This document discusses principles of potentiometry and redox titrations. It summarizes key concepts such as: 1) Potentiometric methods measure potential of electrochemical cells under zero current conditions using the Nernst equation. Reference electrodes must be stable, reversible, and reproducible. 2) Indicator electrodes include metallic electrodes and ion-selective electrodes that respond to specific ions like hydrogen, calcium, fluoride, or ammonium. Glass electrodes are commonly used for pH measurements. 3) Redox titrations involve the oxidation-reduction reaction between an analyte and titrant. Potentiometric titration curves can be used to locate the equivalence point, and redox indicators may change color at the

1. 1
CHAPTER II. POTENTIOMETRY AND REDOX TITRATIONS
I. Principles of Potentiometry
Potentiometric methods of analysis are based upon measurements of the potential
of electrochemical cells under conditions of zero current, where the Nernst equation
governs the operation of potentiometry.
O + ne → R
E = E° + (RT/nF)⋅In{(O)/(R)} where 2.303RT/F = 0.0592
FIGURE 2-1. “Skoog” Fig. 18-1 (p. 387).
This cell can be depicted as
Reference electrode⏐salt bridge⏐analyte solution⏐indicator electrode
Eref Ej Eind
Eref is independent of the concentration of analyte or any other ions in the solution.
Eind depends upon the activity of the analyte.
Ecell = Eind − Eref + Ej
The salt bridge prevents components of analyte solution from mixing with those of
reference solution. The two potentials develop across the liquid junctions at each
end of the salt bridge tend to cancel one another if mobilities of cations and anions
in the bridge solution are about the same. Net Ej is therefore usually less than a few
millivolts. This uncertainty in junction potential places a limit on accuracy of
potentiometric analysis.
II. Reference Electrodes
Requirements:
1. Stable
2. Reversible
3. Reproducible
i/. Standard Hydrogen Electrode (SHE)

2. 2
Pt
2H+
+ 2e ←⎯→ H2; E° = 0 V
ii/. Calomel Electrode
FIGURE 2-2. “Harris” Fig. 15-5 (p. 317).
Hg⎪Hg2Cl2(sat’d), KCl(x M)⎟⎜
Hg2Cl2 + 2e = 2Hg(l) + 2Cl−
; E° = +0.2682 V
E(sat’d KCl) = +0.2415 V
The potential is governed by Cl−
ion activity.
The most common type is saturated calomel electrode (SCE).
iii/. Silver/Silver Chloride Electrode
FIGURE 2-3. “Harris” Fig. 15-3 (p. 316).
Ag⎪AgCl(sat’d), KCl(x M)⎟⎜
AgCl(s) + e = Ag(s) + Cl−
; E° = +0.2223 V
E(sat’d KCl) = +0.197 V
The potential is governed by Cl−
ion activity.
III. Indicator Electrodes
(A) Metallic indicator electrodes
Metal electrodes develop an electric potential in response to a redox reaction at the
metal surface, e.g., Pt, Au, and C, they are relatively inert.
(B) Ion-Selective Electrodes (ISE)
i/. Thermodynamics of ISEs
ISEs do not involve redox processes and often have a thin membrane ideally
capable of binding only the intended ion.
FIGURE 2-4. “Harris” Fig. 15-8 (p. 383).
−RT⋅In(a1/a2) = −nFE
∆G due to activity difference ∆G due to charge imbalance

3. 3
(n = charge of ion)
⇒ E = (0.05916/n) ⋅log(a1/a2)
ii/. Glass Electrodes for pH measurements
FIGURE 2-5. “Harris” (p. 323).
FIGURE 2-6. “Harris” Fig. 15-3 (p. 316).
H+
+ Na+
Gl−
= Na+
+ H+
Gl−
soln. solid soln. solid
FIGURE 2-7. “Harris” Fig. 15-12 (p. 325).
FIGURE 2-8. “Harris” Fig. 15-13 (p. 325).
The reaction in which H+
replaces metal cations in glass is an ion-exchange
equilibrium. This equilibrium constant is so large that surfaces of hydrated glass
membrane consist of entirely silicic acid (H+
Gl−
).
Eb = E1 − E2 = 0.0592⋅log(a1/a2)
where a1 = activity of analyte solution
a2 = activity of internal solution
i.e., Eb = −0.0592⋅log(a2) − 0.0592⋅pH = constant − 0.0592⋅pH (1)
Alkaline Error: The apparent pH is lower than true pH.
Some glass membranes also respond to concentration of alkaline metal ions.
M+
+ H+
Gl−
= H+
+ M+
Gl−
soln. solid soln. solid
where M+
represents some singly charged cation, such as sodium ion.
Kex = (a1b1’)/(a1’b1)
where a1 and b1 are activities of H+
and M+
in solution, respectively
a1’ and b1’ are activities of H+
and M+
in gel surface, respectively
Kex is usually small in value except when [H+
] is low and [M+
] is high.
Selectivity Coefficients:
The effect of an alkaline metal ion on potential across a membrane can be

