1. 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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2. Electrodes and Potentiometry
Potential change only dependent on one ½ cell concentrations
Reference electrode is fixed or saturated  doesn’t change!
Ecell=Ecathod-Eanod
Anod is conventionally reference electode
Fe3+ +e- Fe2+
AgCl(s) + e- → Ag + Cl-
Reference electrode, [Cl-] is constant
Potential of the cell
only depends on [Fe2+] & [Fe3+]
Unknown solution of
[Fe2+] & [Fe3+]
Pt wire is indicator electrode whose potential responds to [Fe2+]/[Fe3+]
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3. 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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4. Electrodes and Potentiometry
Reference Electrodes
1.) Silver-Silver Chloride Reference Electrode
Eo = V
Activity of Cl- not 1E(sat,KCl) = V
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5. Electrodes and Potentiometry
Reference Electrodes
2.) Saturated Calomel Reference Electrode (S.C.E)
Saturated KCl maintains constant [Cl-] even with
some evaporation
Eo = V
Activity of Cl- not 1E(sat,KCl) = V
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6. 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

7. 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
i. Involves single reaction
ii. Detection of catione derived from the metal used in the electrode
iii. Example: use of copper electrode to detect Cu2+ in solution
½ reaction: Cu2+ + 2e-  Cu (s)
Eind gives direct measure of Cu2+:
Eind = EoCu – (0.0592/2) log aCu(s)/aCu2+
since aCu(s) = 1:
Eind = EoCu – (0.0592/2) log 1/aCu2+
or using pCu = -log aCu2+:
Eind = EoCu – (0.0592/2) pCu
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8. 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-  Ag(s) + Cl- EO = V
Eind gives direct measure of Cl-:
Eind = Eo – (0.0592/1) log aAg(s) aCl-/aAgCl(s)
since aAg(s) and aAgCl(s)= 1
& Eo = V:
Eind = – (0.0592/1) log aCl-
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9. 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+ + e-  Ce3+
Eind responds to Ce4+:
Eind = Eo – (0.0592/1) log aCe3+/aCe4+
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10. 2) Membrane Indicator Electrodes a) General
i. electrodes based on determination of cations or anions
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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11. 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
C+ diffuses across the membrane due to concentration gradient resulting in charge difference across membrane
Potential across outer membrane depends on [C+] in analyte solution
A difference in the concentration of C+ exists across the outer membrane.
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Remember an electric potential is generated by a separation of charge

12. 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 the membrane due to concentration gradient resulting in charge difference across membrane
A difference in the concentration of C+ exists across the inner membrane.
Potential across inner membrane depends on [C+] in filling solution, which is a known constant
Electrode potential is determined by the potential difference between the inner and outer membranes:
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

13. 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:
where [C+] is actually the activity of the analyte and n is the charge of the analyte
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14. Combined electrod 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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15. 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

16. -log aH+ (on exterior of probe or
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
in analyte solution)
constant
Selective binding of cation (H+) to glass membrane
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17. Cations (Na+) bind oxygen in SiO4 structure
Electrodes and Potentiometry
pH Electrodes
Glass Membrane
Irregular structure of silicate lattice
Cations (Na+) bind oxygen in SiO4 structure
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18. Electrodes and Potentiometry
pH Electrodes
Glass Membrane
Two surfaces of glass “swell” as they absorb water
Surfaces are in contact with [H+]
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19. 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
Potential is determined by external [H+]
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Constant and b are measured when electrode is calibrated with solution of known pH

20. develops due to the preferential adsorption of H+ onto the glass
iii. pH is determined by formation of boundary potential across glass membrane
At each membrane-solvent interface, a small local potential
develops due to the preferential adsorption of H+ onto the glass
surface.
Glass Surface
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21. 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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22. ‚ H+ not only cation that can bind to glass surface
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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23. ‚ Errors at low pH (Acid error) can give readings that are too high
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+
ii. Used to make ISE’s for Na+, Li+, NH4+
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24. SCE||CrO42- (xM), Ag2CrO4 (sat’d)|Ag
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
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25. 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 electrode.
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26. There are three distinct regions in the titration of iron(II) with standard cerium(IV), monitored potentiometrically with Pt and calomel electrodes.
Before the equivalence point, where the potential at Pt is dominated by the analyte redox pair.
At the equivalence point, where the potential at the indicator electrode is the average of their conditional potential.
After the equivalence point, where the potential was determined by the titratant redox pair.
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27. At the equivalence point: needs both redox pairs to calculate (why?)
Before the equivalence point: using analyte’s concentration to calculate E+
At the equivalence point: needs both redox pairs to calculate (why?)
E of the cell
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28. 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, both half-reactions are used simultaneously to find the voltage.
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29. Titration curve.xlsx
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