Faraday Discuss. Chem. Sac., 1982, 74, 129-140 Catalytic Influence of the Environment on Outer-sphere Electron-transfer Reactions in Aqueous Solutions BY H. BRUHN, S . NIGAM AND J. F. HOLZWARTH Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-1000 Berlin 33, West Germany Received 28th June, 1982 The continuous-flow method with integrating observation (CFMIO) has been used to investigate irreversible electron-transfer (ET) reactions between negatively charged, substitution-inert transition- metal complexes. Special attention has been paid in order to distinguish between the different contributions to the energy of activation such as size of reactants, long-range charge interactions, influence of the free energy of reactions (difference in redox potential) and the composition (electro- lytic content) of the solutions.We selected the ET reaction between Fe(CN)6Hx"-4 and IrCli- to demonstrate the catalytic rate enhancement caused by the addition of mono-, di- and tri-valent cations. Increasing protonation of Fe(CN),H:-4 decreases the rate of ET; strong association with M2+ and M3+ (where M indicates the metal) has no catalytic effect. All alkali-metal ions show an increas- ing catalytic effect with increasing size; the four tetra-alkylammonium ions show the opposite. The Arrhenius plot of the above-mentioned ET reactions in the presence of cations is strongly curved ; the decreasing slope at higher temperatures indicates a complex reaction mechanism. In the ET reaction between silvertetraphenylporphyrin tetrasulphonate and IrCli- , ET occurs at the axial position of the complex, far away from the negatively charged sulphonate groups.A catalytic effect similar to that found in the reaction with Fe(CN)z- is observed ; this result precludes the cations having a bridge-like function during ET. Monovalent cations of varying size show a maximum rate enhancement when their ionic radius is ca. 0.23 nm. If long-range Coulomb inter- actions are shielded, and a situation in which the free-energy change of reaction is zero is simulated, we extrapolate a maximum for the ET rate constant of 10" dm3 mol-' s-'. Progress in the understanding of electron-transfer (ET) reactions is mainly due to theoretical work by Marcus and Levich and Dogonadze and experimental work by Sutin and T a ~ b e .~ A recent summary of the present state can be found in Ulstrup's In this paper we concentrate on outer-sphere electron-transfer reactions between ligand-substitution-inert anionic transition-metal complexes in the presence of different concentrations of electrolyte, to separate the primary salt effect (the electro- static influence on encounter rates) from other effects the electrolytic content of the solution might have. The unusual kinetic behaviour of such anionic complexes in ET has been observed by several groups before and is summarized for electrodes by Peter et aZ.,6 and Scherer et aZ.,7 and by Holzwarth et aZ.,8 Indelli 9n and Wahl 9b for homo- geneous solution. The transition state of these ET reactions carries a high negative charge, causing a high cation concentration in the surrounding solution.If we apply the formalism of Marcus we can expect that any change in the so-called reorganization energy of the transition state caused by different cations can be detected. The measurements described in the following sections give clear evidence that cations strongly influence the activation energy for ET.130 CATALYTIC EFFECTS O N ELECTRON TRANSFER EXPERIMENTAL All rate constants reported here were measured using the continuous-flow method with integrating observation (CFMIO). The time resolution of this method has been demons- trated by measuring half-lives of first- and second-order reactions as low as 5 x s.l0 The complexes used were prepared according to the literature." HC1O4, NaClO,, HCI, all metal chlorides and Na21rC16 were of Pro Analysis or Suprapure grade and purchased from Merck A.G.; Serva (Heidelberg) supplied silver