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332 Modern Analytical Chemistry
formal potential
The potential of a redox reaction for a point, the potential is easiest to calculate using the Nernst equation for the titrant’s
specific set of solution conditions, such
as pH and ionic composition.
The number of redox titrimetric methods increased in the mid-1800s with the
2–
2–
–
introduction of MnO 4 , Cr 2 O 7 and I 2 as oxidizing titrants, and Fe 2+ and S 2 O 3 as
reducing titrants. Even with the availability of these new titrants, however, the rou-
tine application of redox titrimetry to a wide range of samples was limited by the
lack of suitable indicators. Titrants whose oxidized and reduced forms differ signifi-
cantly in color could be used as their own indicator. For example, the intensely pur-
–
2+
ple MnO 4 ion serves as its own indicator since its reduced form, Mn , is almost
colorless. The utility of other titrants, however, required a visual indicator that
could be added to the solution. The first such indicator was diphenylamine, which
was introduced in the 1920s. Other redox indicators soon followed, increasing the
applicability of redox titrimetry.
9D.1 Redox Titration Curves
To evaluate a redox titration we must know the shape of its titration curve. In an
acid–base titration or a complexation titration, a titration curve shows the change
+
in concentration of H 3 O (as pH) or M n+ (as pM) as a function of the volume of
titrant. For a redox titration, it is convenient to monitor electrochemical potential.
You will recall from Chapter 6 that the Nernst equation relates the electro-
chemical potential to the concentrations of reactants and products participating in a
redox reaction. Consider, for example, a titration in which the analyte in a reduced
state, A red , is titrated with a titrant in an oxidized state, T ox . The titration reaction is
A red + T ox t T red + A ox
The electrochemical potential for the reaction is the difference between the reduc-
tion potentials for the reduction and oxidation half-reactions; thus,
E rxn = E Tox/Tred – E Aox/Ared
After each addition of titrant, the reaction between the analyte and titrant reaches a
state of equilibrium. The reaction’s electrochemical potential, E rxn , therefore, is
zero, and
E Tox/Tred = E Aox /Ared
Consequently, the potential for either half-reaction may be used to monitor the
titration’s progress.
Before the equivalence point the titration mixture consists of appreciable quan-
tities of both the oxidized and reduced forms of the analyte, but very little unreacted
titrant. The potential, therefore, is best calculated using the Nernst equation for the
analyte’s half-reaction
RT [ A red ]
°
E A ox / = EAA red - ln
A red ox
nF [ A ox ]
is the standard-state potential for the analyte’s half-reaction,
Although E˚ Aox /Ared
a matrix-dependent formal potential is used in its place. After the equivalence
half-reaction, since significant quantities of its oxidized and reduced forms are
present.
RT [ T red ]
= ° – – ln
E T ox / E T T red
T red ox
nF [ T ox ]