THE RATES AND MECHANISMS OF REACTIONS OF Cr(bip):+ WITH Co(JII) COMPLEXES * BY A. M. ZWICKEL? AND HENRY TAUBE George Herbert Jones Laboratory, University of Chicago, Chicago 37, Illinois, U.S.A. Received 18th January, 1960 Cr(bip):+ is shown to react with complexes of the type CoIII(NH3)sL (L = NH3, OH2, OH-, C1-, Br-) by an outer sphere activated complex. Salt, ligand, and isotope effects have been investigated and are discussed. A useful criterion for classifying and, through this, for improving the under- standing of mechanisms of electron transfer reactions is provided by the geometry of the activated complex. Some activated complexes are characterized by inter- penetration of the first coordination spheres of the reactants in the activated com- plex. These, which have been named the bridged activated complexes, have been demonstrated in the reactions of chromium(I1) with a great variety of oxidants inert to ligand substitution.1 This demonstration is made possible by the behaviour of chromium toward substitution when reduced and when oxidized.Chromium is perhaps unique among aquo ions in that it is labile to substitution when reduced but inert when oxidized. Thus, progress with other aquo ions as reducing agents awaits the development of less direct means of classifying the mode of attack. A second activated complex, which has been called the outer sphere activated complex, is defined by the requirement that the number and identity of the ligands in the first coordination spheres of the reactants remain unchanged when the reactants enter the activated complex.Since this activated complex perhaps must of necessity operate in reactions where both reactants are inert to substitution, it has been found in more systems than has the bridged activated complex.1 One method of attack on the systems which have thus far resisted classification may be a discrimination on the basis of the chemical and isotopic effects characteris- tic of the two activated complexes. Some effects of this kind have been elucidated for reactions involving the bridged activated complex. Analogous effects have now been in part determined for the outer sphere activated complex by study of the reactions of Cr(bip);+ (bip = a&-bipyridine) with various complexes of cobalt(I1I). These oxidants were chosen for study in order to provide comparisons with the data which have been observed for the reactions which they undergo with Cr:.In all the reactions studied thus far using oxidizing agents of the class of present interest, except when L = NH3, C r l l reacts by means of the bridged activated complex. EXPERIMENTAL Due to the air-sensitivity of the reductant, all work was done in an atmosphere of nitrogen scrubbed with Ce; to remove traces of oxygen. The reductant was generated by addition of C<$ (electrolytically produced) to a solution of a,a’-bipyridine. The reductant was added to the deoxygenated solution containing oxidant, neutral salts to * Contribution from the George Herbert Jones Laboratory, University of Chicago. -f present address : Department of Chemistry, Florida State University, Tallahassee, Florida.42A . M. ZWICKEL AND 11. TAUBB 43 fix the ionic strength, and miscellaneous reactants (e.g. acid). 'The mixture was stirrcd by bubbling with nitrogen and pumped into a deoxygenated spectrophotometer cell. The cell and the mixing vessel wcre thermostatted by immersion in a water bath. After mixing, the cell was isolated, dried, and transferred to the thermostatted cell compartment of a Cary model 14 spectrophotometer, and the optical density of the solution as a function of time was recorded. At 562.5 mp, the extinction coefficient of the reductant, 4340 cm-1 mole-1 l., was ca. 100 times that of any other speciesIpresent. Thus, the sccond-order rate law could be used in the form where D is the optical density of the subscripted time, E the extinction coefficient of the reductant, and I the optical path length of the cell.The differentiation with respect to time was performed