Electrochemical rate constants k
el and
volumes of activation ΔV
el
⧧ for
self-exchange at an electrode of the
aqueous couples Co(phen)3
3+/2+,
Co(en)3
3+/2+,
Fe(H2O)6
3+/2+,
Co(diamsar)3+/2+,
Co(diamsarH2)3+/2+,
Co(sep)3+/2+,
Co(ttcn)2
3+/2+,
Fe(phen)3
3+/2+,
Mo(CN)8
3-/4-, and
Fe(CN)6
3-/4- have been measured by
high-pressure AC voltammetry
over the range 0.1−200 MPa at 25 °C; the respective values of
ΔV
el
⧧ are −9.1, −8.3,
−5.5, −3.5, −3.8, −3.0, −2.8,
−1.6, +7.3, and +11 cm3 mol-1.
Although the theory of Marcus (Electrochim. Acta
1968, 13, 1005) suggests that
ln k
el should be linearly related to
1/2 ln k
ex, where
k
ex is the rate constant of the corresponding
homogeneous
(bimolecular) self-exchange reaction, ln k
el is
often sensitive to the nature of the working electrode and the
supporting
electrolyte and is only weakly correlated with ln
k
ex, with slope ≈0.1. In contrast,
ΔV
el
⧧ = (0.50 ±
0.02)ΔV
ex
⧧, in
precise agreement with an extension of Marcus' theory, regardless of
the nature of the electrode and the supporting
electrolyte. This result implies that electron transfer in these
couples occurs adiabatically on direct ion−ion and
ion−electrode contact (i.e., within the outer Helmholtz plane), and
also that ΔV
el
⧧ values are
predictable in the
manner described elsewhere (Can. J. Chem.
1996,
74, 631) for ΔV
ex
⧧.
Conversely, where ΔV
ex
⧧
cannot be measured
for technical reasons (e.g., where paramagnetism of both reactants
precludes NMR measurements of k
ex), it can
be
reliably estimated as
2ΔV
el
⧧.