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Chapter 21
Potentiometry
Definition
Potentiometric methods are based upon measurements of the potential of electrochemical cells in the absence of appreciable currents.
an equilibrium measurement
the Nernst equation is applicable.
Instrumental Configuration
All equipment is simple: an indicator electrode, a reference electrode and a potential measuring device.
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Reference electrode |salt bridge | analyte solution | indicator electrode
Eref Ej Eind
( ) ( ~ )cell ind ref j jE E E E E mV
Applications of Potentiometry
Billions of these measurements are made annually. Importance in environmental and medical applications.
For example,
pH, Conductivity, ion selective electrodes (Cl-, Ca2+,HCN, SO2, NH3), blood gas analysis (O2, CO2).
Reference Electrodes
Purpose: provide stable potential against which other potentials can be reliably measured
Criteria:stable (time, temperature)
reproducible (you, me)
potential shouldn’t be altered by passage of small current
easily constructed
convenient for use
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SHE (NHE)Pt, H2 (1.0 atm)|H+ (aH+ = 1.00 M)
Advantages
International standard E0 0 V at ALL temperature.
One of most reproducible potentials, ±1 mV
Disadvantages
InconveniencePt black easily
poisoned by organics, sulfide, cyanide, etc.
Hydrogen explosive
Sulfuric and hydrochloric strong acids
Practical Reference Electrodes(Secondary Ref. Electrodes)
Aqueous
SCE (Saturated Calomel Electrode)
Ag/AgCl (KCl, x M) Ferrocene methanol--
Fc-CH2OH—water soluble,
added directly to the analyte solution.
Non-aqueous
Ag/Ag+ (x M AgNO3) Pseudo (Quasi)
referencesPt, Ag wires
Ferrocene—Internal standard potential ref.
added directly to the analyte solution.
Saturated Calomel Electrodes (SCE)
Hg(l)|Hg2Cl2|KCl(Sat’d)||
E0 = 0.241 V vs. SHE @ 25°C
Disadvantages
Hg toxic
solubility of KCl temperature dependent dE/dT= -0.67 mV/K (must quote temperature)
Advantages
Most polarographic data ref’d to SCE
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Calomel Electrodes
-Hg Cl /Cl2 2
--2 2 Hg Cl /Cl2 2
-2 2
- 02 2
02Hg Cl /Cl
-
Hg Cl /Cl
Hg Cl (s) + 2e = 2Hg(l) + 2Cl = 0.268 V vs SHE
1ln 0.268 0.0592lg
2 ( )
, . (Satured KCl, [Cl ]~4.5 M)
ClCl
Cl
E
RTE E a
F a
a E
Electrode Acronym Potential vs. SHE
Hg(l)/Hg2Cl2(s)/KCl (0.1 M) 0.3356 Hg/Hg2Cl2(s)/KCl (1 M) NCE 0.2801
Hg(l)/Hg2Cl2(s)/KCl (sat'd) SCE 0.2444 Hg(l)/Hg2Cl2(s)/ NaCl (sat'd) SSCE 0.2360
(298K)
Ag/AgCl
Ag wire coated with AgCl(s), immersed in NaCl or KCl solution
E0 = 0.222 V vs. SHE @ 25°C
Disadvantages
solubility of KCl/NaCl temperature dependent dE/dT = -0.73 mV/K (must quote temperature)
Advantages
chemical processing industry has standardized on this electrode
convenient
rugged/durable
Sat’dAgCl/KCl
-
0/
0
/
AgCl + e = Ag + Cl
10.0592lg
0.0592lg
, .
Ag AgCl
Cl
Cl
Ag AgClCl
E Ea
E a
a E
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Precautions in Useof Ref. Electrodes
Level of liquid inside reference electrode above analyte level to minimize possible contamination;
Place the electrode into the electrolyte solution when not use;
Replace the inside electrolyte solution and/or vycor (the tip) if necessary;
Use a second salt bridge (double electrolyte) to avoid reactions between the analyte and the first electrolyte.e.g., SCE|ClO4
-: K+ + ClO4- KClO4 (s)
Solution : SCE|NaNO3| ClO4-
Reference Electrodewith two salt bridges
SCE Electrode/KCl
NaNO3
Vycor
Hg/Hg2Cl2/KCl
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Liquid Junction Potentials
Differences in ion mobility give rise to junction potentials.Unequal distribution.
Solution: salt bridge containing a high concentration of KCl or NaNO3
Indicator Electrodes
Electrode used with reference electrode to measure potential of unknown solution.
For a good indicator electrode (working electrode)
potential proportional to the analyte ion activity;
specific (one ion) or selective (several ions).
