CHRONOPOTENTIOMETRY

Experiment 2

15 DE DICIEMBRE DE 2016

Haeri LEE Supervisor: Prof. Galier

Pol SALLÉS
1 INTRODUCTION – OBJECTIVES
The objective of this practice is mainly to study a solution of potassium hexacyanoferrate (II) by
constant-current chronopotentiometry. By using this technique, we want to be able to
determine the diffusion coefficient of potassium hexacyanoferrate (II).

2 PRINCIPLE
The experiment is carried out by applying a constant current between the working and the
auxiliary electrodes with a current source, and recording the potential between the working and
reference electrodes. This technique is called constant-current chronopotentiometry.

By studying the potential obtained as a function of time for a specific steady current, it can be
obtained a characteristic transition time for these conditions. The transition time obtained and
the current applied can be related linearly by Sand equation I/C0 = f (1/τ1/2), therefore plotting it
for several constant currents, a straight line can be obtained and from the slope of this line, the
diffusion coefficient of potassium hexacyanoferrate (II) can be deduced.

3 THEORETICAL PART
Constant-current chronopotentiometry1,2

The chronopotentiometry consist on the measurement of potential as a function of time, in this

case for a constant current. In order to understand how the potential can vary in time for a given
current, it can be used the concentration profile depending on the time as it is illustrated in the
Figure 1 it can be observed the concentration profiles for chronopotentiometry.

Figure 1. Concentration profiles for chronopotentiometry

1
https://www.basinc.com/manuals/EC_epsilon/Techniques/CPot/cp
2
Adrian W. Bott. Controlled Current Techniques, Current Separations 18:4 (2000)
Let us consider the electron transfer reaction O + e- ↔ R. Initially, there is a given concentration
of R, which is the same at the electrode surface and in the bulk solution (i.e., 5 mM). Because
the system is not composed of a redox couple if not only of O, the corresponding potential is
null. When an oxidizing current is applied through the system, as soon as R is oxidized and there
is O at the electrode surface the potential switch to the Nernst potential (Corresponds to the
first increase of potential observed at Figure 2). R is oxidized to O at the electrode surface in
order to support the applied current, and the concentration of R at the electrode surface
therefore decreases. This sets up a concentration gradient for R between the bulk solution and
the electrode surface, and molecules of R diffuse down this concentration gradient to the
electrode surface. The potential is close to the redox potential for O + e- ↔ R, and its precise
value depends upon the Nernst equation:
𝑅𝑇 [𝑂]
Nernst equation 𝐸 = 𝐸 𝑜 + 𝑛𝐹 𝑙𝑛 [𝑅]𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑑𝑒
𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑑𝑒

Where [𝑂]𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑑𝑒 and [𝑅]𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑑𝑒 are the surface concentrations of O and R, respectively.
These concentrations vary with time, so the potential also varies with time, which is reflected in
the finite slope of the potential vs. time plot at this stage. Once the concentration of O at the
electrode surface is zero, the applied current can no longer be supported by this electron
transfer reaction, so the potential changes to the redox potential of another electron transfer
reaction. If no other analyte has been added to the solution, the second electron transfer
reaction will involve reduction of the electrolyte; that is, there is a large change in the potential.

In our specific experiment, O is Fe(II) and R is Fe (III). As there are no more analytes in solution,
once the concentration of Fe(II) is zero at the electrode’s surface, the potential will increase to
the oxidation of water, which is the solvent.

Transition time

The time required for the concentration of O at the electrode surface to reach zero is
characterized by the transition time τ (see Figure 2). The magnitude of τ depends upon the
applied current; for example, an increase in the applied current i leads to a decrease in τ.

