Pressure effects on the rate of electron transfer between tris(1,lO-phenanthroline)iron(II) and -(IIT) in aqueous solution and in acetonitrile

HIDEO DOINE AND THOMAS WILSON SWADDLE' Department of Chemistry, The University of Calgary, Calgary, Alta., Canada T2N IN4

Received May 25, 1988

I

HIDEO DOINE and THOMAS WILSON SWADDLE. Can. J. Chem. 66, 2763 (1988). Proton nrnr line-broadening experiments at ambient and elevated (to 215 MPa) pressures show that the rate of electron transfer

between F e ( ~ h e n ) ~ ~ + and Fe(phen)33+ as bisulfates in D20/D2S04 is represented by the activation parameters (at ionic strength I - 0.4molkg-I) AH* = 1.6 ? 0.5kJmol-I, AS* = -102.2 ? 1.6 J K - ~ ~ o I - ' , k(276K) = 1.31 x 107kgmol-Is-', and (at I - 0.3 mol kg-' and a mean pressure of 100 MPa) AV* = -2.2 2 0.1 cm3 mol-I. For the same reaction of the perchlorate salts (total [Fe] 0.046-0.065 mol kg-') in CD3CN, AH* = 11.0 I+- 1.0 kJ mol-I, AS* = -72.5 2 3.6 J K-I mol-I, k(277 K) = 8.0 X 106kg mol-I s-I, and AV* = -5.9 2 0.5 cm3 mol-l. For water as solvent, AV* is satisfactorily accounted for by a classical theory of the Stranks-Hush-Marcus type. Volumes of activation for electron self-exchange are shown to provide criteria for non-adiabaticity and for dominance of (non-aqueous) solvent reorganizatlon dynamics; on this basis, it is seen that neither of these factors is important in the title reactions.

HIDEO DOINE et THOMAS WILSON SWADDLE. Can. J. Chem. 66, 2763 (1988). Des experiences d'klargissement de raies dans les spectres rmn du proton, effectuies a la pression ambiante et a des pressions

allant jus u'i 215 MPa, permettent de demontrer que la vitesse de transfert d'Clectron, entre les ions Fe(phen)32+ et le 4 . . F e ( ~ h e n ) ~ + q u ~ exlstent sous la forme de bisulfates dans une solution de D20/D2S04, peut &tre representte par les paramktres d'activation suivants : (a une force ionique de I - 0,4 mol kgp'), AH* = 1,6 ? 0,5 kJ mol-', AS* = -102,2 &

1,6 J K-' mol-I, k(276 K) = 1,31 X 107kg mol-Is-' et (a I = 0,3 mol kg-' et une pression moyenne de 100 MPa) AV* = -2,2 * 0,1 cm3 mol-I. Pour la m&me reaction des perchlorate ([Fe] totale de 0,046 a 0,065 mol kg-') dans le CD3CN AH * = 11,O 2 1,O kJ mol-l, AS' = - 72,5 t 3,6 J K-' mol-I, k(277 K) = 8,O X lo6 kg mol-' s-' et AV* = -5,9 2

0 , l cm3 mol-'. Lorsque l'eau est le solvant, on peut facilement expliquer la valeur du AV* par une thCorie classique du type Stranks-Hush-Marcus. On dCmontre que les volumes d'activation pour l'auto-Cchange des electrons fournissent des critkres pour expliquer les propriCtCs non-adiabatiques ainsi la dominance de la dynamique de reorganisation des solvants non-aqueux; sur cette base, on peut comprendre pourquoi aucun de ces facteurs n'est important dans les reactions mentionnCes dans le titre.

[Traduit par la revue]

Introduction tris(1 , 10-phenanthroline)iron(II) and -(III)

A continuing theme in the work of our laboratory has been the quantitative prediction, tested by experimental measurement, of the effects of pressure on the rates of inorganic reactions in solution (1-5). Outer-sphere electron transfer reactions are particularly attractive subjects in this respect, since the Stranks- Hush-Marcus ("SHM") theory (6) allows one, in principle, to calculate the effect of pressure on the rate constant k (expressed as the volume of activation Av* = -RT(a In k/aP)=) from basic physical properties of the reactants and the solvent. The initial apparent success (6) of simple SHM theory for self- exchange reactions of metal complexes in aqueous solution, however, has been shown to have been fortuitous (7,8), and we have therefore undertaken a re-evaluation of this approach.

