Electroanalytical Chemistry
Lecture #2
An Interfacial Process
? For,O + ne- = R
? 5 separate events must occur:
– O must be successfully transported from bulk
solution (mass transport)
– O must adsorb transiently onto electrode surface
(non-faradaic)
– CT must occur between electrode and O (faradaic)
– R must desorb from electrode surface (non-
faradaic)
– R must be transported away from electrode surface
back into bulk solution (mass transport)
What is an Electrode?
? Electrical double layer
Electrode Classification
? Based on the nature and number of phases
between which electron transfer occurs
? 3 Classes:
– Electrodes of the First Kind
– Electrodes of the Second Kind
– Electrodes of the Third Kind
Electrode of the First Kind
? Metal in contact with its cations or non-
metal in contact with its anions
? EXAMPLES:
– Cu2+ /Cu(s)
– Zn2+/Zn(s)
– SHE
– Ag+/Ag (nonaqueous reference electrode)
– Cl-/Cl2(g)/Pt
Electrodes in Daniell cell
Electrode of the First Kind
(cont’d)
? Electrode response given by Nernst
equation (Nernstian):
– E = E0 + (RT/nF) ln a(M2+)
? NOTE,Fe,Al,and W electrodes are NOT
electrodes of the First Kind
– these have relatively thick surface oxide
coatings
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)
Electrode of the Second Kind
? Electrode response given by:
? E = E0 - (RT/F) ln a(Cl-)
? NOTES,
– anion activity determines potential
– make great reference electrodes because of low
solubility of salt (potential very stable)
The Calomel Reference Electrode
E lec tr od e Acr on y m Potential vs,
SHE
Hg(l) /Hg
2
Cl
2
( s)/ KCl ( 0.1 M ) 0.33 37
Hg/Hg
2
Cl
2
( s)/ KCl ( 1 M ) NCE 0.28 01
Hg(l) /Hg
2
Cl
2
( s)/ KCl ( sat'd) SCE 0.24 12
Hg(l) /Hg
2
Cl
2
( s)/ NaCl ( sat'd) SSCE 0.23 60
Note,concentrations typically high ?? concentrations small ? electrode
doesn’t become polarized ? potential constant
Electrode of the Third Kind
? Electrodes that merely serve as sources or
sinks for electrons
? Common names,redox,inert,unattackable
? EXAMPLES:
– metals,Pt,Au,GC,graphite,HOPG,Hg
– semiconductors,Si,GaAs,In-SnO2/glass
? Response:
– for Pt in contact with Fe2+,Fe3+ in solution:
– E = E0- 0.059 (V) log ([Fe2+]/[Fe3+])
Electrode of the Fourth Kind
? Electrodes that cannot be classified as 1-3
? EXAMPLES:
– Chemically modified electrodes (CME’s)
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 = not polarizable
– easily constructed
– convenient for use
SHE
Advantages
? International standard
E0 ? 0 V
? One of most
reproducible potentials
+ 1 mV
Disadvantages
? Convenience
– Pt black easily
poisoned by organics,
sulfide,cyanide,etc.
– Hydrogen explosive
– Sulfuric and
hydrochloric strong
acids
Practical Reference Electrodes
Aqueous
? SCE
? Ag/AgCl
Nonaqueous
? Ag+/Ag
? pseudoreferences
– Pt,Ag wires
? Ferrocene
SCE
? Cl-(aq)/Hg2Cl2/Hg(l)
? Hg22+ + 2e- = 2Hg(l)
? E0 = 0.24 V vs,SHE @ 250C
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 From BAS www-site,
http://www.bioana
lytical.com/
Ag/AgCl
? Ag wire coated with
AgCl(s),immersed in NaCl
or KCl solution
? Ag+ + e- = Ag(s)
? E0 = 0.22 V vs,SHE @ 250C
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
From BAS www-
site,
http://www.bioana
lytical.com/
Ag+/Ag
? Ag+ + e-= Ag(s)
? requires use of internal potential
standard
Disadvantages
? Potential depends on
– solvent
– electrolyte (LiCl,
TBAClO4,TBAPF6,
TBABF4
? Care must be taken to
minimize junction
potentials
Advantages
? Most widely used
? Easily prepared
? Works well in all
aprotic solvents:
– THF,CAN,DMSO,
DMF
From BAS www-
site,
http://www.bioana
lytical.com/
Pseudo-References
? Pt or Ag wire (inert)
? Idea:
in medium of high resistance,low
conductivity,wire will assume reasonably
steady,highly reproducible potential (+ 20
mV)
? Advantage,no solution contamination
? Limitation,must use internal potential
standard (ferrocene)
Can Aqueous References Be
Used in Nonaqueous Media?
