ELECTROANALYTICAL
TECHNICS
I
COULOMETRY
m = AQ = A I t = (M/nF) I t
 An analytical method for determining the amount (m)
of a substance released during electrolysis in which
the number of coulombs (nF) used is measured.
 Coulometry is an absolute measurement similar to
gravimetry and requires no chemical standards or
calibration. It is therefore valuable for making
absolute concentration determinations of standards.
m …… amount of electroactive substance
A …… electrochemical equivalent
M …… molar weight
I …… current
t …… time
Charles Augustin de Coulomb (1736 –1806)
Definition
One Coulomb C is the quantity of
charge transported by an electric
current of one Ampere (A) during one
second (s).
1 C = 1 A • 1 s
To produce one mol of a chemical
compound, using one electron,
96 484 C are required.
Michael Faraday, 1834 – the relation between the
amount of electricity consumed and the amount of metal
produced in solid form from solutions
Laszlo Szebelledy, Zoltan Somogyi 1938 – the basis for
coulometric analysis used in electroanalytical methods coulometry
as a new electroanalytical method
Panta S. Tutundžić – coulomb as the primary
standard
Very high precision of charge measurement is possible with a
chemical coulometer. However, chemical coulometers are
always less convenient to use than electronic integration
instrumentation. As a consequence chemical coulometers are no
longer commonly used in the electrochemical laboratory. The
types of chemical coulometer which are most precise are :
the silver
the iodine
the hydrogen-oxygen gas
the hydrogen-nitrogen gas
coulometer
0.1%
Measurement of Charge Using Chemical Coulometers
Measurement of Charge Using Electronic Integration
Analog method of integrating charge
the most common method - electronic integration of the
instantaneous charge (which is proportional to current) be built
up as actual charge on a capacitor over a period of time,
the voltage across the capacitor, which is a measure of the
charge held, is then determined; if the quality of the capacitor is
such that no significant charge leaks off during the period of
charge accumulation,
this method is capable of results of good precision; a useful
integrator circuit consists of an operational amplifier with an
integrating capacitor in the feedback loop.
Digital method of integrating charge
can be used if the current being measured is applied as a series of
identical small current pulses. If the number of coulombs in a
single pulse is accurately known, multiplication by the number of
pulses (which can easily be counted by a digital counter) gives the
charge passed with the same relative error as the relative error
with which the charge of a single pulse is known, provided that the
number of pulses is sufficiently large.
highly practical for coulometric titrations, since often
electrogeneration conditions can be established which are not
adversely affected by the pulsating nature of the current.
 this method should not be used without care both as to the
apparatus and as to the electrochemical reactions being employed.
Measurement of Charge Using Electronic Integration
can be performed as a constant-potential or a constant-current technique.
Constant-potential coulometry can be used both as a technique of analysis and as
a means for determining the value n (number of electrons per molecule).
By Faraday's law, the total quantity of chemical change produced at an electrode is
directly proportional to the quantity of electricity passed. The fundamental requirement
for a controlled-potential coulometric analysis is that the electrode reaction under
investigation proceeds with 100% current efficiency. If this condition is satisfied, the
amount of electricity produced or consumed can be related to the concentration by
Faraday's law.
In the constant-potential coulometry the electrode potential should be maintained
constant using a potentiostat. In additional to general potentiostats used for various
applications, special potentiostats for constant-potential coulometry (particularly,
constant-potential coulometric titrations) have been designed.
POTENCIOSTATIC COULOMETRY
COULOMETRY
POTENCIOSTATIC COULOMETRY AMPEROSTATIC COULOMETRY
integratorpotentiostat
diaphragm
W……..Pt, Au, Hg and vitreous carbon
ISES (Intelligent
School Electronic
System)
Determination of metal ions, actinides, organic substances (coulometric detector in
combination with HPLC)

t
IdtQ
0
.constE 
catholyte
anolyte
A…….. auxiliary Pt
R…….. Ag/AgCl/KCl or Hg/Hg2Cl2/KCl
Determination of SO2 a NO2
POTENCIOSTATIC COULOMETRY
COULOMETRIC METHODS
DIRECT COULOMETRY

t
IdtQ
0
DIRECT COULOMETRY

t
IdtQ
0
0.01% I
DIRECT COULOMETRY
The Nernst diffusion layer δ is:
• independent of time
• inversely dependent on square
root of stirring rate





