Electrochemical Kinetics of Cyanometalate Complexes in Aqueous Solution at High Pressures

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".