The lab report below was submitted as part of the coursework for
CM3292 Advanced Experiements in Analytical and Physical Chemistry. Please do not plagiarise from it as
plagiarism might land you into trouble with your university. Do note
that my report is wellcirculated online and many of my juniors have
received soft copies of it. Hence, please exercise prudence while
referring to it and, if necessary, cite this webpage.
AIM
(A) To determine the E^{0}’ value and n for the Fe^{III}(CN)_{6}^{3}/ Fe^{II}(CN)_{6}^{4} couple in 0.1M KNO_{3} from the 2mM cyclic voltammogram
(B) To determine the effect of scan rate on peak height of the cyclic voltammogram
(C) To determine the concentration of unknown K_{3}Fe(CN)_{6} solution using a calibration graph of concentration vs. peak height
(D) To determine the effect of the supporting electrolyte on the cyclic voltammogram
(A) To determine the E^{0}’ value and n for the Fe^{III}(CN)_{6}^{3}/ Fe^{II}(CN)_{6}^{4} couple in 0.1M KNO_{3} from the 2mM cyclic voltammogram
(B) To determine the effect of scan rate on peak height of the cyclic voltammogram
(C) To determine the concentration of unknown K_{3}Fe(CN)_{6} solution using a calibration graph of concentration vs. peak height
(D) To determine the effect of the supporting electrolyte on the cyclic voltammogram
RESULTS and CALCULATIONS
Preparation of varying concentrations of K_{3}Fe(CN)_{6}
solutions
Concentration /mM

Volume of 50mM K_{3}Fe(CN)_{6}
solution used / mL

Volume of 0.1M KNO_{3}
solution used / mL

Final volume / mL

2

2.00

48.00

50.00

4

4.00

46.00

50.00

6

6.00

44.00

50.00

8

8.00

42.00

50.00

10

10.00

40.00

50.00

(A) Determine the E^{0}’ value
and n
From the cyclic voltammogram of 2mM K_{3}Fe(CN)_{6} in 0.1M KNO_{3}, E_{pa} = 0.268 V, E_{pc} = 0.185 V.
From the cyclic voltammogram of 2mM K_{3}Fe(CN)_{6} in 0.1M KNO_{3}, E_{pa} = 0.268 V, E_{pc} = 0.185 V.
Therefore, E^{0}’ = (E_{pa}
+ E_{pc}) ÷ 2 = (0.268 + 0.185) ÷ 2 = 0.2265 V ≈ 0.227 V
Percentage
difference between literature value and experimental value = (0.2270.225) /
0.225 x 100% =0.667 %. This small percentage difference between the literature
and experimental value implied that the E^{0}’
obtained experimentally has a rather high degree of accuracy.
ΔE_{p} = E_{pa} – E_{pc}
=_{ }(0.268 – 0.185)≈ 0.059 ÷ n
n ≈ 0.059 ÷ 0.144 ≈ 0.410 ≈ 1
n ≈ 0.059 ÷ 0.144 ≈ 0.410 ≈ 1
Hence, the number of electrons
transferred in the reaction for Fe^{III}(CN)_{6}^{3}/
Fe^{II}(CN)_{6}^{4}couple in
0.1M KNO_{3} is deduced to be 1.
(B)
Determine the effect of scan rate on peak height
4mM K_{3}Fe(CN)_{6} in
0.1M KNO_{3} was used. From the cyclic voltammograms at different scan
rates,
Scan Rate, v (mV/s)

i_{pa} (×10^{4}A)

i_{pc} (×10^{4}A)

li_{pa}/i_{pc}l

v^{1/2} (mV/s)^{1/2}

20

3.514

2.821

1.26

4.47

50

5.279

4.541

1.16

7.07

75

6.223

5.440

1.14

8.66

100

6.970

6.102

1.14

10

Table 1 – Results for Scan Rate and
Peak Height for 4mM K_{3}Fe(CN)_{6} in 0.1M KNO_{3}
From Table 1, the graphs of i_{pa} and i_{pc} vs. v^{1/2}
are plotted:
Figure 1 – Graph of
i_{pa} and i_{pc} against v^{1/2}

Both the graph of i_{pc} and i_{pa} against v^{1/2}
gave a linear plot with R^{2} greater than 0.99. This indicates that
the i_{pc} and i_{pa} were directly proportional to the
square root of the scan rate. From the graph, it also shows that as the scan
rate increases, the peak current also increases.

