2579
Correlation of Self-Exchange and Electrochemical Rate Data
Correlation of Homogeneous Self-Exchange and Electrochemical Rate Data. Further Evidence for Anomalously Low Reorganizational Barriers in Electron Transfer Reactions of Cobalt Complexes1a John F. Endicott, Ronald R. Schroeder," Dale H. Chidester, and Donald R. Ferrierlb Department of Chemistry, Wayne State University, Detroit, Michigan 48202 (Received October 12, 7977; Revised Manuscript Received August 8, 7973) Publication costs assisted by the Public Health Service
The staircase voltammetric technique has been applied to the determination of the standard heterogeneous rate constants ( k , ) for one electron reductions of several coordination complexes. Some of these determinations together with literature data suggest a correlation between k , and the homogeneous selfexchange rate constants (kexch) similar in form to that suggested by Marcus: log kexch = (2.0 i 0.5) log k , (4.0 f 1). Contrasting behavior is exhibited by cobalt(1II) complexes for which little variation in k , is found for complexes whose self-exchange rates vary by more than a factor Similar behavior has previously been reported for outer-sphere homogeneous reduction of cobalt(II1) complexes. It must be concluded that the reorganizational barriers which are so important in cobalt(II1)-(11) self-exchange reactions are not as significant in cross reactions of cobalt complexes.
+
Owing to their apparent simplicity, electron transfer reactions of coordination complexes have been the subject of many experimental and theoretical studies.2 Although most of the systematic investigations have dealt with homogeneous reactions, the theoretical treatment of MarC U S ~ ~ suggests % ~ , ~ a relationship (1) between the homoge-
neous self-exchange rate constant ( e . g . , for the Ru(NH3)e3+s2+exchange reaction), k e x c h , the standard (reference to Eo for the exchange related couple) heterogeneous rate constant, k,, and the homogeneous and heterogeneous diffusion rates ( 2 and Zel, respectively). Although Marcus' arguments have been in the literature for several years, there does not appear to have been any previous attempt to systematically examine the validity of (1)or to examine the possibility that there may be a general empirical correlation between hexch and k,. The studies reported in the present manuscript were undertaken to complement studies of the outer-sphere electron transfer reactions of cobalt complexes in homogeneous aqueous solutions? ,4-8 The Marcus-type free energy correlations (2) have not been precisely applicable to ho-
mogeneous electron transfer reactions of cobalt complexe~.2a-d,~-8 Several studies5x8 have demonstrated that the major discrepancy between (2) and observed behavior arises because reorganizational barrier in cross reactions is much smaller than would be inferred from the usua12a,b relation, A12 = % ( A l l + A221 = %(Ac, + A22). Rate parameters from heterogeneous reactions provide a more direct means of examining this anomalous behavior of cobalt complexes. The present study examines the relationship between k e x c h and k,, and is a result of our interests in the energetics of homogeneous, outer-sphere electron transfer
reactions4 ,738 and in the development of convenient and accurate methods for determining standard heterogeneous rate c o n ~ t a n t s . ~ - ~ l It is to be noted that the widely ~ i t e d ~ - success ~ , ~ J in ~ correlating heterogeneous rates of reduction of CoIII( NH3)5X complexes with outer sphere homogeneous reduction rate constants is probably due to the fact that Vlcek12 referred all his heterogeneous rate constants to a common reference potential (since standard potentials, EO, are unknown for these complexes) and variations in the cross reaction rates whether homogeneous or heterogeneous depend strongly on AG12. Experimental Section Three different instrument systems were used to obtain the staircase voltammetry data.9J1J3 Each system was composed of an electrolysis cell, a potentiostat, a central timing unit, a staircase waveform generator, a current sampler, and a data recording device. The same cell potentiostat and waveform sources were used with each