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Kinetics of reduction of hexakis(acetamide)- and hexakis(dimethylacetamide)-iron(III) by tris(3,4,5,6,7,8-hexamethyl-1,10-phenanthroline)iron(II) in acetonitrile |
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Dalton Transactions,
Volume 1,
Issue 15,
1995,
Page 2473-2478
Eva Vallazza,
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摘要:
z z z z Kinetics of Reduction of Hexakis(acetamide)- and Hexakis(dimethy1acetamide)-iron( 111) by Tris(3,4,5,6,7,8- hexamethyl-I ,I 0-phenanthroline)iron(ii) in Acetonitrile t Eva Vallazza and Roland Schmid" Institute of Inorganic Chemistry, Technical University of Vienna, A - I060 Vienna, Getreidemarkt 9, Austria The kinetics of outer-sphere electron transfer between [ Fe( hmphen),]*+ (hmphen = 3,4,5,6,7,8- hexamethyl-1.1 0-phenanthroline) and substitutionally labile Fe3+ introduced as [FeL,I3+ [L = dma (dimethylacetamide) or aa (acetamide)] in acetonitrile has been studied at 25 "C with the salts added as the perchlorates. Both reactions can be described by one mechanism implying that the acidic hydrogens of aa d o not appreciably complicate the issue. To accommodate the variations in the redox rate constants, three rapid solvation pre-equilibria [FeLJ3+ [FeL3I3+ + 3 L (co-ordinated MeCN is omitted) have to be invoked where, for driving-force reasons, only [FeL,I3+ and [FeLJ3+ are redox- active. Further, the acceleration with salt is well described by ion pairing and ion tripling of the trivalent ions with perchlorate, treated in terms of the reduction in Coulombic repulsion in forming the precursor complexes.For the solvate speciation, the overall reaction rates are controlled by both the reactivities of the reacting species and their availabilities. In the context of previous work, the differences between the two reactions are as follows: the redox rate constants of the aa species are larger than those of the corresponding dma species, which is primarily a driving-force effect with dma being the stronger Lewis base; on the other hand, the availabilities of the reacting species are higher in the case of dma, contrary to expectation.On the balance of the experimental evidence available, it does appear that the stabilities of the [FeL,J3+ solvate species are not a function of the donor strength of L but rather of its size tentatively expressed by the effective molecular hard-sphere diameter. This is another of our 'particularly heroic attempts'' to analyse the kinetics of non-aqueous, outer-sphere electron transfer between transition-metal complexes in which one reactant is substitution labile, exchanging ligands with solvent mole- cules.2 ' In these studies 3--6 we have been using trivalent Fe3 + (and Mn3+ as well) as the oxidants, complexed by strong oxygen donors L such as dimethylformamide (dmf).The reducing agents, and simultaneously the indicators of the progress of reaction, were ferroins [equation (l)], where X is a [FeLh13+ + [Fe(X~hen)~]~+ =products (1) methyl group introduced so as to shift the potential for quantitative conversion. All salts were added as the perchlorates. The reactions were all run in one solvent viz. acetonitrile (MeCN), in order to minimise non-co-ordinating (outer-sphere) solvent effects and to focus on co-ordinating (inner-sphere) solvent effects. At the outset, we, naively, did not expect appreciable competition from MeCN with L for co-ordination to a triply charged cation, in the framework of hard-soft considerations.One of our goals in measuring electron-transfer rates of simple solvate complexes has been to investigate to what extent they follow the order of empirical solvent-basicity parameters such as the donor number, and eventually to undertake comparisons with theoretical predictions through structural parameters. However, the kinetics of reactions (1) was found to be especially complex because of the occurrence of typically three solvation (fortunately fast) pre-equilibria (2 j ( 4 ) (in the following, co- ordinated MeCN is omitted). Consequently, these systems seem to be a poor choice for the determination of definite outer- ? Non-SI units employed: A = 100 pm, dyn = I 0-5 N. [FeL6I3+ &[FeL,13+ + L [FeL,J3+ P"[FeLJ3+ + 2L (3) sphere electron-transfer rate constants.Thus, we changed the emphasis of our experiments to more qualitative aspects highlighting the problems of studies in non-aqueous solvents. Nevertheless, the variations of the experimental rate constant with concentration actually are very sensitive probes of both the solvate and the ionic speciations because each speciation leads to large changes in reactivity. The individual solvate species react at highly different rates due to the different natures of MeCN, which is a x-acid stabilising the divalent state, and hard L which stabilises the trivalent state. Thus, rates are strongly decreased upon small additions of extra L. For the ionic speciation, the + 3/ + 2 charge type of redox reactions causes a strong Coulombic repulsion to be overcome in forming the precursor complex.The work against repulsion is reduced by ion association with the counter ions, affecting a strong acceleration of the rate when extra salt is added. Our method of analysing the kinetic data is to study several dependencies of the pseudo-first-order rate constant on the concentrations of oxidant, extra added salt and extra added L and fit them simultaneously by a unique rate constant equation featuring solvation equilibrium constants, ion-pairing constants and rate constants as parameters. This procedure in connection with the above-mentioned sensitivity of the fits to the individual parameters would appear to afford an adequate analysis despite2474 J. CHEM. SOC. DALTON TRANS. 1995 the large amount of parametrisation. In fact, the values of p obtained from the kinetic fits alone yield mean co-ordination numbers nicely consistent with those derived from 'H NMR spectroscopy revealing ligated and free L in CD,CN.,., Furthermore, the ion-pairing constants were satisfactorily complemented numerically by conductance measurements.ti In the present paper we compare the reduction kinetics of Fe3 + complexed by dimethylacetamide (dma) and acetamide (aa) again in MeCN as the solvent. The purpose is twofold. (i) The role of acidic hydrogens in non-aqueous outer- sphere electron transfer is elucidated further. In the case of the reduction kinetics of [Mn(OC(NH2)2f,]3 + and [M~~(dmso),]~ + (dmso = dimethyl sulfoxide) it was found that perchlorate association is similar for both despite the presence of acidic hydrogens in urea.The question arises whether this result is of more general validity. (ii) The work adds to the data on the corresponding systems [Fe(dmf),13' and [Fe(tmp),] + (tmp = trimethyl phosphate) reported previously. 3*4 Of the various parameters involved, the possibility of gathering values of for various L is an intriguing one. This addresses a long-standing question as to the relevance of the donor number of L to the stability of unmixed [ML,]" + complexes when both leaving and non-leaving ligands are the same. In the simple picture of the donor-acceptor model it was argued that, since five co-ordinated solvent molecules contribute to the overall acceptor strength of the remaining [ML,]"+ moiety, but only one ligand leaves for exchange, the latter might more readily dissociate the higher is the donor number of L.7 This proposal has been offered to explain the order of solvent-exchange rates for a few unmixed complexes of Ni2+ and Co2+.