4. 4
accounted for by inserting an additional term in Equation (1) to give
Eb = constant + 0.0592⋅log(a1 + KH,Mb1) (2)
where KH,M = Kex is the selectivity coefficient for the electrode.
Acid Error: The apparent pH is higher than true pH.
Perhaps because glass surface is saturated with H+
in strong acid and cannot be
protonated at any more sites.
iii/. Glass Electrodes for Cations other than pH
By varying the chemical composition of glass, glass electrodes can be prepared that
are differentially responsive to other cations (primarily monovalent), e.g., Na+
, K+
,
NH4
+
, Rb+
, Cs+
, Li+
, and Ag+
.
iv/. Solid State Electrodes
FIGURE 2-9. “Harris” Fig. 15-16 (p. 331).
TABLE 2-10. “Harris” Table 15-5 (p. 332).
e.g., Fluoride electrode
Europium doped LaF3 single crystal; internal electrolyte: NaF/NaCl.
FIGURE 2-11. “Harris” Fig. 15-17 (p. 331).
E = constant − 0.0592⋅log(aF
−)
At low pH, F−
forms HF (pKa ≈ 3) and interferes; at pH > 8, OH−
interferes.
v/. Liquid-Membrane Electrodes
FIGURE 2-12. “Harris” Fig. 15-20 (p. 333).
TABLE 2-13. “Harris” Table 15-6 (p. 334).
e.g., Calcium ion-selective electrode based on a liquid ion exchanger
TABLE 2-13. “Harris” Table 15-6 (p. 334).
[(RO)2PO2]2Ca = 2(RO)2PO2
−
(dialkylphosphate) + Ca2+
E = constant + (0.0592/2)⋅log(aCa
2+)

5. 5
vi/. Gas-Sensing Probes
e.g., FIGURE 2-14. “Harris” Fig. 15-22 (p. 335).
Other acidic or basic gases, including NH3, SO2, H2S, NOx (nitrogen oxides), and
NH3, can be detected in the same manner.
IV. Redox Titrations
A redox titration is based on an oxidation-reduction reaction between analyte and
titrant.
i./. Potentiometric Titrations
A potentiometric titration involves measurement of the potential of a suitable
indicator electrode as a function of titration volume.
e.g., Titration of Fe(II) with standard Ce(IV),
FIGURE 2-15. “Harris” Fig. 16-1 (p. 349).
Titration reaction: Ce4+
(titrant) + Fe2+
(analyte) → Ce3+
+ Fe3+
K ≈ 1017
in 1 M HClO4
Reference half-reaction: 2Hg(l) + 2Cl−
= Hg2Cl2(s) + 2e
At the Pt indicator electrode, there are two reactions that come to equilibrium,
Indicator half-reaction: Fe3+
+ e = Fe2+
E° = 0.767 V (1)
Indicator half-reaction: Ce4+
+ e = Ce3+
E° = 1.70 V (2)
FIGURE 2-16. “Harris” Fig. 16-2 (p. 353).
a) Region 1: Before the Equivalent Point
Prior to equivalent point, amounts of Fe2+
and Fe3+
are both known, therefore, it is
convenient to calculate cell potential by using Reaction 1 instead of Reaction 2.
E = Ecathode − Eanode = E+ − E−
= {0.767 − 0.0592⋅log([Fe2+
]/[Fe3+
])} − 0.241
= 0.526 − 0.0592⋅log([Fe2+
]/[Fe3+
])
When volume of titrant, V = Ve/2, where Ve = amount required to reach equivalent