Our early considerations (4) suggested that, subject to some minor modifications (notably the treatment of the separation u between the reacting metal-ion centres as a pressure-sensitive variable), the SHM theory might prove adequate for self- exchange reactions of transition metal complexes containing large ligands with extended T-electron systems. In such cases, fully adiabatic electron transfer (i.e., electronic transmission coefficient x , ~ - 1) might be expected, and the solvent should be adequately represented as a continuous dielectric with relative permittivity equal to the bulk value D throughout.

I Indeed, Braun and van Eldik (9) reported that AV* for electron transfer between C~(terpy) ,~+ and C ~ ( b i p y ) ~ ~ + in water comes

I close to the predictions of simple SHM theory (this is, however, a net reaction rather than self-exchange).

An appropriate test case is the self-exchange reaction of

I 'TO whom all correspondence should be addressed.

the ambient-pressure kinetics of which were mapped out for various solvents by Wahl and co-workers with 'H nrnr line- broadening (10, 11). We report here a high-pressure study of this system in water and acetonitrile, in addition to refinements of some of the measurements of Larsen and Wahl(10, 11). An attractive feature of this widely-used couple is that the Fe-N bond lengths are identical in the oxidized and reduced species (12), so that the contributions of internal reorganization AVIR* and hGIR* to AV* and the free energy of activation AG*, respectively, should be negligible, thereby permitting simplifi- cation of the theoretical calculations.

Experimental Preparation of materials

[ F e ( ~ h e n ) ~ ] (C104)' and [ F e ( ~ h e n ) ~ ] (C104), were made by the methods of Chan and Wahl(11). [Fe(phen)-,]S04.9H20 was prepared by dissolving FeSO4.7H20 (0.9 g) in 15 mL water to which phen.H20 (3 g) was added. The mixture was stirred for 1 h in the dark and then filtered; to the filtrate, 200 mL acetone was added. The combined precipitates were recrystallized twice from ethanol-acetone. All complex salts were shown spectrophotometrically to be >99% pure, and were stored in vacuo over PZo5.

For the kinetic studies in aqueous media, Fe(~hen)3~+ could not be introduced as a solid salt (the sulfate could not be obtained pure, and the perchlorate caused precipitation of [Fe(phen)3](C104)2) and was therefore generated ,in solution by oxidation of [ F e ( ~ h e n ) ~ ] S O ~ in aqueous sulfuric acid with the stoichiometric amount of ammonium hexanitratocerate(1V) (G. Frederick Smith Chemical Co., 99.98%). It was shown by spectrophotometric titration that the oxidation was quantitative in the time required for solution preparation, and further-

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2764 CAN. J . CHEM. VOL. 66, 1988

more that ~ e ( ~ h e n ) 3 ~ + was stable enough in solution in aqueous sulfuric acid (0.1 rnol L-I) below 5°C for completion of a cycle of pressurized nmr experiments (ca. 8 h); significant decomposition of the iron(II1) complex in solution, however, precluded reliable kinetic measurements under pressure at higher temperatures (cf. refs. 11 and 13). In acetonitrile, on the other hand, [Fe(phen)3](C104)3 proved to be very stable even at room temperature.

