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Development and Use of a Cyclic Voltammetry Simulator To Introduce Undergraduate Students to Electrochemical Simulations Jay H. Brown* Science Department, Southwest Minnesota State University, 1501 State Street, Marshall, Minnesota 56258, United States S Supporting Information *

ABSTRACT: Cyclic voltammetry (CV) is a popular technique for the study of electrochemical mechanisms because the method can provide useful information on the redox couple. The technique involves the application of a potential ramp on an unstirred solution while the current is monitored, and then the ramp is reversed for a return sweep. CV is sometimes introduced in undergraduate chemistry laboratories. The CV waveform is dependent on several processes including charge transfer, diffusion, and coupled homogeneous reactions. Computer simulations are sometimes used to study these effects. An easy-to-use CV simulator was written in Microsoft Excel for the purpose of teaching undergraduate students and to serve as an entryway to more sophisticated electrochemical simulations. KEYWORDS: Upper-Division Undergraduate, Analytical Chemistry, Physical Chemistry, Hands-On Learning/Manipulatives, Electrochemistry

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INTRODUCTION Cyclic voltammetry (CV) is often used to study electrochemical processes because the technique can provide valuable information on the redox couple.1 The method is sometimes incorporated into undergraduate chemistry laboratories.2 CV involves the application of a potential ramp on an unstirred solution while the resulting current is monitored, and then the ramp is reversed for a return sweep (Figure 1). The cyclic voltammogram of benzophenone (Figure 1b) consists of a reduction current peak obtained during the initial sweep and an inverted oxidation current peak produced during the return scan. Measuring the potential difference between the two peaks provides 0.065 V, suggesting a single reversible electron transfer.3 The absolute value of the oxidation current peak is smaller than the current peak for reduction. A possible reaction scheme involves an EC2 mechanism in which a second order homogeneous chemical reaction occurs after the electron transfer (Scheme 1),4 where kf and kb are the forward and backward heterogeneous rate constants for electron transfer at the electrode surface, and k2 is the second order homogeneous rate constant for benzopinacol dimer formation that removes a portion of the benzophenone in the vicinity of the working electrode, thus reducing the magnitude of the oxidation current peak.

parameters in the spreadsheet, which is a valuable feature for the learning process. The potential ramp of a CV experiment is simulated in the spreadsheet using the following eq (Table 1):5

E = E1 ± vt

where E is the potential being ramped, and E1 is the starting potential. The potential is first ramped in the negative direction (−vt) until it reaches a predetermined switching potential (E2). The potential is then ramped in the positive direction (+vt) for the return sweep back to E1. The heterogeneous rate constants for the redox couple are then calculated using the following Butler−Volmer relationships:3 o

k f = koe−αnF(E − E ′)/RT k b = koe(1 − α)nF(E − E

o

′)/RT

(2) (3)

where kf, kb, and ko are the forward, backward, and standard heterogeneous rate constants for electron transfer, respectively. Note that kf and kb equal ko when the applied potential (E) equals the formal potential Eo′. Also note that heterogeneous rate constants correspond to reactions at the electrode surface and have units of cm/s as compared to first or second order homogeneous rate constants for chemical reactions that occur in solution and have units of s−1 and cm3/mol s, respectively (discussed in the following). Reactions at the electrode surface generate concentration gradients resulting in diffusion. Several techniques can be used to simulate this process.1,3,5 A simple approach called the point method was adopted for the spreadsheet.5 The method is based on a diffusion grid where each line represents an array of concentration values (Figure 2).

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THEORY Computer simulations of CV data can be helpful in obtaining additional information on the redox couple.1,3,5 An easy-to-use CV simulator was written in Microsoft Excel for use in undergraduate chemistry laboratories (see Supporting Information). Excel was selected as the platform for this work because of its wide availability; spreadsheets can be easily modified as needed, and spreadsheets allow students to see all the calculations involved in the simulations. The students receive instantaneous visual feedback as they change the simulation © XXXX American Chemical Society and Division of Chemical Education, Inc.