 













)x(bulk
x
)x(
)x(
cc
D
x
c
D)flux(f
0
0
0
)x(nFAfi 0

)x(bulk cc
nFADi
0


bulk
lim
c
nFADi 
where n number of electrons, Faraday constant F = 96 485 C.mol-1, A electrode area
[cm2], D diffusion coefficient [cm2 s-1],  Nernst layer [cm]
diffusion
POTENCIOSTATIC COULOMETRY
ktcln  0tcln kt
t ecc 
 0
ktIln  0tIln kt
t eII 
 0
or
t time, i current, Q charge
tinFVc tt 
2) Advantages:
- more specific than amperostatic coulometry
- avoids redox of species that may interfere with amperostatic coulometry
- can be used for over 55 elements without major interference
3) Disadvantages
- does take longer than amperostatic titration
- current (i) decreases with time
- conversion becomes slower as less analyte around to oxidize or reduce
It = Ioe-kt
k = AD/V
where:
D = diffusion coefficient
A = electrode surface area
V = volume
 = thickness of the surface layer
where concentration gradient exists
Potentiostatic Coulometry
Coulometric Methods
Potentiostatic Coulometry
Basics:
-detection of analyte in solution by using Coulometry at fixed potential to
quantitatively convert analyte to a given form
- current controlled by contents of cell.
Based on Measurement of Amount of Electricity (or charge, in coulombs) Required to
Convert Analyte to Different Oxidation State
Q = It for constant current with time
where:
Q = charge required (coulombs = A. s)
I = current (A)
t = time of current (s)
for variable current from 0 to t :
Relate charge (coulombs, C) to moles of e- passing electrode by Faraday constant
Faraday (F) = 96,485 Coulombs (C)/mole
If know moles of e- produced and stoichiometry of ½ cell reaction:
Ag (s)  Ag+ + e- (1:1 Ag+/e-)
gives moles of analyte generated, consumed, etc.
Coulometric Methods