35

30

25 t2

20
Time (s)

15
τ
10

5
t1
0
0 0,2 0,4 0,6 0,8
Potential (V)/REF
Figure 2. Example of transition time measurement for a
potential-time plot
The relation between the current applied and the transition time is given by Sand equation:

𝐼𝜏 1/2 𝑛 𝐹 𝑆 𝐷1/2 𝜋 1/2

=
𝐶𝑜 2
Where I is the constant current, τ the transition time, Co the Fe(II) concentration, S the electrode
surface and D the diffusion coefficient. The parameter iτ½ is a useful diagnostic parameter for
chronopotentiometry, as it is constant for redox processes that are not complicated by coupled
chemical reactions or adsorption.
4 EXPERIMENTAL PART

4.1 MATERIALS AND METHODS

1) Materials

Chemical materials:

- K4(Fe(CN)6): as precursor of Fe(CN)64-. Yellow solid (M=422.41 g/mol)

- KNO3: ionic salt of potassium ions K+ and nitrate ions NO3− which is used as supporting
electrolyte. (M= 101.1 g/mol)

Electrochemical cell:

All the experiments have been carried in a three-electrode cell, with the three electrodes
connected to a potentiostat whose parameters are controlled by using a computer.

- Working electrode (WE) - Platinum rotating disc electrode: the electrode rotates during
experiments inducing a flux of analyte to the electrode. The electrode includes a
conductive disk made of Pt (2mm diameter => S = π mm2) embedded in an inert non-
conductive polymer attached to an electric motor that control of the electrode's
rotation rate. These working electrodes are used in electrochemical studies when
investigating reaction mechanisms related to redox chemistry, among other chemical
phenomena. During our experiments, the variation of the WE potential vs. RE is
studied and the redox reaction which is studied will take place on its surface.
- Reference electrode (RE) - Saturated calomel reference electrode (SCE): reference
electrode based on the reaction between elemental mercury and mercury(I) chloride.
When saturated, the redox potential of SCE is +0.244 V vs. SHE (at 25ºC). The cell
notation is: Cl- (4M)|Hg2Cl2 (s) | Hg(l) | Pt. It will be used as reference potential. In order
to use it, it is kept in KNO3 0,5 M.
- Counter electrode (CE) - Platinum wire: provides a surface for a redox reaction to
balance the one occurring at the surface of the working electrode. The current will flow
through the WE and the CE.

2) Preparation of the solutions

In order to do the experiment, a solution of potassium hexacyanoferrate (II) at 10-2 mol/L and
KNO3 0,5 mol/L was prepared in a total volume of 100 mL. The same solution was prepared for
two different concentrations of potassium hexacyanoferrate (II): 0,8·10-2 mol/L and 1,2·10-2
mol/L.

The mass weighted of potassium hexacyanoferrate (II) was calculated for a MW= 422,41 g/mol.
After weighting the compound on the balance, it was put in a volumetric flask where finally a
solution of KNO3 0,5 mol/L was added until 100 mL. The data used to prepare the solutions is
included in Table 1.

m = C·MW·V (C= concentration; MW= molar weight; V= total volume)

 Compound Molar weight C = Concentration m = Weight of specie Weight of specie
(g/mol) (mol/L) calculated (mg) weighted (mg)
0,01 422,2 422,1 ± 0,1
Fe(CN)6K4 422,41 0,008 337,7 338,5 ± 0,1
0,012 506,6 507,0 ± 0,1
Table 1. Data used for calculating the mass need of each specie to prepare the solution. Final weight is also included.

3) Experimental set-up

Figure 3 Schematics of experimental set-up

In order to prepare the experiment to study it, the solution to analyse is introduced in the conic
beaker. The volume introduced has to be enough to be in contact with the three electrodes but
it needs to be lower than the maximum allowed for the working electrode. Once the
electrochemical cell is prepared and all the electrodes are connected to the potentiostat, it has
to be checked if “CELL ENABLE” sign is on (This sign has to be on while the measurement but has
to be off when stop measurement and clean or change the solutions).