mesotetraphenylporphyrin tetrasulphonate (AgTPPTS4-), and Kodak (Rochester) the tetra-alkylammonium chlorides. All measure- ments were performed in triply distilled water using reactant concentrations between lo-' and mol dmd3. Stock solutions were never kept for more than 10 h, and special care was taken to avoid photochemical decomposition by the light used to monitor the progress of reaction inside the CFMIO apparatus. RESULTS AND DISCUSSION The electron-transfer (ET) rate constants between IrCIg- as the oxidizing species and Fe(CN);- as the reducing compound were measured by adding different con- centrations of metal chlorides to the solutions.In fig. 1 the results are summarized by plotting the rate constants kET against the root of the ionic strength I. Above the dashed line the solution pH was 5 : below the line 1 rnol dm-3 HC1 (not included in I ! ) was always present, making the pH zero. Only the open symbols show measurements at varying pH values; here fne HCl concentration ranged from to 1 mol dme3. All rate constants at pH 5 show a marked increase with increasing ionic strength of added metal chlorides. Measurements with the same cations (Na+ or K+) and differ- ent anions, such as NO,, PF, or SO:-, instead of C1- never varied by more than 40% at an ionic strength of 0.1 rnol dme3; therefore we have only reported results using metal chlorides. At low ionic strength the rate enhancement increased in the series M+ < M2+ < M3+.At ionic strengths of 0.1 M2+ and M3+ have already reached a I 01 5 10 20 30 40 50' 75 100 102(I&+/mol dm-3)* FIG. 1.-Influence of cations on the rate constants for electron transfer between IrCli- and Fe(CN):- at different ionic strengths ( I ) . Above the dashed line the pH is 5, below the dashed line the pH is 0 (1 mol dm-3 HCl present). A, Increasing concentration of HCl from lo-, to 1 mol dm-3. Tem- perature = 298 K.H . BRUHN, S . NIGAM AND J . F . HOLZWARTH 131 limit for kET, unlike the alkali ions, which still showed an increase in kET at higher ionic strength up to 1 mol dm-3; no limit in kET could be observed for M+. The pronounced decrease in slope for M2+, and at even lower ionic strength Z for M3+, occurs in a concentration range where ion-pair formation with Fe(CN)%- is observed.12 In the series Mg2+ < Ca2+ < Sr2+ < Ba2+ the increase in kET is only small; almost no difference was measured between La3+ and Ce3+.Unexpected behaviour was observed if we increased the concentration of H + from to 1 rnol dm-3. After a small increase in kET around pH 4 we found a decrease in kET which levels to a con- stant value at pH 2. Experiments with a constant concentration of 1 mol dm'3 HCl and increasing amounts of K+ showed an increase in kET similar to the rate at high K+ concentrations without the addition of HCl; 0.1 mol dmW3 Rb+ was slightly more effective than 0.1 mol dm-3 K+ ; Ce3+ and Ca2+ are less effective. To explain the results in fig. 1 we have to take into account that both reactants are negatively charged.This means that the electrostatic repulsion influences the encounter rate. Only at an ionic strength above 0.5 mol dm-3 can we expect that this ET rate-decreasing effect is no longer important l1 (see also fig. 6). The most sur- prising result was measured with an increasing concentration of H+. To gain more insight into the reason for this unusual behaviour we have measured the rate of ET between Fe(CN)z- and IrCli- at a constant ionic strength of 0.93 mol dm-3 and changing electrolytic content from 0.93 mol dm-3 HCIO, to 0.93 mol dm-3 NaC10,. In this way we have shielded the electrostatic repulsion completely but the pH of solutions was gradually shifted from 0.03 to 5. The results are reported in fig.2. FIG. 2.