(1)

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Figure 1. (a) Potential ramp and (b) cyclic voltammogram of 9.8 × 10−8 mol/cm3 benzophenone (background subtracted) at pH = 2.0 with initial potential = 0.20 V, switching potential = −0.30 V, and scan rate = 0.04 V/s. See Experimental section for additional acquisition parameters.

Scheme 1. Possible Reaction Scheme for the Electrochemical Reduction of Benzophenone

Figure 2. Section of a diffusion grid used for the point method.

The total time of a CV experiment (ttotal) equals twice the potential range divided by the scan rate. The time increment (Δt) equals the total time divided by the number of time increments in the grid (Figure 2). The total distance is calculated as xtotal = 6(Dttotal)1/2. This corresponds to about four

times the root-mean-square distance a species diffuses throughout the course of an experiment.1,3 The distance increment (Δx) equals the total distance divided by the number of distance increments in the grid. The variable Cj is a predicted concentration of a diffusing species located at a

Table 1. Symbols, Definitions, Values (Where Appropriate), and Units Symbol

Definition

Value and Units

A α, α1, α2 C, Cj, Ci, COx,0, etc. D E, E1, E2, Eo′, E1o′, E2o′ F iTotal JOx, JRed k1, k1,1, k1,2, k2

Surface area of the working electrode Transfer coefficient for redox couple, analogous for first and second redox couple in a series Various concentrations used in the simulations (see Theory section for details on subscripts) Common value for the diffusion coefficients Potential value, starting potential, switching potential, formal potential for redox couple, analogous for first and second couple in a series, respectively Faraday constant Total faradaic current for the simulation Fluxes for the oxidized and reduced forms of a redox couple, respectively First order homogeneous rate constant, analogous for first and second homogeneous reactions, and second order homogeneous rate constant, respectively Heterogeneous forward, backward, and standard rate constant for electron transfer, respectively Simulation parameter for a diffusion grid Number of electrons, number of electrons in initial charge transfer, number of electrons in first and second redox couple in a series, respectively Gas law constant Time, total time of CV experiment, and time increment of a diffusion grid, respectively Temperature Scan rate of a CV experiment Distance, total distance of a diffusion grid, and distance increment of diffusion grid, respectively

cm2 ≈ 0.5 (unitless) mol/cm3 ≈ 1 × 10−5 cm2/s V

kf, kb, ko λ n, na, n1, n2 R t, ttotal, Δt T v x, xtotal, Δx

B

96485 C/mol A mol/cm2 s s−1, cm3/mol s cm/s unitless often 1 or 2 (unitless) 8.31451 J/K mol s K V/s cm

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Eq 9 was derived by writing the relationship between the flux of the oxidized form, diffusion coefficient, and the concentration gradient at the electrode surface in discrete form (JOx = −D[COx,1 − COx,0]/Δx).1,3 Unfortunately, this equation cannot be used directly in the simulation because the concentration of the oxidized form at the electrode surface (COx,0) is an unknown boundary condition required for the point method outlined earlier. However, the equation can still be rearranged to give COx,0 = COx,1 + (JOxΔx/D). Likewise, CRed,0 = CRed,1 + (JRedΔx/D). Because the flux of the oxidized form can also be written as a rate equation (JOx = kf COx,0 − kb CRed,0), substitution of the two previous equations into the rate equation followed by rearrangement gives eq 9. The surface concentrations of the oxidized and reduced forms can now be calculated using the two equations below:1,3

specific time and distance increment (e.g., 2Δx and 2Δt) calculated from three earlier data points (Ci−1, Ci, and Ci+1) on the grid (Figure 2). Fick’s Second Law of Diffusion (eq 4) is approximated in discrete form (eq 5) and then solved for the concentration of interest (eq 6) where the time and distance increments Δt and Δx were defined above and the simulation parameter λ = DΔt/ Δx2:1,3,5 δC δ 2C =D 2 δt δx

Cj − Ci Δt

=

(4)

D[Ci − 1 − 2Ci + Ci + 1] Δx 2

Cj = Ci + λ(Ci − 1 − 2Ci + Ci + 1)

(5) (6)