graphically. Linearity of the above plots under widely varying initial conditions of concentration was taken as proof of the validity of the treatment of the data and specifically of the assumed second-order rate law. RESULTS THE FORMULA OF THE C ~ ~ + - B ~ ~ I D I N E COMPLEX Evidence that the predonlinant form of Cr(U) in the reactant solutions is a complex containing 3 molecules of bipyridine for each atom of chromium was provided by a mass-action analysis of the colour of solutions containing 1.0 x 10-4 M Cr(II), 5 x 10-4 M HC1 and various concentrations of bipyridine. The extinction coefficient of the terminal complex at high bipyridine concentration was determined using a solution containing a large excess of the base.Using the extinction coefficient thus determined, the concentration of the terminal complex was calculated from the measured optical density of the intermediate solutions, the concentration of Cri: then being obtained by difference. The concentration of free bipyridine was also determined by difference, using the value of Harkins and Freiser2 for the acidity of the bipyridinium ion. The data and the results of the calculations are shown in table 1. TABLE ~.-D~ERMINATIoN OF THE COMPOSITION OF THE Cr(II) COMPLJX temp., 23" total bip., M 2.2 x 10-4 3.7 x 10-4 5.6 XlO-4 Cr(bip);', M 2-26 x 10-5 5.32 x 10-5 8-75 x 10-5 Cr:gf, M 7.74 x 10-5 4.68 x 10-5 1.25 x 10-5 calc.for n = 1 2.4 x 10-5 5.9 ~ 1 0 - 5 1.2 x 10-4 n = 2 2.1 x 10-5 3.8 ~ 1 0 - 5 7.4 x 10-5 n = 3 1.6 x 10-5 2.6 x 10-5 4.6 x 10-5 free bip, M 0.8 x 10-4 1-51 x 10-9 1-40 x 10-14 0 . 5 2 ~ 10-4 1 a26 X 10-9 0.17 x 10-4 0.83 x 10-9 1-28 x 10-14 It is apparent from the results shown in table 1 that the assumption that the formula of the complex is Cr(bip)z+ does account satisfactorilyfor the data, and that44 REACTIONS OF Cr( bip)z+ WITH Co(I1 I ) COMPLEXES it is the only simple assumption that does. In the solutions used in the rate experiments, the total concentration of bipyridine was at least 9 times as great as in the experiments outlined in table 1 so that it can safely be assumed that unless the acidity is too great the predominant form of Cr(1I) in the solutions is the com- plex Cr(dip)g+.EVIDENCE ON THE GEOMETRY OF THE ACTIVATED COMPLEX The reaction of Cr(dip):+ with the Co(1II) complexes studied was found to be nicely first order in the reducing agent and in the oxidizing agent at least for all the oxidants with which it was possible to get fairly extensive kinetic data. The rate of reaction of Cr(dip):+ with Co(NH&+ was also shown to be independent of total bipyridine concentration over a considerable range from 0.002 M total to greater than 0.01 M total (Cr(I1) total at ca. 5 x 10-5 initial, pH approximately 4). With Co(NH3);' as reactant, and with bipyridine in good excess, the rate of reaction was shown to be independent of pH in the range 3.5 to 5.6; with the aquo complex as reactant, the rate of reaction was shown to be independent of pH in the range 3.0 to 5.0.For both systems it can therefore be taken as proved that the reactant is Cr(dip):+ rather than an ion containing less bipyridine per Cr(I1). (It should be mentioned, however, that an increase in the rate of reaction is noted when the pH is lowered to 1.5. Presumably a species such as Cr(dip)2+ or Cr(dip)g+ is present at low pH, and it reacts more rapidly with Co(NH&+ than does Cr(dip):+.) TABLE ~ . - c o ( N H ~ > ~ + AS OXIDIZING AGENT Total [bip] 0.002 or greater ; [initial Cr(II)] ca. 5 x from 5 x 10-6 to 1 x lO-3M [Co(NH,)3,+], temp. 25 25 25 25 25 25 4 4 4 25 24 24 24 23 4 24 0.01 (NaCl) 0.05 (NaCl) 0.096 (NaC1) 0.20 (NaCl) 0 2 0 (NaCl) 0 2 0 (NaCl) 0.01 (NaCl) 0.05 (NaCl) 0-20 (NaCl) 020 (NaCl) 0-01 (NaC104) 0.05 ( N ~ C I O ~ ) 0.10 (NaC104) 0-20 (NaRr) 0.20 (NaBr) 0.20 (KCl) k x 10-3 M-1 min-1 2.4 6.8 10.8 14.9~ 15*2b 11-oc 0.43 1-48 3.9d 20.0e 5-6 21.3 41 36 9.6 15.6 a average of 5 determinations, with an average deviation from the mean of 5 %. b using 94.8 % D20 as solvent, mean of two values.c using