* Apart from this, experimental evidence is still missing owing to the lack of appropriate reaction systems.Experimental Hexakis(dimethylacetamide)iron(IrI) perchlorate was prepared by dissolving iron(r1i) perchlorate hydrate (5 g) (Aldrich) in purified dimethylacetamide (30 cm3), with the temperature kept below 30°C. Anhydrous diethyl ether was added until the solution turned cloudy and a heavier layer was observed. Upon keeping the solution at - 20 "C overnight a microcrystalline precipitate formed. It was collected on a glass frit and washed with cold anhydrous diethyl ether.The yellow crystals were dried in vacuo at ambient temperature ( ~ 9 0 % yield). This procedure was repeated twice. The product seems to be slightly hygroscopic in the solid state (Found: C, 32.95; H, 6.30; C1, 12.00; N, 9.40. Calc. for C,4H,,C~3FeN,01,: C, 32.85; H, 6.20; CI, 12.25; N, 9.60%). Hexakis(acetamide)iron(m) perchlorate was synthesised by adding an excess of acetamide (ten-fold excess) (Merck, reagent grade) to a solution of iron(iI1) perchlorate hydrate (5 g) (Aldrich) and acetic acid anhydride (1 : 6 v/v) in MeCN. The green product was precipitated with diethyl ether, filtered off and dried in uacuo (yield 92%). It was recrystallised twice from MeCN (Found: C, 20.55; H, 4.30; Cl, 15.10; N, 12.00. Calc. for C12H3,C13FeN,018: C, 20.35; H, 4.25; C1, 15.00; N, 11.85%).The complex [Fe(hmphen),][ClO,], (hmphen = 3,4,5,6,7,8-hexamethyl- 1,IO-phenanthroline) was prepared as described. The solvents acetonitrile and dimethylacetamide were purified and dried by standard methods.' Tetrabutylammonium perchlorate was synthesised from tetrabutylammonium hydroxide (Riedel de Haen) and perchloric acid (Loba, p.a.) and recrystallised from 50% (vjv) anhydrous ethanolaiethyl ether.' CAUTION: Owing to the hazardous nature of metal perchlorates containing organic ligands, the drying temperature was kept below 50°C. Only small amounts were synthesised at a time and handled with extreme care. The kinetic measurements were done on a Durrum D-110 stopped-flow spectrophotometer at 25 k 0.1 "C (equipped with a MGW Lauda TUK 30 thermostat and a MGW Lauda R42/2D thermosensor) using a 2 mm cell by following the consumption of [Fe(hmphen),]'+ (Amax = 513 nm, E = 16 000 dm3 mol-' crr-').Pseudo-first-order conditions were maintained by taking a 10-100 fold excess of [Fe(dma),I3+ or [Fe(aa),I3+ over the reductant concentration ( ~ 5 x mol dmP3). Absorbance data were processed as b e f ~ r e . ~ Proton NMR measurements were carried out on a Bruker AC 250 instrument operating at 250.13 MHz. Temperature was controlled within k 1 "C by using a Eurothenn AC TBL temperature controller. Temperature readings were calibrated against the temperature dependence of the proton chemical shift of ethylene glycol. l o Deuteriated acetonitrile (CD,CN, 99.95%; Aldrich) was used as the solvent, which was dried over 3 A molecular sieves and purged with N, in order to remove oxygen. The cyclic voltammetric experiments were done as before., Conductance measurements were done with a WTW- LF535 microprocessor conductivity meter fitted with a WTW- LTA 1 electrode.Results Speciation ofFe3 +.-As in previous ~ o r k , ~ , ~ . ~ attempts have been made to assess the speciation by means of 'H NMR spectroscopy. For [Fe(dma),][ClO,], dissolved in CD,CN ( M 17 mmol dm 3 ) , resonances of co-ordinated dma (6 70-30 and lOto -5)andbulkdma(63.17,3.11 and 1.94),relativetothe residual protons of the solvent (6 1.93 us. SiMe,), were resolved at room temperature. Unfortunately the substantial peak overlap defies a definite analysis. Qualitatively, however, from a comparison with spectra recorded for the [Fe(dmf)J3' analogue where peak separation was feasible, it can be implied that the loss of dma and dmf from the respective compounds is similar but probably greater in the case of dma.For [Fe(aa),][ClO,],, on the other hand, no free aa could be detected in the CD,CN solution obviously because of a superimposition of the bulk methyl protons by the solvent signal. Actually acetamide dissolved in CD3CN exhibits a sharp singlet at 6 1.84, very close to that of the residual protons of the solvent. Beyond that, the signals of the amide protons are not suitable for studying the speciation because of broadening due to quadrupole relaxation of the adjacent 14N. Kinetics. -Since both the oxidants considered behave quite similarly, they are described together, termed as Fe"'.Throughout the iron(Ii1) oxidant was taken in at least ten-fold excess, giving pseudo-first-order rate constants, kobs. In addition, quantitative conversions were ascertained from the absorbance changes. Values of kobs were measured under a variety of conditions. They were found to increase non-linearly with [Fe"'] when no electrolyte was added and to pass through a maximum when the variation in perchlorate concentration was compensated for by the addition of NBu,C104 (Fig. 1). The variation in rate constant with NBu,CIO, at fixed [Fe"'] is shown in Fig. 2 . Finally, the rate constants decrease notably when extra L was added (Fig. 3), independently of whether L was admixed to the Fe"' or the [Fe(hmphen),12+ reactant solutions before the react ion.Electrochemical Dam-Redox potentials are available for the unmixed complexes only (Table 1). Thus, a strong shift of E" is expected upon the addition of L to a MeCN solution of [Fe(MeCN),I3+. This is in fact found but a detailed study is not worthwile because of the occurrence of an electrochemical- chemical4ectrochemicalLchemical mechanism' ' with too many unknowns (different solvation equilibria at both Fe2 + and Fe3+). Conductance Data.-The molar conductivities (S cm2 mol-') measured in MeCN at 25 "C for concentrations (mmol dmP3) in parentheses are as follows: [Fe(dma),][CIO,],, 402 (0.998),J. CHEM. SOC. DALTON TRANS. 1995 6 - 4 - 2475 - 6 4 2 I I I J o o o * O * 0 4 20 I 1 I I I 0 5 10 15 20 25 [Fell']T/mmol dm3 Fig. 1 Observed rate constant as a function of iron(rrr) concentration under different conditions.Curves: (a) without adding NBu,CIO,; (b) at constant total perchlorate concentration. L = dma (upper), [Fe(hrnphen),'+]T = 0.20 mmol dm-3; aa (lower), [Fe(hmphen),'+], = 0.02 mmol dm '. Points are experimental, solid lines are calculated with equation (1 0) and parameters given in Table 2 Table 1 Redox potentials" in acetonitrile at 25 "C Complex E+ b/V Ref. [Fe(aa)J3' 2 c 1.22,' This work [Fe(drna),], + ' ' 1 .30Td This work [Fe(hmphen),] ' + I 2 + 1.52, 2 [Fe(MeCN),] + j' + 2.56, 1 " The potentials are referenced to [Cr(C,H,Ph),]'/+ ( - 1.11 8 us. ferrocene-ferrocenium). Potentials represent the mean of the cathodic and the anodic peak potentials from cyclic voltammograms (scan rate 0.1 V s I , electrolyte 0.1 mol dm-, NBu,CIO,, reactant concen- tration = I mmol dm ,).Measured in MeCN saturated with aa. Measured in dma. 'V I 5 9 - 30 - 20 - I I I I 1 0 50 100 150 200 250 [CI041T/mmol dm-3 Fig. 2 Observed rate constants as a function of NBu,CIO, salt concentration. Upper: [Fe(dma),3+], = 2.0 mmol dm-j, [Fe(hmphen),Z+]T = 0.20 mmol dm '. Lower: [Fe(aa),3+], = 2.0 mmol dm-3, [Fe(hmphen),'+], = 0.02 mmol drn-,. Other details as in Fig. 1 pairs Fe(C10,)2 +-Fe3 + and Fe(CIO,), +-Fe(C104)2 + was set at 0.8 : 1 from past experience. Owing to the high experimental concentrations chosen, values of both Klo and A,(; FeL63f), where h, is the equivalent ionic conductivity, depend dramatically on r . Taking r = 9 A, the Fuoss ratio, K10/K2', is equal to 5.27 and the results were, for [Fe(dma),][ClO,],, K,' = 740 dm3 mol-', h,[iFe- (dma)63+] = 83.9 S cm2 mol-' and, for [Fe(aa),][CIO,],, Klo = 1410 dm3 mol-', ho[$Fe(aa)63'] = 79.0 S cm2 mol '.With r set at 10 A (the Fuoss link is 4.46), the results were, for [Fe(drna),][C10,],, K,' = 630 dm3 mol ', h,[:Fe- (dma),3+] = 78.9 S cm2 mol-' and, for [Fe(aa),][CIO,],, Klo = 1090 dm3 mol-', ho[iFe(aa)63+] = 69.9 S cm2 mol-'. 367 (2.002), 345 (3.000), 331 (3.998), 319 (5.002), 309 (5.999), 302 (6.997). 