Page 77 - Analytical Electrochemistry 2d Ed - Jospeh Wang

62 CONTROLLED-POTENTIAL TECHNIQUES

potential step. Such a charge measurement procedure, known as chronocoulometry,
is particularly useful for measuring the quantity of adsorbed reactants (because of the
ability to separate the charges produced by the adsorbed and solution species). A
plot of the charge (Q) vs. t 1=2 yields an intercept at t ˆ 0 that corresponds to the sum
of the charge due to the reaction of the adsorbed species and the double-layer
charging. The former can be estimated by subtracting the intercept obtained in an
identical experiment carried out in the blank solution.

3-2 POLAROGRAPHY

Polarography is a subclass of voltammetry in which the working electrode is the
dropping mercury electrode (DME). Because of the special properties of this
electrode, particularly its renewable surface and wide cathodic potential range (see
Section 4-5 for details), polarography has been widely used for the determination of
many important reducible species. This classical technique was invented by J.
Heyrovsky in Czechoslovakia in 1922, and had an enormous impact on the progress
of electroanalysis (through many subsequent developments). Accordingly, Heyr-
ovsky was awarded the 1959 Nobel Prize in Chemistry.
The excitation signal used in conventional (DC) polarography is a linearly
increasing potential ramp. For a reduction, the initial potential is selected so that
the reaction of interest does not take place. The potential is then scanned
cathodically while the current is measured. The current is proportional to the
slope of the concentration±distance pro®le (see Section 1-2.1.2). At a suf®ciently
negative potential, reduction of the analyte commences, the concentration gradient
increases, and the current rises rapidly to its limiting (diffusion-controlled) value. At
this plateau, any analyte particle that arrives at the electrode surface instantaneously
undergoes an electron-transfer reaction, and the maximum rate of diffusion is
achieved. The resulting polarographic wave is shown in Figure 3-2. The current
oscillations re¯ect the growth and fall of the individual drops.
To derive the expression for the current response, one must account for the
variation of the drop area with time:

2=3

3mt
A ˆ 4p ˆ 0:85 mt† 2=3 3-2†
4pd
where t is the time and m and d are the mass ¯ow rate and density of mercury,
respectively. By substituting the surface area (from equation 3-2) into the Cottrell
equation (equation 3-1), and replacing D by 7=3D (to account for the compression of
the diffusion layer by the expanding drop), we obtain the Ilkovic equation for the
limiting diffusion current (1):
t
i ˆ 708nD 1=2 m 2=3 1=6 C 3-3†
d
1
1
2
Here, i will have units of amperes (A) when D is in cm s , m is in g s , t is in
d
3
seconds and C is in mol cm . This expression represents the current at the end of