Page 94 - Academic Press Encyclopedia of Physical Science and Technology 3rd Analytical Chemistry

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Encyclopedia of Physical Science and Technology EN005M-206 June 15, 2001 20:25

172 Electrochemistry

FIGURE 2 Potential-time profile that is used for polarography and linear-sweep voltammetry (solid line) and cyclic
voltammetry (both solid and dashed lines).

This then can be substituted into Eq. (50) to give a calcu- rial produced by the electrolysis reaction, these quantities
lated diffusion current for the dropping mercury electrode, can be directly related to the concentration of the species
at the electrode surface. For a generic reduction process
b
2/3 1/6
1/2
(i t ) calc = 462nC D m t . (53)
[Eq. (45)], the potential of the electrode is given by the
Actually, experimental results indicate that the constant Nernst equation
√
in Eq. (53) is too small by a factor of 7/3, due to the
growth of the mercury drop into the solution away from RT C ox(0,t)
◦
E = E + ln . (56)
the capillary orifice. Thus, the correct diffusion current nF C red(0,t)
expression for a dropping mercury electrode is
Initially, the solution contains only ox (concentration,
b
t
i = 706nC D 1/2 m 2/3 1/6 , (54) b
C ). When a potenital is applied and reductive current
ox
which gives the current at any time up to the lifetime of the flows, the oxidized form of the electroactive species dif-
drop. If the drop time, t d , is substituted, the well-known fuses toward the electrode. From Eq. (63) it follows that
Ilkovic equation results,
b 1/2 2/3 1/6
i = 706n C ox − C ox(0,t) D ox m t d
2/3 1/6
b
i d = 706nC D 1/2 m t d , (55)
t
= i d − 706nC ox(0,t) D 1/2 m 2/3 1/6 . (57)
−3
ox
2 −1
d
b
where i d is in A if D is in cm s , C is in mol cm , m
−1
in mg s , and t is in s. Alternatively, i d is in µA when Hence,
b
C is in mM.
The polarographic current-potential wave that is illus- i d − i
C ox(0,t) = . (58)
1/2
trated by Fig. 3 conforms to the Nernst equation for re- 706nD ox m 2/3 1/6
t
versible electrochemical processes. However, it is more
convenient to express the concentrations at the electrode Afterreductionofox,itsreducedform(red )diffuseseither
surface in terms of the current, i, and diffusion current, into the bulk of solution or into the mercury to form an
i d . Because i d is directly proportional to the concentra- amalgam. In either case,
tion of the electroactive species in the bulk and i at any
b 1/2 2/3 1/6
point on the curve is proportional to the amount of mate- i = 706n C red(0,t) − C D m t . (59)
red red d