4.2 EXPERIMENTAL STUDIES

1. Potentiometric mode
In the potentiometric mode, linear voltammetry is the technique that has been used, applying a
range of potential, and the current obtained is measured. This experiment is carried out with
and without stirring. From the current-potential curves obtained, it will be determined the
optimal currents for the study of different transition times easily measurable.

Operational conditions: VWE/ref 0 V to 1.4 V

Scan rate 0.01 V/s
Stirring 0 and 1500 rpm
 Without stirring
25

Ipeak
Current (μA) 20

15

10
Idiff
5

0
0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6
Potential (V)/RE

Figure 4. Current-potential curve obtained for linear voltammetry without stirring for 10-2M
K4(Fe(CN)6).

The Figure 4 corresponds to the current-potential curve obtained for linear voltammetry
without stirring. Studying it as the potential increase, it can be observed an increase of current
due to oxidation of Fe(II) to Fe(III). First a peak is reached (Ipeak≈ 20 μA) and then the current is
stabilized (Idiff ≈ 8 μA) until a potential E > 1,2 V, when there is an exponential increase of current
due to water oxidation. Focusing on the reason why we obtained the peak, it is because in this
case as there is not convection, the mass transfer is only given by diffusion and therefore it is
slower. It implies for small potentials applied the diffusion will be fast enough to distribute a
certain amount of current, and the C(Fe(II))electrode > 0 but if the potential keeps increasing, the
diffusion layer will also increase, and the kinetics will be limited by mass transfer with a current
obtained proportional to the Fe(II) arriving by diffusion (C(Fe(II))electrode 0). Therefore, for
higher potentials the current will be limited by diffusion (Idiff).

Stirring 1500 rpm

200

150
Current (μA)

100

50

0
0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6
Potential (V)/RE

Figure 5. Current-potential curve obtained for linear voltammetry stirring at 1500 rpm for 10-2M
K4(Fe(CN)6).
The Figure 5 corresponds to the current-potential curve obtained for linear voltammetry with
stirring. Studying it as the potential increase, it can be observed first activation limitation, giving
an exponential increase of the current, and then diffusion limitation, where the current gets a
constant value (Ilim ≈ 170 μA). In this case mass transfer is given by both diffusion and convection,
and the limiting current obtained will be proportional to the concentration according to the
following equation:

Ilim = (nFSD/δ)·Csolution

n = Number of electrons / mol D = Diffusion coefficient

F = Faraday constant δ = Diffusion layer

S = Electrode’s surface Csolution= [K4(Fe(CN)6)]solution

From the curves obtained in Fig. 4 and Fig. 5, a discussion follows in order to choose the correct
values of current which need to be applied to obtain good transition times (τ):

- On one hand, focusing on Fig. 4, if Iapplied < Idiff => τ  ∞ Because the concentration
of Fe(II) at the electrode’s surface would never reach 0.
- On the other hand, focusing on Fig.5, if Iapplied = Ilim => τ  0 Because in our
experiments there is not stirring, so the system would run out of Fe(II) at the electrode’s
surface too fast.

Therefore, it has been decided to start from a current of 15 μA, which is a little bit higher than
Idiff = 8 μA, and the current will be increased by 5 μA until the transition time becomes
unmeasurable.

2. Intentiostatic mode
A constant current is applied between WE and CE and the variation of the potential WE/RE is
measured along time. The current chosen to study the reproducibility of the measurements has
been 15 μA. This value has been chosen after the potentiostatic mode study, because it is a value
a little bit higher than diffusion current so it is expected a transition time easily measurable and
not too long.

