Discrimination of Inner- and Outer-Sphere Electrode Reactions by

From a mechanistic perspective, electron-transfer reactions are generally classified into inner- and outer-sphere pathways. There have been a number o...
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Laboratory Experiment pubs.acs.org/jchemeduc

Discrimination of Inner- and Outer-Sphere Electrode Reactions by Cyclic Voltammetry Experiments Sachiko 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 are studying homogeneous and heterogeneous electron-transfer reactions is described. Heterogeneous or electrode reaction kinetics can be examined by using the electrochemical reduction of three FeIII/FeII redox couples at platinum and glassy carbon disk electrodes. Cyclic voltammetric measurement is suitable for determining the electrode-reaction rate constants. The dependence of the rate constant on the electrode materials enables the students to discriminate and discuss the mechanism of the electrode reaction. The experiment is completed in a 5-h laboratory period for pairs of students in analytical chemistry lab class. This material is also suitable for an inorganic 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

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he electron-transfer reactions or redox reactions of metal complexes in solution are a basic subject of study in inorganic chemistry and bioinorganic chemistry. The thermodynamic aspects of redox reactions are of fundamental importance. The difference in the standard electrode potential of two redox couples is the driving force in these reactions. From a mechanistic perspective, electron-transfer reactions are generally classified into inner- and outer-sphere pathways. There have been a number of studies on the mechanism of electron-transfer reactions involving the theories proposed by Marcus and the experimental data has been provided by many researchers.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+ in hydrochloric acid solution is classified as an inner-sphere reaction.1 Electrode reactions are similarly distinguished as inner- and outer-sphere electron-transfer reactions at electrodes.2,3 In an outer-sphere electrode reaction, electron transfer between the electrode and the oxidant or reductant takes place at the plane separated by at least a solvent layer from the electrode, which is called the outer Helmholtz plane (OHP) (Figure 1). Thus, the reactant−electrode interactions should be weak. The approach used for the quantitative theoretical treatment of such electrode reactions can be similarly applied to homogeneous outer-sphere self-exchange reactions. The well-known relation between the rate constants ko and kex for the corresponding electrode and homogeneous self-exchange reactions is © 2013 American Chemical Society and Division of Chemical Education, Inc.

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

⎛ k ⎞1/2 ko = ⎜ ex ⎟ Ze ⎝ Zh ⎠

(1)

where Ze and Zh are the collision frequencies for the electrode and self-exchange reactions and are roughly 104 cm s−1 and 1011 dm3 mol−1 s−1, respectively.3 Alternatively, in an inner-sphere electrode reaction, a coordinated ligand of electroactive metal complexes is bound to the electrode surface and electron transfer may take place through the ligand adsorbed on the electrode, the inner Helmholtz plane (IHP). Therefore, the rate constant of an inner-sphere electrode reaction should be highly Published: April 26, 2013 778

dx.doi.org/10.1021/ed200604m | J. Chem. Educ. 2013, 90, 778−781

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Laboratory Experiment

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

dependent on the electrode material, whereas that of an outersphere electrode reaction should be less dependent. Cyclic voltammetry (CV) is one of the most useful techniques for electrochemical measurements.4−7 The equipment used for voltammetric measurements is readily available. The measured voltammograms, current or charge versus potential curves, can be easily digitized and stored on a personal computer instead of being drawn on an xy recorder. CV measurements are widely used to determine the redox potential of redox couples of interest and to elucidate electrode reaction mechanisms including chemical reactions that accompany the electrode reaction. Thus, CV is often used in laboratory experiments in inorganic and analytical chemistry courses for undergraduate students. The structure of electrical double layer including potential profile on the electrode is a main subject of electrochemistry and controls the electrode reaction rate. From the viewpoint of the experimental course in inorganic and analytical chemistry the focus is on (i) the easy estimation of the electrode reaction constants by CV, (ii) the dependence of the electrode materials on 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 which undergraduate students can elucidate the mechanism of an electrode reaction by estimating the rate constants of different FeIII/FeII redox systems at different electrodes with the aid of CV measurements. This approach can also be used to show how instrumental electrochemical methods including chronocoulometry and cyclic voltammetry can be used to obtain the electrode reaction rate constants for some electrochemically quasi-reversible one-electron redox couples. The students work in pairs for a five hour lab period in this experimental course.