Nuclear magnetic resonance measurements All nmr spectra were taken on a Bruker WH-90 spectrometer with

quadrature detection. The spectra of the separate ~e(phen)?+ and ~ e ( ~ h e n ) ~ ~ + complexes in solution were in good agreement with those in the literature ( 1 1, 13). The required quantities were the full widths W at half height and chemical shifts 6 of the protons in the 2 and 9 positions on the phenanthroline ligands. Temperature dependence studies were made with a standard Bruker 'H probehead, and spectra at elevated pressures (to 215 MPa) were obtained with the pressurizable assembly described previously (5). For measurements on aqueous systems, the solutions were prepared from [Fe(phen)3]S04.9H20 and D2SO4 (Sigma, 98 atom%) in D 2 0 (Aldrich, 99.8 atom%). Ammonium hexanitratocerate(1V) in D20/D2S04 was used to produce ~ e ( ~ h e n ) ~ ~ + , and DSS (sodium 3-(trimethylsilyl)propanesulfonate; MSD) was introduced as an internal standard. For measurements in acetonitrile, the requisite amounts of [ F e ( ~ h e n ) ~ ] ( C l O ~ ) ~ and [Fe(phen)3](C104)3 were dissolved in CD3CN (Aldrich, 99 atom%) which had been dried over a 4A molecular sieve.

Results Aqueous solutions at variable temperature

The rate constant k for reaction [ l ] was obtained from the "fast exchange" expression (5, 11)

where f p is the fraction of the total iron concentration [ F e l ~ corresponding to the paramagnetic ~ e " ' species (calculated as in ref. 5), Av is the difference in chemical shift between the 2,9-proton resonances of the Feu and ~ e " ' complexes in separate solutions, and W D P , W D , and W p are respectively the linewidths of these resonances in the reaction mixture, in a corresponding solution containing the Feu complex without ~ e " ' , and in a solution containing the Feu' complex without ~ e " . Equation [2] is applicable only in the "fast exchange limit" and is appropriate here because the criterion k[FeIT/2.rrAv >> 1 was satisfied in all the experiments reported in this paper. At 11.2"C, Av = 5055 and W p = 298.5 Hz; at l.O°C, the corresponding values were 5244 and 309.6 Hz. Thus, W p follows Curie's law. Values of Av and W p for other tempera- tures were obtained by interpolation. The assumption implicit in eq. [2], that the effects on W of coupling of the 2,9 with the 3,8 and 4,7 protons can be neglected, was shown to be valid; like Chan and Wahl (1 l) , we calculated that this contribution to W would in no case exceed 10%.

Measurements were made with [FeIT ranging from 0.0608 to 0.1485, [D2SO4] from 0.100 to 0.201, and ionic strength I from 0.22 to 0.48 rnol kg-'. Surprisingly, the twenty values of k so obtained, calculated from eq. [2] and subject to an estimated error of less than +5%, ranged only from 1.26 x lo7 to 1.37 X lo7 rnol kg-' s-' over the accessible temperature range -2.4 to + 11.2"C and showed no discernable dependence on I. Full details are given in the Supplementary ~ a b l e s ? but values of k

2~upplementary tables S1-S5 may be purchased from the Depository of Unpublished Data, CISTI, National Research Council of Canada, Ottawa, Ont., Canada KIA 0S2.

are well represented by the Eyring equation

[3] k = (%kg Tlh) exp ((AS*/R) - (AH*/RT))

where AH* = 1.6 + 0.5 kJ mol-I, AS* = -102.2 &

1.6 J K- ' mol-' , transmission coefficient x = 1 (assumed), and the other symbols have their unusual meaning^.^ At 25"C, the extrapolated value of k is 1.49 x lo7 kg mol-' s-'. Chan and Wahl reported k = (3.6 & 1.0) x lo7 and (4.9 -C 1.5) x lo7 L mol-' s-' for reaction [I.] at 5 and 17"C, respectively, but the counterion in their experiments was chloride rather than HS04-, and the rate data may have been affected by decomposition of the Fe"' complex (1 1).

Acetonitrile solutions at variable temperature In acetonitrile, the perchlorate salts of ~ e ( ~ h e n ) ~ ~ + and