294 (8.001), 287 (8.999) and 282 (9.997); [Fe(aa),][ClO,],, 281 (3.999), 267 (5.002), 258 (6.000), 249 (7.002), 240 (7.998), 234 (9,001) and 229 (9.998). These results were analysed by the exact Lee-Wheaton equation l 2 because no fit was obtained unless both higher terms were included.Various parameters were fixed before fitting: (i) the second- stage association constant K20 was linked to the fitted value of K,' by the Fuoss ratio [equation ( 5 ) : D, is the static dielectric constant and r the approach distance in A]; (ii) the molar Kl0/K,* = exp (56O.75/Dsv) ( 5 ) conductance of perchlorate was taken as 103.8 S cm2 mo1-';13 (iii) the ratio of the conductance of the ion to that of the ion Discussion In accordance with previous report^,^-^ the decrease in rate when extra L is added, shown in Fig. 3, is indicative of solvation equilibria between L and MeCN co-ordinated at Fe3+, with ions of higher L content being less reactive. The large effect of small additions of L would further suggest that not much ligand is lost from either complex.Moreover, since the effect of L is independent of the mode of addition (i.e., either to the reductant or the oxidant solutions), these equilibria are rapid compared to the redox processes. The various solvate species available should have highly different reactivities. On the basis of Table 1, the reduction potential difference could well be about 0.2 V for the replacement of one L by MeCN. In addition to the solvate speciation, also the ion speciation leads to large changes in reactivity. The problem of deconvoluting simultaneously these two kinds of speciation, is2476 J. CHEM. SOC. DALTON TRANS. 1995 2.5 r -i 0- I 40 80 1 20 s o 121- 4 -L , o , 0 I 0 1 0 20 40 60 80 [Lldmmol dm4 Fig. 3 Observed rate constants as a function of the concentration of extra added ligand.Upper: [Fe(dma),3+]T = 10.0 mmol dm-3, [Fe(hmphen)3Z+]T = 0.20 mmol dm-3. Lower: [Fe(aa)63+]r = 10.0 mmol dm-3, [Fe(hmphen),'+], = 0.025 mmol dm-3. Other details as in Fig. 1 tackled by the reaction model successfully applied before with all the assumptions made outlined as follows: (i) The two kinds of speciation do not affect each other, that is ion association is qualitatively and quantitatively the same for all solvate species and vice uema (in the following, X- = ClO,-), equations (6) and (7). [FeL,] + + X - [FeL,X] + (6) [FeL,XI2+ + X- &[FeL,X,]+ (7) (ii) The reaction rate of each solvate species is considered to vary with both ionic strength and counter-ion concentration. Ionic strength effects are treated by Coulombic work terms with extrapolation to infinite ionic strength.Ion-pairing equilibrium constants are approximated as real constants within the experimental ionic strength range. Ion pairing lowers the electrostatic work needed to bring the reactants together by reducing the charge type of the reaction. Relative to this effect, ion pairing does not alter the electron-transfer reactivity. The ion-pairing constants calculated from the kinetic analyses should be connected with those derived from the conductance measurements via equation (8) valid for MeCN (D, = 37.5, T = 298 K, z1 and z2 are the charges of the reactants, and Y is the distance parameter in A).14 A justification of all these approximations has been given before. 5 + 6 In addition to equations (6) and (7), slight ion pairing was also allowed for the ferroin reactant, equation (9), with K3 fixed [Fe(hmphen),12+ + X- [Fe(hmphen),X]+ (9) at 3 dm3 mol-' as before.3*4 Along these lines six ionic paths are considered for each solvate species, represented in turn by the six terms in the numerator of equation (lob) where the charge type enters uia the exponential terms [e.g. the term e6A stands for the free-ion path, etc. A is defined as in equation ( ~OC)]. In this framework, the reactivity of each solvate species is characterised by a single electrostatics-free rate constant, independent of the number of anions attached. For our two reactions the kinetics appear to be very similar as judged from the experimental rate constant plots in Figs. 1-3. One difference nevertheless is in the dependence of kobs on [Fe'"], of Fig.1, measured at constant total perchlorate concentration. Whereas kobs passes through a maximum in the case of dma, saturation behaviour is displayed in the case of aa. In terms of the various assumptions outlined above, the shape of these plots results from two combined effects: (i) the variation in the active species concentration with [Fe"'],, as determined by the solvation equilibrium constants, and (ii) the decrease in free [C104-] due to ion association, as determined by the association constants. Since either ligand, dma and aa, is similar to dmf in both structure and donor strength, both reactions were analysed in terms of Scheme 1, by analogy to the Fe"'4mf system., (Here and in the following, the subscripts to the rate constants denote the number of L ligands bound.) That [FeL4I3+ is the first species in the series to react in either case is reasonable in the context of the reduction potentials given in Table 1.If the potential is tentatively assumed to be a linear function of st~ichiometry,'~,'~ [FeL4I3+ is indeed the first species in the series that has a potential more positive than that of the ferroin oxidant. The expression for the pseudo-first-order rate constant with all assumptions described above included is given by equation (10a). The approach distance Y was taken uniformly as 14 8( as e6A + Kl[X-]e4A + K3[X-]e3A + K,K2[X-]2e2A (1 + K3[X-])(1 + KJX-1 + K1K2[X-I2) + Q = (lob) K , K3[X -I2e2* + K , K2K3[X-] 3eA (1 + K3[X-])(I + K,[X-] + K1K2[X-J2) 15 1 + 0 . 4 8 r l r Y - _ 7.12I* A = b e f ~ r e , ~ .~ in the absence of structural data for the solvate complexes. It may be noted that the results of the calculations [FeL,I3+ [FeLSl3' e [FeL4l3+ \ + [FeLjI3+ / ".\ P + [Fe( hmphen) 3] ' ' 1 Fe" + [Fe(hmphen) j]3 ' Scheme 1 L = dma or aaJ. CHEM. SOC. DALTON TRANS. 1995 - - - - - 2477 6.0 5.6 b 5.2 Table 2 Summary of association constants, solvation equilibrium constants and electrostatics-free rate constants for the oxidation of [Fe(hmphen),12+ in acetonitrile at 25 "C 28 26 24 [Fe(dma)6I3 +I2 + K,/dm'mol ' 100 2 20 P2/mo12 dm ti K2/dm3 mot-' 36.8 f 6.3 Pl/mol dm-3 (1.72 f 0.2) x p3/mo13 dm (9.68 f 1.6) x lo-* k,/dm3 mol ' s-' (6.18 f 1.3) x lo3 k,/dm3 mol s (1.70 f 0.5) x lo4 (2.11 f 0.5) x 10-5 r [Fe(aa),13 + I 2 + 180 ? 30 11.6 ? 2 (6.56 2 0.6) x (1.37 f 0.4) x (1.41 f 1.3) x lo-'' (5.70 f 1.6) x lo4 (8.37 k 3.2) x lo5 were not sensitive to moderate changes in the distance parameter.In fitting the kinetic data by use of equation (lo), both the free proligand and the free perchlorate concentrations were supplied from the roots of the respective material-balance equations through Newton's method as before. The results of the fits are shown by the solid lines in Figs. 1-3, with the best-fit parameters listed in Table 2. Overall, the fits are quite acceptable apart perhaps from the rather poor reproduction of the saturation behaviour displayed by the aa system [lower plot (6) of Fig. 11. As can be calculated from the p values of Table 2, for either ligand, both active species increase in concentration as [Fe"'], increases (in contrast to the dmf case for which [Fe(dmf),,+] actually is found to decrease (see Fig.5 in ref. 3)). Thus the shapes of curves (b) in Fig. 1 are largely governed by the extent of ion association reducing [ClO, -Ifree as [Fen'], increases under the condition of constant [CIO4-IT. Therefore, to obtain rate saturation instead of a maximum, the computer analysis based on equation (10) reduces K , for aa relative to that ofdma, in contrast to expectation. What might be expected, however, is that K , be higher for aa similar to the K , values (Table 2), in accordance with theconductance data. For the latter, on the other hand, the Fuoss link [equation (5)] employed in treating them is likewise highly suspect. There is increasing evidence from various lines of inquiry, conducto- that the driving force in the ion-association process does not derive from the energy of the interaction between the cation and the anion, but instead from solvent-solute restructuring.Thus the occasional agreement between experimental association constants and those calculated from the Fuoss equation would seem to be rather fortuitous due to a compensation of various effects. Anyway, the above comparisons may be taken to signal some additional complicating features inherent in the aa system, perhaps connected with the acidic hydrogens of aa, not accounted for by the reaction model employed here. Therefore, the physical significance of the numerical value of K , for the aa system cannot be taken too seriously.On the other hand, the differences in behaviour between the aa