(C) Determine the concentration of unknown K_{3}Fe(CN)_{6}
solution
From the cyclic voltammograms at
concentrations of K_{3}Fe(CN)_{6},
[K_{3}Fe(CN)_{6}] (mM)

i_{pa} (×10^{4}A)

i_{pc} (×10^{4}A)

li_{pa}/i_{pc}l

2

1.784

1.595

1.12

4

3.514

2.821

1.25

6

5.299

 4.764

1.11

8

6.820

6.099

1.12

10

8.365

7.506

1.11

Table 2 – Results for Peak Height at
varying concentrations of K_{3}Fe(CN)_{6}
From Table 2, the graphs of i_{pa} and i_{pc} vs. [K_{3}Fe(CN)_{6}] are plotted:
Figure 2 – Graph of i_{pa} and i_{pc} against [K_{3}Fe(CN)_{6}]
From the cyclic voltammogram of the
unknown solution, the peak heights are determined to be:
i_{pa}
= 4.378 ×10^{4}A, i_{pc} = 4.002 ×10^{4}A
Using i_{pa} calibration
graph, the
equation of the bestfit line is determined to be y = 0.823x + 0.216
Substituting the i_{pa} value for the unknown solution, the concentration of the unknown solution was determined to be 5.057mM.
Substituting the i_{pa} value for the unknown solution, the concentration of the unknown solution was determined to be 5.057mM.
Using i_{pc} calibration graph, the equation of the bestfit line is
determined to be y = 0.755x – 0.027
Substituting the i_{pc} value for the unknown solution into the equation, the concentration of the unknown solution was determined to be 5.265mM.
Substituting the i_{pc} value for the unknown solution into the equation, the concentration of the unknown solution was determined to be 5.265mM.
Thus, average value for the
concentration of the unknown K_{3}Fe(CN)_{6} solution
= (5.265 + 5.057) ÷2 = 5.161mM
= (5.265 + 5.057) ÷2 = 5.161mM
(D) Determine the effect of the
supporting electrolyte
From
the cyclic voltammogram in different supporting electrolytes,
Solution

Scan Rate
(mV/s) 
E_{pa}
(V) 
E_{pc}
(V) 
i_{pa}
(×10^{4}A) 
i_{pc}
(×10^{4}A) 
E^{0}’
(V) 
ΔE_{p}
(V) 
4mM K_{3}Fe(CN)_{6} in 0.1M KNO_{3}