of the three instrument systems. The cell was of the conventional three electrode type composed of a working electrode (either a hanging mercury drop, a platinum wire, or a slowly dropping mercury electrode), a platinum wire counter electrode, and a saturated calomel reference electrode connected to the cell by a salt bridge and capillary probe. The cell was a 50-mm diameter weighing bottle with a snug-fitting Teflon cap which held the electrodes and the nitrogen gas inlet tube. The potentiostat was an operational amplifier based adder-controller of conventional design and included a voltage follower input to which the reference electrode was connected, a dc voltage source for setting the initial potential, and a precision resistor for current monitoring. The staircase generator was a binary up-down counter, triggered by the central timing unit. The counter output was connected to a digital to analog converter to produce the staircase waveform. The staircase waveform consisted of 128 steps of 5 , 10, or 20 mV amplitude. The Journal of Physical Chemistry, Vol. 77, No. 21, 7973
2580
The first instrument systenigJ1 used for preliminary and qualitative work included a square wave signal generator as the central timer. The differentiated square wave triggered the waveform counter and a delay timer; the delay timer in turn triggered the current sampling by modulating the electron beam of an oscilloscope. The delay timer turned “on” the beam during each step only a t the preselected current sampling time. The voltammogram was recorded using an oscilloscope camera with a Polaroid back using 3000 speed film. The second instrument systeml13l3 utilized a transient recorder (Biomation 610, Biomation Inc., Palo Alto, Calif.) as the central timer and as a digital recorder. A delay timer connecting the transient recorder and the waveform counter provided the delay needed for selectable current sampling times. The voltammogram was stored in the transient recorder memory as 128 six-bit binary words. A teletype inferfaced to the transient recorder provided a punched paper tape recording of the voltammogram. This tape recording was processed through the university’s IBM 360/67 time-shared system to produce decimal output. Programs stored in the time-shared system were used for signal averaging, peak finding, automatic baseline correction, unit conversion, and plotting. The third system13 used a minicomputer (JRA.5 spectrum computer, JOEL, Inc., Tokyo, Japan) as the central timer and data gathering device. This system provided up to five current samples per step a t five preselected times and was used with the slow dropping mercury electrode. The computer averaged the data from five experiments (one experiment per DME drop) and provide a punched paper tape output identical in form with the previously described system except in providing eight-bit binary numbers. Solutions were prepared from reagent grade chemicals using distilled solvents. The cobalt macrocyclic complexes were kindly donated by Dr. D. P. Rillema.14 Other cobalt complexes were prepared by standard literature proced u r e ~ . The ~ ~ ,[Ru(NH3)6](C104)3 ~ ~ used was obtained as the chloride salt from Mathey-Bishop, Malvern, Pa., and recrystallized from perchloric acid. All solutions used in the staircase studies were shown by polarography to contain no significant impurities. The solutions for voltammetric studies were made up just before use to be approximately millimolar or less in the complex and either 0.05 or 0.1 M in NaC104 or HC104. For each complex, voltammograms were run on solutions containing 0.05 and 0.1 M perchlorate. Voltammograms were recorded using several step times and at least five step to sampling time r a t i o ~ . ~The - ~ ~data % ~ were ~ used to determine experimental i, values. These were compared with i, values calculated from the theory presented by Ferrier and Schroeder.lo The theoretical k, values giving i, corresponding most closely to the experimental values were chosen. These results are listed in Table I. The measured k , values were corrected for double layer effects using the data of Wroblowa, Kovac, and Bockris for NaC104.l7 For this purpose graphs of the outer Helmholtz plane potential, 4, us. applied potential (referenced t o sce) were constructed for several perchlorate concentrations18 (see Figure 1).For each set of voltammograms, run in either 0.05 or 0.1 M perchlorate, a 6 value corresponding to the peak potential was selected and a corrected k , value was calculated. Corrections were made according to eq 3 The Journal of Physical Chemistry, Vol. 77, No. 21, 1973