--l)ependence of the rate constants for electron transfer between H,Fe(CN)f-4 and IrCIi- on the pH at a constant ionic strength of 0.93 mol dm-3 and temperature of 295 K. AkET/kET = f5 %. The kET value starts at 2.6 x lo5 dm3 mol-' s-' (as in fig. 1 at 1 rnol dm-3 HC1) and levels into a constant value of 2.1 x lo8 dm3 mol-' s-l above pH 3. In fig. 3 we have plotted the redox potentials of the two reactant couples IrCl;2'-3 and Fe(CN)c3jm4 under the same experimental conditions. Furthermore, we have included the con- centration of the protonated forms of H,Fe(CN)z-4 using the equilibrium constants given in the figure, which were extrapolated from measurements of Jordan and Ewing.13 As we learn from fig. 3, three different forms of H,Fe(CN)Z-, are present,132 CATALYTIC EFFECTS ON ELECTRON TRANSFER PH FIG. 3.-Relative concentrations of the three ions (a) H,Fe(CN);-, (6) HFe(CN);- and (c) Fe(CN)i-, and the redox potentials of 11Cl;-'~- and H,Fe(CN)f-4/3- in the pH range 0-5.Temperature = 295 K. but only the form IrClg- is an electron acceptor in the pH range investigated. The small increase in the redox potential of IrClg-'3- below pH 1 is due to a catalytic influence of Na+ replacing H+. With the results from fig. 3 we can now set up a mechanism for the oxidation of H,Fe(CN),"-4 by IrC1:- (see scheme 1). The three forms of the iron complex, connected by fast protonation/deprotonation equilibria, react with IrClg- to give the same products Fe(CN)g- and IrClg-. In table 1 we have calculated the reorganization energy AI2 using the formalism of Marcus: AG,*, == A2/4 + AG,",/2 + (AG1"2)2/4&2 + AG& The electrostatic interaction term AGX2 (free enthalpy) can be neglected, because the constant ionic strength of 0.93 mol dmq3 shields all long-range Coulomb interactions; SCHEME 1.-Mechanism of the oxidation of H,Fe(CN)f-4 by IrCIi-,H .BRUHN, S . NIGAM A N D J . F . HOLZWARTH 133 this was demonstrated before8*" and can be seen from fig. 6 later. AG,", was cal- culated from the measured differences between the redox potentials of the reactants given in fig. 3. AGf2 is connected with the experimental kET value by the transition- state equation k = 7cZexp(-AGF2/RT). IC was taken as 1, assuming an adiabatic outer-sphere electron transfer with an inter- action energy of 1-2 kJ between the redox orbitals.2, the highest possible ET rate constant in aqueous solution, was taken equal to 10" dm3 mo1-I s-l, and is governed TABLE DEPENDENCE OF THE OXIDATION OF H,Fe(CN):-, BY IrClg- ON pH AT 298 K AND CONSTANT IONIC STRENGTH (0.93 mol dm-3 NaClO, + HCIO,) ~~ ~~ with AGY2 = 0 (Marcus) * I \ PH k E T l AGT2I AG21 AG,*,"l A121 -log[H&,,] dm3 mol-ls-' kJ mol-1 kJ mol-' kJ mol-' kJ mol-' 0.03 0.16 0.33 0.49 0.64 1.03 1.15 1.33 1.64 2.03 2.16 2.33 2.64 3.03 3.33 4.03 5.0 2.6 x 105 4.4 x 105 8.5 x 105 1.6 x lo6 2.3 x lo6 6.2 x lo6 8.8 x lo6 1.3 x 107 2.7 x 107 4.7 x 107 6.1 x 107 8.7 x lo8 1.3 x 10' 1.6 x lo8 1.8 x lo8 1.9 x 10' 2.1 x lo8 31.5 30.3 28.6 27.0 26.2 23.8 22.9 21.9 20.4 18.8 18.2 17.3 16.3 15.8 15.5 15.4 15.1 - 20.9 -23.4 - 26.4 -28.9 -31.5 -35.1 - 36.4 - 37.4 - 40.1 -42.8 -43.4 -44.1 -45.3 - 46.3 -46.6 - 46.7 -46.8 41.3 41.1 40.8 40.3 40.1 39.4 38.9 38.4 37.8 37.1 36.7 35.9 35.3 35.1 34.9 34.8 34.6 165.2 164.4 163.1 161.0 160.4 157.5 155.8 153.5 151.3 148.5 146.6 143.8 141.1 140.5 139.6 139.2 138.2 by the concerted rotations of water dipoles in the dynamic structure of liquid water caused by short-lived hydrogen bridges between the water molecules.The recom- bination reaction of Hkq, and OH,,, with a rate of 1.2 x lo1' dm3 mol-' s-' at 298 K l4 is a good estimate for 2, although there could be some differences because of the charge neutralization. During the reorganization of the reactants in the encounter complex before the electron will actually be transferred (Franck-Condon restriction) ion-dipole and dipole-dipole interactions dominate in the surrounding solution. AG&O is the calculated free enthalpy of activation if the reduction of the measured AGT2 caused by the thermodynamic differences in the free energy between reactants and products AGf2 is taken into account.In this way we simulate conditions under which there is no thermodynamic differ- ence in the energy