Co(ND3);' in 93.8 % D20, mean of two values. dmean of 3 values, average deviation, 5 %. e 0.005 M Na2SO4. The kinetic evidence cited implies that the chromium reaction product is Cr(dip)i+, for bipyridine is not lost from the Cr(II) complex prior to reaction, andA . M. ZWICKEL AND H . TAUBE 45 since Cr(II1) is usually quite inert to substitution, the base is probably not lost after the electron transfer reaction is consummated.This prediction based on kinetic considerations is supported by the following evidence. The spectrum of the reaction product is identical with that obtained for a solution of Cr(dip)z+ which has been oxidized by air, and that of a solution prepared by prolonged heating of Cr(HzO);+ in the presence of excess bipyridine. The reaction product cannot be eluted from a column of Dowex-50-X4 ion exchange resin by 1 M HC104, but is eluted by 4 M HC104 so that it probably has a charge of +3. The arguments just presented show that the coordination sphere of the Cr(I1) complex is not disrupted when it reacts. The well-known inertia to substitution of the Co(II1) complex studied ensures that the oxidizing agents also keep the co- ordination sphere intact, so that the mode of attack is limited to that corresponding to the geometry of the outer-sphere activated complex.SUMMARY OF KINETIC DATA The results of experiments with Co(NH&+ as oxidizing agent and covering a range of conditions are summarized in table 2 and for certain other oxidizing agents in table 3. Table 4 shows the activation parameters computed from the data obtained on the reaction of Co(NH3>;+ with Cr(dip)i+ at different temperatures. TABLE 3.-REA(=TION OF Cr(dip)$+ WITH A VARIETY OF OXIDIZING AGENTS Concentrations in the range used for experiments of table 2, NaCl to maintain p, pH-4 oxidant temp., O C P k, M-1 min-rx 10-3 Co(en$+ 25 0.10 2.2 Co(en): + 25 0.20 3.8 CO(NH~)~(OH~)~-~ 4 0.05 126* CO(NH3)5(OH2)3 + 4 0.05 486 CO(m3)5(OH2)3 + 4 0.05 73= Co(NH3)5(OH2)3+ 4 0.01 39 Co(NH3)5Br2+ 4 00001 > 103 CO(NH~)~CP+ 4 0.01 630 a mean of 9 values (variable pH), average deviation from mean of 4 %.b In 93.8 % D20, making a linear extrapolation to 100 % D20. In D20 deuteration of the H20 molecule on Co(NH3)sH203+ takes place, but not immediate deuteration of NH3. An additional experiment using completely deuterated aquopentamminecobalt (111) showed the rate to be the same as that with only H20 deuterated. c at pH = 7.25. TABLE 4.-AcTIVATION PARAMETERS FOR THE REACTION CO(NH3);' WITH Cr(dip);+ medium AH+, kcal AS+, cal/molc deg. 0.20 (NaCl) 9.9 - 14 0.05 (NaCl) 11.3 -11 0.01 (NaCI) 13.0 - 10 0.20 (NaBr) 10.8 - 9 DISCUSSION The actual mechanism of the reactions investigated is most probably a quantum- mechanical tunnelling process.In support of this hypothesis may be cited the46 REACTIONS OF Cr( hip):+ WITH Co(ll1) COMPLEXES result that Cr(bip);+ reacts with Co(en):+ several times less rapidly than it does with Co(NH3):'. The decreased rate observed with ethylenediamine as compared to NH3 as ligand on the oxidant can on this basis be ascribed to the greater size of the ethylenediamine rnoleqle resulting in greater tunnelling distance and consequently lowering the probability for barrier penetration. It is interesting that even for the outer-sphere activated complex, the rates of reaction are very sensitive to the nature of the groups associated with the oxidizing agent. The comparison of the reaction rates for two ions of like charge, namely Co(NH3);' and Co(NH3)5Hz03+ is particularly significant.The increased rate when H20 is substituted for NH3 implies that the electron transfer process makes particular use of Iigands in these reactions also, and that the electron transfer proceeds through the ammonia ligand only when it has no other choice. Results then for ions of fixed charge type, can be interpreted as measuring the " conduc- tivity " of each ligand, or on the tunnelling model, the permeability of each ligand for electrons. The rate of reaction of Cr(bip):+ with Co(NH3)50H2+ may be