J . Endicott, R. Schroeder, D. Chidester, and D. Ferrier
where z is the formal charge on the reacting species, CY is the transfer coefficient, and 78, is the number of electrons involved in the rate determining portion of the electron transfer reaction.18~9 Our measurements showed that ana was close to 0.5 for the various reactions studied here and this value was used for all corrections.z0 Corrected k , values and the measured values for each complex in each supporting electrolyte are listed in Table I. Significance of the k, Values. The measured k , values and the corresponding corrected h, values listed in Table I warrant some further discussion in regard to reliability and consistency of the results. From the h, values listed all of the complexes studied would be polarographically reversible, a conclusion consistent with previous observations in thisg,ll and other laboratories.Z1-ZZIn fact the results given here serve merely to support with quantitative data a trend previously noted for numerous cobalt complexes. The effects of chemical reactions and adsorption on the measured h, values are considered minimal. For the species studied here, cyclic voltammograms taken a t moderate scan rates have shown both cathodic and anodic waves indicating that chemical decomposition of the electron transfer products is slow on the relevant experimental time scale.z3 Adsorption peaks or other anomalous peaks where observed were sufficiently removed from the normal voltammetric wave to allow its complete characterization uia normal means. The trend in peak current with variations in sampling time was entirely consistent with the behavior predicted by the staircase t h e ~ r y . ~ , l o For R u ( N H ~ ) ~the ~ + h, value reported is the upper limit measurable by the staircase technique with the apparatus currently available. For cases where a measured k , value was obtained, we feel the values in Table I and I1 are accurate to within Ct30%. The double layer corrections merit additional comment. Our anticipation of somewhat dissimilar results a t the two perchlorate concentrationsz4 was not entirely satisfied as similar results were generally obtained. Corrections for double layer effects should have reduced any dissimilarities but instead increased them. Thus, the uncorrected results for any one complex seem more consistent than do the corrected values. It should be noted, however, that the
I 0
-0.1
-0.2
-0.3
-0.4
-0.5
-0.6
VOLTS vs. SCE
Figure 1. The potential at the outer Helmboltz plane, 6 , vs. the applied potential (in volts vs. sce) for various concentrations of NaC104. Based on the data presented in ref 17.
Correlation of Self-Exchange and E l e c t r o c h e m i c a l Rate
Data
2581
TABLE I: Measured and Corrected k , Values for Several Metal Complexes Complexa Co( [14]dieneN4) ( N H 3 ) t 3 +
C o ( [ 1 4 ] t e t r a e n e N 4 ) (NH3)z3+
C o ( e n ) 33+
Electrolyteb
0.050 M HC104
-0.08
0.10 M HC104
-0.06
0.050 M HC104
-0.56
0.01 M HC104
-0.54
0.050 M NaClO
-0.47
0.10 M NaC104
-0.47
0.10 M NaC104
-0.21
a For complex abbreviations see ref 25. values in volts. g Uljing eq 3.
iq
EPC
All in HzO, at 25 f 0.1".
1.22 1.30 1.42 1.24 1.33 1.41 1.17 1.24 1.29 1.37 1.21 1.28 1.35 1.53 1.27 1.36 1.37 1.28 1.46 1.66 1.30 1.51 1.81 1.94
iq(theor)- k,' 1.22 1.30 1.37 1.23 1.32 1.40 1.18 1.24 1.29 1.33 1.21 1.29 1.35 1.42 1.26 1.36 1.47 1.30 1.47 1.65 1.33 1.54 1.85 2.45
Volts vs. sce.
4'
kse
lo-'
kscorre'g
1.0
2.45 X
0.9
2.2 X
0.55
1.35 X
-0.067
2 X
0.75
1.84 X
-0.063
4 X
1.2
2.94 X
-0.043
4 X
2.5
6.5 X
-0.043
9 X
Rev
>1
0.085
>1
0.044
>1
>> 1
4-0.013
From ref 9, k,' = k,t/;yana/v'B. e Cm/sec.
r
TABLE I I: Standard Heterogeneous Rate Constants lor Reduction of Several Coordination Complexes Complexa
Solventb
E,, ve
k,,d c m sec-'
From Figure 1,
-.