content of reactants and products. That the formula of Marcus given above is suitable to calculate the influence of the differences in the free energy AG,", was shown by Sutin et al.15 and Holzwarth et a1.I6 From the A12 term in table 1 we can now obtain the free energy of activation AGTF under the conditions AG& = 0. With the relation from the transition-state theory mentioned previously k& can easily be calculated.In fig. 4 the calculated rate constants for ET using AGT; as the activ-134 CATALYTIC EFFECTS ON ELECTRON TRANSFER ation energy are plotted against the pH of solution. We learn from this plot that the kgT value now varies from 5 x lo3 to 8 x lo4 dm3 mol-' s-l, which is markedly less than the change of lo3 in fig. 2. This is due to the effect of the thermodynamic differ- ence in the free energy of the reaction AGi2. These results can be explained by assum- ing that as the pH is shifted below 3 the protonation of Fe(CN)t- becomes important and at a pH of 0 the dominating species is H,Fe(CN):-. If we accept the mechanism given we conclude that ET becomes more difficult as soon as Fe(CN):- is protonated.We can calculate kiT for the three different reaction couples as k&(Fe) = 8 x lo4 dm3 1 0 ~ ~ 0 0 4 I v) I I I I 1 0 1 2 3 4 5 lo3 PH FIG. 4.-Calculated electron-transfer rate constants of the reaction H,Fe(CN):-4 + IrClz- using the activation energy in table 1, where the influence of the difference in redox potential is taken into account (AG:z = 0). For all three lines k&(H2Fe) = 3.3 x lo3 dm3 mol-' s-' and kgT(Fe) = 8 x 104 dm3 mol-'s-'; k&(Hk) varies from 2 x lo4 dm3 mol-'s-' in (a) to 8 x lo3 dm3 mol-'s-' in T = 295 K. Ionic strength = 0.93 mol dm-3. MiT = f 11 %. (6). mo1-l s-l, kgT(HFe) = 1.4 x lo4 dm3 mo1-l s-l and kiT(H2Fe) = 3.3 x lo3 dm3 mol-l s-l. The solid line in fig. 4 was calculated using these rate constants. The accuracy of the computation can be seen from the dashed lines; while calculating (a) kgT(HFe) was taken as 2 x lo4 dm3 rno1-I s-l; for (b) k&(HFe) = 8 x lo3 dm3 mol-1 s-' with both kET(H2Fe) and kgT(Fe) were kept constant.The reason for the slower ET rates of the protonated forms H,Fe(CN)Zm4 is certainly the dissociation of one or two protons connected with ET. Fe(CN)z- is not protonated in the pH range above zero. We cannot decide from these experiments whether the protons have to be completely dissociated before the electron can be transferred (consecutive reaction) or the tran- sition state is better described by a weakening of the proton-ferrocyanide interaction (concerted reaction). However, knowing the ET rates of H,Fe(CN)g- with the very fast Fe-phenanthroline complexes measured before l6 we can exclude the consecutive reaction path because these rate constants are three to four orders higher than the value of kET with IrClg-, and the differences in the redox potentials of the Fe- phenanthroline complexes are reflected in the kET values as predicted by Marcus theory; this would not be the case if the proton dissociation occurs before the electron transfer governing the rate.We therefore believe that we are justified in assuming three parallel ET pathways connected by two proton equilibria which control theH . BRUHN, S . NIGAM AND J . F . HOLZWARTH 135 concentration of the three forms of H,Fe(CN)gm4, as shown in scheme 1. The un- expected behaviour of the ET rate from Fe(CN)z' to IrC1;- in fig. 1 for increasing HCl concentrations between and 1 mol dm-3 (open symbols) can now be explained by the superposition of the increasing electrostatic shielding of the negative charges of the reactants (increasing kET) and the lowering of the difference in redox potential (decreasing kET) as well as the increasing reorganization energy A with increasing degree of protonation (decreasing kET).These three opposing effects result in a kET value which does not change between proton concentrations from to 1 mol dm-3 if no other cations are added. No attempt was made to separate