Operational conditions: Pretreatment: -15 μA (1 s)

Current applied: 15 μA
Total time: 60 s
Interval time: 0,1 s

Pre-treatment

In order to study the transition time of our system, it is important to start with the rest potential,
so the slope from rest potential to Nernst Potential will allow us to determine the beginning of
the transition time (t1). The rest potential is only got when there is no presence of Fe(III) in
solution and there is only Fe(II). Therefore, to get this condition a cathodic current (I < 0) is
applied in order to reduce all the possible Fe(III) near the electrode.
Measurement of transition time

The process followed to measure the transition time of a curve is explained here for one of the
curves as example. The current used in this case is IA= 15 μA, and the corresponding potential-
time curve obtained is shown in Fig. 6A. From this plot, with the same program Gpes, we can do
transition time analysis, which is done in a plot with the time as a function of the potential (Fig.
6B). By extrapolation we are able to measure a transition time τ = t2 – t1. In this case, it
corresponded to τ = 25,0 s. The same process has been followed for all the other transition time
measurements.

A) 1 B) 35
0,8
30
0,6
25 t2
Potential (V)/REF

0,4
20

Time (s)
0,2

0 15
0 10 20 30
-0,2 τ
10
-0,4
5
-0,6
t1
-0,8 0
0 0,2 0,4 0,6 0,8
Time (s) Potential (V)/REF
Figure 6. (A) Potential vs time plot obtained for IA = 15 μA; (B) Plot obtained exchanging axis of plot (A) in order to
measure the transition time τ= t2-t1

Reproducibility

Analysing the same solution several times, the obtained results differed each other as we can
observe in Fig. 7. By analysing the plot obtained with transition time analysis, we can get the
transition time for each measurement. The results are included in Table 2, where we can
observe that the reproducibility of the experiment is really low, as the values differ a lot between
them while they were expected to be almost equal.
 1,5

1
Potential (V)/REF

0,5
15 uA (A)
15 uA (B)
0
15 uA (C)
0 5 10 15 20 25 30 35

-0,5

-1
Time (s)

Figure 7. Potential-time curve for I= 10.2 μA without stirring before the measurement

The reason of this low reproducibility is due to the fact the concentration of Fe(II) near to the
electrode is different each time, depending on the time we wait between experiments. After
doing a measurement, the amount of Fe(II) near to the electrode is lower because it has been
oxidized to Fe(III). If there is no stirring between measurements, the Fe(II) concentration will be
equilibrated again only by diffusion, which is a slow mass transfer. Therefore, if we don’t wait
time enough, [Fe(II)]electrode < [Fe(II)]solution which would imply a lower transition time.

A possible way to solve this problem is stirring the solution between experiments. In this way,
mass transfer is much faster allowing to homogenise the Fe(II) concentration before starting the
experiment. It was corroborated by doing three measurements for the same operational
conditions, but this time stirring between measurements. The results can be observed in Fig. 8.
and the corresponding transition time is in Table 2.

0,8

0,7

0,6
Potential (V)/REF

0,5

0,4 15 uA (D)

0,3 15 uA (E)
15 uA (F)
0,2

0,1

0
0 5 10 15 20 25 30 35
Time (s)

Figure 8. Potential-time curve for I= 10.2 μA with stirring before the measurement
 Without stirring between Stirring between experiments
experiments
Measurement A B C D E F
Transition time (s) 25,0 20,2 11,5 24,3 23,9 24,6
Table 2. Transition time obtained for each measurement with I = 15 μA.

Analysing the results summarized in Table 2 we can observe how the reproducibility is much
better in the case we stir between experiments. Therefore, from here the solution have been
stirred before each measurement.

Application of different currents

With the objective of finding the diffusion coefficient from Sand equation, a constant current
have been applied and the corresponding EWE/REF have been measured along time. By plotting E-
t curve, the transition time have been obtained from its analysis. Different constant currents
have been used in this section of the experiment. The currents used are the ones chosen after
studying the I-V curves in the potentiometric mode.

Operational conditions: Pretreatment: -15 μA (1 s)

Current applied: Ix
Total time: 60 s (100 s for I10)
Interval time: 0,1 s

Where Ix is: I10 = 10 μA; I15 = 15 μA; I20 = 20 μA; I25 = 25 μA; I30 = 30 μA; I35 = 35 μA

0,8

0,7

0,6

0,5
Potential (V)/ref

0,4

0,3
10 uA 15uA
0,2
20 uA 25 uA
0,1
30 uA 35 uA
0
-5 5 15 25 35 45 55 65 75
-0,1

-0,2
Time (s)

Figure 9. Potential-time curves obtained for different constant currents applied to our system.