t
IdtQ
0
Coulometry: electrochemical method based on the quantitative oxidation or reduction
of analyte
- measure amount of analyte by measuring amount of current and time
required to complete reaction
charge = current (i) x time in coulombs
- electrolytic method  external power added to system
Coulometric Titration:
of Cl-
use Ag electrode to produce Ag+
Ag (s) Ag+ + eAg+
+ Cl- AgCl (ppt.)
- measure Ag+ in solution by 2nd electrode
- only get complete circuit when Ag+ exists in solution
- only occurs after all Cl - is consumed
- by measuring amount of current and time required
to complete reaction can determine amount of Cl Coulometric
Methods
Example : Constant current of 0.800 A (A) used to deposit Cu at the cathode and
O2 at anode of an electrolytic cell for 15.2 minutes. What quantity in grams
is formed for each product?
Coulometric Methods
4) Two Types of Coulometric Methods
a) amperostatic (coulometric titration)
- most common of two
b) potentiostatic
Fundamental requirement for both methods is 100% current efficiency
- all e- go to participate in the desired electrochemical process
- if not, then takes more current  over-estimate amount of analyte
Amperostatic Methods (Coulometric Titrations)
1)Basics: titration of analyte in solution by using coulometry at constant current
to generate a known quantity of titrant electrochemically
- potential set by contents of cell
- example:
Ag (s)  Ag+ + e- for precipitation titration of Cl-
To detect endpoint, use 2nd electrode to detect buildup of titrant after
endpoint.
Coulometric Methods
2) Applications
a) Can be used for Acid-Base Titrations
- Acid titration
2H2O + 2e-  2OH- + H2 titrant generation reaction
- Base titration
H2O  2H+ + ½ O2 + 2e- titrant generation reaction
b) Can be used for Complexation Titrations (EDTA)
HgNH3Y2- + NH4
+ + 2e-  Hg + 2NH3 +HY3HY3-
 H+ + Y4c)
Can be used for Redox Titrations
Ce3+  Ce4+ + eCe4+
+ Fe2+  Ce3+ + Fe3+
Coulometric Methods
3) Comparison of Coulometric and Volumetric Titration
a) Both have observable endpoint
- Current (e- generation) serves same function as a standard titrant solution
-Time serves same function as volume delivered
- amount of analyte determined by combining capacity
- reactions must be rapid, essentially complete and free of side reactions
b) Advantages of Coulometry
- both time and current easy to measure to a high accuracy
- don’t have to worry about titrant stability
- easier and more accurate for small quantities of reagent
small volumes of dilute solutions  problem with volumetric
- used for precipitation, complex formation oxidation/reduction or neutralization reactions
- readily automated
c) Sources of Error
- variation of current during electrolysis
- departure from 100% current efficiency
- error in measurement of current
- error in measurement of time
- titration error (difference in equivalence point and end point)
Coulometric Methods
Coulometric vs Volumetric Titrations
Coulometric Volumetric
Preparation of standard solutions None Yes
Standardization of titrant None Yes
Storage of titrant None Yes
Use of labile reagents Trivial Difficult
free KOH or NaOH titrants Trivial Possible
Dilution effects during titration None Yes
Addition of microquantities of analyte Trivial Difficult
Determination of microamounts of analyte Yes Difficult
Determination of microvolumes Yes Difficult
Accuracy of titration High O.K.
Economy of reagent Maximal Depends
Automation Perfect Possible
Remote control Perfect Possible
End-point detection Same for both modes
Price Similar
Comparison of Coulometric and Volumetric Titration
4) Change in Potential During Amperostatic Methods
a) In constant current system, potential of cell will vary with time as analyte is
consumed
- Cell “seeks out” electrochemical reactions capable of carrying the
supplied current
Cu2+ + 2e-  Cu (s) initial reaction
-Nernst Equation
Ecathode = Eo
Cu2+/Cu – 0.0592/2 .log (1/aCu2+)
Note: Ecathode depends on aCu2+. As
aCu2+ decreases  (deposited by
reaction) Ecathode decreases.
Coulometric Methods
& Ag (s) vs. Cl- in solution
- when all Cu2+ is consumed, current is carried by another electrochemical reaction
& generation of H2 (g) if reduction takes place
2H+ + 2e-  H2 (g)
& breakdown of water if oxidation
2H2O  H2O2 + 2H+ + 2eH2O2
 O2 + 2H+ + 2e-
not a problem as long as other species don’t co-deposit
- or if have a large excess of species being used in titrant generation vs. titrated analyte
4) Change in Potential During Amperostatic Methods
Coulometric Methods
0.8 1.0 1.2 1.4 1.6 1.8 2.00.6
0
2
4
6
8
10
E, V vs SCE
j,mA/cm2
(1)
(2)
j lim
2
Br - e = 1/2Br-
1/2H O - e = H + 1/4O2
+
2
Experimental current-potential curve for oxidation of bromides at a rotating disk electrode. Composition of solution: 10 mM KBr, 60 mM HClO4
and 0.1 M KNO3. Area of the electrode: 0.16 cm2. Rotating rate: 400 rpm.
This will be exemplified by a current-potential curve obtained in stirred solution containing 10 mM KBr. Due to the stirring
of the solution, a constant amount of electroactive material reaches the electrode and the plots are time independent. At
potentials around +1.0 V vs SCE the oxidation of Br- takes place; at more positive potentials water is oxidized. The oxidation
