POTENTIOMETRY
Prof. K. A. S. Pathiratne
Department of Chemistry
University of Kelaniya
1
Basic Setup
A). An electrochemical cell of the type below must
be constructed
Potentiometer or
a digital
voltmeter
Reference
electrode
Indicator
electrode
Analyte solution (electrolyte)
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POTENTIOMETRY
Key Components:
Reference electrode
 Indicator electrode (e.g. pH electrode, F- electrode,
etc.)
 Solution containing analyte
 Potentiometer to measure e.m.f. of the cell
 Oxidizable / reducible species as analyte
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B). Note:
1. Analyte is in the electrolytic solution
2. One of the two electrodes used must be a reference
electrode
eg. Ag(s) / AgCl(s) / KCl(aq)
Hg(l) / Hg2Cl2(s) / KCl(aq)
3. The other electrode should be an indicator electrode
C). e.m.f. of the cell, i.e. cell potential when no current flow
must be measured.
A potentiometer or a digital voltmeter with a high
internal resistance must be used.
Requirement: Cell current should be zero
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The cell notation
Reference electrode /salt bridge / analyte solution / indicator electrode
E ref
E LJ
E ind
Potentiometer or a digital voltmeter
Salt bridge
Ag
Indicator electrode
AgCl
Analyte solution
(electrolyte)
Sat. KCl solution
E cell = E ind – E ref + E LJ
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 E cell value is measured
 E ref value is known.
 Experimental conditions are arranged in such a
way to reduce the value of ELJ .Therefore Eind value
can be obtained. It contains the information on the
concentration of the analyte.
Note: By convection reference electrode is taken to be
the anode.
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Reference electrode
• The potential of the electrode does not depend on the
concentration of analyte. It is a constant.
• An ideal reference electrode has a potential which is,
1. Accurately known
2. Constant
3. Completely insensitive to the content in the analyte
solution
• Also,
1. Electrode must be rugged
2. Easy to assemble
3. maintain a constant potential while passing a small
current.
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EXAMPLE FOR REFERENCE ELECTRODES
1). Standard hydrogen electrode in principle can be used.
But troublesome.
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2). Calomel Electrode (CE) or Saturated Calomel Electrode
(SCE)
3). Silver / Silver Chloride electrode
Either lab made or commercial ones are used.
(a) Saturated Calomel electrode
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2Hg (l) + 2Cl-
Hg2Cl2 (s) + 2e
1
E
SCE
= E0 + RT ln [Hg2Cl2(s)]
; Nernst equation for the
2F [Hg(l)]2 [Cl-(aq)]2 above equilibrium
1
E SCE = E0 - RT ln [Cl-(aq)]
F
 Depends only on [Cl- ].
 Use 1 M or Saturated KCl. Therefore its potential
remains constant.
E SCE = + 0.244 V at 25 0C.
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(b) Silver / Silver Chloride electrode
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AgCl(s) + e
E = E0 AgCl/Cl- + RT ln
F
Ag(s) + Cl-(aq)
[AgCl]
[Ag] [Cl-]
E Ag = E0 + RT ln 1
F
[Cl-]
 Therefore its potential too remains constant as long as
KCl (Ci-) concentration remains constant.
Note : E0AgCl /Ag = + 0.222 V
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E0 AgCl/Ag = + 0.199 V at 25 oC for saturated KCl (~4.6 M)
Note; These two electrodes can be fabricated in the
laboratory
 A salt bridge to avoid mixing of the electrolyte in the
reference electrode with those in the analyte solution.
 In a U tube, a salt bridge can be prepared.
 5 g of agar, a heteropolysaccharide dissolved by heating in
100 ml water containing 35 g of KCl. Allow to cool to room
temperature. You will get a gel in the tube.
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Double junction reference electrode
 Like in a salt bridge, if two junctions are incorporated the
value of ELJ is reduced.
 It is a varying quantity which introduces an error.
Ag wire
Outer tube containing
KCl solution or if Clmust not be there, use
KNO3
AgCl, KCl
AgCl precipitate
Junction 1
Junction 2
 Two junctions nearly cancels the ELJ
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• With a salt bridge or double junction reference electrode,
ELJ reduces to few milli volts.
• It gives a fundamental limit to the accuracy of the
potentiometric measurement.
Indicator Electrode
 Ideally it must respond to changes in concentration of an
analyte or group of analytes rapidly and reproducibly.