By the analysis of Figure 9 the transition time can be obtained for each potential-time plot. All
the obtained results are included in the Table 3.
 Current applied (μA) 10 15 20 25 30 35
Transition time (s) 59,9 24,6 12,8 7,8 5,2 3,9
Table 3. Transition time obtained for each measurement at different currents.

As it can be observed, the higher is the current applied, the shorter is the transition time
obtained. That corresponds to the expected results, as the higher is the current, the faster will
be consumed the Fe(II) near to the electrode. In this case a current of 10 μA has been also used,
which is closer to the diffusion current (obtained in the potentiostatic mode), so the
corresponding transition time is quite longer.

Different concentrations

In accordance to the Sand equation, plotting I/C0 = f (1/τ1/2) the results should be the same
independently of the concentration used. Therefore, in order to check that the results obtained
are reproducible also with different concentrations of Fe(II), some measurements have been
done with hexacyanoferrate (II) at 0,8·10-2 mol/L and at 1,2·10-2 mol/L. In both cases the
potential-time curve has been plot for two constant currents: I = 15 μA and I = 25 μA. The plots
obtained are gathered and compared with the ones obtained for hexacyanoferrate (II) at 1·10 -2
mol/L in the Figure 10. From this curves, the transition time have been calculated as in the
previous cases and the corresponding values are included in the Table 4.

0,9

0,8

0,7
Potential (V)/ref

0,6

0,5

0,4

0,3

0,2 [Fe(II)]=0,012 M / I= 15uA [Fe(II)]=0,012 M / I= 25uA

[Fe(II)]=0,01 M / I= 15uA [Fe(II)]=0,01 M / I= 25uA
0,1
[Fe(II)]=0,008 M / I= 15uA [Fe(II)]=0,008 M / I= 25uA
0
0 5 10 15 20 25 30 35 40 45 50
Time (s)

Figure 10 Potential-time curves obtained for different concentrations of Fe(II) precursor, for two different constant
currents (15 μA and 25 μA)
 [Fe(CN)64-] (10-2 mol/L) 1,2 1 0,8
Current applied (μA) 15 25 15 25 15 25
Transition time (s) 38,7 12,5 24,6 7,8 15,9 5,5
Table 4. Transition time obtained for each measurement at different concentrations for constant currents of 15 μA
and 25 μA

The obtained results in Figure 10 shows how, for a given current, the higher is the concentration
of Fe(II), the higher is the transition time. The reason is that for higher concentrations of Fe(II) if
the current applied is the same, there will be a higher amount of Fe(II) near to the electrode
capable of providing the flux of electrons required for that electrode, so the time needed to
oxidize all the Fe(II) near to the electrode surface will be longer.
5 INTERPRETATION
After studying the proper conditions to analyse the system and obtain the transition time,
several experiments at different currents and at different concentrations of precursor have been
done. The transition potential has been measure for each one of the measurements and the
obtained results are included in the Tables 3 and 4.

Now, in order to verify the Sand equation, these results have been used to plot I/C0 = f (1/τ1/2)
where I is the constant current applied, C0 is the initial concentration of hexacyanoferrate (II)
and τ the transition time obtained; the resulting plot correspond to the Figure 11. According to
the Sand Equation, if the development of the semi-infite diffusion equations is correct, this
relation should follow a straight line with a certain slope and a null intersection point. Knowing
all the other parameters, the diffusion coefficient (D) can be determine from the slope.