and dma systems, overall, are not so large so as to warrant a further analysis particularly since no simple modification of equation (10) is obvious. A prior comparison between the reduction kinetics of [Mn(dmso),13 + and [Mn{OC(NH2),}6]3+ did not reveal any particular effect of the acidic hydrogens of urea. Let us now discuss the other parameters listed in Table 2. It should be emphasised that, because of the amount of parametrisation, the parameters themselves must have inherently rather large error limits. Particularly the error associated with the [FeL3I3+ path (p,, k,) is large. The mean co-ordination number of dma calculated from the p values for 8 mmol dm of the dma salt is 5.05. For the aa salt of the same concentration the values point to a significantly higher value of 5.62.In view of such high co-ordination numbers, clearly the fits of the kinetic data cannot be sensitive to p3. An unexpected result is that the values of p are larger for [Fe(aa),13+ than for [k(dma),I3 ' despite the lower donor number of aa (26.0, see Appendix) compared to dma (27.8). In Fig. 4 are plotted values spectroscopic l 9 and 221 I 1 1 1 14.8 log P1 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 Fig. 4 Plot of log p1 us. donor number and o of the ligands of [FeL,], + 5.51 mp \ - x = 3 \ a a \ \ \ \ 1 Y \ o------o 3.5 1 I I I I I I 22 24 26 28 Donor number Fig. 5 Plot of log k , and log k , us. donor number of PI (these are the most reliable ones, but similar plots are obtained using P2 or p3) versus the donor number including those for the complexes [Fe(dmf)6]3 + and [Fe(tmp),13 + dealt with As is seen, there is definitely no relationship.Instead, there is a trend between and the ligand size tentatively expressed in terms of the effective hard-sphere diameter o (see Although the ligand size is certainly not the only parameter determining the stability of complexes, this trend can be related to the size-dependent lability of the first co-ordination sphere to ligand substitution. Since local structural rearrangement is involved, such processes might better be described in terms of molecular packing effects rather than bond-strength parameters. Recently, there has been increasing appreciation of the fundamental importance of packing effects in liquid-state phenomena.,' 30 In a forth- coming study we will try to add to the number of data points in Fig.4 by searching specifically for the effect of size by replacing the methyl groups in [Fe(dmf),13 + by higher homologues up to butyl. For the (electrostatics-free) rate constants k , and k,, finally, the complexes containing aa are more reactive towards reduction compared to the dma analogues. This may largely be a driving-force effect, aa being the weaker base thus stabilising the trivalent state to a lesser extent. However, the relationship between the rate constants and the ligand donor number is very poor as seen in Fig. 5. An additional remark is in order here. In previous iron(Ir1) the experimental rate constants could not be fitted satisfactorily by equation (10) or a similar one unless the assumption was introduced that the various solvate species react oia different ion-paired paths.This was rationalised in terms of the competition of the driving force changing with the inner-sphere composition and of the Coulombic work changing with ion pairing. In fact, the change in driving force for the2478 J. CHEM. SOC. DALTON TRANS. 1995 replacement of one L by MeCN could well be comparable in magnitude to the reduction in Coulombic work in changing the charge type from +2/+3 to +2/+, that is, when [FeLJ3+ reacts as such or as the triplet. Therefore, the overall reactivity of e.g. [FeL3I3+ might be comparable to that of [FeL,X,]+. In the present iron(m) reactions, however, no improvement of the fits was attained upon this procedure.Appendix Determination of the Donor Number of aa.-This was done by a solvatochromic method reported recently." Thus, the broad absorption peak at h z 602 nm ( C z 16 61 1 cm-') displayed by [Cu(tmen)(acac)]CIO, (tmen = N,N,N',N- tetramethylethane-l,2-diamine, acac = acetylacetonate) dis- solved in nitromethane, saturated with aa, gives donor number = 26.0 from the empirical equation, D, = 195.5 - 0.0102 +, shown in the appendix of ref. 3 1. Determination of the Hard-sphere Diameters o.--(a) Of aa. This is done on the basis of the crystal structure of orthorhombic acetamide having dimensions a = 7.76, b = 19.00, c = 9.51 A and 2 = Hence the number density is p = (abc/z)-' = 1.14 x 10' A '. From this, o can be calculated from the equation q = 7cpo3/6 if the packing fraction q is known.Assumin closest packing, that is taking the maximum value of q = n$/6 = 0.74, we obtain CT = 4.99 A. Owing to the assumption of closest packing, this value should represent an upper estimate. (h) Of tmp. For liquids, the hard-sphere diameter can be calculated by means of equation (29) of ref. 26, using experimental values of the isothermal compressibility PT, the molar liquid volume, the gas-phase dipole moment, and the vapour pressure. However, QT for trimethyl phosphate has not been measured. Thus we calculated PT from the surface tension (36.92 dyn cm-') and the mass density (d25 = 1.2144 g cm ') according to ref. 33, giving QT = 6.88 x lo-'' Pa-'. From this we get o = 5.90 A. To check this, we used another empirical method, described in ref.24, based on the molar refraction, requiring the refractive index n = 1.3939 and the number density p = 5.204 x 10 k3. From these values the volume V, can be evaluated from [(n2 - l)/(n2 + 2)]/p as 45.956 A3, and from the empirical correlation Vhs = 2.473 ( V , - 5.53) the hard-sphere volume vhs = 99.974 A3. Finally, vh, = (7r/6)03 giving o = 5.77 A. Thus we adopt for tmp, in Fig. 4, a value of CT = 5.83 A as the mean. Acknowledgements This work was supported by thf: Fonds zur Forderung der wissenschaftlichen Forschung in Osterreich (Project No. 8 126). Also, thanks go to Professor A. D. Pethybridge (Reading, UK) for calculating the ion-association constants from conductance data, to Dr. K. Kirchner for doing the NMR spectroscopic measurements, and to Dr.L. Han for some of the kinetic measurements. References 1 S. Wherland, Coord. Chem. Rev., 1993,123, 169. 2 R. Schmid, K. Kirchner and F. L. Dickert, Znorg. Chem., 1988,27, 3 R. Schmid, K. Kirchner and V. N. Sapunov, Znorg. Chem., 1989,224, 4 R. Schmid, L. Han, K. Kirchner and V. N. Sapunov, Monatsh. 5 R. Jedlicka, K. Kirchner and R. Schmid, J. Chem. Soc., Dalton 6 S. Dasgupta, E. Vallazza and R. Schmid, J Chem. Soc., Dalton 7 V. Gutmann, The Donor-Acceptor Approach to Molecular 8 W. J. MacKellar and D. B. Rorabacher, J. Am. Chem. Soc., 1971,93, 9 D. D. Perrin and L. W. F. Armarego, Purijicution of Laboratory 10 D. S . Raiford, C. L. Fisk and E. D. Becker, Anal. Chem., 1979,51, 1 1 K. Kirchner, R. Jedlicka and R. Schmid, Monatsh. Chem., 1992,123, 12 A.D. Pethybridge, Z. Phys. Chem. (Munich), 1982,133, 143. 13 R. L. Kay, B. J. Hales and G. P. Cunningham, J. Phys. Chem., 1967, 14 R. Schmid, Rev. Znorg. Chem., 1991, 11,255. 15 D. P. Poe, Znorg. Chem., 1988,27, 1280. 16 C. M. Duff and G. A. Heath, Znorg. Chem., 1991,30,2528. 17 F. Lukacs and K. Burger, J. Chem. Soc., Furaday Trans., 1992,88, 18 L. Reichstadter, E. Fischerova and 0. Fischer, J. Solution Chem., 19 D. D. Chingakule, P. Gans, J. B. Gill and P. Longdon, Monatsh. 20 K. Kirchner, H. W. Dodgen, S. Wherland and J. P. Hunt, Znorg. 21 D. C. Gaswick and S. M. Malinak, Inorg. Chem., 1993,32, 175. 22 T. G. Braga and A. C. Wahl, J. Phys. Chem., 1985,89, 5822. 23 R. M. Nielson and S. Wherland, Inorg. Chem., I984,23, 1338. 24 D. Ben-Amotz and D. R. Herschbach, J.Phys. Chem., 1990, 94, 25 D. Ben-Amotz and K. G. Willis, J. Phys. Chem., 1993,97,7736. 26 R. Schmid and D. V. Matyushov, J. Phys. Chem., 1995,99,2393. 27 Y. Yoshimura, Y. Kimura and M. Nakahara, Ber. Bunsenges. Phys. 28 Y. Yoshimura and M. Nakahara, Ber. Bunsenges. Phys. Chem., 1986, 29 Y. Yoshimura and M. Nakahara, J. Chem. Phys., 1984,81,4080. 30 R. Ravi, L. E. S. de Souza and D. Ben-Amotz, J. Phys. Chem., 1993, 31 R. W. Soukup and R. Schmid, J. Chem. Educ., 1987,64,904. 