 No indicator electrode is absolutely specific and behave as
above.
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Metallic electrodes
Indicator Electrode
Membrane electrodes
Metal Electrodes
•
•
•
•
Metal electrodes of the 1st kind
Metal electrodes of the 2nd kind
Metal electrodes of the 3rd kind
Redox electrodes
Membrane Electrodes
• Ion selective electrodes (ISE)
• Molecular selective electrodes (MSE)
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Metal electrodes of the 1st kind
• A pure metal is in direct equilibrium with its own cation in
a solution
Mn+(aq) + ne
M(s)
M(s)
This is an oxidation / reduction
equilibrium
Mn+ (aq)
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Nernst equation:
E = E0 Mn+/ M + RT log
nF
a Mn+
aM
Note: Activity must be used in the Nernst expression
a = γI C
a = activity
γI = activity coefficient
C = concentration
 γI varies with the ionic strength of the medium
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• Usually potential is expressed as a p function.
E ind = Eo - RT pM
nF
Where, pM = - log10 aMn+
E ind
Intercept = EoMn+/ M (Standard electrode potential)
Slope = - RT = - 0.059
n
nF
pM
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• Electrodes of the first kind are not widely used due
to several reasons.
1). They respond not only to their own cations, but also to
other ions. e.g. Cu electrode can respond to Ag(I)
2). Zn, Cd can be used only in neutral or basic solutions.
In acidic medium, the metal dissolves.
3). Other metals also oxidized. Therefore, limited only to
deaerated solutions.
4). Certain harder metals (eg. Fe, Cr, Co, Ni), do not
provide reproducible potentials
5). E vs. pM do not give theoretically expected slope of
– 0.059
n
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Usable first kind electrodes
• Ag+ / Ag
• Hg22+ / Hg
In neutral solutions
• Cu2+ / Cu
• Bi3+ / Bi
•
•
•
•
Zn2+ / Zn
Tl+ / Tl
Cd2+ / Cd
Pb2+ / Pb
In deaerated solutions
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Electrodes of the second kind
• Metals not only respond to its own cations, but also to
anions which form stable, but sparingly soluble salts with
the metal ion:
eg. Ag+ forms sparingly soluble AgCl
Pb2+ forms sparingly soluble PbSO4
Hg forms sparingly soluble EDTA – Hg
complex
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e.g.
AgCl(s) + e
Ag(s) + Cl-(aq) ;
EoAgCl = 0.222 V
Eind = EoAgCl - 0.059 log aCl-
EoAgCl + 0.059 pClEind
Slope = 0.059
1
Intercept = EoAgCl
pCl-
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Electrodes of the third kind
• A metal can respond to the concentration of another metal
ion in which it is in contact
• This electrodes are rarely used
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Redox electrodes
• An inert metallic conductor,
eg. Pt, Au, Pb or Carbon
• Respond to the potential of redox system
eg. Ce(IV) and Ce(III)
E = EoCe4+/Ce3+ + RT log a Ce 4+
a Ce 3+
F
• Good for redox titrations.
Its potential depends on the ratio of the concentrations
of ion at 2 oxidation states.
• Useful for redox titrations of transition metals
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Membrane Electrodes
• Also called p-ion electrodes
• Fundamentally different from metal electrodes both in
design and in principle.
• Two types of membrane electrodes:
• Ion selective electrodes (ISE)
• Molecular selective electrodes (MSE)
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Several types of ISE
• Glass membranes for H+ and several monovalent cations
• Solid state electrodes based on inorganic salt crystals
• Liquid based electrodes (A hydrophilic polymer membrane
saturated with hydrophobic ion exchanger)
• ……………………………………………………………
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Basic components of an ion selective electrode
(III). Internal
reference
electrode
(II). Internal standard solution
(I). Ion sensitive membrane
I. A membrane sensitive only to the ion of interest
II. Standard solution kept inside of the membrane ( internal standard)
III. A reference electrode dipped in the internal standard solution
( internal reference electrode)
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e.g. for ISE : pH electrode
DVM
Internal reference
electrode- Ag wire
Internal std
solution [1 M HCl]
AgCl coating
H+ sensitive glass
membrane
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Schematic representation
reference electrode 2
External soln
SCE // [H3O+]= a1 / Glass / [H3O+]= a2 , [Cl-] = 1.0 M, AgCl (sat’d) / Ag
membrane
reference
Internal reference solution
electrode 1
Glass electrode
 Glass membrane : specific to H+ up to pH ~9
 Corning 015 glass
22% Na2O
6% CaO
Excellent specificity to H+ up to a pH limit
72% SiO2
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• A potential develops across the membrane, due to an
ion exchange process.