COx,0 = COx,1 +

Eq 6 cannot be used to predict the concentrations for the first column, last column, or bottom row of a diffusion grid because these three arrays lack earlier concentration(s) necessary for the calculations. Instead, these regions are filled with concentration values using boundary conditions.1,3,5 The first column of the grid contains concentrations at the working electrode surface. These are calculated values discussed in the following. The last column contains concentrations furthest from the electrode surface. This array is filled with the bulk concentration. The bottom row of the grid contains concentration values at the start of the simulation. This array is filled with the bulk concentration as well. Eq 6 is then used to fill the remaining grid locations. The spreadsheet uses several 200Δt by 50Δx diffusion grids for various species in the simulation. The following modifications of eq 6 were incorporated into the diffusion grids associated with the reduced form to account for first and second order coupled homogeneous reactions that occur in solution during EC and EC 2 mechanisms, respectively:1,5 Cj = Ci + λ(Ci − 1 − 2Ci + Ci + 1) − k1ΔtCi

(7)

Cj = Ci + λ(Ci − 1 − 2Ci + Ci + 1) − 2k 2ΔtCi 2

(8)

C Red,0 = C Red,1 +

i Total = −nFAJOx

JOx = −JRed

k f Δx D

+

k bΔx D

(11)

JRed Δx

(13)

Graphing the total current (y-axis) versus potential (x-axis) displays the simulation (Figure 3). The potential is graphed in

Figure 3. Cyclic voltammogram of benzophenone and EC2 simulation with parameters: COx,Bulk = 6.1 × 10−8 mol/cm3, Eo′ = 0.013 V, n = 1, D = 1 × 10−5 cm2/s, A = 2.54 × 10−2 cm2, v = 0.04 V/s, ko = 1 cm/s, and k2 = 1.6 × 106 cm3/mol s.

k f COx,1 − k bC Red,1 1+

D

(12) D where COx,0 and CRed,0 are the concentrations of the oxidized and reduced forms at the electrode surface, respectively. The total faradaic current that corresponds to each time increment is finally calculated using:1,3

where k1 is the first order rate constant for a homogeneous chemical reaction (s −1 ), and k 2 is the second order homogeneous rate constant (cm3/mol s). The rate constants can also be set to zero if a homogeneous chemical reaction does not occur after reduction. The rate of mass transfer to the electrode surface is then described in the simulator using the following flux equations:1,3 −JOx =

JOx Δx

(9)

the reverse direction and current graphed in the positive direction. This common display convention for CV results in upright reduction current peaks and more difficult reductions (requiring greater negative potentials) results in peaks located further to the right.3 The display can be easily changed by altering the graphic options in the spreadsheet. The broadening observed in the experimental voltammogram may be the result of capacitance effects, which are not included in the simulation.5 These and other limitations of the spreadsheet are outlined in the Results section. The spreadsheet can also be used to demonstrate important aspects of CV such as the separation in potential between the

(10)

where JOx and JRed are fluxes, and COx,1 and CRed,1 are concentrations of the oxidized and reduced forms one distance increment away from the electrode surface, respectively. Note the fluxes for the oxidized and reduced forms are always in equal but opposite directions (eq 10). The sign conventions of eq 10 indicate that the reactant (e.g., the oxidized form during reduction) migrates toward the electrode surface, while the product (i.e., the reduced form, respectively) migrates away from the electrode surface. C

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The spreadsheet mechanism labeled as EC with na allows the simulation of two or more overlapping EC waveforms of the same shape.3 The modified mechanism requires two separate values for the number of electrons. The number of electrons in the initial charge transfer step (na, generally 1 or 2) automatically replaces the number of electrons (n, Table 1) in the Butler−Volmer calculations (eqs 2 and 3). This controls the shape of the overlapping waveforms. The total number of electrons (n), which can now be any integer value, is used in the calculations of the faradaic currents (eq 13). This governs the area of the overlapping waveforms. For example, using na = 2 and n = 4 simulates the shape and area of two overlapping two-electron waveforms located at Eo′. Combining two EC simulations together provides an ECEC mechanism in which the two homogeneous reactions remove portions of the two reduced species as electropassive products. The product of the first redox couple is used as the reactant for the second couple in the series by adding the fluxes of the first reduced form (eq 10) to the corresponding surface concentration calculations of the second oxidized species (eq 11). Setting E1o′ > E2o′ with n1 and n2 = 1 provides two oneelectron waveforms at the two Eo′ values (Figure 6).1 Setting