~ e ( ~ h e n ) ~ ~ + were used, as they are both sufficiently soluble and stable at room temperature. The quantities Av and W p in eq. [2] had the values 5105 and 239 Hz at 19OC, and 5564 and 261 Hz at - 5. 1°C, respectively, in good agreement with previous reports (11, 12). Thus, they conformed to Curie's law, and values for other temperatures were obtained by interpolation. Determinations of the rate constant k were made from eq. [3] for five temperatures ranging from - 8.9 to + 15.9OC for three different solutions ([FeIT = 0.0646,0.0651,0.0463 mol kg-'; I = 0.19,0.20,0.14 rnol kg-') but the results were independent of concentration within the experimental error. The data (Supplementary ~ a b l e s ~ ) are represented by AH * = 11.0 2 1.OkTmol-' and AS* = -72.5 + 3.6JK-'mol-' if x = 1, so that k = 1.20 X lo7 kg mol-' s-' at 25OC. These agree satisfactorily with the results of Chan and Wahl(11) for reaction [I.] in CD3CN with perchlorate as counterion (note different concentration units and [FeIT).

Aqueous solutions at variable pressure Here, the anions were again HS04- and S042-. It was not

possible to determine accurately the effect of pressure on the contact shifts and line widths of the pure paramagnetic ~ e " ' species, since the high pressure probehead is relatively insensi- tive and because small amounts of the Feu complex tended to form, with consequent exchange broadening, on the longer timescale of the high pressure experiments. The Debye equa- tion, however, suggests that W p should be proportional to the viscosity q of the solvent at a given temperature (14). Water is an anomalous fluid in that q is only slightly affected (it is actually decreased and then increased (15, 16)) by rising pressure under the conditions of our experiments (3.0°C, 0.1-215 MPa), so that the pressure dependences of Av and W p in aqueous solutions can be safely neglected.

Values of the rate constant k obtained for reaction [ I ] at various pressures P at 3.0 1- 0.3"C are given in the Supple- mentary Material and are summarized in Fig. 1. There is no evidence of any dependence of k on concentrations or ionic strength (I - 0.17-0.32 rnol kg- '), and the In k vs. P plot can be regarded as linear within the experimental error, giving AV* = -2.2 ? 0.1 cm3 mol- ' for the mean conditions P = 100 MPa, I = 0.3 rnol kg-', and T = 3.0°C; k p = o = 1.29 X lo7 kg mol-I s-' , in excellent agreement with the variable- temperature result. Data obtained at the lower [FeIT are less precise and hence more scattered in Fig. 1.

Acetonitrile solutions at variable pressure The perchlorate salts of the complexes were used. In

3 ~ x c e p t where otherwise indicated, uncertainties cited in this paper are standard deviations.

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DOINE AND SWADDLE 2765

FIG. 1. Pressure dependence of the rate of reaction [ l ] in aqueous acidic (D20/D2S04) solution at 3.0'. Filled circles: [FeIT = 0.0352, [D2SO4] = 0.1001, I = 0.17 mol kg-'. Filled squares: [FeIT = 0.0621, [D2SO4] = 0.1351, I = 0.26 mol kg-'. Open circles: [FeIT = 0.0706, [D2SO4] = 0.1351, I = 0.28 mol kg-'. Open squares: [FeIT = 0.1050, [D2SO4] = 0.1001, I = 0.32mol kg-'.

acetonitrile, ~e(phen)3~+ is sufficiently stable that the pressure dependence of the linewidth Wp could be measured, and the results over the range 0.1-205 MPz at 3.8OC and [Fe] = 0.042 mol kg-' are represented adequately by

where P is in MPa. This type of relationship reflects the behavior of acetonitrile as a normal fluid (5). There was no detectable variation of Av with pressure (5380 + 60 Hz).

The data (Supplementary ~ables') are summarized in Fig. 2. The scatter is worse than for the acidic aqueous systems, but again there is no discernable concentration effect over the admittedly limited range [FeIT = 0.0468 to 0.0677 mol kg-'. The In k vs. P plot may be taken to be linear within the experi- mental uncertainty, giving AV* = -5.9 + 0.5 cm3 mol- ' and kP=,, = 8.1 X lo6 kg mol-' s-I (cf. 7.9 X lo6 kg mol-' s-' from the temperature dependence study) at 3.8OC and I - 0.18 molkg-'.

Discussion Three models were considered in interpreting the above

kinetic data for reaction [ I 1: (a) a two-sphere, weakly adiabatic, continuous-dielectric model of the SHM type, developed elsewhere (3-5) from principles laid down by Sutin (17); (b) an adaptation of model (a) with allowance for possible non-adiabaticity (3); and (c) following recent developments (18-22), a model in which solvent reorganization dynamics are important.