32 W. C. Hamilton, Acta Crystallogr., 1965, 18, 866. 33 I. C. Sanchez, J. Chem. Ph.ys., 1983,19, 405. 1530. 4167. Chem., 1993,124,493. Trans., 1993,417. Trans., 1993, 2387. Interactions, Plenum, New York, 1978. 4379. Chemicals, 3rd edn., Pergamon, Oxford, 1988. 2050. 203. 71, 3925. 3345.1993, 22, 809. Chem., 1992,123,52 1. Chem., 1990, 29, 238 1. 1038. Chem., 1988,92, 1095. 90, 58. 97, 11842. Received 23rd March 1995; Paper 5/0188OCz z z zKinetics of Reduction of Hexakis(acetamide)- andHexakis(dimethy1acetamide)-iron( 111) by Tris(3,4,5,6,7,8-hexamethyl-I ,I 0-phenanthroline)iron(ii) in Acetonitrile tEva Vallazza and Roland Schmid"Institute of Inorganic Chemistry, Technical University of Vienna, A - I060 Vienna, Getreidemarkt 9, AustriaThe kinetics of outer-sphere electron transfer between [ Fe( hmphen),]*+ (hmphen = 3,4,5,6,7,8-hexamethyl-1.1 0-phenanthroline) and substitutionally labile Fe3+ introduced as [FeL,I3+ [L = dma(dimethylacetamide) or aa (acetamide)] in acetonitrile has been studied at 25 "C with the salts addedas the perchlorates.Both reactions can be described by one mechanism implying that the acidichydrogens of aa d o not appreciably complicate the issue. To accommodate the variations in the redoxrate constants, three rapid solvation pre-equilibria [FeLJ3+ [FeL3I3+ + 3 L (co-ordinated MeCN isomitted) have to be invoked where, for driving-force reasons, only [FeL,I3+ and [FeLJ3+ are redox-active. Further, the acceleration with salt is well described by ion pairing and ion tripling of thetrivalent ions with perchlorate, treated in terms of the reduction in Coulombic repulsion in forming theprecursor complexes. For the solvate speciation, the overall reaction rates are controlled by both thereactivities of the reacting species and their availabilities.In the context of previous work, thedifferences between the two reactions are as follows: the redox rate constants of the aa species arelarger than those of the corresponding dma species, which is primarily a driving-force effect with dmabeing the stronger Lewis base; on the other hand, the availabilities of the reacting species are higherin the case of dma, contrary to expectation. On the balance of the experimental evidence available, itdoes appear that the stabilities of the [FeL,J3+ solvate species are not a function of the donorstrength of L but rather of its size tentatively expressed by the effective molecular hard-spherediameter.This is another of our 'particularly heroic attempts'' to analysethe kinetics of non-aqueous, outer-sphere electron transferbetween transition-metal complexes in which one reactant issubstitution labile, exchanging ligands with solvent mole-cules.2 ' In these studies 3--6 we have been using trivalent Fe3 +(and Mn3+ as well) as the oxidants, complexed by strongoxygen donors L such as dimethylformamide (dmf).Thereducing agents, and simultaneously the indicators of theprogress of reaction, were ferroins [equation (l)], where X is a[FeLh13+ + [Fe(X~hen)~]~+ =products (1)methyl group introduced so as to shift the potential forquantitative conversion. All salts were added as theperchlorates. The reactions were all run in one solvent viz.acetonitrile (MeCN), in order to minimise non-co-ordinating(outer-sphere) solvent effects and to focus on co-ordinating(inner-sphere) solvent effects.At the outset, we, naively, did not expect appreciablecompetition from MeCN with L for co-ordination to a triplycharged cation, in the framework of hard-soft considerations.One of our goals in measuring electron-transfer rates of simplesolvate complexes has been to investigate to what extent theyfollow the order of empirical solvent-basicity parameters suchas the donor number, and eventually to undertake comparisonswith theoretical predictions through structural parameters.However, the kinetics of reactions (1) was found to be especiallycomplex because of the occurrence of typically three solvation(fortunately fast) pre-equilibria (2 j ( 4 ) (in the following, co-ordinated MeCN is omitted).Consequently, these systems seemto be a poor choice for the determination of definite outer-? Non-SI units employed: A = 100 pm, dyn = I 0-5 N.[FeL6I3+ &[FeL,13+ + L[FeL,J3+ P"[FeLJ3+ + 2L (3)sphere electron-transfer rate constants. Thus, we changed theemphasis of our experiments to more qualitative aspectshighlighting the problems of studies in non-aqueous solvents.Nevertheless, the variations of the experimental rate constantwith concentration actually are very sensitive probes of both thesolvate and the ionic speciations because each speciation leadsto large changes in reactivity.The individual solvate speciesreact at highly different rates due to the different natures ofMeCN, which is a x-acid stabilising the divalent state, and hardL which stabilises the trivalent state.Thus, rates are stronglydecreased upon small additions of extra L. For the ionicspeciation, the + 3/ + 2 charge type of redox reactions causes astrong Coulombic repulsion to be overcome in forming theprecursor complex. The work against repulsion is reduced byion association with the counter ions, affecting a strongacceleration of the rate when extra salt is added.Our method of analysing the kinetic data is to study severaldependencies of the pseudo-first-order rate constant on theconcentrations of oxidant, extra added salt and extra added Land fit them simultaneously by a unique rate constant equationfeaturing solvation equilibrium constants, ion-pairing constantsand rate constants as parameters. This procedure in connectionwith the above-mentioned sensitivity of the fits to the individualparameters would appear to afford an adequate analysis despit2474 J.CHEM. SOC. DALTON TRANS. 1995the large amount of parametrisation. In fact, the values of pobtained from the kinetic fits alone yield mean co-ordinationnumbers nicely consistent with those derived from 'H NMRspectroscopy revealing ligated and free L in CD,CN.,.,Furthermore, the ion-pairing constants were satisfactorilycomplemented numerically by conductance measurements. tiIn the present paper we compare the reduction kinetics ofFe3 + complexed by dimethylacetamide (dma) and acetamide(aa) again in MeCN as the solvent. The purpose is twofold.(i) The role of acidic hydrogens in non-aqueous outer-sphere electron transfer is elucidated further.In the caseof the reduction kinetics of [Mn(OC(NH2)2f,]3 + and[M~~(dmso),]~ + (dmso = dimethyl sulfoxide) it was foundthat perchlorate association is similar for both despite thepresence of acidic hydrogens in urea. The question ariseswhether this result is of more general validity. (ii) The workadds to the data on the corresponding systems [Fe(dmf),13'and [Fe(tmp),] + (tmp = trimethyl phosphate) reportedpreviously. 3*4 Of the various parameters involved, thepossibility of gathering values of for various L is anintriguing one. This addresses a long-standing question as to therelevance of the donor number of L to the stability of unmixed[ML,]" + complexes when both leaving and non-leaving ligandsare the same. In the simple picture of the donor-acceptor modelit was argued that, since five co-ordinated solvent moleculescontribute to the overall acceptor strength of the remaining[ML,]"+ moiety, but only one ligand leaves for exchange, thelatter might more readily dissociate the higher is the donornumber of L.7 This proposal has been offered to explain theorder of solvent-exchange rates for a few unmixed complexes ofNi2+ and Co2+.