6. 6
point, [Fe2+
] = [Fe3+
] and E+ = E° for the Fe3+
/Fe2+
couple.
The point at which V = Ve/2 is analogous to the point at which pH = pKa when V =
Ve/2 in an acid-base titration.
b) Region 2: At the Equivalent Point
Exactly enough Ce4+
has been added to react with all the Fe2+
. Virtually all cerium
is in the form Ce3+
and virtually all iron is in the form Fe3+
. Tiny amounts of Ce4+
and Fe2+
are present at equilibrium.
i.e., [Ce3+
] = [Fe3+
] and [Ce4+
] = [Fe2+
].
At any time, Reactions 1 and 2 are both in equilibrium at the Pt electrode.
Hence, both reactions contribute to the cell potential at the equivalent point,
E+ = 0.767 − 0.0592⋅log([Fe2+
]/[Fe3+
]) (1)
E+ = 1.70 − 0.0592⋅log([Ce3+
]/[Ce4+
]) (2)
Adding Equations 1 and 2,
2E+ = 2.467 − 0.0592⋅log([Fe2+
][Ce3+
]/[Fe3+
][Ce4+
])
Because [Ce3+
] = [Fe3+
] and [Ce4+
] = [Fe2+
] at the equivalent point,
2E+ = 2.467 ⇒ E+ = 1.23 V
The cell voltage potential is
E = E+ − E(calomel) = 1.23 − 0.241 V = 0.99 V
In this particular titration, the equivalence-point potential is independent of
concentrations and volumes of reactants.
c) Region 3: After the Equivalent Point
Now both [Ce3+
] and [Ce4+
] are known, it is convenient to calculate cell potential
by using Reaction 2 instead of Reaction 1.
E = {1.70 − 0.0592⋅log([Ce3+
]/[Ce4+
])} − 0.241
= 1.46 − 0.0592⋅log([Ce3+
]/[Ce4+
])}
At the special point when V = 2Ve, [Ce3+
] = [Ce4+
] and E+ = E° for the Ce4+
/Ce3+
couple.
After the equivalence point, the cell potential levels off near 1.46 V.

7. 7
e.g., Titration of Tl+
by IO3
−
in 1.00 M HCl.
Titration reaction: IO3
−
+ 2Tl+
+ 2Cl−
+ 6H+
→ ICl2
−
+ 2Tl3+
+ 3H2O
Indicator half-reaction: IO3
−
+ 2Cl−
+ 6H+
+ 4e = ICl2
−
+ 3H2O E° = 1.24 V
Indicator half-reaction: Tl3+
+ 2e = Tl+
E° = 0.77 V
FIGURE 2-17. “Harris” Fig. 16-3 (p. 353).
When the stoichiometry of the reaction is not 1:1, the curve is not symmetric. Still,
negligible error is introduced if center of steepest portion is taken as end-point.
Less change in voltage near equivalence point as compared to last titration curve!
i.e., clearest results are achieved with strongest oxidizing and reducing agents.
ii/. Redox Indicators
A redox indicator changes color when it goes from its oxidized to its reduced state.
TABLE 2-18. “Harris” Table 16-2 (p. 355).
To predict the potential range over which the indicator color will change, write a
Nernst equation for the indicator.
In(oxidized) + ne = In(reduced)
E = E° − (0.0592/n)⋅log{[In(reduced)]/[In(oxidized)]}
The color of In(reduced) will be observed when
[In(reduced)]/[In(oxidized)] ≥ 10/1
and the color of In(oxidized) will be observed when
[In(reduced)]/[In(oxidized)] ≤ 1/10
i.e., The color change will occur over the range
E = (E° ± 0.0592/n) V
e.g., ferroin, E° = 1.147 V
FIGURE 2-19. “Harris” (p. 354).
The color change is expected to occur in the approximate range 1.088 V to 1.206 V
with respect to standard hydrogen electrode.

8. 8
The larger the difference in standard potential between titrant and analyte, the
sharper the break in titration curve at equivalent point. A redox titration is usually
feasible if the difference between analyte and titrant is ≥ 0.2 V. If the difference in
formal potentials is ≥ 0.4 V, then a redox indicator usually gives a satisfactory end
point. Otherwise, the end point should be detected potentiometrically.
iii/. Gran Plot
The Gran plot uses data from well before the equivalent point (Ve) to locate Ve.
Potentiometric data close to Ve are the least accurate because electrodes are slow to
equilibrate with species in solution when one member of a redox couple is nearly
used up.
e.g., For the oxidation of Fe2+
to Fe3+
, the potential prior to Ve is
E = [E°’ − 0.0592⋅log([Fe2+
]/[Fe3+
])] − Eref (1)
If volume of analyte is V0 and volume of titrant is V, and if the reaction goes “to
completion” with each addition of titrant, then
[Fe2+
]/[Fe3+
] = (Ve − V)/V (2)
Substituting (2) into (1) and rearranging,
V⋅10−nE/0.0592
= −(V − Ve)⋅10−n(Eref
− E°’)/0.0592
A graph of V⋅10−nE/0.0592
versus V should be a straight line whose x-intercept is Ve.
FIGURE 2-20. “Harris” Fig. 16-4 (p. 356).
iv/. Adjustment of Analyte Oxidation State
Sometimes it is necessary to adjust oxidation state of analyte before it can be
titrated. Preadjustment must be quantitative and the excess preadjustment reagent
must be removed or destroyed.
a) Preoxidation
1. Peroxydisulfate (Persulfate)
S2O8
2−
is a strong oxidant that requires Ag+
as a catalyst.
S2O8
2−
+ Ag+
→ SO4
2−
+ SO4
−
+ Ag2+

