a In T ) = -1.4. Thus, AGO = -8.9 kJ mol-l
A brief review of ion pairing equilbria between organic anion radicals and simple cations is given in part 1.' B. G. Chauhan, W. R. Fawcett, and A. Lasia, J . Pbys. Cbem., 81, 1476 (1977). M. Szwarc and J. Jagur-Grodzinski in "Ions and Ion Pairs in Organic Reactions", Vol. 2, M. Szwarc, Ed., Wiley-Interscience, New York, N.Y., 1974, Chapter 1. A. E. J. Forno, M. E. Peover, and R. Wilson, Trans. Faraday Soc., 66, 1322 (1970). H. Kojima and A. J. Bard, J . Am. Chem. Soc., 97,6317 (1975). V. G. Levich, Adv. Electrochem. Nectrocbem. Eng., 4,249 (1966). R. R. Dogonadze in "Reactions of Molecules at Electrodes", N. S. Hush, Ed., Wiley-Interscience, New York, N.Y., 1971, Chapter 3. P. P. Schmidt in "Electrochemistry, Specialist Periodical Reports", Vol. 5, H. R. Thirsk, Ed., Chemical Society, London, 1975, Chapter 2
Reaction Modes of 1,3-Cyclohexadiene Radical Anion M. E. Peover and J. S. Powell, J. €/echoanal. Chem.,20,427 (1969). H. Kojima and A. J. Bard, J. Nectroanal. Chem., 63, 117 (1975). J. E. B. Randles, Discuss. Faraday Soc., 1, 1 1 (1947). R. de Levie and A. A. Husovsky, J. €/echoanal.Chem., 22,29 (1969). H. Moreira and R. de Levie, J. Electroanal. Chem., 29,353 (1971). T. G. McCord, H. L. Hung, and D. E. Smith, J . Electroanal. Chem.,
21,5 (1969). M. Sluyters-Rehbach and J. H. Sluyters, J . Electroanal. Chem., 26,
237 (1970). Ya. Doylido, R. V. Ivanova, and B. B. Damaskin, Elektrokhimiya,6,
3 (1970). K. J. Vetter, “Electrochemical Kinetics”, Academic Press, New York, N.Y., 1967,p 432. According to eq 9,double layer effects are assumed to be given by the classical Frumkin model,lg that is, the reactant and product are assumed to experience the average potential on the outer Helmholtz plane when at the reaction site. P. Dehhay, ”Double Layer and Electrode Kinetics”, Wiley-Interscience, New York, N.Y., 1965,Chapters 3 and 9. W. R. Fawcett and J. 8. Sellan, unpublished results. N. Tanaka and R. Tamamushi, Electrochim. Acta, 9,963 (1964). P. J. Zandra and S. I. Weissman, J. Am. Chem. Soc., 90,3611
(1968). M. Szwarc, Acc. Chem. Res., 5, 169 (1972). T. Kitagawa, T. Layloff, and R. N. Adams, Anal. Chem., 36, 925
(1964). P. A. Malachesky, T. A. Miller, T. Layloff, and R. N. Adams, Exch. React., Proc. Symp., 151 (1965). B. A. Kowert, L. Marcoux, and A. J. Bard, J. Am. Chem. Soc., 94,
5538 11972). T. M. Krygowski, M. Lipsztajn, and Z. Galus, J. Electroanal. Chem.,
42,261 (1973).