kexch, M - l sec-'
A. C o b a l t ( l l 1 ) Complexes C o ( [14]aneN4) ( C N ) 2 + Co([l4]dieneN4) (CN)2+ C o ( [ l 4 ] d i e n e N 4 ) (NH3)23+ C o ( [14]dieneN4)CIz+ Co([14]dieneN4) Br2+ C o ( [14]tetr.aeneN4)( N H3)z3+ Co (e17)3~+ Co (EDTA) C0(NH3),j3+
-1.1 -1.1
0.01-0.02 0.01-0.02 0.023
-0.06 +0.05
10-9e
0.005 0.005
4-0.16
0.01 5 0.040 0.01-0.02 0.5-1.3 X
-0.56 -0.47 -0.04
1 0'
x 10-5 10-6 3 x 10-'2h 5
B. Other Metallo Complexes
x 10' 103 4 1.0 x 1 0 - 2 ( 1 0 - 3 ) ~ 1 x 10-4 2 X 10-5(3 X 10-7)k 5
-0.21
>1 5 x 10-3' 3 x 10-3' 2 x 10-4:
10-5
a For ligand abbreviations see ref 25. AN = acetonitrile. Peak potential vs. sce. Values taken from ref 2c or 24 except as indicated. e Based on the self-exchange rate observed for trans-Co([14]dieneN4) ( O H Z ) ~ ~ + (ref , ~ + 4d). Based on the self-exchange rate observed for Co([141tetraeneNa(OH2)23+,2+(ref 4d). From the rate constant for the Ru(NH3)6*+ reduction of trans-Co([14]tetraeneN4 ( " 3 ) 2 3 f , 4 C we estimate that kexch = 10°.4*0.8 M - ' s e c - l . g Reference 25. Reference 24. ' Reference 19. J T. J. Meyer and H. Taube, inorg. Chern., 7, 2369 (1968); G. Navon and KJ. Meyerstein, J. Phys. Chem., 7 4 , 4067 (1970). 'Values in parentheses estimated from cross reactions with f l i ~ ( N H 3 ) 6 ~using the Marcus relation, k12 = (kllk22k12. f12)"? See ref 4 .
correction applied (eq 3) is in fact an overcorrection for double layer effects, and that the actual k , for each complex lies between the corrected and uncorrected values. It is our opinion, though not supported by existing theories, that the uncorrected values more closely approximate the true k , value than do the corrected ones. Furthermore, considering the similarities in the complexes one would expect them to exhibit some similarities in behavior and
C,
here again the uncorrected k , values appear to be more reasonable than the corrected ones.
and Discussion Values of the standard heterogeneous rate constant, k,, for reduction of several cobalt complexes are listed in Table II.25 To facilitate comparisons we have also included, where possible, estimates of the homogeneous self-exThe Journalof Physical Chemistry, Voi. 77, No. 2 1 , 1973
J. Endicott, R. Schroeder, D. Chidester, and D. Ferrier
2582
cognizance of the relatively poor quality of the values of and k, currently available the agreement between (4) and (1) is far better than might have been expected. Such problems as reactant adsorption in the heterogeneous reactions and specific ion effects in the homogeneous reactions may require that empirical relations of type (4) are intrinsically imprecise. The very large difference in the magnitude of the variations observed in k , and k e x c h for cobalt complexes suggest some differences in the fundamental physical parameters determining the rates of the two kinds of one electron reductions, heterogeneous and self-exchange. On the other hand, the outer sphere (e.g., with R u ( N H ~ ) ~ ~ + or V2+) reduction rates of these same cobalt complexes in homogeneous solution exhibit a similar independence of the cobalt self-exchange rates.E It seems necessary to conclude that the rate constants for cobalt(II1)-(11) self-exchange reactions are limited by some factor (or factors) which is less significant in heterogeneous or homogeneous cross reactions of cobalt complexes. At the present time it does not appear that there are significant “spin restrictions” on the cobalt(II1)-(11) self-exchange rates.8333-37 Much of the variation in these self-exchange rates has been rationalized in terms of ligand reorganizational barriers a view that has received much experimental support and has been widely accepted.2-s, 2 8 , 2 9 , 3 5 , 3 8 In the sense that (l),a prediction based on such a theory, is consistent with the experimental correlation (4) of k e x c h and k,, the present study further corroborates this model. However, we do not find a basis within the context of this model for rationalizing the order observed for self-exchange rates (or standard heterogeneous reduction rates) even of all the