Potentiometric Methods
A.) Introduction:
1.) Potentiometric Methods: based on measurements of the potential of electrochemical
cells in the absence of appreciable currents (I →0)
2.) Basic Components:
a) reference electrode: gives reference for potential measurement
b) indicator electrode: where species of interest is measured
c) potential measuring device
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Electrodes and Potentiometry
Potential change only dependent on one ½ cell concentrations
Reference electrode is fixed or saturated  doesn’t change!


Ecell=Ecathod-Eanod
E cathod  E cathod –
0.059
oxi
Log
n
red
Anod is conventionally reference electode
E anod  E anod –
0.059
oxi
Log
n
red


 [ Fe 2  ]  
0.05916
   0.222  0.05916 log[ Cl  ]
E cell  0.771 
log 
 [ Fe 3  ]  
1



Fe3+ +e- Fe2+
AgClReference
Ag + Cl(s) + e →
electrode,
Potential of the cell
only depends on [Fe2+]
& [Fe3+]
[Cl-] is constant
Unknown solution of
[Fe2+] & [Fe3+]
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Pt wire is indicator
electrode whose
potential responds
to [Fe2+]/[Fe3+] 2
B.) Reference Electrodes: (Instead of SHE)
Need one electrode of system to act as a reference against which potential
measurements can be made  relative comparison.

Standard hydrogen electrodes are cumbersome
-
Requires H2 gas and freshly prepared Pt surface
Desired Characteristics:
a) known or fixed potential
b) constant response
c) insensitive to composition of solution under study
d) obeys Nernest Equation
e) reversible
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Electrodes and Potentiometry
Reference Electrodes
1.) Silver-Silver Chloride Reference Electrode
Eo = +0.222 V
Activity of Cl- not 1E(sat,KCl) = +0.197 V
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Electrodes and Potentiometry
Reference Electrodes
2.) Saturated Calomel Reference Electrode (S.C.E)
Eo = +0.268 V
Activity of Cl- not 1E(sat,KCl) = +0.241 V

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Saturated KCl maintains constant [Cl-] even with
some evaporation
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Electrodes and Potentiometry
Indicator Electrodes
1.) three Broad Classes of Indicator Electrodes

1) Metal Electrodes
-

Develop an electric potential in response to a redox reaction at the metal surface
2) Ion-selective (Membrane) Electrodes
-
Selectively bind one type of ion to a membrane to generate an electric potential
3) Molecular Selective Electrode
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Remember an electric potential is generated by a separation of charge
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1) Metallic Indicator Electrode (3 Main Types)
a) Metallic Electrodes of the First Kind
b) Metallic Electrodes of the Second Kind
c) Metallic Redox Indicators
a) Metallic Electrodes of the First Kind
i. Involves single reaction
catione
ii. Detection of
derived from the metal used in the electrode
iii. Example: use of copper electrode to detect Cu2+ in solution
½ reaction: Cu2+ + 2eEind gives direct measure of Cu2+:
since aCu(s) = 1:
or using pCu = -log aCu2+:
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
Cu (s)
Eind = EoCu – (0.0592/2) log aCu(s)/aCu2+
Eind = EoCu – (0.0592/2) log 1/aCu2+
Eind = EoCu – (0.0592/2) pCu
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b) Metallic Electrodes of the Second Kind
i. Detection of
anion
derived from the interaction with metal ion
(Mn+)
from the electrode
ii. Anion forms precipitate or stable complex with metal ion (Mn+)
iii. Example: Detection of Cl- with Ag electrode
½ reaction: AgCl(s) + e- 
Eind gives direct measure of Cl-:
Ag(s) + Cl- EO = 0.222 V
Eind = Eo – (0.0592/1) log aAg(s) aCl-/aAgCl(s)
since aAg(s) and aAgCl(s)= 1
& Eo = 0.222 V:
Eind = 0.222 – (0.0592/1) log aCl-
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c) Metallic Redox Indicators
i. Electrodes made from inert metals (Pt, Au, Pd)
ii. Used to detect oxidation/reduction in solution
iii. Electrode acts as e- source/sink
iv. Example: Detection of Ce3+ with Pt electrode
½ reaction: Ce4+ + eEind responds to Ce4+:
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
Ce3+
Eind = Eo – (0.0592/1) log aCe3+/aCe4+
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2) Membrane Indicator Electrodes
a) General
cations anions
i. electrodes based on determination of
or
by the selective adsorption of these ions to a membrane surface.
ii. Often called Ion Selective Electrodes (ISE) or pIon Electrodes
iii. Desired properties of ISE’s
1) minimal solubility – membrane will not dissolve in solution during measurement.
– silica, polymers, low solubility inorganic compounds , (AgX) can be used
2) Need some electrical conductivity
3) Selectively binds ion of interest
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Electrodes and Potentiometry
Indicator Electrodes
Ion-Selective Electrodes