calculated as 6 x 10 4 M-1 min-1 from the experiment with the aquopentammine system done at pH 7.25 under which conditions ca. 80 % of the aquo complex is dissociated to the hydroxy form. The comparison of the relative rate of reaction of Co(NH3)50H2+ and Co(NH3)50Hi+ with Cr(bip);+ on the one hand and with Crzl on the other is particularly significant.When Cr: is reactant, with both oxidizing agents a bridged activated complex is involved,3 and the hydroxo ion reacts at least 106 times more rapidly than does the aquo.4 But by the " outer-sphere " mechanism, the hydroxy ion in fact reacts less rapidly than the aquo. This implies that in the many systems in which the hydroxy form of the oxidizing agent reacts more rapidly than the aquo, the hydroxy ion is serving as a bridging group. In the bridged activated complex, it performs two functions, acting as a binding ligand, and conducting the electron. Its superiority over H20 in stabilizing a binuclear com- plex apparently far outweighs its somewhat lessened conductivity. The result for OH- as ligand observed in the system under present study is consistent with the observations made for the halide ions as ligands.By extrapolating the specific rates observed for Br- and C1- as ligands, the rate for (NH3)5CoF2+ reacting with Cr(dip):' is expected to be of the same order as it is for (NH3)5CoOH2+, and OH- and F- are perhaps expected to resemble each other in permeability to electron transport. It is also profitable in the context of these remarks to draw attention to the great increase in reactivity that takes place when H20 on Cr2+ is replaced by bipyridine. The rate of reaction of Crx,* with Co(NH&+ at 25" and p = 0.40 (NaC104) is 5-3 x 10-3 M-1 min-1.5 This reaction presumably also proceeds through an outer-sphere activated complex. Thus it is known that a proton is not lost from the oxidizing ion when it enters the activated complex, as would be required to expose an electron pair for use in bridging.The reaction has an activation enthalpy of 14.7 kcal and activation entropy of - 30 cal/mole deg. Part of the reason for the greater speed at which Cr(dip>g+ compared to C<$ reacts with Co(NH3);+ is the more fwourable entropy associated with the formation of the activated com- plex. On the tunnelling model, the entropy of activation may be interpreted as the sum of the classical entropy of formation of the activated complex from the reac- tants, and a term - R Ink,, where k , is the probability of barrier penetration.6 The function of the bipyridine molecule can in part be construed as being to bring the electrons to the surface of the molecule, thereby increasing the probability of barrier penetration.However, it must be recognized that the electronic con- figurations of Crz: and Cr(bip>:+ differ, the former having three d electrons in orbitals of t2g symmetry and one in an e, orbital 7 while the latter has four t2g electrons.8 Thus the electron which transfers from the bipyridine complex is inA. M. ZWICKEL AND H . TAUBE 47 an orbital which can overlap the 7r orbitals of the ligands, and thus can be brought to the surface of the molecule with consequent enhancement of reactivity to electron transfer. That such 7r orbitals areused as indicated by the result of George and lrvine 9 showing that the 5-nitro - 1,lO-phenanthroline complex of Fe(I1) reacts with Ce(IV) less rapidly than does the 1 ,lo-phenanthroline complex.This dif- ference presumably appears because the use of the ligand 7r orbitals by the nitro substituent renders them less available for use by the d electrons of the metal. The absence of a solvent isotope effect for the reaction of Co(NH3);' with Cr(dip):+ is interesting and implies that electron transfer occurs, at best, through the solvent and not to it. Indeed, it appears unlikely that the solvent plays any role at the mimediate site of attack, electron transfer most probably occurring directly from complex to complex without intervening layers of solvent.10 But even granting this, it is