current peaks of a redox couple increases as the standard heterogeneous rate constant (ko) decreases; redox couples with fast electron transfer (i.e., large ko values) exhibit electrochemically reversible behavior indicated by current peak potentials that are independent of scan rate (v), and irreversible systems with small ko values coupled with fast homogeneous reactions on the experimental time scale (i.e., large k1 or k2 values) provide current peaks that shift toward negative potentials with increasing scan rates (Figures 4 and 5).

Figure 4. Effect of reducing the standard heterogeneous rate constant (ko) using the EC mechanism with k1 = 0 s−1 and v = 0.1 V/s.

Figure 6. Effect of setting E1o′< E2o′ in ECEC mechanism with v = 0.05 V/s. Parameters: (a) E1o′ = 0.1 V, E2o′ = −0.1 V, n1 = 1, n2 = 1. (b) E1o′ = −0.1 V, E2o′ = 0.1 V, n1 = 1, n2 = 1.

E1o′ < E2o′ with n1 and n2 = 1 results in a single two-electron waveform located at the average Eo′ value. When E1o′ < E2o′, the simulator automatically adds the number of electrons and averages the two Eo′ values of the two redox couples in the Butler−Volmer calculations (eqs 2 and 3). The first column of simulation parameters on the ECEC mechanism page of the spreadsheet is designated as the first redox couple in the series. The second column of parameters is for the second redox couple.

Figure 5. Effect of increasing the scan rate (v) on an irreversible EC system with ko = 0.01 cm/s and k1 = 10 s−1.

The current peak potential shift with the scan rate is related to the flux through diffusion and Butler−Volmer kinetics. Large scan rates (v) result in small values for Δx (see Figure 2 and subsequent discussion). Small ko values result in small values for kf and kb (eqs 2 and 3). The flux depends on Δx, kf, and kb (eq 9). The current depends on the flux (eq 13). When kf and kb are small, the minimum and maximum JOx flux values shift toward negative and positive potentials, respectively, with increasing scan rate. The difference in potential between the two current peaks increase, and the waveform becomes extended. This is electrochemically irreversible behavior. When kf and kb are large, the minimum and maximum JOx values and the separation in potential between the two current peaks become insensitive to the scan rate resulting in electrochemically reversible behavior.

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EXPERIMENTAL SECTION Ethanol (Pharmco; 200-proof), benzophenone (Mallinckrodt; 99%), sodium sulfate (Fisher; 99%), sulfuric acid (Fisher; 98%), and mercury (Bethlehem; 99.9995%) were used without further purification. The water was distilled twice using a glass still. A stock solution of 0.1 M sodium sulfate electrolyte was prepared in a 500 mL volumetric flask and transferred to a plastic storage bottle. A benzophenone stock solution (9.8 × 10−7 mol/cm3) was made by placing 0.0179 g of benzophenone into a 100 mL volumetric flask and dissolving to mark with 200-proof ethanol. Samples were prepared by pipetting 10 mL of benzophenone D