(a) Adiabatic continuous-dielectric model In this case, the rate coefficient k is given by

0 100 200

PRESSLIRE / MPa FIG. 2. Pressure dependence of the rate of reaction [ l ] in aceto-

nitrile (counterion: perchlorate) at 3.8OC. Open circles: [FeIT = 0.0468 mol kg-'. Open squares: [FeIT = 0.0668 mol kg-'. Filled circles: [ ~ e ] ~ = 0.0677 mol kg-'.

where K A is the formation constant for the precursor assembly {Fe(~hen)~'+, ~ e ( p h e n ) ~ ~ + ) , v, is the nuclear frequency factor, and AGIR4 and AGos* are the contributions to the free energy AG* of activation from reorganization within the reactants and from the surrounding solvent, respectively, in the activation process. For reaction [l] , AGIR* will be negligible because neither the Fe-N bond lengths (12) nor the stretching frequencies (23) change significantly on going from Fe" to FelI1. The formation of the precursor assembly involves exponential factors AGcouL* and AGDH* representing the Coulombic work and Debye-Huckel effects, respectively, which can be combined with the solvent reorganization term AGSR* to give AG* while K A is replaced by 4000.rrNu3/3 (in L mol-' s-', for u in metres) where u is the Fe-Fe separation and N is Avogadro's number (17). For consistency with transition state theory (eq. [3]), v, may be set equal to kBT/h. We have, in SI units and symbols,

where r is the effective radius of the reactant ions approximated to spheres (here, r is the same for each), n is the refractive index of the solvent (for convenience, taken to be the Na-D-line value commonly tabulated), and D is the relative permittivity (dielectric constant) of the solvent. If a is the distance of closest approach of the reactant cations (charges zl and z2) to the counter-ions, we have

where B and C are the usual Debye-Huckel parameters. The approximation of Fe(~hen)~"+ to a sphere is obviously

crude, but values of r - 700 pm and a - 900 pm seem reasonable (1 1, 12), and in any event it turns out that the calculated values of k are not very sensitive to these choices. Similarly, although u is to be regarded as variable (4, 17), it transpires that k changes very little as u is allowed to vary from 1.0 to 1.8 nm; for u = 2r = 1.4 nm, k = 8.2 X

10l0kg mol-' s-', AGSR* = 13.7, AGCOUL4 = 6.9, and

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2766 CAN. J . CHEM. VOL. 66 , 1988

AGDH* = -6.6 kJ mol-' in water at 3"C, 0.1 MPa and I = acetonitrile, since the pressure dependence of its refractive 0.3 kg mol-I. In view of the simplicity of the model, the index is not known, and furthermore there are indications (11) discre~ancv between the calculated and the observed value of that anion-cation association influences the reaction rate. k (l .? x h7 kg mol-' s-') is not excessive. It may be noted that the coulombic and Debye-Hiickel terms tend to cancel at the ionic strengths used in this study.

For acetonitrile as the solvent with the same choices of r, u , and a , but with I = 0.2 mol kg-' and T = 25.0°C, eqs. [5]-[8] predict k = 2 x 10" kg mol-' s-', with AGsR* = 13.1, AGcouL* = 16.4, and AGDH* = - 16.2 kJ mol-' . Although the latter two terms are much larger than for aqueous solution, once again they cancel at the relevant ionic strength, and indeed the measured k, though lo4-fold smaller than predicted, is almost the same in the two solvents because AGsR* is little affected. Our failure to detect the acceleration of reaction [ l ] in acetonitrile by the perchlorate counter-ion as reported by Chan and Wahl (11) may mean that F e ( ~ h e n ) ~ ~ + - C l O ~ - pairing was approaching saturation in our concentration range (which, however, was narrow). Indeed, recent measurements by Schmid et a1. (24) indicate that Fe(~hen)~~+-ClO,- pairing would be about 90% complete in our acetonitrile solutions at 25°C.