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HAZARDS K3[Fe(CN)6], FeCl3, and Fe3(SO4)2 are harmful if swallowed and cause irritation to the eyes and skin if contacted. The concentrated acids are corrosive.

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CALCULATIONS The electrode reaction rate constants ko′ are calculated from the ΔEp in the voltammograms with the aid of Table 1 and eq Table 1. Relationship between ψ Function Parameter and Peak Potential Separation ΔEpa

π

ΔEp/mV

6.0 5.0 4.0 3.0 2.0 1.0 0.75 0.50 0.35 0.25

220 288 382 454 525 620 691 763 857 929

Ψ 0.10 5.0 × 2.0 × 1.0 × 5.0 × 2.0 × 1.0 × 5.0 × 2.0 × 1.0 ×

10−2 10−2 10−2 10−3 10−3 10−3 10−4 10−4 10−4

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

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Q=

Ψ

61.6 62.5 63.8 66.0 70.3 82.8 90.6 105 123 144 a

3. Table 1 is reconstructed by utilizing the digital simulation package DigiSim 3.0 (Bioanalytical Systems) with the conditions of n = 1 where n is the number of the electrons involved in the electrode reaction, DO = DR, where DR is the diffusion 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′ is adopted as Eλ because some measured values of ΔEp exceed 200 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 the scan rate of 200 mV s−1 as shown in Figure 2A. The measured value of ΔEp was 66 mV which corresponds to 3.0 of the dimensionless rate parameter Ψ from Table 1.11 The parameter Ψ is expressed as

EXPERIMENTAL PROCEDURE The 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 measurements were performed with a three-electrode system combined with a voltammetric analyzer (CV-50W, Bioanalytical Systems). A platinum 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 M NaCl) 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 from the slope of the Q versus t1/2 plot according to eq 2 in potential step chronocoulometry 2FADO1/2CO*t 1/2 1/2

ΔEp/mV

ψ= (2)

ko′ = f (ΔEp) [πDOv(F /RT )]1/2

(3)

Then, the k ′ 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 along with thermodynamic (Eo′) and mass transfer (DO) parameters. The Eo′ values can be properly calculated by averaging Epa and Epc because the αc values for all redox couples studied are near 0.5.12 o

where Q is the charge passed upon electrolytic reduction of the FeIII species, F is the Faraday constant, A is the electrode surface area, DO and CO* are the diffusion coefficient and the concentration of the reducible FeIII species, respectively, and t is the time. The surface area of the Pt and GC disk electrodes were determined by chronocoulometry according to eq 2 using the 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 the Pt and GC electrodes. The scan rate of each voltammogram was chosen as the separation of anodic and cathodic peak potentials, ΔEp = Epa − Epc, becomes larger than 65 mV. The

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RESULTS AND DISCUSSION The redox couple of [Fe(CN)6]3‑/[Fe(CN)6]4‑ is known to be an electrochemically reversible system at platinum and some 779

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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 3‑

[Fe(CN)6] / [Fe(CN)6]4‑ 1.0 M KCl Fe3+/Fe2+ 1.0 M HCl Fe3+/Fe2+ 0.50 M H2SO4

ΔEp/mV (v/V s−1)

ko′/cm s−1 −2

Pt

66 (0.2)

4.1 × 10

GC Pt GC Pt GC

86 (0.2) 86 (0.05) 392 (0.05) 107 (0.05) 512 (0.05)