of Br- can proceed at a maximum current density of 5 mA/cm2. If the current forced through the electrodes corresponds to a
current density lower than that value, say 2.5 mA/cm2 (dotted line (1), the only reaction that takes place is the oxidation of
Br-. If, however, a larger current density is applied, say 7.5 mA/cm2 (dotted line (2), only 5 mA/cm2 are contributed by the
oxidation of Br-. An additional 2.5 mA/cm2 are due to the oxidation of water.
The problem is evident - the current
efficiency of the generation of Br2 is
not 100% any more.
To ensure 100% current efficiency, the generation
of titrant should be the only process, taking place
at the generating (working) electrode. The current
by which the titrant is generated has to be smaller
than the limiting current of the electrode process
of interest. If this condition is not maintained,
some unwanted electrode process could take place
and bring to the reduction of the current
efficiency.
Microcoulometry -
0,05 ml (in a drop),
c = 10-11 až 10-9 g
1 m C
INDIRECT COULOMETRY
COULOMETRIC TITRATIONS
 The technique of coulometric titration was originally
developed by L. Szebelledy and Z. Somogy in 1938.
 The method differs from volumetric titration in
that the titrant is generated in situ by electrolysis and
then reacts stoichiometrically with the substance
being determined.
 The amount of substance reacted is calculated from
the total electrical charge passed, Q, in coulombs,
and not, as in volumetric titration, from the volume
of the titrant consumed.
COULOMETRIC TITRATIONS
Princip:
 na pracovní elektrodě se z pomocné látky P konstantním
proudem generuje činidlo X, s nímž analyt A reaguje na
produkt Y:
reakce na elektrodě: P ± ne  X
reakce v roztoku: A + X  Y
Například: 2 Br
–
- 2 e  Br2
AsIII + Br2  AsV + 2 Br
–
 činidlo je generováno tak dlouho, aby s ním analyt právě
kvantitativně zreagoval, tj. byl jím ztitrován
 v elektrochemické cele musí být vhodný indikační systém
(např. fotometrický, elektrody pro potenciometrickou,
amperometrickou indikaci aj.)
Coulometric titration
Constant-current coulometry
CCC - is often used for coulometric titrations
the titrant is generated in the solution by the application of a
constant current
measurement is made of the time of current generation, and
the product of the current and the time yields coulombs Q=I t
by application of Faraday's law, the equivalents of titrant can
be calculated directly m = AQ = A I t = (M/nF) I t
the electrode reaction proceeds with 100% current efficiency.
The titrant that is generated should react rapidly and
stoichiometrically with the substance being determined.
AMPEROSTATIC COULOMETRY
 obsah analytu se určí pomocí Faradayova zákona
z množství činidla vygenerovaného nábojem Q = I·t a
ze známé stechiometrie chemické reakce v roztoku
Ig
čas, t0
konec
elektrolýzy
Q
stir bar
indicatication
(potentiometry,
amperometry)
membrane
time
generator
of const.
current
generation current ( 10mA/cm2)
INDIRECT COULOMETRY
COULOMETRIC TITRATIONS
 Coulometric analyses can in fact be carried out according
to two different techniques: controlled-current
coulometry (galvanostatic coulometry) or controlledpotential
coulometry (potentiostatic coulometry).
 A fundamental requirement for a coulometric titration is
100 percent current efficiency at the electrodes of the
electrolysis cell.
 The reagent generated (titrant) must react
stoichiometrically and preferably rapidly and irreversibly
with the substance being determined (analyte).
 The reagent can be generated in situ, i.e. in the analysis
solution, or in an external vessel with continuous flow.
In practice, most commonly used coulometric titrations
allow the direct determination of substances that are
not reduced or oxidized at the generator electrodes.
COULOMETRIC TITRATION EXPERIMENTS
 100 % conversion or current efficiency at the generator electrodes is, how
can 100 % efficiency be ensured? …..no other reactions can take place - by
controlling the applied voltage or through a suitable choice of the electrolyte.
 The electrolyte solution must be inert and have a sufficiently high
concentration.
 The geometry of the measuring cell and the stirrer speed (rapid
homogeneity of the analysis solution) also play a very important role. The
reagent generated must be dispersed as rapidly as possible throughout the
measuring cell. Efficient and rapid mixing of the analysis solution with the
titrant leads to steady state conditions at the electrodes (sensors) being
attained more quickly.
 The electrode material of the generator electrodes and their arrangement in
the measuring cell are important.
 The hydrogen overvoltage - on mercury and platinum. Platinum is also
suitable as an electrode substrate because it is chemically stable and
corrosion-resistant in most electrolyte solutions.
COULOMETRIC TITRATIONS - requirements
 the equivalence point or end point of a coulometric titration can be determined as in
any other titration (color indication, potentiometry, amperometry)
 constant current sources for the generation of titrants are relatively easy to make
 the electrochemical generation of a titrant is much more sensitive and can be much
more accurately controlled than the mechanical addition of titrant using a burette
(I=10 µA for 100ms ~ 10-8 mol or few micrograms of titrant)