* Apart from this, experimental evidence is stillmissing owing to the lack of appropriate reaction systems.ExperimentalHexakis(dimethylacetamide)iron(IrI) perchlorate was preparedby dissolving iron(r1i) perchlorate hydrate (5 g) (Aldrich) inpurified dimethylacetamide (30 cm3), with the temperature keptbelow 30°C.Anhydrous diethyl ether was added until thesolution turned cloudy and a heavier layer was observed. Uponkeeping the solution at - 20 "C overnight a microcrystallineprecipitate formed. It was collected on a glass frit and washedwith cold anhydrous diethyl ether. The yellow crystals weredried in vacuo at ambient temperature ( ~ 9 0 % yield). Thisprocedure was repeated twice. The product seems to be slightlyhygroscopic in the solid state (Found: C, 32.95; H, 6.30; C1,12.00; N, 9.40. Calc. for C,4H,,C~3FeN,01,: C, 32.85; H, 6.20;CI, 12.25; N, 9.60%).Hexakis(acetamide)iron(m) perchlorate was synthesised byadding an excess of acetamide (ten-fold excess) (Merck, reagentgrade) to a solution of iron(iI1) perchlorate hydrate (5 g)(Aldrich) and acetic acid anhydride (1 : 6 v/v) in MeCN.Thegreen product was precipitated with diethyl ether, filtered offand dried in uacuo (yield 92%). It was recrystallised twice fromMeCN (Found: C, 20.55; H, 4.30; Cl, 15.10; N, 12.00. Calc. forC12H3,C13FeN,018: C, 20.35; H, 4.25; C1, 15.00; N, 11.85%).The complex [Fe(hmphen),][ClO,], (hmphen =3,4,5,6,7,8-hexamethyl- 1,IO-phenanthroline) was prepared asdescribed. The solvents acetonitrile and dimethylacetamidewere purified and dried by standard methods.'Tetrabutylammonium perchlorate was synthesised fromtetrabutylammonium hydroxide (Riedel de Haen) andperchloric acid (Loba, p.a.) and recrystallised from 50% (vjv)anhydrous ethanolaiethyl ether.'CAUTION: Owing to the hazardous nature of metalperchlorates containing organic ligands, the drying temperaturewas kept below 50°C.Only small amounts were synthesisedat a time and handled with extreme care.The kinetic measurements were done on a Durrum D-110stopped-flow spectrophotometer at 25 k 0.1 "C (equipped witha MGW Lauda TUK 30 thermostat and a MGW LaudaR42/2D thermosensor) using a 2 mm cell by following theconsumption of [Fe(hmphen),]'+ (Amax = 513 nm, E =16 000 dm3 mol-' crr-'). Pseudo-first-order conditions weremaintained by taking a 10-100 fold excess of [Fe(dma),I3+ or[Fe(aa),I3+ over the reductant concentration ( ~ 5 x moldmP3). Absorbance data were processed as b e f ~ r e . ~Proton NMR measurements were carried out on a BrukerAC 250 instrument operating at 250.13 MHz.Temperature wascontrolled within k 1 "C by using a Eurothenn AC TBLtemperature controller. Temperature readings were calibratedagainst the temperature dependence of the proton chemicalshift of ethylene glycol. l o Deuteriated acetonitrile (CD,CN,99.95%; Aldrich) was used as the solvent, which was dried over3 A molecular sieves and purged with N, in order to removeoxygen. The cyclic voltammetric experiments were done asbefore., Conductance measurements were done with a WTW-LF535 microprocessor conductivity meter fitted with a WTW-LTA 1 electrode.ResultsSpeciation ofFe3 +.-As in previous ~ o r k , ~ , ~ . ~ attempts havebeen made to assess the speciation by means of 'H NMRspectroscopy. For [Fe(dma),][ClO,], dissolved in CD,CN( M 17 mmol dm 3 ) , resonances of co-ordinated dma (6 70-30and lOto -5)andbulkdma(63.17,3.11 and 1.94),relativetotheresidual protons of the solvent (6 1.93 us.SiMe,), were resolvedat room temperature. Unfortunately the substantial peakoverlap defies a definite analysis. Qualitatively, however, froma comparison with spectra recorded for the [Fe(dmf)J3'analogue where peak separation was feasible, it can be impliedthat the loss of dma and dmf from the respective compoundsis similar but probably greater in the case of dma. For[Fe(aa),][ClO,],, on the other hand, no free aa could bedetected in the CD,CN solution obviously because of asuperimposition of the bulk methyl protons by the solventsignal. Actually acetamide dissolved in CD3CN exhibits a sharpsinglet at 6 1.84, very close to that of the residual protons of thesolvent.Beyond that, the signals of the amide protons are notsuitable for studying the speciation because of broadening dueto quadrupole relaxation of the adjacent 14N.Kinetics. -Since both the oxidants considered behave quitesimilarly, they are described together, termed as Fe"'.Throughout the iron(Ii1) oxidant was taken in at least ten-foldexcess, giving pseudo-first-order rate constants, kobs. Inaddition, quantitative conversions were ascertained from theabsorbance changes.Values of kobs were measured under a variety of conditions.They were found to increase non-linearly with [Fe"'] when noelectrolyte was added and to pass through a maximum when thevariation in perchlorate concentration was compensated for bythe addition of NBu,C104 (Fig.1). The variation in rateconstant with NBu,CIO, at fixed [Fe"'] is shown in Fig. 2 .Finally, the rate constants decrease notably when extra L wasadded (Fig. 3), independently of whether L was admixed to theFe"' or the [Fe(hmphen),12+ reactant solutions before thereact ion.Electrochemical Dam-Redox potentials are available forthe unmixed complexes only (Table 1). Thus, a strong shift ofE" is expected upon the addition of L to a MeCN solution of[Fe(MeCN),I3+. This is in fact found but a detailed study isnot worthwile because of the occurrence of an electrochemical-chemical4ectrochemicalLchemical mechanism' ' with toomany unknowns (different solvation equilibria at both Fe2 + and Fe3+).Conductance Data.-The molar conductivities (S cm2 mol-')measured in MeCN at 25 "C for concentrations (mmol dmP3)in parentheses are as follows: [Fe(dma),][CIO,],, 402 (0.998)J.CHEM. SOC. DALTON TRANS. 19956 -4 -2475- 642I I I Jo o o * O * 0420I 1 I I I0 5 10 15 20 25[Fell']T/mmol dm3Fig. 1 Observed rate constant as a function of iron(rrr) concentrationunder different conditions. Curves: (a) without adding NBu,CIO,;(b) at constant total perchlorate concentration. L = dma (upper),[Fe(hrnphen),'+]T = 0.20 mmol dm-3; aa (lower), [Fe(hmphen),'+],= 0.02 mmol dm '. Points are experimental, solid lines arecalculated with equation (1 0) and parameters given in Table 2Table 1 Redox potentials" in acetonitrile at 25 "CComplex E+ b/V Ref.[Fe(aa)J3' 2 c 1.22,' This work[Fe(drna),], + ' ' 1 .30Td This work[Fe(hmphen),] ' + I 2 + 1.52, 2[Fe(MeCN),] +j' + 2.56, 1" The potentials are referenced to [Cr(C,H,Ph),]'/+ ( - 1.11 8 us.ferrocene-ferrocenium).Potentials represent the mean of the cathodicand the anodic peak potentials from cyclic voltammograms (scan rate0.1 V s I , electrolyte 0.1 mol dm-, NBu,CIO,, reactant concen-tration = I mmol dm ,). Measured in MeCN saturated with aa.Measured in dma.'V I 5 9 -30 -20 -I I I I 10 50 100 150 200 250[CI041T/mmol dm-3Fig. 2 Observed rate constants as a function of NBu,CIO, saltconcentration. Upper: [Fe(dma),3+], = 2.0 mmol dm-j,[Fe(hmphen),Z+]T = 0.20 mmol dm '. Lower: [Fe(aa),3+], = 2.0mmol dm-3, [Fe(hmphen),'+], = 0.02 mmol drn-,.Other details asin Fig. 1pairs Fe(C10,)2 +-Fe3 + and Fe(CIO,), +-Fe(C104)2 + was set at0.8 : 1 from past experience.Owing to the high experimental concentrations chosen,values of both Klo and A,(; FeL63f), where h, is the equivalentionic conductivity, depend dramatically on r . Taking r = 9 A,the Fuoss ratio, K10/K2', is equal to 5.27 and the results were,for [Fe(dma),][ClO,],, K,' = 740 dm3 mol-', h,[iFe-(dma)63+] = 83.9 S cm2 mol-' and, for [Fe(aa),][CIO,],,Klo = 1410 dm3 mol-', ho[$Fe(aa)63'] = 79.0 S cm2 mol '.With r set at 10 A (the Fuoss link is 4.46), the resultswere, for [Fe(drna),][C10,],, K,' = 630 dm3 mol ', h,[:Fe-(dma),3+] = 78.9 S cm2 mol-' and, for [Fe(aa),][CIO,],,Klo = 1090 dm3 mol-', ho[iFe(aa)63+] = 69.9 S cm2 mol-'.367 (2.002), 345 (3.000), 331 (3.998), 319 (5.002), 309 (5.999),302 (6.997).294 (8.001), 287 (8.999) and 282 (9.997);[Fe(aa),][ClO,],, 281 (3.999), 267 (5.002), 258 (6.000), 249(7.002), 240 (7.998), 234 (9,001) and 229 (9.998). These resultswere analysed by the exact Lee-Wheaton equation l 2 becauseno fit was obtained unless both higher terms were included.Various parameters were fixed before fitting: (i) the second-stage association constant K20 was linked to the fitted valueof K,' by the Fuoss ratio [equation ( 5 ) : D, is the static dielectricconstant and r the approach distance in A]; (ii) the molarKl0/K,* = exp (56O.75/Dsv) ( 5 )conductance of perchlorate was taken as 103.8 S cm2 mo1-';13(iii) the ratio of the conductance of the ion to that of the ionDiscussionIn accordance with previous report^,^-^ the decrease in ratewhen extra L is added, shown in Fig.3, is indicative of solvationequilibria between L and MeCN co-ordinated at Fe3+, withions of higher L content being less reactive. The large effect ofsmall additions of L would further suggest that not much ligandis lost from either complex. Moreover, since the effect of L isindependent of the mode of addition (i.e., either to thereductant or the oxidant solutions), these equilibria are rapidcompared to the redox processes. The various solvate speciesavailable should have highly different reactivities. On the basisof Table 1, the reduction potential difference could well beabout 0.2 V for the replacement of one L by MeCN.In addition to the solvate speciation, also the ion speciationleads to large changes in reactivity.The problem ofdeconvoluting simultaneously these two kinds of speciation, i2476 J. CHEM. SOC. DALTON TRANS. 