Page 57 - Analytical Electrochemistry 2d Ed - Jospeh Wang

42 STUDY OF ELECTRODE REACTIONS

mechanisms and kinetics. Such experiments are particularly useful when the reactant
and product have suf®ciently different spectra.
Consider, for example, the general redox process:

O ‡ ne „ R 2-16†

When the potential of the OTE is stepped to a value such that reaction (2-16)
proceeds at a diffusion-controlled rate, the time-dependent absorbance of R is given
by

t
2C e D 1=2 1=2
O R
O
A ˆ 2-17†
p 1=2
where e is the molar absorptivity of R and D and C are the diffusion coef®cient
R
O
O
and concentration of O, respectively. Hence, A increases linearly with the square root
of time (t 1=2 ), re¯ecting the continuous generation of R at a rate determined by the
diffusion of O to the surface. Equation (2-17) is valid when the generated species is
stable. However, when R is a short-lived species (i.e., in an EC mechanism), the
absorbance response will be smaller than that expected from equation (2-17). The
rate constant for its decomposition reaction can thus be calculated from the decrease
in the absorbance. Many other reaction mechanisms can be studied in a similar
fashion from the deviation of the A±t curve from the shape predicted by equation
(2-17). Such a potential-step experiment is known as chronoabsorptometry.
Thin-layer spectroelectrochemistry can be extremely useful for measuring the
formal redox potential (E ) and n values. This is accomplished by spectrally

determining the concentration ratio of oxidized to reduced ([O]=[R]) species at
each applied potential (from the absorbance ratio at the appropriate wavelengths).
Since bulk electrolysis is achieved within a few seconds (under thin-layer condi-
tions), the whole solution rapidly reaches an equilibrium with each applied potential
(in accordance to the Nernst equation). For example, Figure 2-11 shows spectra for
the complex [Tc(dmpe) 2 Br 2 ] ‡ in dimethylformamide using a series of potentials
[dmpe is 1,2-bis(dimethylphosphine)ethane]. The logarithm of the resulting concen-
tration ratio ([O]=[R]) can be plotted against the applied potential to yield a straight
line, with an intercept corresponding to the formal potential. The slope of this
Nernstian plot (0.059= n V) can be used to determine the value of n.
Besides potential-step experiments, it is possible to employ linear potential scan
perturbations of an OTE (27). This voltabsorptometric approach results in an optical
analogue of a voltammetric experiment. A dA=dE vs. E plot (obtained by differ-
entiating the absorbance of the reaction product with respect to the changing
potential) is morphologically identical to the voltammetric response for the redox
process (Figure 2-12). Depending upon the molar absorptivity of the monitored
species, the derivative optical response may afford a more sensitive tool than the
voltammetric one. This concept is also not prone to charging-current background
contributions and holds considerable promise for mechanism diagnosis and kinetic
characterization of coupled chemical reactions.