1.2 5.0 1.0 2.7 3.3

carbon electrodes and has been widely used for the first CV measurement in laboratory experimental classes.4,5,7,13 In this experiment, CV measurements of three FeIII/FeII redox couples involving [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 conducted and 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 electrodes with a scan rate of 200 mV s−1. Both voltammograms are electrochemically quasi-reversible systems, in which the potential difference between the cathodic and anodic peak potentials, ΔEp, is more than 59 mV. Panels B and C of Figure 2 show the cyclic voltammograms at the Pt and GC disk electrodes for the Fe3+/Fe2+ redox couples in 1.0 M hydrochloric acid and 0.50 M sulfuric acid, respectively. The electrochemical parameters obtained for these redox couples are 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 a reversible electrochemical process at a slow scan rate such as 100 mV/s, although the value at the Pt electrode is about three times larger than that at the GC electrode. Consequently, the electrode reaction of this redox couple proceeds by an outersphere mechanism. On the other hand, the cyclic voltammograms at the GC electrode in HCl and H2SO4 show broad peaks with large ΔEp, whereas comparatively sharp peaks appear in the voltammograms at the Pt electrode in both acid solutions. The ko′ values at the Pt electrode in HCl and H2SO4 are 50- and 100-fold greater than those at the GC electrode, respectively. The great dependence of ko′ on the electrode material indicates that the electrode reaction at the Pt electrode for the Fe3+/Fe2+ redox couple in HCl and H2SO4 follows an inner-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 Figure 1 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,

× × × × ×

10−2 10−3 10−4 10−3 10−5

mechanism

Eo′/V

DO/cm2 s−1

outer sphere

0.278

7.63 × 10−6

inner sphere inner sphere

0.280 0.442 0.439 0.418 0.410

4.96 × 10−6 5.18 × 10−6

in the right illustration of the inner-sphere mechanism for the Fe3+/Fe2+ couple at Pt electrode in HCl or H2SO4. The reduction of [Fe(CN)6]3‑ takes place at the plane separated by at least one water molecule from the Pt or GC electrode. In contrast, Fe3+ in HCl is easily reducible through the bridging of a chloride or sulfate anion that is adsorbed on the Pt electrode and coordinates concurrently to one Fe3+ cation. The slow electrode reaction rate for the reduction of Fe3+ at the GC electrode is due to the slight adsorption of chloride or sulfate ions on the electrode.

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CONCLUSION A lab experiment is presented for advanced analytical chemistry students. The students measure the voltammograms of three different FeIII/II redox couples at two different working electrodes. The kinetic ko′, thermodynamic Eo′, and mass transfer DO parameters are determined from the voltammogram of each redox system. The dependence of ko′ on the working electrode materials of platinum and glassy carbon leads to the discrimination of electrode reaction mechanisms. The illustration of electrode reaction mechanisms helps the students to learn the reaction path in the Helmholtz planes at the electrode. The students can also realize at a glance the differences of these mechanisms from the shape of voltammogram such as ΔEp. The experiment is completed in a 5-h laboratory period for pairs of students when the instructor can measure the diffusion coefficient of each oxidant before class. If a voltammogram simulation software package is available, the students can better understand cyclic voltammetry from the comparison of measured and simulated voltammograms.

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ASSOCIATED CONTENT

S Supporting Information *

Student handout. This material is available via the Internet at http://pubs.acs.org. 780

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Laboratory Experiment

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Lappin, A. G. Redox Mechanisms in Inorganic Chemistry; Ellis Horwood: 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: Fundamentals and 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 experiments and calculate the diffusion coefficients in advance if the class does not have enough time to do these experiments. (9) Sawyer, D. T.; Sobkowiak, A.; Roberts, J. L., Jr. Electrochemistry for Chemists, 2nd ed.; Wiley: New York, 1995, p 219. (10) A similar table is referred in the case of Eλ − Epc = 112.5 mV and ΔEp values ≤ 212 mV.14 (11) For 0.3 < αc < 0.7, the ΔEp values are nearly independent of αc and depend only on Ψ.14 (12) The values of αc were estimated by fitting the measured voltammograms to the corresponding simulated voltammograms using αc as the fitting parameter with the help of DigiSim 3.0 (Bioanalytical Systems). (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; pp 242−243.

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