E glass = L - 0.059 pH
L – combination of three constants (Not standard electrode potential)
Note : Contribution to L is different from those obtained
for metal electrodes.
i.e.
Junction potentials, potential of external reference,
potential in internal reference and boundary potential
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ERRORS
1. Alkaline error
In basic solutions:
• glass electrode respond to alkali metal ions (Na+) in
addition to H+
observed pH < actual pH
• Occur above ~ pH 9
2. Acid error
observed pH > actual pH
• pH < ~ 0.5
• Reasons are not well understood
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Glass electrodes for other cations
• Na+, Li+, K+, Cs+, Rb+, Ag+, NH4+ have been developed.
3. Dehydration may cause erratic behavior
4. Variation in junction potential
A fundamental source of uncertainty that for which a
correction can not be applied, which results due to
differences in concentration of standards and samples.
5. Errors in the pH of standard buffer.
Any error in the preparation or any change in the
composition or during storage of buffers can cause error
e.g. Action of bacteria on organic buffer
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6. Errors in low ionic strength solutions
e.g. Lake or stream water
Non reproducible junction potential due to partial
clogging of fitted plug between salt bridge and analyte
solution.
Electrodes with FFJ (Free Flow Junction) are used for
these types of application
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Response of Ion Selective Electrode
nx n
y
E = const ± β RT log [ax + Σy kX,y ay
nx F
]
Where:
β ~ 1
ax = activity of the ion to be determined
ay = activity of any interfering ion
kxy = selectivity coefficient
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Kxy =
Response of electrode to any interfering ion y
Response of electrode to the interested ion x
nx, ny = charges of the ions, x and y respectively
• k Na+,H+ ≈ 1/36 for pH electrode
Refer the other methods of measuring k x,y ; David Harvey
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Solid State Electrodes
• Based on inorganic salt crystals (mostly for anions)
e.g. F- electrode
• A crystal of LaF3 doped with EuF2 is used here.
• Single crystal – e.g. LaF3
• Poly crystalline - e.g. Ag2S, etc.
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Ag wire
Ag/AgCl electrode
AgCl coating
0.1 M NaF + 0.1 M NaCl
Crystalline membrane
E = L – β (0.05916) log aF- - (out side)
β ≈1
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Mechanism of operation
 F- actually move from one side of the membrane to the
other side by occupying vacant sites present in EuF2 sites.
 A charge separation and a potential difference
therefore is created
Range : 10-6 M
 KF-, other
1M
≈ 103
 At high pH ~ 8, response to OH- is high (error)
 At low pH ~ 4, H+ + F Usable pH range is pH ~4
HF
~8
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• For other examples : Refer Daniel C. Harris, pg. 401
Cl-, Br-, I- , SCN-, CN- , S2Crystals of AgCl, AgBr, AgI, Ag2S for Cl-, Br-, I- and
S2- respectively
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Liquid Based ISE
 For polyvalent cations (e.g. Ca2+) and certain anions
(e.g. NO3-)
e.g. For Ca2+ ion , the above electrode can be used.
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 Ca 2+ ions outside the membrane form chelate with liquid
ion exchanger and moves across in to the inner tube
establishing a potential
Comparison of a liquid membrane calcium electrode with a
glass electrode
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 Liquid ion exchanger, an example is (Ca2+) Ca dialkyl
phosphate is dissolved in an immiscible organic liquid.
