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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.

1

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.