In this section we consider how quantitative and qualitative information may be extracted from a voltammogram.

**Quantitative and Qualitative Aspects of
Voltammetry**

Earlier we described
a voltammogram as the electrochemical equivalent of a spec-
trum in spectroscopy. In this section we consider how quantitative and qualitative
information may be extracted from a voltammogram. Quantitative information is
obtained by relating current to the concentration of analyte in the bulk solution.
Qualitative information is obtained from the voltammogram by extracting the standard-state potential for the redox
reaction. For simplicity we only consider voltammograms similar
to that shown
in Figure 11.33a.

Let’s assume
that the redox
reaction at the working
electrode is

O+
*ne*– < = = = =
> R** ……………11.34**

and that initially only O is present in the bulk solution. The current is determined
by the rate at which O diffuses
through the fixed diffusion layer (see Figure 11.32),
and is given by equation
11.33, or

*i *=
*K*_{O}([O]_{bulk} – [O]_{x}_{=0})**
……………11.35**

where *K*_{O} is a constant
equal to *nFAD*_{O}/
δ. When the limiting current
is reached, the concentration of O at the electrode surface is zero,
and this equation simplifies to

*i*_{lim} = *K*_{O}[O]_{bulk}**
……………11.36**_{}

Thus, the limiting
current, *i*_{lim}, is a linear function
of the concentration of O in bulk solution, and a quantitative analysis is possible
using any of the standardization methods. Equations similar
to equation 11.35
can be devel- oped for other forms of voltammetry, in which peak currents are related to the ana- lyte’s concentration in bulk solution.

To extract the standard-state potential, or formal
potential, for reaction
11.34 from a voltammogram, it is necessary to rewrite the Nernst equation

11.37

in terms of current instead of the concentration of O and R.
Substituting equation 11.36 into equation
11.35 and rearranging gives

11.38

To derive a similar equation for the concentration of R at the electrode surface we note that

Since the concentration of R in bulk solution is zero, this equation
simplifies to

*i *= *K*_{R}[R]_{x}_{=0}

11.38

where *E*_{1/2} is the half-wave potential (Figure 11.34).
If *K*_{O} is approximately equal to *K*_{R}, which is often
the case, then the half-wave potential is equal
to the standard-state potential. Note that equation
11.41 is only valid if the redox reaction is electrochemically
reversible. Voltammetric techniques giv-
ing peak potentials also can
be used to determine a redox reaction’s standard- state potential.

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