Page 92 - 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

170 Electrochemistry

where the activity coefficient can be determined by the at the half-equivalence point; the half-reaction potential,
Debye-Huckel equation. assuming activities are equal to concentrations, is given
Another important application is the use of potentio- directly by the potential of the indicator electrode relative
metric measurements for the evaluation of thermodynamic to the reference electrode. If the latter is a standard hydro-
◦
equilibrium constants. In particular, the dissociation con- gen electrode, the measured potential is equal to the E for
III
II
3+
stants for weak acids and weak bases in a variety of sol- the Fe (OH 2 ) /Fe (OH 2 ) 2+ couple. The evaluation of
6 6
◦
vents are evaluated conveniently with a pH electrode mea- the E for a half reaction provides a direct measure of the
suring system. The most precise approach is to perform free energy for the half reaction relative to the free energy
an acid-base titration such that the titration curve can be for the reduction of hydronium ion to hydrogen gas. Like-
◦
recorded.Obviously,onecouldmeasurethepHofaknown wise, a combination of any pair of E values or of the free
concentration of a weak acid and obtain a value of its energy values permits the evaluation of the equilibrium
hydronium-ion activity which would permit a direct eval- constant and the standard free energy for a redox reaction.
uation of its dissociation constant. However, this would From a practical standpoint it is often useful to have the
be a one-point evaluation and subject to greater errors observed potential in the medium of measurement for the
than by titrating the acid halfway to the equivalence point. condition of equal concentrations of the oxidized and re-
The latter approach uses a well-buffered region where the duced species of a half reaction. Such potentials are known
pH measurement represents the average of a large num- as formal potentials, E , rather than standard potentials
◦
ber of data points. Similar arguments can be made for the and are not purely thermodynamic quantities. The term
evaluation of solubility products and stability constants of “formal potential” comes from the tradition of having the
complex ions. supporting electrolyte at a one formal concentration. How-
In the use of potentiometry for the evaluation of stability ever, other stated solution conditions also are included in
constants for complex ions, the expressions can become many listings. Thus, the indicated potential is what one
extremely complicated if multi-equilibria are present. For would expect at the half-equivalence point under actual
a simple one-to-one complex, a direct potentiometric titra- titration conditions. In other words, activity corrections
tion curve again provides the most satisfactory route to an have not been made.
accurate evaluation of the constant. The curve looks sim-
ilar to that for an acid-base titration, and the appropriate III. CONTROLLED-POTENTIAL
pointtopickisthehalf-equivalencepoint.Ifthecomplexis ELECTROLYSIS AND VOLTAMMETRY
extremely stable, then the amount of free metal ion at this
point on the titration curve (ligand titrated with metal ion)
For chemists, the second important application of elec-
is sufficiently low that it can be disregarded. Assuming it
trochemistry (beyond potentimetry) is the measurement
is a stable complex, at the first half-equivalence point the
of species-specific [e.g., iron(III) and iron(II)] concentra-
concentration of complexed metal ion will be equivalent to
tions. This is accomplished by an experiment whereby the
that of the free ligand. The potential will give a direct mea-
electrolysis current for a specific species is independent of
sure of the free metal ion and allow the stability constant
applied potential (within narrow limits) and controlled by
for the complex to be evaluated at the half-equivalence
mass transfer across a concentration gradient, such that
point, e.g.,
it is directly proportional to concentration (i = kC). Al-
I
[Ag (en) ] though the contemporary methodology of choice is cyclic
+
. (44)
K f = I
+
Ag (OH 2 ) [en] voltammetry, the foundation for all voltammetric tech-
2
niques is polarography (discovered in 1922 by Professor
Potentiometry also is a direct means to evaluate the
Jaroslov Heyrovsky; awarded the Nobel Prize for Chem-
standard potential for half reactions (E ) and has been ap-
◦
istry in 1959). Hence, a historical approach is used with
plied for appropriate reversible systems. Such measure-
a recognition that cyclic voltammetry will be the primary
ments require corrections for activity coefficients or ex-
methodology for most chemists.
trapolation of the data to infinite dilution. Again, direct
measurements in which equal molar concentrations of the
oxidized or reduced species are introduced into the sys- A. Principles and Fundamental Relations
tem provide a simple approach to such evaluations and
1. Diffusion to a Planar Electrode
are as precise as those obtained by less direct methods.
However, E values also can be extracted from poten- The basic approach in controlled-potential methods of
◦
tiometric titration data. For example, in the titration of electrochemistry is to control in some manner the poten-
II
III
IV
Fe (OH 2 ) 2+ ion with Ce (OH 2 ) 4+ ion, the Fe (OH 2 ) 3+ tial of the working electrode while measuring the resultant
6 n 6
II
ion concentration equals the Fe (OH 2 ) 2+ concentration current, usually as a function of time. When a potential
6