? Yes with caution!
– May be significant junction potentials
? Requires use of internal standard
– May be greater noise
? Electrolyte may precipitate/clog electrode frit
– Don’t forget about your chemistry
? Chemistry may be water sensitive
Electrodes
? Metal
– solid
? Pt,Au,Ag,C
– liquid
? dropping mercury electrode (DME)
? Semiconductors
– Si,GaAs
– In-SnO2/glass (optically transparent)
Carbon
? Paste
– With nujol (mineral oil)
? Glassy carbon (GC)
– Amorphous
? Pyrolytic graphite - more ordered than GC
– Basal Plane
– Edge Plane (more conductive)
Electrode Materials
? Different Potential Windows
? Can affect electron transfer kinetics
Electrodes
? Size
– Analytical macro
? 1.6 - 3 mm diameter
– Micro
? 10-100 ?m diameter
From BAS www-site,
http://www.bioanalytical.com/
Electrode Geometry
Geometry is critical and affects how the data
are analyzed and interpreted
? Disk
– area,?r2
? wire (cylinder)
– area,l(2 ?r) ?r2
? Mesh
– optically transparent
? Sheet
Note,Geometric area <
effective surface area
Cleanliness IS Next to Godliness
in Electrochemistry
? Working electrode must be carefully
cleaned before each experiment
– Mechanical
? Abrasion with alumina or,diamond” polish
– Chemical
? Sonicate in Alconox
? Soak in HNO3
– Electrochemical
? Cycle in 0.5 M H2SO4 (Pt)
Electrochemical Cleaning
Taken from Table 4-7 in Sawyer,D.T.; Roberts,Jr.,J.L,Experimental
Electrochemistry for Chemists Wiley,New York,1976.
Counter Electrode
? Area must be greater
than that of working
? Usually long Pt wire
(straight or coiled) or
Pt mesh (large surface
area)
? No special care
required for counter
From BAS www-site,
http://www.bioanalytical.com/
Ew = Ecell - iRcell - Epolarization
When is iR large?
?I is high,I > 10 ?A
?large electrodes
?solvents with low conductivity
?relatively polar organic solvents
Two Common Configurations
? 2-electrode cell
– iR must be small < 1 mV
(microelectrodes)
? 3-electrode cell
– Avoids internal polarization
of reference electrode
– Compensates for major
potion of cell iR drop
From BAS www-site,
http://www.bioanalytical.com/
2-Electrode Cell
? 2-electrode cell
– Working
– Reference electrode
? Current passed between working and
reference
3-Electrode Cell
? 3-electrode cell
– Working
– Reference
– Counter/auxilliary
? Current is passed between working and
counter
? High impedance placed in front of reference
(low current) so ref,Potential constant
Potentiostat/Galvanostat
? Potentiostat
– Control potential
– Cyclic voltammetry,
chronoamperometry,
etc.
? Galvanostat
– Control current
– Potentiometry
From BAS www-site,
http://www.bioanalytical.com/
Evolution of the Electrode
Double Layer Models
? Time-Line:
– Helmholtz 1879
– Guoy-Chapman 1910-13
– Stern 1924
– Grahame 1947
Helmholtz Model
? Interface between electrolyte solution and
electrode behaves like a capacitor in its
ability to store charge
elec
trode
+
+
+
+
_
_
_
_ solution
Double Layer Distance from electrode
?
Potential dies off
sharply as we
move away from
electrode
Helmholtz Model
? Double charge layer = electrically neutral
interface
? Defects:
– No interactions occur further away from first
layer of adsorbed ions
– [Electrolyte] - no effect
Guoy-Chapman Model
? Idea,Diffuse double
layer - Double layer
not compact but of
variable thickness with
ions free to move
? Accounts for effects of
applied potential and
[electrolyte]
Distance from electrode
?