Responds Selectively to one ion
-

Contains a thin membrane
capable of only binding the
desired ion
Does not involve a redox process
Membrane contains a ligand (L) that
specifically and tightly binds analyte of
interest (C+)
The counter-ions (R-,A-) can’t cross the
membrane and/or have low solubility in
membrane or analyte solution
+ exists
C+ diffuses
across
the
dueof
to
A
difference
themembrane
concentration
Potential
across
outerinmembrane
depends
onC[C+]
concentration
gradient
resulting in charge difference
across
the
outer membrane.
in analyte
solution
across membrane
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Remember an electric potential is generated by a separation of charge
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Electrodes and Potentiometry
Indicator Electrodes
Ion-Selective Electrodes

Responds Selectively to one ion
-

Contains a thin membrane
capable of only binding the
desired ion
Does not involve a redox process
C+ diffuses
across
dueoftoC+ exists
A difference
in the
the membrane
concentration
Potential concentration
across inner membrane
depends
[C+] difference
in
resulting in on
charge
across thegradient
inner membrane.
filling solution,
is a known constant
acrosswhich
membrane
Electrode potential is determined by the potential
difference between the inner and outer membranes:
E  E outer  E inner
where Einner is a constant and Eouter depends on the
concentration of C+ in analyte solution
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Remember an electric potential is generated by a separation of charge
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Electrodes and Potentiometry
Indicator Electrodes
Ion-Selective Electrodes

Responds Selectively to one ion
-

Contains a thin membrane
capable of only binding the
desired ion
Does not involve a redox process
Electrode Potential is defined as:
0.05916
E  constant 
log[C  ]
n
where [C+] is actually the activity of the analyte and n is
the charge of the analyte
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pH Electrode
i. most common example of an ISE
based on use of glass membrane that preferentially binds H+
ii. Typical pH electrode system is shown
pH sensing element is glass tip of Ag/AgCl electrode
Two reference electrodes here
one SCE outside of membrane
one Ag/AgCl inside membrane
Combined electrod
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Electrodes and Potentiometry
pH Electrodes
1.) pH Measurement with a Glass Electrode
Ag(s)|AgCl(s)|Cl-(aq)||H+(aq,outside) H+(aq,inside),Cl-(aq)|AgCl(s)|Ag(s)
Outer reference
electrode
[H+] outside
(analyte solution)
[H+] inside
Inner reference
electrode
Glass membrane
Selectively binds H+
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Electric potential is generated by
[H+]
difference across glass membrane
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iii. pH is determined by formation of boundary potential across glass membrane
Boundary potential difference (Eb) = E1 - E2 where from Nernst Equation:
Eb = c – 0.592pH
-log aH+ (on exterior of probe or
constant
in analyte solution)
Selective binding of cation (H+) to glass membrane
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Electrodes and Potentiometry
pH Electrodes
Glass Membrane

Irregular structure of silicate lattice
Cations (Na+) bind oxygen
in SiO4 structure
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Electrodes and Potentiometry
pH Electrodes
Glass Membrane