20

0.275

0.173

3.514

2.821

0.224

0.102

4mM K_{3}Fe(CN)_{6} in 0.1M KCl

20

0.278

0.182

3.424

3.000

0.230

0.096

Table 3 – Results for the two
supporting electrolytes: KNO_{3} and KCl
From Table 3, it can be seen that the E_{pa}
and E_{pc} values for both electrolytes are similar. The peak height
values, i_{pa} and i_{pc}, are slightly lower for the KCl
electrolyte.
DATA ANALYSIS
(A)
Determine the E^{0}’ value and n
The E^{0}’ value from the experiment was determined to be 0.227V. The experimental value deviates slightly from the literature value of 0.225V (by 0.667%). This may be due errors in the extrapolation of the baseline in the cyclic voltammogram. The temperature at which the experiment was conducted could be different from the conditions used for the literature value. A difference in temperature can affect the current flow through the solution and result in a deviation. These random errors should be minimised by taking more readings.
The E^{0}’ value from the experiment was determined to be 0.227V. The experimental value deviates slightly from the literature value of 0.225V (by 0.667%). This may be due errors in the extrapolation of the baseline in the cyclic voltammogram. The temperature at which the experiment was conducted could be different from the conditions used for the literature value. A difference in temperature can affect the current flow through the solution and result in a deviation. These random errors should be minimised by taking more readings.
(B)
Determine the effect of scan rate on peak height
Voltammetric currents depend on the concentration gradient that is established very near the electrode during electrolysis. This is called the Nernst diffusion layer. The relationship between the scan rate and the current peak height can be explained by considering the size of the diffusion layer and the time taken to record the scan^{[1]}.
Voltammetric currents depend on the concentration gradient that is established very near the electrode during electrolysis. This is called the Nernst diffusion layer. The relationship between the scan rate and the current peak height can be explained by considering the size of the diffusion layer and the time taken to record the scan^{[1]}.
The
cyclic voltammogram will take longer to record as the scan rate is decreased.
At a slow scan rate, the diffusion layer will grow much further from the
electrode as compared to a fast scan. This leads to a concentration gradient to
the electrode surface that is much lower as compared to a fast scan. Thus, the
magnitude of the current is directly proportional to the scan rate^{[2]}.
According to the RandlesSevcik equation^{[3]},
i_{p} = 2.686 × 10^{5}n^{3/2}AD^{1/2}Cv^{1/2}
or simply put, the peak current, i_{p} is directly proportional to the square root of the scan rate, v^{1/2 }when other factors are kept constant. This is confirmed from Figure 1 which shows that the experimental values conform closely to the linear relationship between i_{p} and v^{1/2} (with R^{2} values above 0.99).
i_{p} = 2.686 × 10^{5}n^{3/2}AD^{1/2}Cv^{1/2}
or simply put, the peak current, i_{p} is directly proportional to the square root of the scan rate, v^{1/2 }when other factors are kept constant. This is confirmed from Figure 1 which shows that the experimental values conform closely to the linear relationship between i_{p} and v^{1/2} (with R^{2} values above 0.99).
(C)
Determine the concentration of unknown K_{3}Fe(CN)_{6} solution
The relationship between peak current and concentration can be explained by considering the concentration gradient at the diffusion layer. Just outside the diffusion layer, is the bulk solution being analysed. The concentration of the bulk solution is approximately the concentration of the solution and the concentration of the analyte at the surface of the electrode is close to zero (at the potential which peak current occurs). This leads to a concentration gradient and subsequently, the voltammetric current. Thus, a solution of higher concentration will lead to a greater concentration gradient as the difference between the concentration at the electrode surface and the bulk solution is higher. This leads to a higher peak current.
The relationship between peak current and concentration can be explained by considering the concentration gradient at the diffusion layer. Just outside the diffusion layer, is the bulk solution being analysed. The concentration of the bulk solution is approximately the concentration of the solution and the concentration of the analyte at the surface of the electrode is close to zero (at the potential which peak current occurs). This leads to a concentration gradient and subsequently, the voltammetric current. Thus, a solution of higher concentration will lead to a greater concentration gradient as the difference between the concentration at the electrode surface and the bulk solution is higher. This leads to a higher peak current.