Potential dies off
exponentially as
we move away
from electrode
Stern Model
? Combination
of Helmholtz
and Guoy
Chapman
models e
lec
trode
+
+
+
+
_
_
_
_ Bulk
solution
Compact
Layer
+
+
_
__
+
Diffuse
Layer
Grahame Model
? Specifically adsorbed ions
are desolvated,approach
electrode surface closer,and
feel greater potential
? 3 region model
– IHP - Inner Helmholtz Plane
? passes through center of
specifically adsorbed ions
– OHP - Outer Helmholtz Plane
? passes through solvated and non-
specifically adsorbed ions
elec
trode
+_
_
_
_
Bulk
solution
IHP
+
+
_
__
OHP
+
+
+
Au/water
? Pzc (potential of zero charge) 0.18 V
– E negative of pzc ? excess negative charge
(electrostatic interactions possible)
? Normally hydrophobic
– has strong affinity for organic contaminants
? Clean surface hydrophilic
– wettability
Junction Potential
? Electrical potential that develops at the
interface between two solutions
? Since we isolate reference electrode from
working by frit 1 or more junction
potentials exist in cell
Ew = Ecell - Ejunction
Mass Transport
? 3 Modes:
– Diffusion
– Migration
– Convection
? Natural
? Mechanical
? Movement of mass described by Nernst-
Planck equation
Diffusion
? Movement of mass due to a concentration
gradient
? Occurs whenever there is chemical change
at a surface,e.g.,O ? R
Migration
? Movement of a charged species due to a
potential gradient
? Opposites attract
? Mechanism by which charge passes through
electrolyte
Convection
? Movement of mass due to a natural or
mechanical force
? at long times ( > 10 s),diffusing ions set up
a natural eddy of matter
Movement of Ions in Solution
? Can be described in 3 equivalent ways:
– Molar ionic conductivity,?i (electrochemistry)
– Ionic mobility,ui (separations)
– Frictional coefficients,fi (industry/engineering)
? So,short and fat
better than long and
slender
? units,S m2/mol
?????
cRA
L ;
Molar Ionic Conductivity
Io n ? (1 0
-4
S m
2
/mo l)@ in fin ite
d ilu tion,25
0
C
H
+
350
OH
-
200
Ba
2+
127
K
+
74
Cl
-
77
HCO
3
-
45
T BA
+
24
Taken from Table 2.3.2 in Bard,A.; Faulkner,
L,Electrochemical Methods Wiley,New
York,1980.
Questions
Ion ? (10
-4
S m
2
/ m ol)@i nfinit e
diluti on,2 5
0
C
H
+
350
OH
-
200
Ba
2+
127
K
+
74
Cl
-
77
HCO 3
-
45
TBA
+
24
Taken from Table 2.3.2 in Bard,A.; Faulkner,
L,Electrochemical Methods Wiley,New
York,1980.
? What size
conductivities do
electrolyte ions have?
? How do the cation and
anion conductivities
compare in
electrolytes?
Questions
Io n ? ( 10
-4
S
m
2
/ mol ) in
wat er,2 5
0
C
? ( 10
-4
S
m
2
/ mol ) in
CH 3 CN,2 5
0
C
Na
+
50 10 0
K
+
74 84
Cl
-
77 98
n -B u 4 N
+
PF 6
-
10 4
Taken from Table 4-7 in Sawyer,D.T.;
Roberts,Jr.,J.L,Experimental
Electrochemistry for Chemists Wiley,New
York,1976.
? Have we made any
assumptions about
concentration and
ionization?
? Will the conductivity
of ions be the same in
different solvents?