The prediction of k from eqs. [5]-[8] is clearly subject to errors from the numerous assumptions and simplifications, but at least some of these should cancel out in taking the pressure derivative of Ink to obtain AV*. Thus, a model which gives only rough predictions of k may estimate AV* quite accur- ately. Differentiation of eqs. [5]-[8] with respect to pressure gives the following expressions for the volume of activation in the adiabatic two-sphere continuous-dielectric model (3); P is the isothermal compressibility of the solvent, and, for reaction [I 1, AVIR4 is zero.

Parameters such as (an/aP)T, ( ~ 3 D l d P ) ~ , and P are them- selves pressure dependent, with the result that I AV* I must decrease with rising pressure (i.e., a plot of In k vs. P will be a curve tending towards the horizontal) (3-5). This anticipated curvature, however, is often lost within the experimental uncertainty of k, as is the case here (Figs. 1 and 2), and it is then expedient to treat the In k vs. P plot as linear, giving a mean AV* that would be representative of the mid-point of the pressure range - here, 100 MPa. We have therefore evaluated eqs. [9]-[12] for water at 100 MPa, 3.0°C, I = 0.3 mol kg-', r = 700pm, a = 900pm,anda = 1.4nm: AVsR* = -4.18, AVcouL* = -1.81, AVDH* = +2.56, PRT = +0.88, and AV* = -2.5 cm3 mol-'. This last is in close agreement with the observed value of -2.2 cm3 mol-'. The calculations are not significantly affected by the choice of r, and, if a is varied from 1.0 to 1.8 nm with r = 700 pm, opposing trends in AVsR* and AVcouL* result in a very small change in AV* (from -3.0 to -2.3 cm3 mol-'). For I = 0.4 mol kg-', the calculated AV* is -2.2cm3 mol-'.

It is not possible at present to evaluate eqs. [9]-[12] for

(b) Possibility of non-adiabaticity Since eqs. [5]-[8] overestimate k, the possibility should be

considered that reaction [I.] is non-adiabatic with xel - lop4. If non-adiabaticity applies at Fe-Fe separations u greater than a certain value uad, a semi-classical approach (17) can be adopted, noting that AGIR* is negligible for reaction [I]. The electronic coupling factor HAB is given approximately by

whence, if the distance scaling factor a is known, xel is calculable from

[I41 x e ~ = 211 - exp (-ve1/2vn)1/[2 - exp (ve1/2v,)]

where the electronic frequency vel is given by

Thus, from eq. [5], we have

and hence, proceeding as above and in ref. 3, with the assumptions that H A B O , cad , and a are independent of P , the non-adiabatic volume of activation AVNON4 is given by

For reaction [ l ] in water, a is not known, but is probably in the usual range 6 to 25 nm-' (17), in which case AvNON4 lies between -8 and -23 cm3 mol-' for T = 3.0°C, P = 100MPa, I = 0.3molkg-', a = 900pm,anda= 2r = 1.4nm.Clearly, this range is quite inconsistent with the observed value of -2.2 cm3 mol-', and it may be confidently concluded that reaction [ l ] in water is fully adiabatic, as Taube (25) and Chan and Wahl (1 1) have suggested.

Thus, in favorable cases (such as when the components of eq. [9] are all quite small), the pressure effect on the rate of a self-exchange redox reaction can be diagnostic of its adiabaticity. It will be noted that uad and H~~~ need not be known for this purpose; either the reaction is fully adiabatic because a < cad , in which case eq. [9] should account for the observed AV*, or it is non-adiabatic and eq. [17] applies.

