Page 97 - Academic Press Encyclopedia of Physical Science and Technology 3rd Analytical Chemistry

P1: GRB Final Pages
Encyclopedia of Physical Science and Technology EN005M-206 June 15, 2001 20:25

Electrochemistry 175

the current as well as the decay of the concentration of the in the electrode reaction be known, and the concentration
electroactive species is given by the relation of the electroactive species and the area of electrodes be
known. With these conditions satisfied, diffusion coeffi-

i t C t −DA
= = exp t , (72) cients can be evaluated rapidly over a range of tempera-
i t=0 C t=0 V x
tures and solution conditions.
where V is the volume of the solution to be electrolyzed Voltammetric methods also provide a convenient ap-
and x is the thickness of the concentration gradient. proach to establish the thermodynamic reversibility of an
Thus, the current and concentration decay exponentially. electrode reaction and for the evaluation of the electron
Under idealized conditions, 90% of the electroactive stoichiometry for the electrode reaction. As outlined in
species will be electrolyzed in approximately 20 min. In- earlier sections, the standard electrode potential, the dis-
creases in the temperature as well as in the electrode area sociation constants of weak acids and bases, solubility
relative to the solution volume will accelerate the rate of products, and the formation constants of complex ions can
electrolysis. The fundamentals of the controlled-potential be evaluated from polarographic half-wave potentials, if
bulk electrolysis are discussed in recent monographs (see the electrode process is reversible. Furthermore, studies of
Bibliography). half-wave potentials as a function of ligand concentration
provide the means to determine the formula of a metal
complex.
D. Applications of Controlled-Potential Methods
The techniques of voltage sweep and cyclic voltamme-
To date, the most extensive application of electrochemical try provide the analytical and physical chemical capabili-
methods with controlled potential has been in the area of ties of classical voltammetry and, in addition, provide the
qualitative and quantitative analysis. Because a number of means to perform these measurements much more rapidly
monographs have more than adequately reviewed the liter- for a broader range of conditions. Cyclic voltammetry is
ature and outlined the conditions for specific applications, particularly useful for the rapid assessment of thermody-
this material is not covered here. In particular, inorganic namic reversibility and for the evaluation of the stoichiom-
applications of polarography and voltammetry have been etry for the electrode reaction.
discussed in great detail in the classic treatise by Kolthoff
and Lingane.
An important specialized type of voltammetric system IV. ELECTRON-TRANSFER PROCESSES
is a self-contained cell for the determination of ·O 2 · in the
gas or solution phases. This is the so-called Clark elec- In electrochemical cells, electron transfer occurs within
trode, which consists of a platinum or gold electrode in the the electrode/solution interface, with electron removal
end of a support rod that is covered by an ·O 2 ·-permeable (oxidation) at the anode and electron introduction (reduc-
membrane (polyethylene or Teflon) such that a thin film tion) at the cathode. The current through the solution is
of electrolyte is contained between the electrode surface carried by the ions of the electrolyte, and the voltage limits
and the membrane. A concentric tube provides the support are those for electron removal from and electron insertion
+
for the membrane and the means to contain an electrolyte into the solvent/electrolyte {e.g., H 2 O/(H O aq )(ClO − );
4aq
3
I
−
solution in contact with a silver-silver chloride reference [Na (OH 2 ) ](Cl )}
+
6 aq
electrode. The Clark device has found extensive applica-
−
tion to monitor ·O 2 · partial pressure in blood, in the atmo- 2H 2 O −e H 2 O(H 2 O·) + H O
+
3
sphere, and in sewage plants. By appropriate adjustment
+[HO·](E ) pH 0 , + 2.72 V vs NHE
◦
of the applied potential, it gives a voltammetric current
plateau that is directly proportional to the ·O 2 · partial pres- (E ) pH 7 , +2.31 V (73)
◦
sure. The membrane material prevents interference from
−e −
◦
electroactive ions as well as from surface-contaminating HO − [HO·] (E ) pH 14 , +1.89 V (74)
biological materials.
−e −
In addition to the analytical applications discussed Cl − Cl· E , +2.41 V
◦
above, controlled-potential methods are used for the eval-
E ◦ , +2.24 V. (75)
uation of thermodynamic data and diffusion coefficients in MeCN
both aqueous and nonaqueous solvents. Polarographic and In the gas phase, electron removal from atoms is limited
voltammetric methods provide a convenient and straight- by their ionization potential (e.g., H·, 13.6 eV; K·, 4.3 eV;
forward means to the evaluation of the diffusion coeffi- Na·, 5.1 eV; Cu·, 7.7 and 20.3 eV; Ag, 7.6 eV; Fe, 7.9, 16.2,
cients in a variety of media. The requirements are that the and 30.7 eV). However, in the solution phase, electron
current be diffusion controlled, the number of electrons removal (oxidation) from the solvent may be facilitated