Molar Ionic Conductivity
? at infinite dilution,no interionic
interactions,so
molar conductivity of salt = ? ion molar
conductivity
? ?? ?? ACac acAC
EXAMPLE
? Calculate the molar conductivity of KCl and
BaCl2
? ?KCl= ?K+ + ?Cl- = (74 + 77) x 10-4 S m2/mol =
151 x 10-4 S m2/cm
? ?BaCl2= ?Ba+2 + 2?Cl- = (127 + (2*77)) x 10-4 S
m2/mol = 281 x 10-4 S m2/mol
Transference/Transport Numbers
? Useful measure of how much of the current
charge is carried by cations vs,anions
? t+ = c+ ??/ ?CcAa
? t- = a- ?-/ ?CcAa
? where c+?? ? a?-? ?CcAa
? and t+ + t- = 1
EXAMPLE
? Calculate transference numbers for ions in
KCl and BaCl2 (two good electrolytes)
? t+ (KCl) = 74/151 = 0.49
? t+ (BaCl2) = 127/281 = 0.45
? Observation,cations and anions carry
current equally well in good electrolytes
Reminders
? Solvent and concentration
affect ionization and
therefore ionic
conductivity and
transference numbers
? t+ (KClaq) = 0.49 (just
calculated)
? t+ (KCl/DMF) = 0.36
in DMF,?K+ = 31; ?Cl- = 55
t +Electrolyte
@ 0.01
M
@ 0.1 M @ 0.2 M
HCl 0.825 1 0.831 4 0.833 7
NaCl 0.391 8 0.385 4 0.382 1
Taken from Table 2.3.1 in Bard,A.; Faulkner,
L,Electrochemical Methods Wiley,New
York,1980.
Ionic Mobility
? Measure of ion’s velocity in presence of
applied electric field (units,m2/Vs)
? where F is Faraday’s constant (96,485
C/mol) and z is the charge on the ith ion
FE zu
i
ii
i
??? ?
EXAMPLE
? Calculate the ionic mobility of Ba2+
? u (Ba2+) = ?/2F
= (127 x 10-4 S m2/mol)/(2 * 96,485 C/mol)
= 6.6 x 10-8 m2/Vs
? Note on units,C = J/V
Frictional Coefficients
? When ions move through solution they
are subject to a frictional drag force:
? where e is the charge on an electron
(1.6 x 10-19 C)
?
??
i
i
iii
Fez
fF
2
?
Lecture #2
An Interfacial Process
? For,O + ne- = R
? 5 separate events must occur:
– O must be successfully transported from bulk
solution (mass transport)
– O must adsorb transiently onto electrode surface
(non-faradaic)
– CT must occur between electrode and O (faradaic)
– R must desorb from electrode surface (non-
faradaic)
– R must be transported away from electrode surface
back into bulk solution (mass transport)
What is an Electrode?
? Electrical double layer
Electrode Classification
? Based on the nature and number of phases
between which electron transfer occurs
? 3 Classes:
– Electrodes of the First Kind
– Electrodes of the Second Kind
– Electrodes of the Third Kind
Electrode of the First Kind
? Metal in contact with its cations or non-
metal in contact with its anions
? EXAMPLES:
– Cu2+ /Cu(s)
– Zn2+/Zn(s)
– SHE
– Ag+/Ag (nonaqueous reference electrode)
– Cl-/Cl2(g)/Pt
Electrodes in Daniell cell
Electrode of the First Kind
(cont’d)
? Electrode response given by Nernst
equation (Nernstian):
– E = E0 + (RT/nF) ln a(M2+)
? NOTE,Fe,Al,and W electrodes are NOT
electrodes of the First Kind
– these have relatively thick surface oxide
coatings
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)
Electrode of the Second Kind
? Electrode response given by:
? E = E0 - (RT/F) ln a(Cl-)
? NOTES,
– anion activity determines potential
– make great reference electrodes because of low
solubility of salt (potential very stable)
The Calomel Reference Electrode
E lec tr od e Acr on y m Potential vs,
SHE
Hg(l) /Hg
2
Cl
2
( s)/ KCl ( 0.1 M ) 0.33 37
Hg/Hg
2
Cl
2
( s)/ KCl ( 1 M ) NCE 0.28 01
Hg(l) /Hg
2
Cl
2
( s)/ KCl ( sat'd) SCE 0.24 12
Hg(l) /Hg
2
Cl
2
( s)/ NaCl ( sat'd) SSCE 0.23 60
Note,concentrations typically high ?? concentrations small ? electrode
doesn’t become polarized ? potential constant
Electrode of the Third Kind
? Electrodes that merely serve as sources or
sinks for electrons
? Common names,redox,inert,unattackable
? EXAMPLES:
– metals,Pt,Au,GC,graphite,HOPG,Hg
– semiconductors,Si,GaAs,In-SnO2/glass
? Response:
– for Pt in contact with Fe2+,Fe3+ in solution:
– E = E0- 0.059 (V) log ([Fe2+]/[Fe3+])
Electrode of the Fourth Kind
? Electrodes that cannot be classified as 1-3
? EXAMPLES:
– Chemically modified electrodes (CME’s)
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 = not polarizable
– easily constructed
– convenient for use
SHE
Advantages
? International standard
E0 ? 0 V
? One of most
reproducible potentials
+ 1 mV
Disadvantages
? Convenience
– Pt black easily
poisoned by organics,
sulfide,cyanide,etc.