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stock solution into a 100 mL volumetric flask, diluting with 0.1 M sodium sulfate electrolyte, and acidifying with the dropwise addition of concentrated sulfuric acid to pH = 2.0 and a total volume of 100 mL. The pH measurements were made using a pH meter (Orion, Model 370) equipped with a combination glass electrode (Orion, PerpHect Sure Flow). The meter was calibrated using pH 4 and 7 buffers. Samples for the background scans were prepared by using 10 mL of 200proof ethanol in place of the benzophenone stock solution. All samples were prepared fresh daily. The benzophenone stock solution was prepared fresh weekly. The CV experiments were conducted using a BioAnalytical Systems, Inc. (BASi) Epsilon-2 potentiostat. A static drop mercury electrode (SDME) was used as the working electrode (mass, 5.16 × 10−3 g; surface area, 2.54 × 10−2 cm2). The surface area was determined by weighing 10 mercury drops delivered into 20 mL of electrolyte, converting the mass of one drop into a volume using the density of mercury, and then applying the equations for the volume and surface area of a sphere.3 The loss of area at the contact point with the SDME capillary was assumed to be negligible. While solid planar-disk or mercury thin-film electrodes would likely provide currents more consistent with the assumption of linear diffusion in the spreadsheet, the SDME was chosen for this work because the renewable mercury surface requires no preparation (e.g., polishing) prior to use, which is convenient for teaching numerous undergraduate students during a given laboratory period.3,6 The auxiliary electrode was a platinum wire (BASi, MW-1032; length, 7.5 cm; width, 0.5 mm). The reference electrode was Ag/AgCl/NaCl 3 M (BASi, MF-2052). Samples were purged of dissolved oxygen by bubbling with nitrogen gas saturated with solvent for 15 min while being stirred magnetically at 600 rpm. Experiments were then conducted under a nitrogen blanket. Cyclic voltammograms of 9.8 × 10−8 mol/cm3 benzophenone were acquired using the parameters listed in Table 2. All data were acquired at 20 °C.

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HAZARDS Ethanol is an irritant and sensitizer. Avoid inhalation and skin and eye contact. Sodium sulfate is an irritant and desiccant. Avoid skin and eye contact. Benzophenone is an irritant and sensitizer. Avoid skin and eye contact. Sulfuric acid is a corrosive acid that can cause severe burns, eye damage, and blindness. Wear appropriate eye protection, and handle concentrated sulfuric acid with care. Mercury can be absorbed through skin, causes irritation, and can damage the central nervous system. Avoid skin contact, and use in a well-ventilated area. Place trays underneath equipment and work areas to contain spills. Store mercury in approved containers and dispose of properly.

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RESULTS The students acquire and save their CV and background data in a text format compatible with Microsoft Excel. After copying/ pasting their data into the first page of the spreadsheet, the students adjust the background parameters as necessary and then select a mechanism by clicking on a tab at the bottom of the spreadsheet. The students then adjust the simulation parameters until they obtain a good fit based on visual inspection (Figure 3). The EC, EC with na, and EC 2 mechanism pages also graph diffusion profiles so that students can see the generation of various species and their diffusion during the simulation (Figure 7). The diffusion profile graphs

Table 2. CV Acquisition Parameters Parameter

Setting

Initial potential Switching potential Final potential Scan rates Full scale Noise filter Quiet time Sample interval Number of segments

+0.20 V −0.30 V +0.20 V 0.01−0.06 V/s 1 μA 1 Hz 2s 1 × 10−3 V 2

Figure 7. Diffusion profile for the EC2 simulation of benzophenone at −0.30 V during the initial sweep.

are located below the potential ramp on a given mechanism page. The ECEC mechanism page does not graph diffusion profiles to keep the number of required diffusion grids to a minimum. The spreadsheet also contains an optional least-squares-fit optimization macro to aid the simulation process.1 The macro assumes the experimental data have the same potential ramp as the simulation with the starting potential and corresponding current located at the bottom of the columns found in the data page of the spreadsheet. Residuals are calculated in the spreadsheet by subtracting the experimental currents from their corresponding simulation values. The residuals are used to calculate the root-mean-square (RMS) error of the simulation. The macro is started by clicking on a simulation parameter to optimize and then pressing [Ctrl] o. The optimization macro varies the selected parameter using the Excel goal seek (linear

The initial and switching potentials were selected after a wide potential sweep revealed the location of Eo′. An initial potential of about 0.1 V positive of Eo′ was selected so the reduction current would be minimal at the start of the experiment. A switching potential of about 0.4 V negative of Eo′ was chosen to show the decay in reduction current after Eo′ is proportional to t−1/2, which is consistent with a diffusion controlled process.1,3 The background scans were acquired using the same acquisition parameters. Backgrounds were subtracted from the experimental voltammograms in the spreadsheet after applying current gains and offsets to compensate for differences between runs. E