9. 9
Both SO4
−
+ Ag2+
are powerful oxidants. Excess reagent is destroyed by boiling.
boiling
S2O8
2−
+ 2H2O ⎯⎯→ 4SO4
2−
+ O2 + 4H+
The SO4
−
+ Ag2+
mixture oxidizes Mn2+
to MnO4
−
, Ce4+
to Ce3+
, Cr3+
to Cr2O7
2−
,
and VO2+
to VO2
+
.
2. Silver(II)
Silver(II) oxide (AgO) dissolves in concentrated mineral acids to give Ag2+
, with
oxidizing power similar to S2O8
2−
+ Ag+
combination. Excess Ag2+
can be
removed by boiling.
boiling
4Ag2+
+ 2H2O ⎯⎯→ 4Ag+
+ O2 + 4H+
3. Sodium Bismuthate
Solid NaBiO3 has an oxidizing strength similar to that of Ag2+
and S2O8
2−
.
Excess solid oxidant is removed by filtration.
4. Hydrogen Peroxide
H2O2 is a good oxidant in basic solution. It can transform Co2+
to Co3+
, Fe2+
to
Fe3+
, and Mn2+
to MnO2. In acidic solution it can reduce Cr2O7
2−
to Cr3+
and
MnO4
−
to Mn2+
. Excess H2O2 spontaneously disproportionates in boiling water.
boiling
2H2O2 ⎯⎯→ O2 + 2H2O
b) Prereduction
1. Stannous Chloride
SnCl2 can be used to prereduce Fe3+
to Fe2+
in hot HCl. Excess reductant is
destroyed by adding excess HgCl2.
Sn2+
+ 2HgCl2 → Sn4+
+ Hg2Cl2 + 2Cl−

10. 10
2. Chromous Chloride
CrCl2 is a powerful reductant. Excess Cr2+
is oxidized by atmospheric O2.
3. Sulfur Dioxide and Hydrogen Sulfide
SO2 and H2S are mild reducing agents that can be expelled by boiling in acidic
solution.
4. A Column Packed with a Solid Reducing Agent
Jones Reductor – contains zinc coated with zinc amalgam.
Zn2+
+ 2e = Zn(s) E° = −0.764 V
Zn is such a powerful reducing agent that the Jones reductor is not very
selective.
Walden Reductor – filled with solid Ag and 1 M HCl.
Walden reductor is more selective since reduction potential for Ag⎪AgCl
(0.222 V) is high enough that species such as Cr3+
and TiO2+
are not reduced
and therefore do not interfere in analysis of a metal such as Fe3+
.
Another selective reductor uses granular Cd metal. Passing NO3
−
through a
Cd-filled column reduces NO3
−
to NO2
−
.
iv/. Application of Standard Oxidants
TABLE 2-21. “Skoog” Table 17-3 (p.366).
a) Oxidation with Potassium Permanganate
In strongly acidic solution (pH ≤ 1),
MnO4
−
+ 8H+
+ 5e = Mn2+
+ 4H2O E° = 1.507 V
violet colorless
(permanganate) (manganous)
In neutral or alkaline solution,

11. 11
MnO4
−
+ 4H+
+ 3e = MnO2(s) + 2H2O E° = 1.692 V
brown
(manganese dioxide)
In strongly alkaline solution (2 M NaOH),
MnO4
−
+ e = MnO4
2−
E° = 0.56 V
green
(manganate)
KMnO4 usually serves as its own indicator. If the titrant is too dilute to be seen, an
indicator such as ferroin can be used.
Preparation and Standardization:
KMnO4 is not a primary standard. Aqueous KMnO4 is unstable by virtue of the
reaction
4MnO4
−
+ 2H2O = 4MnO2(s) + 3O2 + 4OH−
which is slow in the absence of MnO2, Mn2+
, heat, light, acids, and bases and
should be stored in a dark glass bottle.
KMnO4 can be standardized by titration of sodium oxalate (Na2C2O4).
2MnO4
−
+ 5H2C2O4 + 6H+
= 2Mn2+
+ 10CO2 + 8H2O
b) Oxidation with Cerium(IV)
Ce4+
+ e = Ce3+
E° = 1.44 V (in 1 M H2SO4)
Ce4+
is yellow and Ce3+
is colorless, but the color change is not distinct enough for
cerium to be its own indicator.
The oxidizing strengths of KMnO4 and Ce4+
are comparable, but Ce4+
in sulfuric
acid is very stable.
Primary-standard-grade salt of Ce(IV) is available.
c) Oxidation with Potassium Dichromate
In acidic solution,
Cr2O7
2−
+ 14H+
+ 6e = 2Cr3+
+ 7H2O E° = 1.36 V