the influence of IrCli' on the reorganization energy L12 from the effect of H,Fe(CN);- because the homo- nuclear electron exchange rate used by other authors of 2 x lo5 dm3 rno1-l s-l 17*18 seems rather low. If we use the Fe(CN):-/4' exchange rate given by Shporer et aZ.19 for a 1.7 mol dm-3 Na+ solution of 5.8 x lo4 dm3 mol-1 s-I we would calculate an almost diffusion-controlled electron exchange for IrCli-'3 - .Nevertheless we can draw the conclusion that the three electron exchange rate constants of H,Fe(CN)g-4/ Fe(CN)i- differ approximately by a factor of 15. The influence on IrCl:-l3- should be very small if H+ is replaced by Na+, as was shown by Holzwarth et To gain more insight into the catalytic effect of cations on the ET rate of anionic transition- metal complexes we have measured the temperature dependence of the reaction IrC1;- + Fe(CN):- on adding 0.1 mol dm-3 of the cations Li+, Na+ and K+. We found no linear relation between 283 and 323 K. This proves that a complex reaction mechanism is acting.For the initial slope we found the activation parameters given in table 2. A- decrease in the activation enthalpy AH* is accompanied by a strong TABLE 2.-MOLAR ACTIVATION PARAMETERS AT 0.1 m01 dm-3 Me+ FOR THE ET REACTION IrC1;- + Fe(CN)%- M+ AH*/kJ mo1-l AS*/J K-' mol-' A/dm3 rn01-'s-~ ~~ ~~~ Li+ ' 3 0 5 3 -3.8 6.3 x 10'' Na+ 25.5 -& 3 - 10.6 2.8 x 10l2 K+ 10.3 =k 2 -55.3 1.3 x lo1* increase in the entropy AS* from Li+ to K+ . Our results show the same trend as the data given by Lemire and Lister 2o for the reaction Fe(CN):- + W(CN):- at a con- centration of M+ of (1.05. The strong increase in entropy from Li+ to K+ shown in fig. 5 is another indication of the participation of the highly catalytic cation K+ in the transition state, as is also expected from the curvature in the Arrhenius plot.The lower value of AH* for K+ might be explained by assuming that this cation does not act in a simple Coulomb type of interaction, which should give higher AH* values, but as a catalyst for the reorientation of the outer sphere in the transition state. In fig. 6 we have included the measurements using silver(I1)tetraphenylporphyrin tetra- sulphonate (AgTPPTS4-) as the electron donor instead of Fe(CN);- in the reaction with IrCli-. We know from experiments with micelles 21 and silverporphyrin com- plexes that AgTPPTS4- transfers electrons via an axial type of reaction rather than through the negatively charged sulphonic acid groups attached to the phenyl rings. If the cations acted as a bridge for ET we should not see a catalytic effect of M+ as in the reactions of fig.1. The results included in fig. 6 show a catalytic ET rate enhancement similar to that in fig. 1. Only at ionic strengths >0.05 mol dm-3 in M+ do the differences between the cations seem to disappear. This can be explained by an aggregation of AgTPPTS at high ionic strength (shown by spectroscopic and other136 CATALYTIC EFFECTS ON ELECTRON TRANSFER evidence) which shields the axial positions of the porphyrin complex in such a way that ET is hindered.21 Besides the reaction of AgTPPTS4- with IrCli- we have also included in fig. 6 results using Os(dipy)g+ as the electron acceptor and W(CN)i- as electron donor to establish very accurate values for completely diffusion controlled ET reactions of this type.These rate constants are necessary to distinguish between the influence of the rate of encounter and the real rate of ET at different ionic strengths 10' r( lo! I fA I 0 3 - E % 'CI . - E: " 2 10' 10' T K 3 20 310 300 290 I r I 3.1 3.2 3 . 3 3 . 