diffusion

Discrimination of Inner- and Outer-Sphere Electrode Reactions byCyclic Voltammetry ExperimentsSachiko Tanimoto and Akio Ichimura*

Department of Chemistry, Graduate School of Science, Osaka City University, Osaka 558-8585, Japan

*S Supporting Information

ABSTRACT: A laboratory experiment for undergraduate students who arestudying homogeneous and heterogeneous electron-transfer reactions isdescribed. Heterogeneous or electrode reaction kinetics can be examined byusing the electrochemical reduction of three FeIII/FeII redox couples atplatinum and glassy carbon disk electrodes. Cyclic voltammetric measure-ment is suitable for determining the electrode-reaction rate constants. Thedependence of the rate constant on the electrode materials enables thestudents to discriminate and discuss the mechanism of the electrodereaction. The experiment is completed in a 5-h laboratory period for pairs ofstudents in analytical chemistry lab class. This material is also suitable for aninorganic chemistry lab class.

KEYWORDS: Upper-Division Undergraduate, Inorganic Chemistry, Analytical Chemistry, Laboratory Instruction,Aqueous Solution Chemistry, Coordination Compounds, Electrochemistry, Instrumental Methods, Kinetics, Oxidation/Reduction,Cyclic Voltammetry

The electron-transfer reactions or redox reactions of metalcomplexes in solution are a basic subject of study in

inorganic chemistry and bioinorganic chemistry. The thermo-dynamic aspects of redox reactions are of fundamentalimportance. The difference in the standard electrode potentialof two redox couples is the driving force in these reactions.From a mechanistic perspective, electron-transfer reactions aregenerally classified into inner- and outer-sphere pathways.There have been a number of studies on the mechanism ofelectron-transfer reactions involving the theories proposed byMarcus and the experimental data has been provided by manyresearchers.1 For example, the self-exchange reaction between[Fe(CN)6]

3‑ and [Fe(CN)6]4‑ is classified as an outer-sphere

electron-transfer reaction and that between Fe3+ and Fe2+ inhydrochloric acid solution is classified as an inner-spherereaction.1

Electrode reactions are similarly distinguished as inner- andouter-sphere electron-transfer reactions at electrodes.2,3 In anouter-sphere electrode reaction, electron transfer between theelectrode and the oxidant or reductant takes place at the planeseparated by at least a solvent layer from the electrode, which iscalled the outer Helmholtz plane (OHP) (Figure 1). Thus, thereactant−electrode interactions should be weak. The approachused for the quantitative theoretical treatment of such electrodereactions can be similarly applied to homogeneous outer-sphereself-exchange reactions. The well-known relation between therate constants ko and kex for the corresponding electrode andhomogeneous self-exchange reactions is

=⎛⎝⎜

⎞⎠⎟

kZ

kZ

o

e

ex

h

1/2

(1)

where Ze and Zh are the collision frequencies for the electrodeand self-exchange reactions and are roughly 104 cm s−1 and 1011

dm3 mol−1 s−1, respectively.3 Alternatively, in an inner-sphereelectrode reaction, a coordinated ligand of electroactive metalcomplexes is bound to the electrode surface and electrontransfer may take place through the ligand adsorbed on theelectrode, the inner Helmholtz plane (IHP). Therefore, the rateconstant of an inner-sphere electrode reaction should be highly

Published: April 26, 2013

Figure 1. Schematic illustration of the mechanism of electrodereactions: (left) outer-sphere mechanism and (right) inner-spheremechanism. IHP is the inner Helmholtz plane and OHP is the outerHelmholtz plane.

Laboratory Experiment

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© 2013 American Chemical Society andDivision of Chemical Education, Inc. 778 dx.doi.org/10.1021/ed200604m | J. Chem. Educ. 2013, 90, 778−781

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dependent on the electrode material, whereas that of an outer-sphere electrode reaction should be less dependent.Cyclic voltammetry (CV) is one of the most useful

techniques for electrochemical measurements.4−7 The equip-ment used for voltammetric measurements is readily available.The measured voltammograms, current or charge versuspotential curves, can be easily digitized and stored on apersonal computer instead of being drawn on an xy recorder.CV measurements are widely used to determine the redoxpotential of redox couples of interest and to elucidate electrodereaction mechanisms including chemical reactions thataccompany the electrode reaction. Thus, CV is often used inlaboratory experiments in inorganic and analytical chemistrycourses for undergraduate students.The structure of electrical double layer including potential