 the preparation of standard solutions and titer determination is no necessary
 chemical substances that are unstable or difficult to handle because of their high
volatility or reactivity in solution can also very easily be used as titrants (bromine,
chlorine, Ti 3+, Sn2+, Cr 2+ and Karl Fischer reagents - iodine)
 are easier to automate because a source of current is appreciably easier to control
than a burette drive
 can also be performed under inert atmosphere or be remotely controlled, e.g. with
radioactive substances
 dilution effects due to the addition of the titrant are of no importance.
COULOMETRIC TITRATIONS - advantages
equivalence point = end point = titration stop
Amperometric titration
Biamperometric titration
Potentiometric titration
Coulometric titration
Bipotentiometric titration
TITRATIONS
chemical reaction and steady state methods
methods controlled parameter measured function
E I = f (V)
U I = f (V)
I E = f (V)
I U = f (V)
I Q = f (V) I = f (t)
Fe2+ (Red1)
BIAMPEROMETRIC TITRATIONS
Mn7+ (Ox2)
Fe3+ (Ox1) Mn2+ (Red2)
rev irrev
50:50
BIAMPEROMETRIC TITRATIONS
50% 100%
rev
irrev
by
BIAMPEROMETRIC TITRATIONS
rev
rev
by
irrev
rev
by
BIPOTENTIOMETRIC TITRATIONS
Two electrodes – as in biamperometric titrations
rev
irrev
by
irrev
rev
by
rev
rev
by
Amperostatic coulometry
COULOMETRIC TITRATIONS
Reduction of further
analyt
on working electrode
Primary coulometric titrationI = const.
Secondary coulometric titration
Cathodic reaction of
first analyt
Coulometric titrations
Analyt Reakce na generační elektrodě
kyseliny, S, C v ocelích i
organických látkách (po
převedení na příslušné kyseliny)
2H2O + 2e  2OH+
H2
anorg. zásady, aminy H2O  2H++ 1/2O2+ 2e
Cl,
Br,
I,
thioly, thiomočvina
(argentometrie)
Ag  Ag+ + e
As3+, Sb3+, SO2, fenoly,
thioly, nenasyc. slouč. ...
2Br
Br2 + 2e
As3+, S2O3
2-, H2S,
H2O (dle K.Fischera),
kys.askorbová...
2I
I2 + 2e
Fe3+,V5+,U6+... TiO2+ + 2H+ + e  Ti3+ + H2O
Ca2+, Cu2+, Pb2+, Zn2+...
(chelatometrie)
HgY2- + 2H+ + 2e  Hg(l) + H2Y2-
Výhody coulometrických titrací:
 snadná titrace i málo stálými a těkavými činidly (Br2,
Ti3+);
 činidla není nutno standardizovat (standardem je
Faradayova konstanta);
 lze stanovovat nižší koncentrace analytů než
klasickou volumetrií
 metodu lze snadno automatizovat
Analyzátor solí
Model SAT-210,
DKK-TOA Corporation,
Japonsko
stanovení:
NaCl nebo chloridů
Indikace ekvivalence:
potenciometrická
Rychlost analýzy:
25 s (1% standard
NaCl)
Coulometrický analyzátor vody metodou Karl Fischer
Cou-Lo Compact
GR Scientific
Bedfordshire, UK
Indikace ekvivalence
Měřící rozsah:
1µg - 100mg H2O
Princip:
I2 + SO2 + 3 C5H5N + H2O + CH3OH  3 C5H5NH+ + CH3OSO3
– + 2 I
(místo
pyridinu lze použít např. dietanolamin příp. jiná báze)
The Karl Fischer reaction uses a coulometric titration to determine the amount of water in a sample. It
can determine concentrations of water on the order of milligrams per liter. It is used to find the amount
of water in substances such as butter, sugar, cheese, paper, and petroleum.
The Pt anode generates I2. The next reaction is
oxidation of SO2 by I2. One mole of I2 is consumed
for each mole of H2O. In other words, 2 moles of
electrons are consumed per mole of water.
B·I2 + B·SO2 + B + H2O → 2BH+I− + BSO3
BSO3 + ROH → BH+ROSO3
−
Karl Fischer
The amount of current needed to generate I2 and reach the end point can then
be used to calculate the amount of water in the original sample.
The end point is detected most commonly by a bipotentiometric method.
I2 + SO2 + 2H2O →2HI + H2SO4
It is the same reaction as the iodometric
titration of sulphur dioxide in water.
However, in order to shift the equilibrium to
the right, it was necessary to neutralise the
acids produced. Originally pyridine was used
as the neutralising base.
titrovaná látka titrační
činidlo
základní elektrolyt pracovní
elektroda
indikace
anilín Br2 KBr, HAc/H2O/Py Pt biamperometricky
As(III) Br2 KBr, H2SO4 GC potenciometricky aj
biamperometricky
NH3
(Kjeldahl)
Br2 borax, HCl, KBr Pt biamperometricky
mg až m g
Ti(IV) Cr2+ HBr, CrBr3 Hg amperometricky
0,5 mg
hydrochinon,
izoniacid,
rezorcín
Ag+ AgNO3, HNO3
–10  C
Au potenciometricky,
biamperometricky
sub mg
a -tokoferol VO4
3– VOSO4 v CH3COOH Pt amperometricky
0,1 - 2 mg
hydrochinon
F obr. 8.5
Co3+ Co(CH3COO)2, CH3COONa
(bezvodý)
v CH3COOH
GC biamperometricky
sub mg
Biampérometrická titrační křivka získaná při coulometrickém stanovení hydrochinonu
coulometricky generovaným Co3+ z nasyceného roztoku (CH3COO)2Co v prostředí bezvodé
CH3COOH - T.J. Pastor, V.V. Antonijevic , J. Barek, Mikrochim. Acta 117, 153 (1995).
CHRONOCOULOMETRY - CC
RedneOx  
jd,l
E1/2
ja
jc
- E + E
E1E2
Steady–state current–potential curve for reduction of a oxidant (Ox)
unstirred solution
Chronocoulogram – the shape of the resulting chronocoulogram can be
understood by considering the concentration gradient
in the solution adjacent to the electrode surface
CHRONOCOULOMETRY - CC
CC involves measurement of the charge vs. time response to an applied
potential step
CC is useful for measuring
1) electrode surface areas
2) diffusion coefficients
3) the time window of an electrochemical cell
4) adsorption of electroactive species
5) mechanisms and rate constants for chemical reactions coupled to
ET reactions
21
21
)t(
cnFAD
)t(I)t(I d