– Hydrogen explosive
– Sulfuric and
hydrochloric strong
acids
Practical Reference Electrodes
Aqueous
? SCE
? Ag/AgCl
Nonaqueous
? Ag+/Ag
? pseudoreferences
– Pt,Ag wires
? Ferrocene
SCE
? Cl-(aq)/Hg2Cl2/Hg(l)
? Hg22+ + 2e- = 2Hg(l)
? E0 = 0.24 V vs,SHE @ 250C
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 From BAS www-site,
http://www.bioana
lytical.com/
Ag/AgCl
? Ag wire coated with
AgCl(s),immersed in NaCl
or KCl solution
? Ag+ + e- = Ag(s)
? E0 = 0.22 V vs,SHE @ 250C
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
From BAS www-
site,
http://www.bioana
lytical.com/
Ag+/Ag
? Ag+ + e-= Ag(s)
? requires use of internal potential
standard
Disadvantages
? Potential depends on
– solvent
– electrolyte (LiCl,
TBAClO4,TBAPF6,
TBABF4
? Care must be taken to
minimize junction
potentials
Advantages
? Most widely used
? Easily prepared
? Works well in all
aprotic solvents:
– THF,CAN,DMSO,
DMF
From BAS www-
site,
http://www.bioana
lytical.com/
Pseudo-References
? Pt or Ag wire (inert)
? Idea:
in medium of high resistance,low
conductivity,wire will assume reasonably
steady,highly reproducible potential (+ 20
mV)
? Advantage,no solution contamination
? Limitation,must use internal potential
standard (ferrocene)
Can Aqueous References Be
Used in Nonaqueous Media?
? Yes with caution!
– May be significant junction potentials
? Requires use of internal standard
– May be greater noise
? Electrolyte may precipitate/clog electrode frit
– Don’t forget about your chemistry
? Chemistry may be water sensitive
Electrodes
? Metal
– solid
? Pt,Au,Ag,C
– liquid
? dropping mercury electrode (DME)
? Semiconductors
– Si,GaAs
– In-SnO2/glass (optically transparent)
Carbon
? Paste
– With nujol (mineral oil)
? Glassy carbon (GC)
– Amorphous
? Pyrolytic graphite - more ordered than GC
– Basal Plane
– Edge Plane (more conductive)
Electrode Materials
? Different Potential Windows
? Can affect electron transfer kinetics
Electrodes
? Size
– Analytical macro
? 1.6 - 3 mm diameter
– Micro
? 10-100 ?m diameter
From BAS www-site,
http://www.bioanalytical.com/
Electrode Geometry
Geometry is critical and affects how the data
are analyzed and interpreted
? Disk
– area,?r2
? wire (cylinder)
– area,l(2 ?r) ?r2
? Mesh
– optically transparent
? Sheet
Note,Geometric area <
effective surface area
Cleanliness IS Next to Godliness
in Electrochemistry
? Working electrode must be carefully
cleaned before each experiment
– Mechanical
? Abrasion with alumina or,diamond” polish
– Chemical
? Sonicate in Alconox
? Soak in HNO3
– Electrochemical
? Cycle in 0.5 M H2SO4 (Pt)
Electrochemical Cleaning
Taken from Table 4-7 in Sawyer,D.T.; Roberts,Jr.,J.L,Experimental
Electrochemistry for Chemists Wiley,New York,1976.