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search) algorithm until the error is reduced from its original value.7 If the optimization fails, the macro returns the parameter to its original setting. Changing the parameter manually before restarting the macro may help the optimization process. A final optimization by visual inspection may be necessary to compensate for effects not included in the simulation. As with many optimization techniques, the results are dependent on the quality of the experimental data, selected model, initial parameters, and require an understanding of the underlying principles of the simulation. The simulator is limited to an initial reduction, two redox couples in series, a common value for the diffusion coefficients, and assumes the initial concentration of the reduced form is zero. Electrochemical reversibility is approximated by using a large value for the standard heterogeneous rate constant in place of utilizing the Nernst equation.5 The spreadsheet does not correct the current for a spherical drop electrode, assumes linear diffusion, and does not account for uncompensated resistance or capacitance effects.3,5 The spreadsheet requires background scans for subtraction from the experimental data.1 A procedure for background scans is outlined in the Experimental section. The reduction current peak in the simulation was 1.5-times greater than the experimental value using the benzophenone sample concentration (9.8 × 10−8 mol/cm3) and a literature value for the benzophenone diffusion coefficient (1 × 10−5 cm2/s) in the spreadsheet calculations.8 The concentration value in the spreadsheet was lowered to 6.1 × 10−8 mol/cm3 to fit the experimental reduction current peak. Increasing the sulfuric acid concentration in the samples increased the reduction current peak and increased the rate of dimerization, requiring faster acquisition scan rates to detect the dimerization process. The discrepancy between the computer simulations and experimental data may be the result of an equilibrium involving the protonation of benzophenone prior to reduction.4 Other possible sources of error include an inaccurate sample concentration, variations in electrode area between runs, using an incorrect diffusion coefficient, and errors associated with the equations used in the spreadsheet.1,5 As a comparison, the software package ESP v. 2.4 provided analogous results as the spreadsheet using similar parameters (Figure 8).9

Some CV simulators occasionally produce current oscillations in the predicted waveforms because of truncation errors from the discrete approximations used in the calculations.5 This problem is sometimes corrected by incorporating dampening functions in the simulators to minimize the oscillations. However, this spreadsheet does not contain a dampening function. Aside from putting the parameters back to their original values, three solutions to this problem have been found empirically. Small oscillations can be minimized by either increasing the scan rate or reducing the scan range of the simulation. Large oscillations can be minimized by increasing the total distance of the diffusion grids (xtotal). However, increasing xtotal should be done sparingly because that increases the distance between grid increments and distorts the shape of the simulated waveform. The spreadsheet will need to be unprotected to increase xtotal (see the following). Despite these limitations, this easy-to-use spreadsheet is helpful for introducing students to CV. More sophisticated simulators are available as interest and needs grow.9 The Excel spreadsheet is run on a Hewlett-Packard HP Pavilion 15p100dx laptop computer with an Intel Core i7 processor (2.0 GHz) and Microsoft Windows 8.1 Office software.

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ASSOCIATED CONTENT

S Supporting Information *

Microsoft Excel spreadsheet (CV_EC Simulator). Experimental and background data can be copied/pasted into the first page of the spreadsheet using Excel. A mechanism is selected by clicking on one of the tabs located at the bottom of the spreadsheet. An example data set was included for practice. Critical cells in the spreadsheet were locked to avoid accidental alterations. The spreadsheet can be operated in protected mode or unprotected and modified as needed. The spreadsheet is provided with no guarantee, and it may not be suitable for all applications. The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.5b00225.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The author declares no competing financial interest.

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ACKNOWLEDGMENTS J.H.B. would like to thank the Minnesota Center for Teaching and Learning (CTL) for the purchase of the electrochemical instrumentation, the Southwest Minnesota State University (SMSU) Faculty Improvement Grant (FIG) Committee for the purchase of components used in the electrochemical cell, and the SMSU Foundation for the purchase of chemical reagents used in this work.