19952.5 r-i 0- I40 80 1 20 s o 121-4 -L, o , 0 I 0 10 20 40 60 80[Lldmmol dm4Fig. 3 Observed rate constants as a function of the concentration ofextra added ligand. Upper: [Fe(dma),3+]T = 10.0 mmol dm-3,[Fe(hmphen)3Z+]T = 0.20 mmol dm-3. Lower: [Fe(aa)63+]r = 10.0mmol dm-3, [Fe(hmphen),'+], = 0.025 mmol dm-3. Other details asin Fig. 1tackled by the reaction model successfully applied before withall the assumptions made outlined as follows:(i) The two kinds of speciation do not affect each other, thatis ion association is qualitatively and quantitatively the samefor all solvate species and vice uema (in the following, X- =ClO,-), equations (6) and (7).[FeL,] + + X - [FeL,X] + (6)[FeL,XI2+ + X- &[FeL,X,]+ (7)(ii) The reaction rate of each solvate species is considered tovary with both ionic strength and counter-ion concentration.Ionic strength effects are treated by Coulombic work terms withextrapolation to infinite ionic strength.Ion-pairing equilibriumconstants are approximated as real constants within theexperimental ionic strength range. Ion pairing lowers theelectrostatic work needed to bring the reactants together byreducing the charge type of the reaction. Relative to this effect,ion pairing does not alter the electron-transfer reactivity.Theion-pairing constants calculated from the kinetic analysesshould be connected with those derived from the conductancemeasurements via equation (8) valid for MeCN (D, = 37.5,T = 298 K, z1 and z2 are the charges of the reactants, and Yis the distance parameter in A).14 A justification of all theseapproximations has been given before. 5 + 6 In addition to equations (6) and (7), slight ion pairing wasalso allowed for the ferroin reactant, equation (9), with K3 fixed[Fe(hmphen),12+ + X- [Fe(hmphen),X]+ (9)at 3 dm3 mol-' as before. 3*4 Along these lines six ionic paths areconsidered for each solvate species, represented in turn by thesix terms in the numerator of equation (lob) where the chargetype enters uia the exponential terms [e.g.the term e6A stands forthe free-ion path, etc. A is defined as in equation ( ~OC)]. In thisframework, the reactivity of each solvate species is characterisedby a single electrostatics-free rate constant, independent of thenumber of anions attached.For our two reactions the kinetics appear to be very similaras judged from the experimental rate constant plots in Figs. 1-3.One difference nevertheless is in the dependence of kobs on[Fe'"], of Fig. 1, measured at constant total perchlorateconcentration. Whereas kobs passes through a maximum in thecase of dma, saturation behaviour is displayed in the case of aa.In terms of the various assumptions outlined above, the shapeof these plots results from two combined effects: (i) thevariation in the active species concentration with [Fe"'],, asdetermined by the solvation equilibrium constants, and (ii) thedecrease in free [C104-] due to ion association, as determinedby the association constants.Since either ligand, dma and aa,is similar to dmf in both structure and donor strength, bothreactions were analysed in terms of Scheme 1, by analogy to theFe"'4mf system., (Here and in the following, the subscripts tothe rate constants denote the number of L ligands bound.)That [FeL4I3+ is the first species in the series to react ineither case is reasonable in the context of the reductionpotentials given in Table 1. If the potential is tentativelyassumed to be a linear function of st~ichiometry,'~,'~[FeL4I3+ is indeed the first species in the series that has apotential more positive than that of the ferroin oxidant.Theexpression for the pseudo-first-order rate constant with allassumptions described above included is given by equation(10a). The approach distance Y was taken uniformly as 14 8( ase6A + Kl[X-]e4A + K3[X-]e3A + K,K2[X-]2e2A(1 + K3[X-])(1 + KJX-1 + K1K2[X-I2) + Q =(lob)K , K3[X -I2e2* + K , K2K3[X-] 3eA(1 + K3[X-])(I + K,[X-] + K1K2[X-J2)151 + 0 . 4 8 r l r Y- _ 7.12I*A =b e f ~ r e , ~ . ~ in the absence of structural data for the solvatecomplexes. It may be noted that the results of the calculations[FeL,I3+ [FeLSl3' e [FeL4l3+ \ + [FeLjI3+ /".\ P + [Fe( hmphen) 3] ' '1Fe" + [Fe(hmphen) j]3 'Scheme 1 L = dma or aJ.CHEM. SOC. DALTON TRANS. 1995-----24776.05.6b5.2Table 2 Summary of association constants, solvation equilibriumconstants and electrostatics-free rate constants for the oxidation of[Fe(hmphen),12+ in acetonitrile at 25 "C282624[Fe(dma)6I3 +I2 +K,/dm'mol ' 100 2 20P2/mo12 dm tiK2/dm3 mot-' 36.8 f 6.3Pl/mol dm-3 (1.72 f 0.2) xp3/mo13 dm (9.68 f 1.6) x lo-*k,/dm3 mol ' s-' (6.18 f 1.3) x lo3k,/dm3 mol s (1.70 f 0.5) x lo4(2.11 f 0.5) x 10-5r[Fe(aa),13 + I 2 +180 ? 3011.6 ? 2(6.56 2 0.6) x(1.37 f 0.4) x(1.41 f 1.3) x lo-''(5.70 f 1.6) x lo4(8.37 k 3.2) x lo5were not sensitive to moderate changes in the distanceparameter. In fitting the kinetic data by use of equation (lo),both the free proligand and the free perchlorate concentrationswere supplied from the roots of the respective material-balanceequations through Newton's method as before.The results of the fits are shown by the solid lines in Figs.1-3,with the best-fit parameters listed in Table 2. Overall, the fitsare quite acceptable apart perhaps from the rather poorreproduction of the saturation behaviour displayed by the aasystem [lower plot (6) of Fig. 11. As can be calculated from thep values of Table 2, for either ligand, both active speciesincrease in concentration as [Fe"'], increases (in contrast to thedmf case for which [Fe(dmf),,+] actually is found to decrease(see Fig. 5 in ref. 3)). Thus the shapes of curves (b) in Fig. 1 arelargely governed by the extent of ion association reducing[ClO, -Ifree as [Fen'], increases under the condition of constant[CIO4-IT.Therefore, to obtain rate saturation instead of amaximum, the computer analysis based on equation (10) reducesK , for aa relative to that ofdma, in contrast to expectation. Whatmight be expected, however, is that K , be higher for aa similar tothe K , values (Table 2), in accordance with theconductance data.For the latter, on the other hand, the Fuoss link [equation (5)]employed in treating them is likewise highly suspect. There isincreasing evidence from various lines of inquiry, conducto-that the drivingforce in the ion-association process does not derive from theenergy of the interaction between the cation and the anion, butinstead from solvent-solute restructuring.Thus the occasionalagreement between experimental association constants andthose calculated from the Fuoss equation would seem to berather fortuitous due to a compensation of various effects.Anyway, the above comparisons may be taken to signal someadditional complicating features inherent in the aa system,perhaps connected with the acidic hydrogens of aa, notaccounted for by the reaction model employed here. Therefore,the physical significance of the numerical value of K , for the aasystem cannot be taken too seriously. On the other hand, thedifferences in behaviour between the aa and dma systems,overall, are not so large so as to warrant a further analysisparticularly since no simple modification of equation (10) isobvious.A prior comparison between the reduction kinetics of[Mn(dmso),13 + and [Mn{OC(NH2),}6]3+ did not reveal anyparticular effect of the acidic hydrogens of urea.Let us now discuss the other parameters listed in Table 2. Itshould be emphasised that, because of the amount ofparametrisation, the parameters themselves must haveinherently rather large error limits. Particularly the errorassociated with the [FeL3I3+ path (p,, k,) is large. The meanco-ordination number of dma calculated from the p values for 8mmol dm of the dma salt is 5.05. For the aa salt of the sameconcentration the values point to a significantly higher valueof 5.62. In view of such high co-ordination numbers, clearly thefits of the kinetic data cannot be sensitive to p3.An unexpectedresult is that the values of p are larger for [Fe(aa),13+ than for[k(dma),I3 ' despite the lower donor number of aa (26.0, seeAppendix) compared to dma (27.8). In Fig. 4 are plotted valuesspectroscopic l 9 and221 I 1 1 1 14.8log P1-3.5 -3.0 -2.5 -2.0 -1.5 -1.0Fig. 4 Plot of log p1 us. donor number and o of the ligands of[FeL,], +5.51 mp\ - x = 3\a a \\\\1 Y\o------o3.5 1 I II I I I22 24 26 28Donor numberFig. 