Counter Electrode
? Area must be greater
than that of working
? Usually long Pt wire
(straight or coiled) or
Pt mesh (large surface
area)
? No special care
required for counter
From BAS www-site,
http://www.bioanalytical.com/
Ew = Ecell - iRcell - Epolarization
When is iR large?
?I is high,I > 10 ?A
?large electrodes
?solvents with low conductivity
?relatively polar organic solvents
Two Common Configurations
? 2-electrode cell
– iR must be small < 1 mV
(microelectrodes)
? 3-electrode cell
– Avoids internal polarization
of reference electrode
– Compensates for major
potion of cell iR drop
From BAS www-site,
http://www.bioanalytical.com/
2-Electrode Cell
? 2-electrode cell
– Working
– Reference electrode
? Current passed between working and
reference
3-Electrode Cell
? 3-electrode cell
– Working
– Reference
– Counter/auxilliary
? Current is passed between working and
counter
? High impedance placed in front of reference
(low current) so ref,Potential constant
Potentiostat/Galvanostat
? Potentiostat
– Control potential
– Cyclic voltammetry,
chronoamperometry,
etc.
? Galvanostat
– Control current
– Potentiometry
From BAS www-site,
http://www.bioanalytical.com/
Evolution of the Electrode
Double Layer Models
? Time-Line:
– Helmholtz 1879
– Guoy-Chapman 1910-13
– Stern 1924
– Grahame 1947
Helmholtz Model
? Interface between electrolyte solution and
electrode behaves like a capacitor in its
ability to store charge
elec
trode
+
+
+
+
_
_
_
_ solution
Double Layer Distance from electrode
?
Potential dies off
sharply as we
move away from
electrode
Helmholtz Model
? Double charge layer = electrically neutral
interface
? Defects:
– No interactions occur further away from first
layer of adsorbed ions
– [Electrolyte] - no effect
Guoy-Chapman Model
? Idea,Diffuse double
layer - Double layer
not compact but of
variable thickness with
ions free to move
? Accounts for effects of
applied potential and
[electrolyte]
Distance from electrode
?
Potential dies off
exponentially as
we move away
from electrode
Stern Model
? Combination
of Helmholtz
and Guoy
Chapman
models e
lec
trode
+
+
+
+
_
_
_
_ Bulk
solution
Compact
Layer
+
+
_
__
+
Diffuse
Layer
Grahame Model
? Specifically adsorbed ions
are desolvated,approach
electrode surface closer,and
feel greater potential
? 3 region model
– IHP - Inner Helmholtz Plane
? passes through center of
specifically adsorbed ions
– OHP - Outer Helmholtz Plane
? passes through solvated and non-
specifically adsorbed ions
elec
trode
+_
_
_
_
Bulk
solution
IHP
+
+
_
__
OHP
+
+
+
Au/water
? Pzc (potential of zero charge) 0.18 V
– E negative of pzc ? excess negative charge
(electrostatic interactions possible)
? Normally hydrophobic
– has strong affinity for organic contaminants
? Clean surface hydrophilic
– wettability
Junction Potential
? Electrical potential that develops at the
interface between two solutions
? Since we isolate reference electrode from
working by frit 1 or more junction
potentials exist in cell
Ew = Ecell - Ejunction
Mass Transport
? 3 Modes:
– Diffusion
– Migration
– Convection
? Natural
? Mechanical
? Movement of mass described by Nernst-
Planck equation
Diffusion
? Movement of mass due to a concentration
gradient
? Occurs whenever there is chemical change
at a surface,e.g.,O ? R
Migration
? Movement of a charged species due to a
potential gradient
? Opposites attract
? Mechanism by which charge passes through
electrolyte
Convection
? Movement of mass due to a natural or
mechanical force
? at long times ( > 10 s),diffusing ions set up
a natural eddy of matter
Movement of Ions in Solution
? Can be described in 3 equivalent ways:
– Molar ionic conductivity,?i (electrochemistry)
– Ionic mobility,ui (separations)
– Frictional coefficients,fi (industry/engineering)
? So,short and fat
better than long and
slender
? units,S m2/mol
?????
cRA
L ;
Molar Ionic Conductivity
Io n ? (1 0
-4
S m
2
/mo l)@ in fin ite
d ilu tion,25
0
C
H
+
350
OH
-
200
Ba
2+
127
K
+
74
Cl
-
77
HCO
3
-
45
T BA
+
24
Taken from Table 2.3.2 in Bard,A.; Faulkner,
L,Electrochemical Methods Wiley,New
York,1980.