Y( )cell indicator refE E E f a
Two General Types of Indicator Electrodes
Metallic Indicator Electrodes; the electrode normally consists of a metal, and the electrode potential is directly correlated to the concentration (activity) of the analyte.Membrane Indicator Electrodes [Ion
Selective Electrodes (ISE)]. a key component of the electrode is a membrane (cystalline or non-cystalline membrane)
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Classification of Metallic Indicator Electrodes
Four Classes:Electrodes of the First Kind
Electrodes of the Second Kind
Metallic redox indicators
Electrode of the First Kind
Metal in contact with its cations or non-metal (via a noble metal) in contact with its anions
EXAMPLES:Cu/Cu2+
Zn/Zn2+
SHE (Pt, H2|H+)
Pt, Cl2(g)/Cl-
Ag /Ag+ (nonaqueous reference electrode)
Electrode response given by Nernst equation (Nernstian):
n+
n+
n+
0
M
0
M
0
M + ne = M (s)
ln
0.0592lg ( 298 )
0.0592 = pM
RTE E a
nF
E E a at Kn
En
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Potential response for an electrode of the first kind
NOTE: Not all metals can form the electrode of the first kind. e.g., Fe, Al, and W electrodes are NOT electrodes of the First Kindthese have relatively thick surface oxide coatings
• In general, electrodes of the first kind:(a) simple; (b) not very selective; (c) some metals easily oxidized (deaerated solutions); (d) some metals (Zn, Cd) dissolve in acidic solutions
Electrode of the Second Kind
Metal in contact with sparingly soluble salt of the metal
Common name: anion electrodes
EXAMPLES:Ag/AgCl(s)
Hg/Hg2Cl2(s)/Cl- (saturated calomel electrode; SCE)
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Electrode of the Second Kind
Electrode response given by:
E = E0 +(0.0592/n) pX
NOTES: anion activity determines potential
make great reference electrodes because of low solubility of salt (potential very stable)
Potential response for an electrode of the second kind
Metallic Redox Indicator Electrodes
Electrodes that merely serve as sources or sinks for electrons
Common names: redox, inert, unattackable
EXAMPLES:
Pt, Au, GC (Glassy Carbon)
Response:For Pt in contact with Fe2+, Fe3+ in solution:
E = E0 + 0.0592lg ([Fe3+]/[Fe2+])
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Membrane (or Ion Selective) Electrodes
Properties of Membrane:
• Low solubility - solids, semi-solids and polymers
• Some electrical conductivity - often by doping
• Selectivity - part of membrane binds/reacts with analyte
Two general types - Crystalline and Non-crystalline membranes
Crystalline membranesSingle crystal - LaF3 for F-
Polycrystalline or mixed crystal – Ag2S for S2- and Ag+
Non-crystalline membranesGlass - silicate glasses for H+, Na+
Liquid - liquid ion exchanger for Ca2+
Immobilized liquid - liquid/PVC matrix for Ca2+ and NO3
-
How does a pH probe work?
https://www.youtube.com/watch?v=P1wRXTl2L3I
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Glass Membrane Electrode
•Contains Two ref. electrodes.•Internal Ag/AgCl electrode is part of glass membrane electrode.•The thin glass membrane is pH sensitive, NOT the Ag/AgCl
“2 in 1” glass pH electrode
Glass Membrane StructureSiO4
4- framework with charge balancing cations- SiO2 72 %, Na2O 22 %, CaO 6 %
Cross-section view of a silicate glass structure. In addition to the 3 Si-O bonds shown, each Si is bonded to an additional O atom, either above or below the plane of the paper.
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In aqueous solutions, ion exchange reactions occur at surface
• H+ carries current near surface• Na+ carries current in interior• Ca2+ carries no current (immobile)
+ + _ + + _H + Na Glass Na + H Glass
soln glass soln glass
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+++++++
_______ +
++++++
_______
Boundary PotentialEb = E1 + E2
glass b internal refFor glass electrode: = + E E E
Boundary Potential
This image cannot currently be displayed.
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1
' '1 2
1 2 1 21 2
'2
2 1 '
'2
2 1 2'
1
2
(sign "-" indicates the opposite current direction v
[ ( 0.0592lg )] ( 0.0592lg )
[ 0.059 0.0
s cell
592l2lg )]
[ 0.0592lg )] 0.0592lg )
cur
g
rent)
b
b
a
a aE E E j j
a a
aE j j
a
aj j a
a
a
1
1
0.0592lg
-0.0592pH
a
K
The pH Meter Potential
internal ref
internal ref
internal ref
cell glass electrode external ref
external ref
external ref
exter
ce
nal ref
ll
1
1
-0.0592pH
= -
( )-
[( ]-
( -
)+
+ 0.0592pH
= 0.0592pH
)
b
E
E K
E E
E E E
E E
EK E
K
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Alkaline Error/Acid Error
At high pH, glass electrode indicates pH less than true value (negative error)
Low pH high [H+] glass electrode indicates pH higher than true value (positive error) (Reason unclear)
- + -
- + -
H (soln) + Glass H -Glass (membrane)
Na (soln) + Glass Na -Glass (membrane)
Most accurate region: pH 0.5 10
Acid Error (pH < 0.5), positive
Alkaline Error
+
Selectivity Coefficients
1 , 1
,
1
' 0.0592lg( )
Where is the
for the electrode
is the activity of the alk
(For all membrane Electrodes
ali metal
)b H B
H B selectivity coefficie
E K a k b
k
b
nt
Range between 0 (no interference) to 1 (as sensitive to alkali and hydrogen ions) to >1 (large interference)
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Precaution in use of pH electrode/meter
Place the new/dry electrode into a distilled water for ~24 h before use.