 
Cottrell equation
 
 
t
dt
)t(
cnFAD
Q
0
21
21
21
2121
2

 ctnFAD
Q
the current from E1 to E2

t
dd dt)t(IQ
0
the Anson plot - the plot of Q vs. t 1/2
the Cottrell plot - the plot of Q vs. t -1/2
Single step chronocoulometry
The real electrode surface area can be determined.
The used relationship for the plot slope is valid for diffusion to a
disk working electrode and it should be modified in case of any
other working electrode geometry.
A plot of Q vs. t 1/2 transforms the data into a linear relationship whose
slope is 2nAFcD1/2/1/2 where n=1 is the number of electrons
transfered in a single electron transfer act, A is a real electrode surface
area and F, c, D are the Faraday constant, ferricyanide concentration
and ferricyanide diffusion coefficient (D = 7.6x10-6 cm2 s-1).
Fe(CN)6
3- is reduced to Fe(CN)6
4-.
The analysis of chronocoulometry (CC) data is based on the Anson
equation, which defines the charge-time dependence for linear diffusion
control: Q = 2nFACD½-½t ½
Single step chronocoulometry
E
I
Q
t
t
t
Ic
E
2
E
1
Id
Qc
Typical
waveform of a
potential step
experiment
Typical
chronoamperometric
response
Typical
chronocoulometric
response
Ic capacity current
Qc capacity charge
E1, E2 potentials
Id diffusion current
Single step chronocoulometry
)e(ECQQ dlsCR/t
dldlC

 1
dsCRtime constant
capacitive charge
12 EEE potential step
)t(Q)t(Q)t(Q)t(Q adsCd 
Oxads nF)t(Q 
total charge
adsorptive charge
estimation of surface concentration
Ox
CR/t
dl nFA)e(CEtnFAD)t(Q dls
 