E.g. BF4-, NO3-, K+
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Compound electrodes or gas sensing electrodes
Essential features (usual) :
1) Reference electrode (internal)
Cell
2) Specific ion electrode (internal)
Note: If an acidic or basic gas to be determined, a
pH electrode can be used as a specific electrode
3). Electrolyte solution (internal)
4). Gas permeable membrane
This represent a complete cell. Therefore it is
called A PROBE rather than an electrode
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A gas sensing probe (Schematic representation)
 The thickness of the membrane ~ 1µm
 Pore size ~ 1µm
 Must permit diffusion of gases through the membrane
 Selectivity is obtained with the type of membrane
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CO2 Sensing Probe
 Consists of an ordinary pH electrode. i. e. Specific ion
electrode is a pH electrode
External reference
electrode
0.1 M KCl with weak
bicarbonate buffer
Spaces
0.1 M HCl
Ag
AgCl
Membrane
 Membrane is made out of polyethylene, rubber or teflon
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 CO2 diffuses through membrane into the weak buffered KCl
 This lowers the pH of the KCl solution
 Note: Ion specificity is obtained using the membrane
with different pore sizes
Other molecules (gases) determined :
SO2, NO2, H+, H2S, HCN, NH3, HN3, O2
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Instrument used for measurement of all
potentials
• Resistance of a membrane ~ 108 ohm
• Internal resistance of a meter should be1000 times larger
than the cell resistance.
• Error ~ 0.1%
• Digital voltmeters with 1011
1012 Ω are commercially
available
• Therefore in place of potentiometers, these digital voltmeters
are used.
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Potentiometric Methods
• Direct potentiometry
Reference electrode - ANODE
Indicator electrode - CATHODE
E cell = E ind – E ref + E LJ
For cations:
Eind = L - 0.0592 px
n
L = standard formal electrode potential for metal electrode
L = some of several constants for membrane electrodes
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For cations : Ecell = K - 0.0592 px
n
Ecell
K
Slope = - 0.0592
n
px
• Increase in px decreases meter reading
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For anions : Ecell = K + 0.0592 pA
n
Ecell
Slope = 0.0592
n
K, intercept
pA
• Increase in pA increases meter reading
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• Electrode Calibration Method
Ecell = K ± 0.0592 pA
n
 ‘K’ can not be computed from theory
 ‘K’ can be determined by measuring Ecell with several
different known concentrations of analyte.
Assumption: K does not vary from standard to standard
and to analyte. i.e. It is the same for ANALYTE and
STANDARDS.
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An inherent error in electrode calibration
• In reality, K is not the same for standards and analyte.
(because of the composition differences)
e.g. 1. Junction potential varies due to variation in ionic
strengths between solutions.
2. Activity also varies due to variation in activity coefficients
with solution composition.
Note : This error can not be avoided
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Activity and Concentration
 Electrode response is related to activity and not to
concentration.
 We are interested in knowing concentration.
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Variation of electrode potential with activity and
concentration
E vs. Activity
E vs. concentration
E
p (activity / concentration)
 Concentration can be converted to activity if activity
coefficients are known. They are rarely known as ionic
strength varies from solution to solution.
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 Activity coefficient decreases with increasing concentration
 Therefore deviation increases with concentration
 For singly charged ions, activity coefficients are less affected
with changes in concentration.
 To overcome,
1. Use the potential vs. concentration calibration curve
(Called Empirical Calibration Curve ). The ionic strength of
the standards and the analyte must be the same. However,
this matching is difficult.
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2. When analyte concentration is not large, add a
measured excess of an inert electrolyte to both standards
and samples. This makes ionic strength of standards and
samples nearly the same. The effects due to sample matrix
is negligible under these conditions.
A buffer known as TISAB (Total Ionic Strength Adjusting
Buffer) to control the ionic strength of the samples and the
standards is used to achieve this purpose.
Essentials
 Electrodes responds to activity
 If the ionic strength is held constant,
Activity α Concentration
 Therefore, a plot of E vs. concentration - LINEAR
Can be used for analytical purposes.
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Note : Electrode responses to the activity of uncomplexed
ions. Therefore, ligands must be masked or absent.
 When matrix is complex or its composition is not known,
use Standard Addition Method.
 Standard addition is best if addition increases analyte
concentration by 1.5 to 3 times.
 Results are more accurate if average of several results are
taken.
58
Note : Three Approaches are used
1). When matrices of unknown and standards are the same,
Use E vs. log concentration curve
2). When composition of the matrix is not known,
a). Use TISAB
or
b). Use standard addition technique
3). For standard addition to be correct, excess of inert
electrolyte must be added to analyte to avoid changes in
ionic strength due to addition of standard.
4). Assume ELJ remain same after standard addition.
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• Q: A cell consisting of a SCE and a Pb ISE gave a
potential of – 0. 4706 V when immersed in 50 ml
solution. A 5.00 ml addition of 0.02 M Pb2+ solution
changed the potential to – 0.449 V.
Calculate the molar concentration of Pb2+ in the sample.
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