5 Plot of log k , and log k , us. donor numberof PI (these are the most reliable ones, but similar plots areobtained using P2 or p3) versus the donor number includingthose for the complexes [Fe(dmf)6]3 + and [Fe(tmp),13 + dealtwith As is seen, there is definitely no relationship.Instead, there is a trend between and the ligand sizetentatively expressed in terms of the effective hard-spherediameter o (see Although the ligand size iscertainly not the only parameter determining the stability ofcomplexes, this trend can be related to the size-dependentlability of the first co-ordination sphere to ligand substitution.Since local structural rearrangement is involved, such processesmight better be described in terms of molecular packing effectsrather than bond-strength parameters.Recently, there has beenincreasing appreciation of the fundamental importance ofpacking effects in liquid-state phenomena.,' 30 In a forth-coming study we will try to add to the number of data pointsin Fig. 4 by searching specifically for the effect of size byreplacing the methyl groups in [Fe(dmf),13 + by higherhomologues up to butyl.For the (electrostatics-free) rate constants k , and k,, finally,the complexes containing aa are more reactive towardsreduction compared to the dma analogues. This may largely bea driving-force effect, aa being the weaker base thus stabilisingthe trivalent state to a lesser extent.However, the relationshipbetween the rate constants and the ligand donor number is verypoor as seen in Fig. 5.An additional remark is in order here. In previous iron(Ir1)the experimental rate constants could not be fittedsatisfactorily by equation (10) or a similar one unless theassumption was introduced that the various solvate speciesreact oia different ion-paired paths.This was rationalised interms of the competition of the driving force changing with theinner-sphere composition and of the Coulombic work changingwith ion pairing. In fact, the change in driving force for th2478 J. CHEM. SOC. DALTON TRANS. 1995replacement of one L by MeCN could well be comparable inmagnitude to the reduction in Coulombic work in changing thecharge type from +2/+3 to +2/+, that is, when [FeLJ3+reacts as such or as the triplet. Therefore, the overall reactivityof e.g. [FeL3I3+ might be comparable to that of [FeL,X,]+.In the present iron(m) reactions, however, no improvement ofthe fits was attained upon this procedure.AppendixDetermination of the Donor Number of aa.-This was doneby a solvatochromic method reported recently." Thus, thebroad absorption peak at h z 602 nm ( C z 16 61 1 cm-')displayed by [Cu(tmen)(acac)]CIO, (tmen = N,N,N',N-tetramethylethane-l,2-diamine, acac = acetylacetonate) dis-solved in nitromethane, saturated with aa, gives donornumber = 26.0 from the empirical equation, D, = 195.5 -0.0102 +, shown in the appendix of ref. 3 1.Determination of the Hard-sphere Diameters o.--(a) Of aa.This is done on the basis of the crystal structure oforthorhombic acetamide having dimensions a = 7.76, b =19.00, c = 9.51 A and 2 = Hence the number density isp = (abc/z)-' = 1.14 x 10' A '.From this, o can becalculated from the equation q = 7cpo3/6 if the packingfraction q is known. Assumin closest packing, that is takingthe maximum value of q = n$/6 = 0.74, we obtain CT = 4.99A.Owing to the assumption of closest packing, this value shouldrepresent an upper estimate.(h) Of tmp. For liquids, the hard-sphere diameter can becalculated by means of equation (29) of ref. 26, usingexperimental values of the isothermal compressibility PT, themolar liquid volume, the gas-phase dipole moment, and thevapour pressure. However, QT for trimethyl phosphate has notbeen measured. Thus we calculated PT from the surface tension(36.92 dyn cm-') and the mass density (d25 = 1.2144 g cm ')according to ref. 33, giving QT = 6.88 x lo-'' Pa-'. From thiswe get o = 5.90 A. To check this, we used another empiricalmethod, described in ref. 24, based on the molar refraction,requiring the refractive index n = 1.3939 and the numberdensity p = 5.204 x 10 k3.From these values the volume V,can be evaluated from [(n2 - l)/(n2 + 2)]/p as 45.956 A3,and from the empirical correlation Vhs = 2.473 ( V , - 5.53) thehard-sphere volume vhs = 99.974 A3. Finally, vh, = (7r/6)03giving o = 5.77 A. Thus we adopt for tmp, in Fig. 4, a value ofCT = 5.83 A as the mean.AcknowledgementsThis work was supported by thf: Fonds zur Forderung derwissenschaftlichen Forschung in Osterreich (Project No. 8 126).Also, thanks go to Professor A. D. Pethybridge (Reading, UK)for calculating the ion-association constants from conductancedata, to Dr. K. Kirchner for doing the NMR spectroscopicmeasurements, and to Dr. L. Han for some of the kineticmeasurements.References1 S. Wherland, Coord. Chem. Rev., 1993,123, 169.2 R. Schmid, K. Kirchner and F. L. Dickert, Znorg. Chem., 1988,27,3 R. Schmid, K. Kirchner and V. N. Sapunov, Znorg. Chem., 1989,224,4 R. Schmid, L. Han, K. Kirchner and V. N. Sapunov, Monatsh.5 R. Jedlicka, K. Kirchner and R. Schmid, J. Chem. Soc., Dalton6 S. Dasgupta, E. Vallazza and R. Schmid, J Chem. Soc., Dalton7 V. Gutmann, The Donor-Acceptor Approach to Molecular8 W. J. MacKellar and D. B. Rorabacher, J. Am. Chem. Soc., 1971,93,9 D. D. Perrin and L. W. F. Armarego, Purijicution of Laboratory10 D. S . Raiford, C. L. Fisk and E. D. Becker, Anal. Chem., 1979,51,1 1 K. Kirchner, R. Jedlicka and R. Schmid, Monatsh. Chem., 1992,123,12 A. D. Pethybridge, Z. Phys. Chem. (Munich), 1982,133, 143.13 R. L. Kay, B. J. Hales and G. P. Cunningham, J. Phys. Chem., 1967,14 R. Schmid, Rev. Znorg. Chem., 1991, 11,255.15 D. P. Poe, Znorg. Chem., 1988,27, 1280.16 C. M. Duff and G. A. Heath, Znorg. Chem., 1991,30,2528.17 F. Lukacs and K. Burger, J. Chem. Soc., Furaday Trans., 1992,88,18 L. Reichstadter, E. Fischerova and 0. Fischer, J. Solution Chem.,19 D. D. Chingakule, P. Gans, J. B. Gill and P. Longdon, Monatsh.20 K. Kirchner, H. W. Dodgen, S. Wherland and J. P. Hunt, Znorg.21 D. C. Gaswick and S. M. Malinak, Inorg. Chem., 1993,32, 175.22 T. G. Braga and A. C. Wahl, J. Phys. Chem., 1985,89, 5822.23 R. M. Nielson and S. Wherland, Inorg. Chem., I984,23, 1338.24 D. Ben-Amotz and D. R. Herschbach, J. Phys. Chem., 1990, 94,25 D. Ben-Amotz and K. G. Willis, J. Phys. Chem., 1993,97,7736.26 R. Schmid and D. V. Matyushov, J. Phys. Chem., 1995,99,2393.27 Y. Yoshimura, Y. Kimura and M. Nakahara, Ber. Bunsenges. Phys.28 Y. Yoshimura and M. Nakahara, Ber. Bunsenges. Phys. Chem., 1986,29 Y. Yoshimura and M. Nakahara, J. Chem. Phys., 1984,81,4080.30 R. Ravi, L. E. S. de Souza and D. Ben-Amotz, J. Phys. Chem., 1993,31 R. W. Soukup and R. Schmid, J. Chem. Educ., 1987,64,904.32 W. C. Hamilton, Acta Crystallogr., 1965, 18, 866.33 I. C. Sanchez, J. Chem. Ph.ys., 1983,19, 405.1530.4167.Chem., 1993,124,493.Trans., 1993,417.Trans., 1993, 2387.Interactions, Plenum, New York, 1978.4379.Chemicals, 3rd edn., Pergamon, Oxford, 1988.2050.203.71, 3925.3345.1993, 22, 809.Chem., 1992,123,52 1.Chem., 1990, 29, 238 1.1038.Chem., 1988,92, 1095.90, 58.97, 11842.Received 23rd March 1995; Paper 5/0188O
ISSN:1477-9226
DOI:10.1039/DT9950002473
出版商:RSC
年代:1995
数据来源: RSC
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