12. 12
orange green
(dichromate) (chromic)
Cr2O7
2−
is a less powerful oxidizing agent than MnO4
−
or Ce4+
.
The orange color of Cr2O7
2−
is not intense enough to serve as its own indicator.
In basic solution, Cr2O7
2−
is converted to yellow chromate ion (CrO4
2−
), whose
oxidizing power is nil.
CrO4
2−
+ 4H2O + 3e = Cr(OH)3(s) + 5OH−
E° = −0.12 V
Primary-standard-grade salt of K2Cr2O7 is available and its solutions are stable.
d) Oxidation with Iodine
Solutions of iodine are weak oxidizing agents that are used for the determination of
strong reductants.
I2(aq) + I−
= I3
−
K = 7×102
(iodine) (iodine) (triiodide)
I3
−
+ 2e = 3I−
E° = 0.536 V
1. Iodimetry
A reducing agent is titrated directly with iodine to produce I−
.
2. Iodometry
An oxidizing analyte is added to excess I−
to produce iodine, which is then
titrated with standard thiosulfate solution.
Starch is the indicator of choice for iodine because it forms an intense blue complex
with iodine.
FIGURE 2-22. “Harris” Fig. 16-6 (p. 356).
Iodine solutions lack stability for several reasons:
1. Volatility of iodine;
2. Iodine slowly attacks most organic materials;
3. Air-oxidation of iodide ion

13. 13
4I−
+ O2(g) + 4H+
→ 2I2 + 2H2O
which is promoted by acids, heat, and light.
Preparation and Standardization:
Standard solution of I3
−
can be prepared by adding iodate (IO3
−
) to a small excess of
KI. Addition of excess strong acid (to give pH ≈ 1) produces I3
−
by quantitative
reverse disproportionation.
IO3
−
+ I−
+ 6H+
= 3I3
−
+ 3H2O
Iodine solutions can be standardized by reaction with primary standard-grade
As4O6.
As4O6(s) + 6H2O = 4H3AsO3
(arsenious oxide) (arsenious acid)
H3AsO3 + I3
−
+ H2O = H3AsO4 + 3I−
+ 2H+
Because the equilibrium constant is small, the concentration of H+
must be kept low
(e.g., by addition of sodium bicarbonate) to ensure complete reaction.
v/. Application of Standard Reductants
Standard solutions of most reducing agents tend to react with atmospheric oxygen
and are seldom used for direct titration of oxidizing analytes. Indirect methods are
used instead.
a) Reduction with Iron(II)
Solutions of Fe(II) are readily prepared from iron(II) ammonium sulfate,
Fe(NH4)2(SO4)2⋅6H2O (Mohr’s salt) or form iron(II) ethylenediamine sulfate,
FeC2H4(NH3)2(SO4)2⋅4H2O (Oespar’s salt).
Air-oxidation of Fe(II) takes place rapidly in neutral solutions but is inhibited in the
presence of acids.
b) Reduction with Thiosulfate
Thiosulfate is a moderately strong reducing agent that is the almost universal titrant

14. 14
for I3
−
.
2S2O3
2−
= S4O6
2−
+ 2e E° = 0.08 V
(thiosulfate) (tetrathionate)
In neutral or acidic solutions,
I3− + S2O3
2−
= 3I−
+ S4O6
2−
S2O3
2−
is usually standardized by reaction with a fresh solution of I3
−
prepared from
KIO3 plus KI.
Acids promotes disproportionation of S2O3
2−
,
S2O3
2−
+ H+
= HSO3
−
+ S(s)
(bisulfite)
Hence, addition of sodium carbonate maintains the pH in an optimum range for
stability of the solution.
Metal ions catalyze atmospheric oxidation of S2O3
2−
,
2Cu2+
+ S2O3
2−
→ 2Cu+
+ S4O6
2−
4Cu+
+ O2 + 4H+
→ 4Cu2+
+ 2H2O
Thiosulfate solutions should be stored in dark.
Bacteria also metabolize S2O3
2−
to sulfite and sulfate as well as elemental sulfur.