4 3.5 103K/T FIG. 5-Temperature dependence of the rate constant for electron transfer between IrCIg- + Fe- (CN)t- at constant ionic strength in the presence of different cations: @, 0.1 mol dm-3 KCI; w, 0.1 mol dm-3 NaCl; A, 0.1 mol dm-' LiCl; a, without additives. for experimental rate constants where both effects are superimposed. The steady state equation k;: = kF$ + kDilff allows one to separate both influences if kDiff is known. The purely electrostatic effect on the encounter rate of AgTPPTS4- (fig. 6) or Fe(CN)z- (fig.1) with IrCIi- can be calculated if we take the sum of the ionic radii as the encounter distance and use the static dielectric constant of water. Under these conditions we expect a maximum for the rate enhancement of 2 x lo2, which agrees well with the measurements in the presence of high concentrations of Li +. All other monovalent cations than H+ show a higher increase in kET than expected from purely Coulomb interactions. In table 3 we have summarized the results of the three electron-transfer reaction couples Fe(CN)i-, W(CN)i- and AgTPPTS4-, with IrCli-. Only kET values with monovalent cations at an ionic strength of 0.1 or 1 mol dm-3 are included in the table. The influence of diffusion (the transport term) was taken into account if this was necessary.In this way we achieved the real rate constants of ET which were then used to calculate the reorganization energy RI2 by applying the for- mula of Marcus together with the differences in redox potential either measured orH . BRUHN, S . NIGAM AND J . F . HOLZWARTH 137 taken from the l i t e r a t ~ r e . ~ ~ ' ~ ~ In the last column of table 3 we have included the now- corrected kET values by subtracting the influence of diffusion and the thermodynamic free energy (AGf2 = zFAE) of these reactions. These kET rate constants are the only ones which are suitable for a comparison between different reactions to show the Zimol dm-3 410'2 0.1 0.25 0.5 1 I 1 I Na' 1 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 I+/rnoI* dm-3/2 FIG. 6.-Influence of cations on the rate constant of electron transfer between silver(1r)meso-tetra- phenylprophyrin tetrasulphonate and IrClE- at different ionic strengths together with completely diffusion-controlled electron-transfer reactions of Os(bipy)3 + and W(CN):-. a, Os(bipy)$ + + W(CN):- ; ., Os(bipy)!+ + Ag"TPPTS4- ; 0, 0, A, x , IrCla- + Ag"TPPTS4- ; v, IrClb- + W(CN): - .catalytic influence of the cations. In fig. 7 these quasi-equilibrium electron-transfer rate constants for the three electron donors W(CN);f-, Fe(CN);- and AgTPPTS4- in reactions with the electron acceptor IrC12- are plotted against the crystallographic radii of several monovalent cations. The first important result from fig. 7 is that there seems to be an optimum value for the radius of monovalent cations around 0.23 & 0.02 nm to cause the maximum rate enhancement possible.All three reactions show the same relative differences between the cations, although their absolute k,, values reflect the nature of the electron donor, giving the highest rate constants for the largest anion (AgTPPTS4-) and the lowest rate constant for the smallest [Fe(CN);-]. The tetra-alkylammonium cations complete the set of data on the side of the larger radii. They could not be used with AgTPPTS4- because of a specific interaction with the porphyrin ring, but experiments with W(CN)i- and N(CH,)Z not included in138 CATALYTIC EFFECTS ON ELECTRON TRANSFER TABLE 3. --CORRECTED ELECTRON-TRANSFER RATE CONSTANTS FOR MONOVALENT CATIONS AT 298 K ionic strength/ experimental results calculated using Marcus mol dm-3 kET(AGi2 # o)/ W 2 l &z/ ~ET(WZ = 0)l A- C+ dm3 mol-'s-' kJ mol-' kJ mol-I dm3 mol-l s-I kE-r C+ IrCIi- + Fe(CN):- - I = 0.1 PH 5 I = 1 PH 5 I = 0.1 PH 5 I = 1 PH 5 1 = 0.1 P H 5 Li + Na+ K+ C1- NH: Rb+ c s + N(CH3): Br- N(C2H5)2 N(C4H9)2 3.5 x 107 4.7 x 107 2.0 x 10% 1.9 x lo8 5.6 x lo8 1.9 x 10% 3.1 x 109 5.1 x 107 1.9 x 107 - 53.4 - 53.4 - 52.5 - 52.5 - 51.6 - 50.4 -55.4 - 57.9 - 59.3 Li + 1.8 x lo8 -47.5 C1- Na+ 2.9 x 10% - 47.1 K+ 1.7 x 109 - 46.9 NHZ 2.0 x 109 - 46.9 kET C + IrClg- + W(CN)i- - H+ 2.8 x 107 - 42.9 Li + 2.8 x 107 -42.9 Na+ 4.3 x 107 - 42.9 C1- K+ 2.3 x 10% - 42.3 Rb+ 5.6 x 10% - 42.1 cs+ 3.1 x 109 -41.7 C1- Na+ 2.4 x 10% - 39.2 R b+ 5.3 x 109 - 39.0 kEr IrCIg- + AgTPPTS4- 7 Li + 7.3 x lo8 -45.3 C1- Na+ 9.8 x 10% -45.3 K+ 1.6 x 109 - 