Electrochemical Kinetics of Cyanometalate Complexes in Aqueous Solution at High Pressures

Abstract

For the aqueous couples Os(CN)(6)(3-/4-), Mo(CN)(8)(3-/4-), and W(CN)(8)(3-/4-), volumes of reaction DeltaV(Ag/AgCl) relative to Ag/AgCl/4.0 mol L(-)(1) KCl and volumes of activation DeltaV(el)() for the electrode reactions are reported. Values of DeltaV(Ag/AgCl) are consistent with a very small increase in the metal-carbon bond length on reduction in each case, the main component of DeltaV(Ag/AgCl) (other than that of the reference electrode) being electrostrictive solvation change. For media in which the cation is 0.5 mol L(-)(1) K(+) or (for Mo) Na(+), DeltaV(el)() is strongly positive (+9.4 +/- 0.7, +7.3 +/- 0.7, and +10.8 +/- 0.4 cm(3) mol(-)(1) for Os(CN)(6)(3-/4-), Mo(CN)(8)(3-/4-), and W(CN)(8)(3-/4-), respectively, at 25 degrees C), whereas the theoretical expectation for a mechanism involving only the cyanometalate anions is -3 +/- 1 cm(3) mol(-1). For Mo(CN)(8)(3-/4-) in Et(4)NCl, however, DeltaV(el)() is -4.2 +/- 0.2 cm(3) mol(-)(1). In all cases, DeltaV(el)() is just one-half of the corresponding parameter DeltaV(ex)() for the homogeneous (bimolecular) self-exchange reaction of the same couple, giving strong confirmation of the "fifty-percent rule" (Fu, Y.; Swaddle, T. W. J. Am. Chem. Soc. 1997, 119, 7137). These and related results are interpreted in terms of a mechanism for both electrode and homogeneous electron-transfer reactions of cyanometalates in which the counterion mediates the electron-transfer process. For alkali metal cations, partial deaquation to permit this mediation results in positive DeltaV(el)() values, whereas for tetraalkylammonium counterions, there are no aqua ligands to be removed and DeltaV(el)() is "normal".

Volumes of activation for electrode processes of various charge-types in nonaqueous solvents

“…Furthermore, for aqueous systems, DV el ‡ is found (1)(2)(3)(4)(5) to be one-half of DV ex ‡ : [1] DV el ‡ = (0.50 ± 0.02)DV ex ‡ which is consistent with the corresponding relationship proposed theoretically by Marcus (6) for the free energies of activation [2] DG el ‡ = DG ex ‡ /2…”

“…in aqueous solution at 25°C, the volumes of activation DV ex ‡ and DV el ‡ (DV ‡ = -RT( ¶ ln k/ ¶P) T , where k is the corresponding rate constant) for the homogeneous self-exchange reaction and the equivalent electrode process respectively have invariably been found to be negative (1)(2)(3)(4)(5). Furthermore, for aqueous systems, DV el ‡ is found (1)(2)(3)(4)(5) to be one-half of DV ex ‡ : [1] DV el ‡ = (0.50 ± 0.02)DV ex ‡ which is consistent with the corresponding relationship proposed theoretically by Marcus (6) for the free energies of activation [2] DG el ‡ = DG ex ‡ /2…”

“…As an "exception that proves the rule," DV ex ‡ and DV el ‡ for electron transfer in water can be positive where the reaction is not of the simple, bimolecular, outer-sphere type -for example, the self-exchange pathway for anionic cyanometalate couples that is mediated by alkali-metal cations (7,8) -but even in such cases eq. [1] still holds with remarkable accuracy.…”

“…[1] as such seems not to apply to nonaqueous systems. On the other hand, DV el ‡ for the nonaqueous systems does correlate loosely with the volume of activation DV diff ‡ for diffusion of the reactants in the particular solvent, and DV diff ‡ can be identified, through the Stokes-Einstein relation [3] D = k B T/6 p h r eff (in which D is the diffusion coefficient of a solute molecule of effective radius r eff in a solvent of viscosity h), with the volume of activation DV visc ‡ for viscous flow of the solvent. The implication is that the electrode reactions in nonaqueous media are either diffusion-controlled (which is highly unlikely, as the rates are generally too low and dependent on the particular system) or controlled by solvent dynamics (solvent "friction").…”

Application of High Pressure in the Elucidation of Inorganic and Bioinorganic Reaction Mechanisms

“…On the basis of other measurements and estimates of outer-sphere metal complex preassociations, the small value of the former parameter was not unexpected. 288,289 In a procedure leading to construction of a volume profile, an estimate of þ 30 cm 3 /mol was made for the reaction volume. This total arose from contributions of þ 5, þ 12, and þ 13 cm 3 /mol from the cyt c II/III couple, from the electrostrictive change from the charge change on the Cu center, and from the loss of a water molecule, respectively.…”