profile on the electrode is a main subject of electrochemistryand controls the electrode reaction rate. From the viewpoint ofthe experimental course in inorganic and analytical chemistrythe focus is on (i) the easy estimation of the electrode reactionconstants by CV, (ii) the dependence of the electrode materialson the reaction rate constants or the shape of CV curves, and(iii) the discrimination of the electrode reaction mechanisms.Here, the details are presented of an experiment by whichundergraduate students can elucidate the mechanism of anelectrode reaction by estimating the rate constants of differentFeIII/FeII redox systems at different electrodes with the aid ofCV measurements. This approach can also be used to showhow instrumental electrochemical methods including chrono-coulometry and cyclic voltammetry can be used to obtain theelectrode reaction rate constants for some electrochemicallyquasi-reversible one-electron redox couples. The students workin pairs for a five hour lab period in this experimental course.

■ EXPERIMENTAL PROCEDUREThe electroactive species for CV measurements were K3[Fe-(CN)6] in 1.0 M (M ≡ mol dm−3) KCl, FeCl3 in 1.0 M HCl,and Fe3(SO4)2 in 0.50 M H2SO4. Voltammetric measurementswere performed with a three-electrode system combined with avoltammetric analyzer (CV-50W, Bioanalytical Systems). Aplatinum disk (diameter = 1.6 mm) and a glassy carbon (GC)disk (diameter = 3.0 mm) were used as working electrodes.The reference and counter electrodes were an Ag/AgCl (3.0 MNaCl) and a platinum wire, respectively.Prior to the CV measurements,8 the diffusion coefficients of

Fe3+ in 1.0 M HCl and 0.50 M H2SO4 were determined fromthe slope of the Q versus t1/2 plot according to eq 2 in potentialstep chronocoulometry

π=

*Q

FAD C t2 O1/2

O1/2

1/2 (2)

where Q is the charge passed upon electrolytic reduction of theFeIII species, F is the Faraday constant, A is the electrodesurface area, DO and CO* are the diffusion coefficient and theconcentration of the reducible FeIII species, respectively, and t isthe time. The surface area of the Pt and GC disk electrodeswere determined by chronocoulometry according to eq 2 usingthe known value of the diffusion coefficient, 7.63 × 10−6 cm2

s−1 of [Fe(CN)6]3‑ in 1.0 M KCl as a standard.9

Cyclic voltammograms of FeIII species were measured on thePt and GC electrodes. The scan rate of each voltammogramwas chosen as the separation of anodic and cathodic peakpotentials, ΔEp = Epa − Epc, becomes larger than 65 mV. The

smaller ΔEp causes some uncertainty in the determination ofthe formal electrode reaction rate constant ko′, which is the rateconstant at Eo′.

■ HAZARDSK3[Fe(CN)6], FeCl3, and Fe3(SO4)2 are harmful if swallowedand cause irritation to the eyes and skin if contacted. Theconcentrated acids are corrosive.

■ CALCULATIONSThe electrode reaction rate constants ko′ are calculated fromthe ΔEp in the voltammograms with the aid of Table 1 and eq

3. Table 1 is reconstructed by utilizing the digital simulationpackage DigiSim 3.0 (Bioanalytical Systems) with theconditions of n = 1 where n is the number of the electronsinvolved in the electrode reaction, DO = DR, where DR is thediffusion coefficient of the reductant, transfer coefficient αc =0.5, and Eλ − Eo′ = −1 V where Eλ is the switching potential.

10

The relatively large negative potential with respect to Eo′ isadopted as Eλ because some measured values of ΔEp exceed200 mV.The calculation is tried using the cyclic voltammogram of 2.0

mM K3[Fe(CN)6] in 1.0 M KCl at the Pt electrode with thescan rate of 200 mV s−1 as shown in Figure 2A. The measuredvalue of ΔEp was 66 mV which corresponds to 3.0 of thedimensionless rate parameter Ψ from Table 1.11 The parameterΨ is expressed as

ψπ

= ′ = ΔkD v F RT

f E[ ( / )]

( )o

O1/2 p

(3)

Then, the ko′ value at 278 K can be calculated to be 4.1 × 10−2

cm s−1 using DO = 7.63 × 10−6 cm2 s−1 and v = 0.2 V s−1

according to eq 3.The values of kinetic parameter ko′ for other redox couples

are similarly calculated and are summarized in Table 2 alongwith thermodynamic (Eo′) and mass transfer (DO) parameters.The Eo′ values can be properly calculated by averaging Epa andEpc because the αc values for all redox couples studied are near0.5.12