𝐼 𝑛 𝐹 𝑆 𝐷1/2 𝜋1/2 1
= · 1/2
𝐶𝑜 2 𝜏
𝑠𝑙𝑜𝑝𝑒

4,00E-06

3,50E-06

3,00E-06

2,50E-06
I/Co (A·L/mol)

2,00E-06 [Fe(II)] = 0,01 M

y = 6,56E-06x + 1,61E-07
R² = 0,9995 [Fe(II)] = 0,008 M
1,50E-06
[Fe(II)] = 0,012 M
1,00E-06

5,00E-07

0,00E+00
0 0,1 0,2 0,3 0,4 0,5 0,6
1/τ1/2 (s-1/2)

Figure 11 Representation of I/Co = f(1/τ1/2) for the three different concentrations (0,01 M, 0,008 M and 0,012 M) and
for the different constant currents applied. A linear regression has been done for 0,01 M whose equation is included
on the graph.

As it can be observed in the obtained results for a concentration of 0,01 M (Fig. 11), doing a
linear regression a line equation is obtained with a coefficient of correlation of almost 1 (0,9995),
which means that the results follow a straight line behaviour with really small deviation.
Therefore, it can be verified that the results follow the Sand equation.

In order to determine the diffusion coefficient of hexacyanoferrate (II), the slope obtained in the
linear regression must be used:
 2
𝑛 𝐹 𝑆 𝐷1/2 𝜋1/2 2 · 𝑠𝑙𝑜𝑝𝑒 −14
𝑑𝑚2 −𝟏𝟎
𝒎𝟐
= 𝑠𝑙𝑜𝑝𝑒 𝐷=( 1 ) = 5,96 · 10 = 𝟓, 𝟗𝟔 · 𝟏𝟎
2 𝑠 𝒔
𝑛𝐹𝑆𝜋 2
where:

- slope = 6,56·10-6 A·s1/2·dm3/mol

- n=1
- F = 96500 C
- S = 12·π mm2 = 3,14·10-4 dm2

Therefore, it has been obtained a diffusion coefficient of hexacyanoferrate (II) of 5,96·10-10 m2/s.
In order to know if the obtained diffusion coefficient of hexacyanoferrate (II) is correct, it has
been compared with the one in the laboratory handbook:

D (K4Fe(CN)6) = 1,183·10-9 m2/s (for a C=0,005 M, T= 25oC)

Comparing the diffusion coefficient obtained experimentally and the one of the handbook, it
can be observed that both of them are in the same range (10-9 – 10-10 m2/s), which confirm the
experimental diffusion coefficient is correct. The difference between both values can be due to
different factors: different temperatures, viscosity of the medium, etc.

On the other hand, if the results obtained with different concentrations are compared, it can be
observed all of them are close to the straight black line of 0,01 M. It is because the plot has been
normalized dividing the current I by the concentration C0. Because in the three cases looks like
the slope would be almost the same, it can be said that the diffusion coefficient in this range of
concentrations is maintained almost constant. This behaviour was the one expected because
the experiments have been done with low concentrations.
6 CONCLUSION
Using constant-current chronopotentiometry, the diffusion coefficient of potassium
hexacyanoferrate (II) dissolved in water has been determined.

A potentiometric mode has been used in order to find the appropriate range of constant
currents which need to be applied to analyse the transition time. Once it has been determined,
several measurements from 10 μA to 35 μA have been applied and the corresponding transition
time measured. The higher was the current applied, the shorter was the transition time. It
should be highlighted that in order to have reproducibility in the results, it has been determined
the necessity of stir the solution before each experiment. By plotting the obtained results in
accordance to the Sand equation, a straight line has been obtained from which it has been able
to calculate the diffusion coefficient of potassium hexacyanoferrate (II).

The effect of different concentrations has been also studied, working with 0,008 M, 0,01 M and
0,012 M of potassium hexacyanoferrate (II). The higher was the concentration, the longer was
the transition time for a given current. It has been concluded it follows the same behaviour
independently on the concentration and if it is plotted normalized to the concentration,
according to the Sand equation, the obtained straight lines overlap each other.