(c) Solvent-dynamical models Grarnpp et a1. (19) have analyzed adiabatic electron exchange

processes in which solvent reorganization dynamics are domi- nant. Consider a solvent of viscosity q, molar volume VM, high frequency dielectric constant Dm (- n2) and longitudinal relaxation time TL. If the Ovchinnikova condition (19, 26)

[18] [AGIR4/(AGIR* + A G ~ ~ * ) ] ' ~ ~ u ~ ~ exp (- AGI~*/RT) > 7L-l

is satisfied, the pre-exponential part of eq. [5] becomes solvent dependent; for reaction [ l ] in water at 3°C and acetonitrile at 25"C, this requires AGIR4 5 200 and 100 J mol-' respec- tively, and these conditions could be met, in view of the insensitivity of the Fe-N bond lengths and stretching frequen- cies to the oxidation state of the iron (12, 23). If AGIR4 is negligible, the solvent frequency vs

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DOINE AND SWADDLE 2767

can be used directly to predict values of k for reaction [ l ]

[20] k = ( 4 0 0 0 1 ~ ~ ~ ~ / 3 ) v ~ exp (-AGos*/RT)

of 1 .2 x 10" and 1.8 x 10" kg mol- ' s- ' for water (3°C) and acetonitrile (25"C), respectively. Thus, regardless of whether condition [I81 is met , this approach gives essentially the same result as model ( a ) .

A solvent-dynamical treatment of pressure effects on k (in the case where AGIR* is negligible) involves the replacement of eq. PI by

1. T. W. SWADDLE. Inorg. Chem. 22, 2663 (1983). 2. H. DOINE, K. ISHIHARA, H. R. KROUSE, and T. W. SWADDLE.

Inorg. Chem. 26, 3240 (1987). 3. 1,. SPICCIA and T. W. SWADDLE. Inorg. Chem. 26, 2265 (1987). 4. T. W. SWADDLE. In Inorganic high pressure chemistry. Edited by

R. van Eldik. Elsevier, Amsterdam. 1986. Chap. 5. 5. H. DOINE and T. W. SWADDLE. Inorg. Chem. 27, 665 (1988). 6. D. R. STRANKS. Pure Appl. Chem. 38, 303 (1974). 7. S. WHERLAND. Inorg. Chem. 22,2349 (1983). 8. L. SPICCIA and T. W. SWADDLE. J. Chem. Soc. Chem. Commun.

67 (1985). 9. P. BRAUN and R. VAN ELDIK. J. Chem. Soc. Chem. Commun.

1349 (1985).

~ 2 1 1 A V + = A V ~ ~ + + A V ~ ~ + + pRT - R T ( ~ lnvs/dP)T 10. D. W. L A R S E N ~ ~ ~ A. C. WAHL. J. Chem. Phys.43,3765 (1965). 11. M.-S. CHAN and A. C. WAHL. J. Phys. Chem. 82,2542 (1978).

= AVOS3 + AVSD* 12. B. B. BRUNSCHWIG. C. CREUTZ. D. H. MACARTNEY. T. K.

where

For water at 3"C, it can be estimated (16) that RT(d In -q/dP)T ranges from -2.9 to +1 .2 cm3 mol-' on going from 0.1 to 200 MPa, and is zero near 120 MPa. Thus, the mean calculated AV* o n the basis of eqs. [ lo ] , [ I l l , [12], [21], and [22] for water at 3°C and I = 0 .3 mol kg-' is about -4.7 cm3 mol-I, which is 2.5 cm3 mol- ' too negative. The discrepancy is not large, but model ( a ) gives a closer prediction.

For "normal" liquids, -q rises monotonically and roughly exponentially with pressure, often doubling between 0.1 and 100 MPa (1 5 , 2 7 ) . Consequently, for non-aqueous solutions, the term RT(d In q / d P ) = will typically make a large (20 cm3 mol-' o r more) positive contribution to AV* where solvent reorgani- zation dynamics are dominant. Since the volumes of activation generated by models ( a ) and (b), and by refinements of these (3), are generally in the range 0 to -20 cm3 mol- I , the observation of a markedly positive Av* for outer-sphere electron transfer in a non-aqueous system may be taken as evidence for dominance of solvent dynamics. Clearly, reaction [ l ] in acetonitrile is not such a case.

Acknowledgement W e thank the Natural Sciences and Engineering Council of

Canada for financial support.

SHAM, and N. SUTIN. Faraday Discuss. Chem. Soc. 74, 113 (1982).

13. R. DESIMONE and R. S. DRAGO. J. Am. Chem. Soc. 92, 2343 (1970).

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