Questions
Ion ? (10
-4
S m
2
/ m ol)@i nfinit e
diluti on,2 5
0
C
H
+
350
OH
-
200
Ba
2+
127
K
+
74
Cl
-
77
HCO 3
-
45
TBA
+
24
Taken from Table 2.3.2 in Bard,A.; Faulkner,
L,Electrochemical Methods Wiley,New
York,1980.
? What size
conductivities do
electrolyte ions have?
? How do the cation and
anion conductivities
compare in
electrolytes?
Questions
Io n ? ( 10
-4
S
m
2
/ mol ) in
wat er,2 5
0
C
? ( 10
-4
S
m
2
/ mol ) in
CH 3 CN,2 5
0
C
Na
+
50 10 0
K
+
74 84
Cl
-
77 98
n -B u 4 N
+
PF 6
-
10 4
Taken from Table 4-7 in Sawyer,D.T.;
Roberts,Jr.,J.L,Experimental
Electrochemistry for Chemists Wiley,New
York,1976.
? Have we made any
assumptions about
concentration and
ionization?
? Will the conductivity
of ions be the same in
different solvents?
Molar Ionic Conductivity
? at infinite dilution,no interionic
interactions,so
molar conductivity of salt = ? ion molar
conductivity
? ?? ?? ACac acAC
EXAMPLE
? Calculate the molar conductivity of KCl and
BaCl2
? ?KCl= ?K+ + ?Cl- = (74 + 77) x 10-4 S m2/mol =
151 x 10-4 S m2/cm
? ?BaCl2= ?Ba+2 + 2?Cl- = (127 + (2*77)) x 10-4 S
m2/mol = 281 x 10-4 S m2/mol
Transference/Transport Numbers
? Useful measure of how much of the current
charge is carried by cations vs,anions
? t+ = c+ ??/ ?CcAa
? t- = a- ?-/ ?CcAa
? where c+?? ? a?-? ?CcAa
? and t+ + t- = 1
EXAMPLE
? Calculate transference numbers for ions in
KCl and BaCl2 (two good electrolytes)
? t+ (KCl) = 74/151 = 0.49
? t+ (BaCl2) = 127/281 = 0.45
? Observation,cations and anions carry
current equally well in good electrolytes
Reminders
? Solvent and concentration
affect ionization and
therefore ionic
conductivity and
transference numbers
? t+ (KClaq) = 0.49 (just
calculated)
? t+ (KCl/DMF) = 0.36
in DMF,?K+ = 31; ?Cl- = 55
t +Electrolyte
@ 0.01
M
@ 0.1 M @ 0.2 M
HCl 0.825 1 0.831 4 0.833 7
NaCl 0.391 8 0.385 4 0.382 1
Taken from Table 2.3.1 in Bard,A.; Faulkner,
L,Electrochemical Methods Wiley,New
York,1980.
Ionic Mobility
? Measure of ion’s velocity in presence of
applied electric field (units,m2/Vs)
? where F is Faraday’s constant (96,485
C/mol) and z is the charge on the ith ion
FE zu
i
ii
i
??? ?
EXAMPLE
? Calculate the ionic mobility of Ba2+
? u (Ba2+) = ?/2F
= (127 x 10-4 S m2/mol)/(2 * 96,485 C/mol)
= 6.6 x 10-8 m2/Vs
? Note on units,C = J/V
Frictional Coefficients
? When ions move through solution they
are subject to a frictional drag force:
? where e is the charge on an electron
(1.6 x 10-19 C)
?
??
i
i
iii
Fez
fF
2
?