still surprising that there is no detectable solvent isotope 11 effect associated with rearrangement of the solvent about the ions.12 The isotope effect found on deuteration of the coordinated ammonia molecules, a decrease in rate by a factor of 1.36, probably does not arise from a stretching of N-H bonds, but from stretching the Co-NH3 bonds. Before electron transfer can take place, excitation of the breathing modes of the complex is likely necessary, in order to set up a potential field in whcih the energy of the electron is the same before and after transfer, as discussed by Libby.13 The Franck-Condon principle requires that the electron transfer process be adiabatic.The isotope effect accompanying deuteration in the first sphere of coordination in Co(NH&+ (diminution in rate by a factor of 1-36) is markedly different from that accompanying deuteration of the water molecule in Co(NH3)50Hi+ (diminution in rate by a factor of 2.6).This again is evidence that particular use is made of special groups also when electron transfer takes place by the " outer-sphere " mechanism. The specific implication is that it is expeditious to distort the co- ordinated water molecule. Since the diminished rate observed when OH- rather than H20 is the conducting group indicates that it is not helpful to remove the proton from water, the most reasonable distortion is a bending rather than a stretching mode. It should be noted that the isotope effect associated with replacing H20 in Co(NH&OH;+ by D20 when attack occurs via an outer-sphere activated complex is not much different from that observed for the bridged activated complex.In the latter case (Cr2+ as reducing agent) a total diminution in rate by a factor of 3.8 is observed.4 Part of the factor of 3.8 is undoubtedly to be attributed to substitution of D20 for H20 in the first sphere of coordination about Cr2+. From the H-D solvent isotope effect observed in 14 the reaction of Cr2+ with (NH3)5CrC12+, this is estimated as contributing a factor of 1.3, so that the effect associated with sub- stituting D20 for H20 in the oxidizing agent is a factor of 2.9 by the bridged activated complex. This comparison for the two kinds of mechanism makes it seem all the more unlikely that the H-D effects can be used in a simple way to distinguish between the two kinds of mechanisms although the results are still of great importance in defining the mechanisms of the processes. The salt effects are in accord with the general ideas discussed by Marcus 10 and by Libby.13 The smallest anion used, C1-, presumably interacts most strongly with solvent and therefore the rearrangement of the ionic atmospheres of the reactants in the activated complex is least easily effected with it.As may be expected for an activated complex formed from cations, substitution of K -I- for Na -I- has a negligible effect on reaction rate at least when the cations are at low concentration. Sheppard and Wahl15 have demonstrated the great sensitivity of the electron exchange re- action between MnO, and Mn0;- to the nature of the cation present in solution. We wish to thank the Atomic Energy Commission (Contract AT(11-1)-378) for support of the reaserch described in this paper.48 REACTIONS OF Cr(bip)g+ WITH Co(1II) COMPLEXES 1 Taube, Can. J. Chem., 1959,37, 129. 2 Harkins and Freiser, J. Amer. Chem. Soc., 1955,77, 1374. 3 Kruse and Taube, J. Amer. Chem. Suc., 1960, 82, OOO. 4 Zwickel and Taube, J. Amer. Chem. SOC., 1959,81, 1288. 5 Zwickel and Taube, to be published. 6 Marcus, Zwolinski and Eying, J. Physic. Chem., 1954, 58, 432. 7 Orgel, J. Chem. Physics, 1955, 23, 1004. 8 Hein and Herzog, 2. anorg. Chem., 1952,267, 337. 9 George and Irvine, J. Chem. SOC., 1954, 587. 10 Marcus, J. Chem. Physics, 1956,24,966. 11 Baker, Basolo and Neumann, J. Physic. Chem., 1959, 63, 371. 12 Marcus, J. Chem. Physics, 1957, 26, 867. 13 Libby, J. Physic. Chem., 1952, 56, 863. 14 Ogard and Taube, J. Amer. Chem. SOC., 1958, SO, 1084. 15 Sheppard and Wahl, J. Amer. Chem. Soc., 1957,79, 1020.