complexes not containing cobalt; i. e., the decrease of k e x c h in the order F e ( c N ) ~ ~ - s ~ -R u ( N H ~ ) ~ ~>+ Fe3+J* %~+ > V3+J+ > Eu3+-J+ > Cr3+92+ is extremely difficult to understand only on the basis of the variation in ligand reorganizational barriers. Despite such reservations the most notable exceptions to reactivity correlations based on (1) or (4) involve reactions of cobalt complexes and these seem most deviant with regard to the reorganizational contributions inferred from cobalt(II1)-(11) self-exchange data. It is possible to postulate that self-exchange and cross reaction rate data are intrinsically unrelatable, but this would again be true only in the case of cobalt and would attribute a very unsatisfying complexity and capriciousness to an intrinsically simple class of reactions. The cobalt(II1)-(11) self-exchange reactions do have the relatively unique feature that both the donor and acceptor orbitals are antibonding xeg. Although it is commonly believed2 that the reactant orbital overlap integrals, J@D@A d7, make a negligible contribution to the reaction energetics, it is also evident that in order for the transmission coefficient K N 1, J@D@* d7 must be greater than some minimum value, y. Since the *eg orbitals are buried within the ligation of the complex ion while the t Z g orbitals are . ~ I y in effect requires shorter not, the condition J 4 ~ 4 d7 distances of closest approach and different activated complex geometries when the donor and acceptor orbitals are both *eg in character than when both are tag in character or when only the acceptor orbital is *eg in character. Thus it seems plausible that variations in cobalt(II1)-(11) selfexchange rates arise in part from the work required to achieve the J@D@A d r I y condition as the ligands are changed. kexch
C]=
-121
-5
-4
-3 -2 LOG k,
0
-I
Figure 2. Correlation of homogeneous self-exchange rate constants with heterogeneous rate constants: circles are data from part B of Table II; squares are entries for cobalt couples (part A , Tabie 1 1 ) . Complexes included are Co([14]tetraeneN4(NH3)z3+s2+ ( I ) , C0(en)3~+,~ (I+ I ) , C O ( E D T A ) - , ~ - ( I l l ) , Co([14]dieneN4)(NH3)z3+,z+ ( i V ) , and C O ( N H ~ ) ~ ~ - -( ’V~) .+ The line is drawn to fit eq 1 assuming Z = 10” M-’ sec-’ and Z,I = l o 4 cm sec-l. Solid circles of squares represent values measured in this work, corrected values are indicated by dashed line squares.
change rates for the appropriate cobalt(II1)-(11) couples and some similar data previously reported for C0(”3)6~+ and other c o m p l e ~ e s . ~ ~ - ~ ~ I t is a most remarkable observation that the measured values of k , vary by no more than a factor of lo2 for a series of cobalt complexes whose homogeneous self-exchange rates vary by a factor of more than In a way this result might have been anticipated since it is known that many cobalt(II1) complexes are polarographically reversibleZ1J2 whereas the corresponding homogeneous self-exchange rates are well known to be very slow; e . g . , both ,2+ and qualitative observations apply to the C0(en)3~+ Co(EDTA)- & couples. However, the magnitude of the discrepancy has certainly not been commonly recognized. Since there has been so much speculation about the kinetic significance of metal ligand interactions in electron transfer cross reactions, whether the interactions be due to bond ~trengths,E.~O crystal field strength^,^^ or metal ligand stretching in the activated c o m p l e ~ it, ~is~very ~~ important to note that k , is relatively independent of the ligands (axial or other) coordinated to cobalt(II1). It seems to be a characteristic of both the heterogeneous and homogeneous reactions that the rates of electron transfer reactions of cobalt complexes are very often faster than predicted by the Marcus cross relation (1or 2 ) . Despite the anomalous behavior noted for cobalt complexes, such limited information as is available suggests that k , and k e x c h are reasonably well correlated by (1) for complexes of many other metals (Figure 2 ) ; for example, the empirical relation 4 is in reasonable agreelog hexch = (2.0 f 0.5) logk,