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REFERENCES

(1) Gosser, D. K. Jr. Cyclic Voltammetry: Simulation and Analysis of Reaction Mechanisms; VCH Publishers: New York, 1993. (2) (a) Kissinger, P. T.; Heineman, W. R. Cyclic voltammetry. J. Chem. Educ. 1983, 60 (9), 702−706. (b) Mabbott, G. A. An introduction to cyclic voltammetry. J. Chem. Educ. 1983, 60 (9), 697− 701. (c) Evans, D. H.; O'Connell, K. M.; Petersen, R. A.; Kelly, M. J. Cyclic voltammetry. J. Chem. Educ. 1983, 60 (4), 290−293. (d) King, D.; Friend, J.; Kariuki, J. Measuring vitamin C content of commercial

Figure 8. ESP and spreadsheet simulations using COx,Bulk = 6.1 × 10−8 mol/cm3, Eo′ = 0.013 V, n = 1, D = 1 × 10−5 cm2/s, A = 2.54 × 10−2 cm2, v = 0.04 V/s, ko = 1 cm/s, and k1 = 0.075 s−1. F

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orange juice using a pencil lead electrode. J. Chem. Educ. 2010, 87 (5), 507−509. (e) Messersmith, S. J. Cyclic voltammetry simulations with DigiSim software: An upper-level undergraduate experiment. J. Chem. Educ. 2014, 91 (9), 1498−1500. (3) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications; Wiley & Sons: New York, 1980. (4) (a) Swann, S., Jr.; Briggs, S. W.; Neklutin, V. C.; Jerome, A. J. The electrolytic reduction of benzophenone in acidic and in alkaline Media. Trans. Electrochem. Soc. 1941, 80 (1), 163−173. (b) Blázquez, M.; Rodríguez-Mellado, J. M.; Ruiz, J. J. EC mechanisms: electrodimerization of benzophenone on mercury electrode. Electrochim. Acta 1985, 30 (11), 1527−1532. (c) Chandrasekaran, M.; Noel, M.; Krishnan, V. Voltammetric behaviour of benzophenone on glassy carbon electrode in aqueous medium - A quantitative evaluation of pH dependent adsorption effects. Bull. Electrochem. 1986, 2 (5), 469−472. (d) Tsierkezos, N. G. Investigation of the electrochemical reduction of benzophenone in aprotic solvents using the method of cyclic voltammetry. J. Solution Chem. 2007, 36 (10), 1301−1310. (5) Britz, D. Digital Simulation in Electrochemistry, 3rd ed.; Springer: Berlin, 2005. (6) (a) Bott, A. W. Practical Problems in Voltammetry: Preparation of Working Electrodes. http://www.currentseparations.com/issues/16-3/ cs16-3b.pdf (accessed May 2, 2015). For additional information regarding the maintenance and polishing of working electrodes, see: (b) Working Electrodes. http://www.basinc.com/mans/LC_epsilon/ Maintenance/Working/working.html (accessed May 2, 2015). (7) For a description of the Microsoft Excel goal seek (linear search) algorithm, see: XL: Method Used by Goal Seek To Find a Solution. https://support.microsoft.com/en-us/kb/100782 (accessed May 12, 2015). (8) (a) Nishiyama, Y.; Fukuda, M.; Terazima, M.; Kimura, Y. Study of the translational diffusion of the benzophenone ketyl radical in comparison with stable molecules in room temperature ionic liquids by transient grating spectroscopy. J. Chem. Phys. 2008, 128, 164514. (b) Terazima, M.; Okamoto, K.; Hirota, N. Transient radical diffusion in photoinduced hydrogen abstraction reactions of benzophenone probed by the transient grating method. J. Phys. Chem. 1993, 97, 13387−13393. (9) (a) Nervi, C. Electrochemical Simulations Package ESP v. 2.4. http://lem.ch.unito.it/chemistry/esp_manual.html (accessed March 21, 2015). (b) BASi DigiSim Simulation Software for Cyclic Voltammetry. http://www.basinc.com/products/ec/digisim/ (accessed March 21, 2015). (c) DigiElch Electrochemical Simulation Software. http://www.gamry.com/products/digielch-electrochemicalsimulation-software/ (accessed March 21, 2015).

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