12 212121
Qd = charge due to electrolysis of solution species
Qads = charge due to electrolysis of adsorbed species
QC or Qdl = double-layer charging
ox = surface concentration of adsorbed species (mol cm-2)
Cottrell plot for a chronoamperometry
experiment
Anson plot for a chronocoulometry experiment
Q vs. t -1/2
Q vs. t 1/2
Single step chronocoulometry
Q
Qc
Qads
t1/2
CC charge vs. time1/2 plot
no adsorption
with adsorption
charge response without reactant
problem : at short times this plot is not linear
Single step chronocoulometry
The intercept of the Anson plot is the sum of Qdl and Qads. One method for
eliminating Qdl from the equation is to run the identical experiment on the
electrolyte alone. However, this approach assumes that Qdl is the same both in
the presence and in the absence of the adsorbed analyte, which is generally not a
valid assumption. The alternative method is to use the double potential step
experiment. If only one of O and R adsorbs, then Qads is the difference of the
intercepts of the Anson plots for the two steps.
Data from the later time domains of the experiment are being used to
investigate behavior that occurred at early time points. This shows that
integration retains information about electrolysis that occurs essentially
simultaneously with the potential step. This is a major advantage of CC, since
direct measurement of such behavior is generally very difficult.
In all the above applications, the initial potential is at a value at which
electrolysis does not occur, and the step potential is at a value at which
electrolysis occurs at a diffusion-controlled rate (the second step is generally
from the step potential back to the initial potential). Therefore, before these
potentials can be determined, the redox potential must first be known. In
general, the simplest way to find these potentials is to record the cyclic
voltammogram of the analyte.
Single step chronocoulometry
Double step chronocoulometry
E
1
E
2E
I
Q
Id
τ
t
t
t
Qr
Chronoamperometry- CA
Chronocoulometry -CC
Double step chronocoulometry
Chronocoulometry (CC) and Chronoamperometry (CA)
Initial Potential - First Step Potential - First Step Time
Final Potential - Second Step Potential - Second Step Time
adsorption phenomena
capacity contribution
kinetics of coupled homogeneous reactions








 212121
21
11
t)t(
cnFAD
)t(I)t(I dRedRe
d
 2121
21
21
2
)t(
cnFAD
)t(Q dRedRe



Double step chronocoulometry








 212121
21
11
t)t(
cnFAD
)t(I)t(I dRedRe
d
 2121
21
21
2
)t(
cnFAD
)t(Q dRedRe



 212121
21
21
2
t)t(
cnFAD
r),t(Q dRedRe



reversal step
)t(Q)(Qr),t(Q 
Double step chronocoulometry
Qads
Qc
Q
τ1 /2 +(t – τ)1/2 - t1/2
t1/2
1
3
2
4
plotting
21
t.vs)t(Q 
 212121
t)t(.vsr),t(Q 
1 and 2
no adsorption
3 and 4
with adsorption
Charge-time response for a double-potential
step chronocoulometry/chronoamperometry
experiment.
CHRONOCOULOMETRY
the later of transient part can be detected more accurately
the better signal-to-noise ratio (integral)
the contribution of charging/discharging to the overall charge
as a function of time can be distinguished from the diffusing
electroreactants
Advantages
Disadvantages
practical problems
- relatively long period of time (straightforward data evolution)
- the decay of the current belonging to the DL charging should be
very fast (Rs = 1 Ω, Cd= 20μF, τ =20μs, 96% Ic for 60μs)
(Rs = 1000 Ω, Cd= 200μF, τ =200ms, 96% Ic for 1 s
the distorsion of the reliable part of the chronoamperometric response)
Rs should be lower and A should be small
the good potentiostat (single step and double step technique)
j
- +
-j
-jd,l
Polarization curves for diffusion controlled processes
j
jj
ln dl
Ox




Fn
RT
ln
Fn
RT
EE Redo
c
- +
j
-j
jd,l,cat
jd,l,anod
Polarization curves for diffusion controlled processes
jd,l
E1/2
ja
jc
- E + E
Diffusion overpotential - polarography
Ox

 Redo
c21 ln
Fn
RT
EE2dljj 
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