+
(4 f 1)
(4)
ment with (1) and is a reasonable representation of data for complexes not containing cobalt. In fact if one takes The Journal of Physical Chemistry, Vol. 77, No. 21, 7973
-
2503
Correlation of Self-Exchange and Electrochemical R a t e Data
Acknowledgment. The authors are grateful to Dr. D. P. Rillema for samples of cyclic complexes and for assistance in preparing some of the nonaqueous solutions. One of the authors (J. F. E,) is indebted to Professor J. K. Beattie for some stimulating discussions and for a preliminary report of some of his work. References and Notes (a) Partial support of this research by the Public Health Service (Grant No. AM 14391) is gratefully acknowledged. (b) N.D.E.A. Fellow 1967-,1969. For recent reviews see (a) R . A. Marcus, Ann. Rev. Phys. Chem., 15, 155 (1969); (b) W. L. Reynolds and R. W. Lumry, "Mechanisms of Electron Transfer," Ronald Press, New York, N. Y., 1966; (c) A. G. Sykes, Advan. Inorg. Chem. Radiochem., 10, 153 (1967): (d) H. Taube, "Electron Transfer Reactions of Complex Ions in Solution." Academic Press, New York, N. y., 1970; (e) J. E. Earley, Progr. Inorg. Chem., 13, 243 (1970); (f) R. G. Linck, MTP Int. Rev. Sci.. Inorg. (;hem., Ser. 1, 9, 303 (1971); (g) N. Sutin, Chem. Britain, 8, 148 (1972). R. A. Marcus, J. Phys. Chem., 67, 853 (1963). J. F. Endicoti and H. Taube, J. Amer. Chem. SOC., 86, 168 (1964). R. J. Campion, N. Purdie, and N. Sutin, Inorg. Chem., 3, 1091 (1964). 86, J. P. Candlin, J. Haipern, and D. D. Trim, J. Amer. Chem. SOC., 109 (1964). R. C. Patel and J. F. Endicott, J. Amer. Chem. SOC.,90, 6364 (1968). (a) D. P. Rillema, J. F. Endicott. and R. C. Patel, J. Amer. Chem. Soc., 94, 394 (1972); (b) D. P. Rillema and J. F. Endicott, lnorg. Chem., 11, 2361 (1972); (c) J. Amer. Chem. Soc.. 94, 8711 (1972). D. R. Ferrier, Ph.D. Thesis, Wayne State University, 1971. D. R. Ferrier and R. R. Schroeder, J. EIectroanaI. Chem., 45, 343 (1973). D. R . Ferrier, D. H. Chidester, and R. R. Schroeder, J. Electroanal. Chem., 45, 361 (1973). (a) A. A. V k e k , "Advances in the Chemistry of Coordination Compounds," Macmillan, New York, N. Y., 1961, p 289; (b) Progr. Inorg. Chem., 5, 21 1 (1963). ' D. H. Childester, Ph.D. Thesis, Wayne State University, 1973. D. P. Rillema, J. F. Endicott, and E. Papaconstantinou, Inorg. Chem., 1 0 , 1'739 (1963). R . Angilici, "Synthesis and Technique of Inorganic Chemistry," W. B. Saunders, Philadelphia, Pa., 1969, p 71 F. P. Dwyer, E. Gwarfas, and D. Meller, J , Phys. Chem., 59, 296 (1955). H. Wroblowa, 2. Kovac, and J. O'M. Bockris, Trans. Faraday Soc.. 61, 1523 (1965). P. Delahay, "Double Layer and Electrode Kinetics," Interscience, New York. N. Y., 1965. Although eq 3 is the standard correction used to correct measured rate constants for double layer effects, its application to the data presented here is subject to question. For lack of a more appropriate correction it has been used. The sources of our concern are the nonequilibriuin double layer involved in the staircase experiment due to the lalrge overall potential changes and the subsequent concentration changes and reactant mass transfer. We anticipate from
these considerations that eq 3 overcorrects the measured values. This overcorrection is probably amplified by the use of the formai charges of the reactants without considering ion pairing, activity effects, or the effects of the reactant on the double layer structure. Thus, the measured and corrected rate constants can be considered only to define the range within which the true value falls This rather large uncertainty in the true rate constant values does not however detract from the conclusions given or from the questions raised in this work. (20) (Actually ana values ranging between 0.4 and 0.6 were estimated from our data: no attempt was made to determine a more accurate ana value. Even a large uncertainty in ana has little effect on the corrected k s values especially considering the large uncertainty in 2).