Always keep the electrode in distilled water after use.
Fill electrolyte solution for external ref. if necessary.
Use suitable buffer solutions (2 buffers, fresh) to calibrate the electrode/meter first.
Avoid using the electrode in strong basic/acid solution (pH 0.5-10,12)
Errors in low ionic strength solutions (e.g., lake sample)
Operational Definition of pH
cell
ss s
cell
s uu
u
s
s
u s s
s
- pH =
0.0592In a standard buffer
- pH = 0.0592pH +
0.0592In a unknown solution
- (0.0592pH + )pH
0.0592 0.0592
= - 0.0592pH
( )pH pH pH
0.0592 0u s
u
E K
E E
K E
K EK E
K
E E
E E E
.0592
Glass Electrodes for Other Cations
Maximize kH,B for other ions by modifying glass surface (usually adding Al2O3 or B2O3)
Possible to make glass membrane electrodes for Na+, K+, NH4
+, Cs+, Rb+, Li+, Ag+ ...
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Crystalline Membrane Electrode
Usually ionic compoundSingle crystalCrushed powder, melted
and formedSometimes doped (Li+) to
increase conductivityOperation similar to glass
membrane
Fluoride ISE Electrode
-
3
+
cell F
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Lanthanum Fluoride (LaF ) single crystal membrane
LaF (s) LaF (
= - 0.0592lg + 0.0592pF
s) + F (Double layer formed)
E K a K
Response down to 1 M F-
Liquid Polymer/Membrane Electrode
Replace the solid state crystal with a liquid ion-exchanger filled membrane
Ions impart a charge across the membrane
The membrane is designed to be SELECTIVE for the ion of interest……
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Universal Equation of Membrane Electrode
2
2+
+
Example: Ca mem
0.0592lg M
0.0592 pM
M
brane el
M
0.0592 0.0592lg Ca Ca
ectro
p
d
2
e
2
ncell
n
n
n
cell
E Kn
Kn
cation with n electrons invloved
anion with n electrons invloved
E K K
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Molecular Selective Electrodes
The electrochemical signal (potential) is related to certain types of molecules
(1) Gas-sensing probese.g., CO2, NH3, NO2
(2) Biocatalytic membrane electrodesImmobilized enzyme bound to gas permeable membrane
e.g., Urea
CO2 Gas-sensing Electrode
Work by the permeation of gas across a selective membrane
The gas changes the pH inside the electrode (on the inside of the membrane) and this signal is proportional to the gas concentration.
pCO2 electrode
mV
Externalreferenceelectrode
CO2(g)
Flow Cell
Electrodeassembly
Gas-permeablemembrane
(silicone rubber)
NaHCO3/H2O
CO2 + H2O HCO3- + H+
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- +3
2
+ -2 23
+
2
2
2 2
- +2 2 3
HCO H
CO
CO COH HCO
H
CO
CO
2
CO (g) CO (aq)
CO (aq) + H O HCO + H
/ '
0.0592lg
= 0.0592lg( ' )
= '' 0.059
'' 0.0
2 lg
592pCO
eq
eq
cell
cell
a aK
a
a K a a K a
E K a
K K a
K a
E K
Instruments for Measuring Cell Potential
Most cells containing membrane electrode have very high electrical resistance (>108
ohms).
The voltmeter must have an electrical resistance that is several orders of magnitude greater than the resistance of the cell being measured.
Loading error: Er = -Rs/(RM+Rs)x100%
Potentiometric Titrations
Precipitation titrations (Cl- with AgNO3).
Neutralization titrations (H+ +OH-H2O, pH change; pKa
determination-pKa=pH at half-titration point).
Complex-formation titrations.
Redox titrations.
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Why is the Potentiometric Titration SO Special?
NO indicator is needed.
Experiments can be run under much wider conditions.
End-point determination very sensitive and precise—eliminate personal errors.
Easy to operate/automation.
A wide range of applications.
Examples
21-1 page 620, Lead concentration…
21-2 page 626, activity/concentration vs.Ka
21-3,4 page 628, Kf and KHP
calculation.