From
the RandlesSevcik equation, the peak current, i_{p} is directly
proportional to the concentration of the solution, C when other factors are
kept constant. This allows us to construct a calibration graph from the anodic
peak current, i_{pa} and the cathodic peak current, i_{pc} to
determine the concentration of the unknown solution. Figure 2 confirms the linear relationship between concentration and
peak current. The experimental data conform to linearity with R^{2}
values higher than 0.995. Thus, the concentration obtained for the unknown
solution is considered quite accurate and determined to be 5.161mM.
(D) Determine the effect of the
supporting electrolyte
A supporting electrolyte is added to reduce the effects of migration of the analyte in the solution. It is most commonly an alkali metal salt that is added in excess which does not react at the working electrode at the potentials being used. The current in the cell is primarily due to charges carried by the excess of ions from the supporting electrolyte instead of the analyte and this reduces the effects of migration. The supporting electrolye also reduces the resistance of the solution^{[3]}.
A supporting electrolyte is added to reduce the effects of migration of the analyte in the solution. It is most commonly an alkali metal salt that is added in excess which does not react at the working electrode at the potentials being used. The current in the cell is primarily due to charges carried by the excess of ions from the supporting electrolyte instead of the analyte and this reduces the effects of migration. The supporting electrolye also reduces the resistance of the solution^{[3]}.
The magnitude of the current is
also determined by the rate of mass transport of ions to the edge of the Nernst
diffusion layer by convection and also the rate of transport of ions from the
outer edge of the diffusion layer to the electrode surface^{[5]}. Ions
of a lower mass should have greater mobility. Thus, the supporting electolyte
which has a lower molecular mass should give a higher current. This is
confirmed by the experimental results. The cation of the two electrolytes are
the same. They differ in their anions: Cl^{} with a molar mass of
35.5g/mol and NO_{3}^{} with a molar mass of 63.0g/mol. Since
the charges on the anions are the same, the difference in their mobilities is thus
due to their molar masses. As expected and observed, the i_{pc} peak
current for the solution with KCl as the supporting electrolyte is higher than that
with KNO_{3}. However, the i_{pa} peak current for the former
is unexpectedly lower than the latter. This erratic result may be due to temperature
fluctuations.
Precautions and Other comments
Before recording the cyclic voltammogram, each solution was swirled to ensure homogenity. However, during the recording of the cyclic voltammogram, it was ensured that the solution was not perturbed in any way to prevent inaccuracies. The electrodes were cleaned and blotted dry before changing the solution to be analysed in order to prevent contamination.
Before recording the cyclic voltammogram, each solution was swirled to ensure homogenity. However, during the recording of the cyclic voltammogram, it was ensured that the solution was not perturbed in any way to prevent inaccuracies. The electrodes were cleaned and blotted dry before changing the solution to be analysed in order to prevent contamination.
The i_{pa}/i_{pc} values of all the cyclic voltammograms
are close to 1. This shows that the Fe^{III}(CN)_{6}^{3}/ Fe^{II}(CN)_{6}^{4}
reaction is a reversible electrode reaction with no other reactions involved. The
accuracy of the experiments may be improved by controlling the temperatures of
the solutions and reducing temperature fluctuations.
CONCLUSION
For the Fe^{III}(CN)_{6}^{3}/ Fe^{II}(CN)_{6}^{4} couple in 0.1M KNO_{3} from the 2mM cyclic voltammogram, the E^{0}’ value is determined to be 0.227V and n is determined to be 1.
For the Fe^{III}(CN)_{6}^{3}/ Fe^{II}(CN)_{6}^{4} couple in 0.1M KNO_{3} from the 2mM cyclic voltammogram, the E^{0}’ value is determined to be 0.227V and n is determined to be 1.
The
concentration of the unknown K_{3}Fe(CN)_{6} solution is
determined to be 5.161mM.
The
current peak height varies linearly with the square root of the scan rate, v^{1/2}.
The supporting electrolyte with the lower molar mass produces a higher peak
current.
REFERENCES
[1]
Skoog et. al., Fundamentals of
Analytical Chemistry, 8^{th} Edition, 2004, Brooks/Cole.
[2]
P.T. Kissinger and W.E. Heineman, Laboratory Techniques in Electroanalytical
Chemistry, 2^{nd} Edition, 1996, Dekker.
[3]
E.Gileadi, E. KirowaEisner and J. Penciner, Interfacial Electrochemistry, QD
571 G54 1975.
Where did you find that literature value for the standard reduction potential you used in your calculations?
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