(21) Polarographic reversibility is usually observed, in the presence of excess ligand, for those complexes where cobalt( I I ) complex formation constants are fairly large. For example, see H. A. Laitinen and M. W. Greib. J. Amer. Chem. SOC.,77, 5201 (1955). (22) See also comments on this point in ref 8 and 14. (23) R. S. Nicholson and I. Shain, Anal. Chem., 34, 706 (1964). (24) If double layer effects are to be significant, then the rather large differences in 6 for the same complex at the two different perchlorate concentration should have caused major differences in the measured k s values. (25) Ligand abbreviations used in this paper are [14]aneNa = 5,7,7,12,14,14-hexamethyl-l,4,7,11 -tetraazacyciotetradecane; [14]dieneN4 = 5,7,7,12,14,14-hexamethyi-l,4.8,1j -tetraazacyclote2,3,9,10-tetramethyltradeca-4.1 I-diene; [14]tetraeneN4 = 1,4,8,1l-tetraazacyclotetradeca-l,3,8,1O-tetraene: en = ethylenediamine: EDTA = ethylenediaminetetraacetate. (26) N. Tanaka and R. Tamamushi, Electrochim. Acta. 9, 963 (1964) cm sec:' for C O ( N H ~ ) has ~ ~ been (27) A value of k s = 0.5-3 X obtained. H. Bartelt and S. Landazury, J. Electroanal. Chem., 22, 195 (1969). A value of 1.3 X cm/sec is ais0 obtained from 'Vlcek's data using an E o of -0.21 1 vs. sce and diffusion coefficient of 7 X 10-6 cm2/sec. (28) N. Sutin, Ann. Rev. Nucl. Sci., 1 2 , 285 (1962). (29) An upper limit of 3.3 X M - ' sec-' for the C O ( N H ~ ) ~ ~ ~ . ~ + self-exchange rate has been estimated in ref 4 from data of D. R. Stranks, Discuss. Faraday Soc., 29, 73 (1960): N. S. Biradar and D. R. Stranks, Trans. Faraday Soc., 58, 2921 (1963). (30) See discussion in ref 2c-f and C. Bifano and R . G. Linck, J. Amer. Chem. SOC.,89, 2945 (1967). (31) P. Benson and A. Haim, J. Amer. Chem. SOC.,87,3826 (1965). (32) H. Diebler, P. H. Dodel, and H. Taube, lnorg. Chem., 5 , 1688 (1966). (33) J. K . Beattie, private communication, 1971, (34) R. Farina and R. G. Wilkins, lnorg. Chem.. 7, 514 (1968) (35) For example, the Co([l4]dieneN4) ( O H Z ) , ~ ~ ~ self-exchange rate is slow ( l o - ' M - ' sec-' at 70") despite the fact that Co([l4]dieneN4) ( O H Z ) ~ ~is' predominantly low spin.36 Recent structural studies have shown that the Co11-OH2 bond lengths are 0.5 ,& longer than the Col**-OH~ bond lengths; M. D. Glick. J. Kuszaj, and J. F. Endicott, J. Amer. Chem. SOC.,95, 5097 (1973) (36) (a) D. D. Rillema, J. F. Endicott, and N. A. D. Kane-Maguire, J . Chem. Soc.. Chem. Commun., 495 (1972); (b) manuscript in preparation. (37) (a) J. T. Yardley and J. K. Beattie, J. Amer. Chem. SOC., 94, 8925 (1972): (b) J. K. Beattie, N. Sutin, D. H. Turner, and G . W. Flynn, ibid., 95, 2052 (1973). (38) For a contrary point of view see H. L. Stynes and J. A. Ibers, Inorg. Chem., 10, 2304 (1971). sZt
The Journal of Physical Chemistry, Vol. 77, No. 2 1, 1973