45.3 c s + 2.7 x 109 -45.3 168.8 165.5 148.0 148.6 134.8 112.7 152.9 171.3 184.4 141.5 135.5 114.9 113.1 155 155 150.1 131.1 120.8 100.5 126.0 90.3 122.6 119.2 113.5 76.9 4.0 x 103 5.6 x 103 3.2 x 104 1.2 x 105 2.0 x 104 3.1 x 103 8.2 x loz 6.0 x 104 1.1 x 105 3.1 x 10' 1.2 x lo6 8.8 x 105 1.1 x 106 1.6 x 104 1.6 x 104 2.6 x 104 1.8 x 105 5.0 x 105 3.1 x 105 1.1 x 107 3.9 x lo6 4.2 x 105 5.9 x 105 4.3 x 107 1.1 x lo6H .BRUHN, S . NIGAM AND J . F. HOLZWARTH 139 fig. 7 showed similar results as Fe(CN)i-. In fig. 7 only measurements at an ionic strength of 0.1 mol dm-3 in M + are included to avoid unwanted complications caused by aggregation of reactants (AgTPPTS4-) or precipitation of reactants [Fe(CN)t- + 1 mol dm-3 Cs+].At an ionic strength of 0.1 mol dm-3 electrostatic repulsion between the reactants is still important; therefore we have included some measurements at 1 mol dm-3 M+ in table 3. A comparison with the same reactions at 0.1 mol dm-3 of similar cations show that the rate constant can still be accelerated by a factor of 20 in i lo9 I I I I I I I I I ;, .ti Is+ I \ \ I I I \ I 1 I I I I \ \ \ I I \ \ I \ ! u Na. Li+ Rcrystlnm FIG. 7.-Calcutated eIectron-transfer rate constants for the reactions between IrCIz- and W(CN)g- ( A), Fe(CN);- (0) or AgTPFTS4- (0) using the results from table 3 (AG,", = 0). Temperature = 298 K, pH 5 and I = 0.1 mol dm-3. the case of Na+, where only a small catalytic effect could be observed. The maximum rate constant for electron transfer extrapolated from fig.7 to 109-1010 dm3 mol-' s-' is in good agreement with the maximum rate of ET possible in aqueous solutions of 10" dm3 mol-l s-' if we add the electrostatic term of 20. The equal results for H+ and Li+ in table 3 for IrClg- + W(CN)4,- prove that the proton behaves like Li+ if it is not strongly bound to the reactants, as in the case of Fe(CN)i- at low pH values. C O NCLU S I ON Our measurements of the rate of electron transfer between anionic substitution-inert transition-metal complexes such as Fe(CN)i-, W(CN);- and AgTPPTS4- with TrCIi- is convincing evidence that cations can accelerate ET. This cannot be explained by a simple increase in the encounter rate due to shielding of the electrostatic repulsion140 CATALYTIC EFFECTS ON ELECTRON TRANSFER between the negatively charged complexes.Strong ion associates, like those between H+ and Fe(CN)%- or between di- and tri-valent cations and the reactants at high con- centrations, show no catalytic activity. A simple bridging mechanism like the one found by Taube for inner-sphere ET reactions is unlikely because identical catalytic effects were observed in the ET reactions of AgTPPTS4- + IrCIi- and Fe(CN)i- + IrC1;- as well as W(CN)i- + IrCli-, although the ion-association behaviour of these complexes is different. The differences between the monovalent cations are almost independent of their concentration between loF3 and lo-' mol dm-3. The temper- ature dependence of the reactions in the presence of cations shows a strong curvature, and the entropy of activation for the catalytic active ion K+ is very high and accom- panied by a low AH* in comparison to Li+, which does not act as a catalyst.This proves that the cations are participating in the transition state but they have to be still mobile to cause the catalytic rate enhancement. We believe that the catalytic influence of cations can be described by three effects acting in concert. (1) They influence the water dipoles in the surrounding solution of the activated complex in such a way that their orientation is faster; (2) they allow for a better adjustment of the ligand central metal bonds before electron transfer; (3) they promote the interaction of the redox orbitals which are involved in the reaction, so that the transfer of charge is facilitated. R. A.Marcus, Annu. Rev. Phys. Chem., 1964,15, 155. Phys. Chem. Sect. (Engl. Transl.), 1959, 124, 9. N. Sutin, Acc. 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