■ RESULTS AND DISCUSSIONThe redox couple of [Fe(CN)6]

3‑/[Fe(CN)6]4‑ is known to be

an electrochemically reversible system at platinum and some

Table 1. Relationship between ψ Function Parameter andPeak Potential Separation ΔEp

a

ΔEp/mV Ψ ΔEp/mV Ψ

61.6 6.0 220 0.1062.5 5.0 288 5.0 × 10−2

63.8 4.0 382 2.0 × 10−2

66.0 3.0 454 1.0 × 10−2

70.3 2.0 525 5.0 × 10−3

82.8 1.0 620 2.0 × 10−3

90.6 0.75 691 1.0 × 10−3

105 0.50 763 5.0 × 10−4

123 0.35 857 2.0 × 10−4

144 0.25 929 1.0 × 10−4

aThe table is constructed by utilizing the digital simulation packageDigiSim 3.0 (Bioanalytical Systems). (One-electron reduction, DO =DR, αc = 0.5, Eλ − Eo′ = −1 V).

Journal of Chemical Education Laboratory Experiment

dx.doi.org/10.1021/ed200604m | J. Chem. Educ. 2013, 90, 778−781779

carbon electrodes and has been widely used for the first CVmeasurement in laboratory experimental classes.4,5,7,13 In thisexperiment, CV measurements of three FeIII/FeII redox couplesinvolving [Fe(CN)6]

3‑/[Fe(CN)6]4‑ in 1.0 M KCl, Fe3+/Fe2+ in

1.0 M HCl, and Fe3+/Fe2+ in 0.050 M H2SO4 are conductedand the redox behaviors are compared.Figure 2A shows the cyclic voltammograms of 2.0 mM

K3[Fe(CN)6] in 1.0 M KCl at platinum and GC disk electrodeswith a scan rate of 200 mV s−1. Both voltammograms areelectrochemically quasi-reversible systems, in which thepotential difference between the cathodic and anodic peakpotentials, ΔEp, is more than 59 mV. Panels B and C of Figure2 show the cyclic voltammograms at the Pt and GC diskelectrodes for the Fe3+/Fe2+ redox couples in 1.0 Mhydrochloric acid and 0.50 M sulfuric acid, respectively. Theelectrochemical parameters obtained for these redox couplesare also summarized in Table 2.For the redox couple of [Fe(CN)6]

3‑/[Fe(CN)6]4‑, ko′ at

both electrodes is large enough for the system to behave as areversible electrochemical process at a slow scan rate such as100 mV/s, although the value at the Pt electrode is about threetimes larger than that at the GC electrode. Consequently, theelectrode reaction of this redox couple proceeds by an outer-sphere mechanism. On the other hand, the cyclic voltammo-grams at the GC electrode in HCl and H2SO4 show broadpeaks with large ΔEp, whereas comparatively sharp peaksappear in the voltammograms at the Pt electrode in both acidsolutions. The ko′ values at the Pt electrode in HCl and H2SO4are 50- and 100-fold greater than those at the GC electrode,respectively. The great dependence of ko′ on the electrodematerial indicates that the electrode reaction at the Pt electrodefor the Fe3+/Fe2+ redox couple in HCl and H2SO4 follows aninner-sphere type mechanism.For the redox couple [Fe(CN)6]

3‑/[Fe(CN)6]4‑ in KCl, MLx

in the left illustration of the outer-sphere mechanism in Figure1 can be replaced by [Fe(CN)6]

3‑/[Fe(CN)6]4‑. Similarly Mn+

and Lm‑ are replaced by Fe3+/2+ and Cl− or SO42‑, respectively,

in the right illustration of the inner-sphere mechanism for theFe3+/Fe2+ couple at Pt electrode in HCl or H2SO4. Thereduction of [Fe(CN)6]

3‑ takes place at the plane separated byat least one water molecule from the Pt or GC electrode. Incontrast, Fe3+ in HCl is easily reducible through the bridging ofa chloride or sulfate anion that is adsorbed on the Pt electrodeand coordinates concurrently to one Fe3+ cation. The slowelectrode reaction rate for the reduction of Fe3+ at the GCelectrode is due to the slight adsorption of chloride or sulfateions on the electrode.