Two surfaces of glass “swell” as they absorb water
-
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Surfaces are in contact with [H+]
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Electrodes and Potentiometry
pH Electrodes
Glass Membrane

H+ diffuse into glass membrane and replace Na+ in hydrated gel region
-
Ion-exchange equilibrium
Selective for H+ because H+ is only ion that binds significantly to the
hydrated gel layer
Charge is slowly carried by
migration of Na+ across
glass membrane
E  constant   (0.05916) pH
Potential is determined by
external [H+]
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Constant and b are measured when electrode is calibrated with solution of known pH
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iii. pH is determined by formation of boundary potential across glass membrane
Si
O-
Glass Surface
At each membrane-solvent interface, a small local potential
develops due to the preferential adsorption of H+ onto the glass
surface.
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Electrodes and Potentiometry
Junction Potential
1.) Occurs Whenever Dissimilar Electrolyte Solutions are in Contact



Develops at solution interface (salt bridge)
Small potential (few millivolts)
Junction potential puts a fundamental limitation on the accuracy of direct
potentiometric measurements
-
Don’t know contribution to the measured voltage
Different ion mobility results in
separation in charge
Again, an electric potential is generated by a separation of charge
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iv. Alkali Error
 H+ not only cation that can bind to glass surface
- H+ generally has the strongest binding
 Get weak binding of Na+, K+, etc
 Most significant when [H+] or aH+ is low (high pH)
- usually pH $11-12
At low aH+ (high pH), amount of Na+ or
K+ binding is significant  increases
the “apparent” amount of bound H+
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v. Acid Error
 Errors at low pH (Acid error) can give readings that are too high
 Exact cause not known
- usually occurs at pH # 0.5
c) Glass Electrodes for Other Cations
i. change composition of glass membrane
 putting Al2O3 or B2O3 in glass
 enhances binding for ions other than H+
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ii. Used to make ISE’s for Na+, Li+, NH4+
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Example 18: The following cell was used for the determination of pCrO4:
SCE||CrO42- (xM), Ag2CrO4 (sat’d)|Ag
Calculate pCrO4 if the cell potential is -0.386.
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16-1 The shape of a redox titration
curve
• A redox titration is based on an oxidation-reduction
reaction between analyte and titrant.
• Consider the titration of iron(II)
with standard cerium(IV),
monitored potentiometrically
with Pt and calomel electrodes.
The potentials show above is in 1 M HClO4
solution. Note that equilibria 16-2 and 16-3
are both established at the Pt http:\\asadipour.kmu.ac.ir
electrode.
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•
There are three distinct regions
in the titration of iron(II) with
standard cerium(IV), monitored
potentiometrically with Pt and
calomel electrodes.
1.
Before the equivalence point,
where the potential at Pt is
dominated by the analyte redox
pair.
2. At the equivalence point, where the
potential at the indicator electrode
is the average of their conditional
potential.
3. After the equivalence point, where
the potential was determined by the
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Before the equivalence point: using analyte’s concentration to calculate E+
At the equivalence point: needs both redox pairs to calculate (why?)
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E of the
cell
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After the equivalence point:
There are two special points during the above titration process: (1)
when V = ½ Ve, [Fe3+] = [Fe2+] and E+ = E°(Fe3+ | Fe2+) ; (2) when V =
2 Ve, [Ce4+] = [Ce3+] and E+ = E°(Ce4+ | Ce3+) = 1.70 V.
•
Summary
The greater the difference in reduction potential between analyze and
titrant, the sharper will be the end point.
•
The voltage at any point in this titration depends only on the ratio of
reactants; it will be independent of dilution.
•
Prior to the equivalence point, the half-reaction involving analyze is used to
find the voltage because the concentrations of both the oxidized and the
reduced forms of analyte are known.
•
After the equivalence point, the half-reaction involving titrant is employed. At
the equivalence point, bothhttp:\\asadipour.kmu.ac.ir
half-reactions are used simultaneously to find 28
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the voltage.
• Titration curve.xlsx
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