The Journal of Physical Chemistty, Vol. 82, No. 70, 1978 1121
(28) A. Jenard and H. D. Hurwitz, J. Electroanal. Chem., 19,441 (1968). (29) H. W. Nurnberg and G. Wolff, J. Electroanal. Chem., 21,99 (1969). (30) W. R. Fawcett, J. Nectroanal. Chem., 22, 19 (1969). (31)T. Kakutani, H. Kinoshta, and M. Senda, Rev. Polarog., 20,15 (1974). (32) W. R. Fawcett and Yu. I. Kharkats, J. Electroanal. Chem., 47, 413 (1973). (33) R. D. Allendoerfer and P. H. Rieger, J . Am. Chem. Soc., 88,371 1 (1966). (34) W. R. Fawcett, J. Chem. Phys., 61,3842 (1974). (35) W. R. Fawcett and C. L. Gardner, J. Electroanal. Chem., 82,303 (1977). (36) R. Dietz and M. E. Peover, Discuss. Faraday Soc., 45,155 (1968). (37) H. D. Hurwitz, A. Sanfeld, and A. Steinchen-Sanfeld, Electrochim. Acta, 9, 929 (1964). (38) W. R. Fawcett and R. 0. Loutfy, Can. J. Chem., 51,230 (1973). (39) N. V. Fedorovich, A. N. Frumkin, and Kh. E. Keys, Collect. Czech. Chem. Commun., 36, 722 (1971). (40) C. K. Mann, Electroanal. Chem., 3, 57 (1969). (41) R. A. Marcus, J. Chem. Phys., 43,679 (1965). (42) J. M. Sav6ant and D. Tessier, J. Elecfroanal. Chem.,65,57 (1975). (43) W. R. Fawcett and T. M. Ktygowski, Can. J. Chem., 54,3283(1976). (44) K. M. Joshi, W. Mehl, and R. Parsons, Trans. Symp. Electrode Processes, 7959, 249 (1961). (45) B. G.Chauhan, W. R. Fawcett, and T. A. McCarrick, J. Electroanal. Chem., 58, 275 (1975). (46) W. R. Fawcett and S.Levine, J. Electroanal. Chem., 43,175 (1973). (47) J. T. Denison and J. B. Ramsey, J. Am. Chem. Sac., 77, 2615 (1955). (48) G.R. Leader and J. F. Gormley, J. Am. Chem. Sac., 73,5731 (1951). (49) S.J. Bass, W. I. Natham, R. M. Meighan, and R. H. Cole, J. Phys. Chem., 68, 509 (1964). (50) M. J. Weaver and F. C. Anson, J. Phys. Chem., 80, 1861 (1976). (51) M. Temkin, Zhur. Fiz. Khim., 22, 1081 (1948).
Competitive Reaction Modes of the 1,3-Cyclohexadiene Radical Anion G. G. Stroebel,
D. Y.
Myers, R. R. Grabbe, and P. D. Gardner”
Department of Chemistty, University of Utah, Salt Lake City, Utah 84 1 72 (Received December 8, 1977) Publication costs assisted by the University of Utah
The 1,3-cyclohexadieneradical anion was generated by sodium-ammonia reduction of the diene. By varying the composition of the medium and observing the variation in product composition,it was possible to determine the various intermediates formed and to assess quantitatively the partitioning of the overall reaction of radical anion among its several competitive modes. These include protonation to 3-cyclohexenyl radical, followed by its dimerization or further reduction, conjugate addition of the radical anion to substrate, and coupling of 3-cyclohexenyl radical with the parent radical anion. This was made possible by the reduction of tricyclo[6.4.0.02,7]dodeca-3,11:diene to its ring-opened radical anion and observing the ratio of isomeric dihydro products so produced since they are common to the reductive dimerization of 1,3-cycohexadiene. A cursory examination of the reduction of 1,3-cyclooctadiene showed that its radical anion is significantly more basic than that of 1,3-cyclohexadieneand that the cyclooctadiene has a significantly smaller electron affinity than cyclohexadiene.
Introduction Rather detailed and elegant studies of radical anions derived from many aromatic hydrocarbons and heterocyclics have provided some understanding of their electronic structures, solvation characteristics and interactions with cations, and certain facets of their chemical behavioral Other than qualitative reduction experiments of an observational nature, relatively little has been done with radical anions derived from simpler nonaromatic hydroc a r b o n ~ due ~ , ~ to their greater reactivity and shorter lifetimes. The radical anion (9) of 1,3-cyclohexadiene (1) has been found4 to have a lifetime of 1-2 s in liquid ammonia a t -78 “ C and was therefore selected as a representative substrate for studying reactions of diene radical ions and the manner in which they vary as reaction conditions are varied. Specifically, we wished to determine the relative importance of radical and radical ion participation in processes leading to dihydro dimers28and the relative importance of radical-radical anion coupling and
radical anion conjugate addition to substrate diene.5
Experimental Section The radical anion (9) of 1,3-cyclohexadiene (1) was generated either by “normal addition”, addition of a solution of l in ether or T H F to a solution of the metal or metal naphthalenide in liquid ammonia-ether (or THF) or THF, or by “inverse addition”,6*6the addition of reductant solution from a vacuum jacketed dropping funnel cooled with dry iceacetone to a similarly cooled three-neck reaction flask equipped with a mechanical stirrer, dry ice condenser, and the usual plumbing required to work in an inert environment. Ratios of reductant to reactant and the use of ethanol as a proton donor and dicyclohexyl18-crown-6 ether (henceforth crown ether) are indicated as appropriate in tabulated data. These ratios were realized by adding a solution of reductant (typically 100 mL) which was approximately 0.03 M in NaO and 1:7 v/v THF-NH, to 25-40 mL of reactant solution prepared in
0022-3654/78/2082-1121$01.00/00 1978 American Chemical Society
