Page 80 - Analytical Electrochemistry 2d Ed - Jospeh Wang

3-2 POLAROGRAPHY 65

where K d is the formation constant. The stoichiometric number can thus be
† vs. In [L]. It is possible to exploit
computed from the slope of a plot of E 1=2 c
equation (3-8) to improve the resolution between two neighboring polarographic
waves, based on a careful choice of the ligand and its concentration.
For reversible systems (with fast electron-transfer kinetics), the shape of the
polarographic wave can be described by the Heyrovsky±Ilkovic equation:

RT i i
d
E ˆ E 1=2 ‡ ln 3-9†
nF i
It follows from equation (3-9) that a plot of E vs. log‰ i i†=iŠ should yield a
d
straight line with a slope of 0.059=n at 25 C. Such a plot offers a convenient method

for the determination of n. In addition, the intercept of this line will be the half-wave
potential. Another way to estimate n is to measure E 3=4 E 1=4 †, which corresponds
to 56.4=n mV for a reversible system. E 3=4 and E 1=4 are the potentials for which
i ˆ 0:75i and i ˆ 0:25i , respectively.) It should be emphasized that many polaro-
d
d
graphic processes, especially those of organic compounds, are not reversible. For
those that depart from reversibility, the wave is ``drawn out,'' with the current not
rising steeply, as is shown in Figure 3-2. The shape of the polarographic response for
an irreversible reduction process is given by

1=2
RT i i t
d
E ˆ E ‡ ln 1:35k f 3-10†
anF i D
where a is the transfer coef®cient and k is the rate constant of the forward reaction.
f
In a few instances, the polarographic wave is accompanied by a large peak (where
the current rises to a maximum before returning to the expected diffusion current
plateau). Such an undesired peak, known as the polarographic maximum, is
attributed to a hydrodynamic ¯ow of the solution around the expanding mercury
drop, and can be suppressed by adding a small amount of a surface-active material
(such as Triton X-100).
When the sample solution contains more than one reducible species, diffusion
currents resulting from each of them are observed. The heights of the successive
waves can be used to measure the individual analytes, provided there is a reasonable
difference (>0.2 V) between the half-wave potentials. The baseline for measuring
the limiting current of the second species is obtained by extrapolation of the limiting
current of the ®rst process. With a potential window of about 2 V, ®ve to seven
individual polarographic waves might be observed. Solution parameters, such as the
pH or concentration of complexing agents, can be manipulated to deliberately shift
the peak potential and hence improve the resolution of two successive waves.
Successive waves are observed also for samples containing a single analyte that
undergoes reduction in two or more steps (e.g., 1,4-benzodiazepine or tetracycline).
The background (residual) current that ¯ows in the absence of the electroactive
species of interest is composed of contributions due to double-layer charging process
and redox reactions of impurities, as well as of the solvent, electrolyte, or electrode.