■ CONCLUSION

A lab experiment is presented for advanced analytical chemistrystudents. The students measure the voltammograms of threedifferent FeIII/II redox couples at two different workingelectrodes. The kinetic ko′, thermodynamic Eo′, and masstransfer DO parameters are determined from the voltammo-gram of each redox system. The dependence of ko′ on theworking electrode materials of platinum and glassy carbon leadsto the discrimination of electrode reaction mechanisms. Theillustration of electrode reaction mechanisms helps the studentsto learn the reaction path in the Helmholtz planes at theelectrode. The students can also realize at a glance thedifferences of these mechanisms from the shape of voltammo-gram such as ΔEp. The experiment is completed in a 5-hlaboratory period for pairs of students when the instructor canmeasure the diffusion coefficient of each oxidant before class. Ifa voltammogram simulation software package is available, thestudents can better understand cyclic voltammetry from thecomparison of measured and simulated voltammograms.

■ ASSOCIATED CONTENT

*S Supporting Information

Student handout. This material is available via the Internet athttp://pubs.acs.org.

Figure 2. Cyclic voltammograms at Pt (red) and GC (black) electrodes: (A) of 2.0 mM K3[Fe(CN)6] in 1.0 M KCl with a scan rate of 200 mV s−1,(B) of 2.0 mM FeCl3 in 1.0 M HCl with a scan rate of 50 mV s−1, and (C) of 1.7 mM Fe2(SO4)3 in 0.50 M H2SO4 with a scan rate of 50 mV s−1.

Table 2. Electrode Reaction Parameters Obtained from Cyclic Voltammetric Measurements

couple electrode ΔEp/mV (v/V s−1) ko′/cm s−1 mechanism Eo′/V DO/cm2 s−1

[Fe(CN)6]3‑/ Pt 66 (0.2) 4.1 × 10−2 outer sphere 0.278 7.63 × 10−6

[Fe(CN)6]4‑

1.0 M KCl GC 86 (0.2) 1.2 × 10−2 0.280Fe3+/Fe2+ Pt 86 (0.05) 5.0 × 10−3 inner sphere 0.442 4.96 × 10−6

1.0 M HCl GC 392 (0.05) 1.0 × 10−4 0.439Fe3+/Fe2+ Pt 107 (0.05) 2.7 × 10−3 inner sphere 0.418 5.18 × 10−6

0.50 M H2SO4 GC 512 (0.05) 3.3 × 10−5 0.410



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■ AUTHOR INFORMATIONCorresponding Author

*E-mail: [email protected]

The authors declare no competing financial interest.

■ REFERENCES(1) Lappin, A. G. Redox Mechanisms in Inorganic Chemistry; EllisHorwood: New York, 1994.(2) Torres, L. M.; Gil, A. F.; Galicia, L.; Gonzalez, I. J. Chem. Educ.1996, 73, 808−810.(3) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentalsand Applications, 2nd ed.; Wiley: New York, 2001; pp 115−124.(4) Kissinger, P. T.; Heineman, W. R. J. Chem. Educ. 1983, 60, 702−706.(5) Van Benschoten, J. J.; Lewis, J. Y.; Heineman, W. R.; Roston, D.A.; Kissinger, P. T. J. Chem. Educ. 1983, 60, 772−776.(6) Baldwin, R. P.; Ravichandran, K.; Johnson, R. K. J. Chem. Educ.1984, 61, 820−823.(7) May, M. A.; Gupta, V. K. J. Chem. Educ. 1997, 74, 824−828.(8) An instructor can conduct the chronocoulometric experimentsand calculate the diffusion coefficients in advance if the class does nothave enough time to do these experiments.(9) Sawyer, D. T.; Sobkowiak, A.; Roberts, J. L., Jr. Electrochemistryfor Chemists, 2nd ed.; Wiley: New York, 1995, p 219.(10) A similar table is referred in the case of Eλ − Epc = 112.5 mV andΔEp values ≤ 212 mV.14

(11) For 0.3 < αc < 0.7, the ΔEp values are nearly independent of αcand depend only on Ψ.14(12) The values of αc were estimated by fitting the measuredvoltammograms to the corresponding simulated voltammograms usingαc as the fitting parameter with the help of DigiSim 3.0 (BioanalyticalSystems).(13) Santos, A. L.; Takeuchi, R. M.; Oliveira, H. P.; Rodrigues, M. G.;Zimmerman, R. L. J. Chem. Educ. 2004, 81, 842−846.(14) Bard, A. J.; Faulkner, L. R. Electrochemical Methods:Fundamentals and Applications, 2nd ed.; Wiley: New York, 2001; pp242−243.



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