Run-D.M.C.: A Mnemonic Aid for Explaining Mass Transfer in

Oct 31, 2013 - Run-D.M.C.: A Mnemonic Aid for Explaining Mass Transfer in. Electrochemical Systems. Deon T. Miles*. Sewanee: The University of the Sou...
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Run-D.M.C.: A Mnemonic Aid for Explaining Mass Transfer in Electrochemical Systems Deon T. Miles* Sewanee: The University of the South, Sewanee, Tennessee 37383-1000, United States ABSTRACT: Electrochemistry is a significant area of analytical chemistry encompassing electrical measurements of chemical systems. The applications associated with electrochemistry appear in many aspects of everyday life: explaining how batteries work, how the human nervous system functions, and how metal corrosion occurs. The most common electrochemical technique performed in an instrumental analysis laboratory is voltammetry. For a measurement of current to occur in a voltammetry experiment, an electroactive species must continuously be moved from the bulk solution to the surface of the working electrode, where the reaction will take place. There are three modes of mass transport to the working electrode surface: diffusion, migration, and convection. These modes of mass transport are important features of the electrochemical process that determines reaction rate. Using the mnemonic aid “RunD.M.C.” helps students recall these different processes. This mnemonic device also aids in the interpretation of a typical concentration profile near the working electrode surface for a hydrodynamic (e.g., rotated disk) voltammetry experiment. The popularity of the hip-hop music group that this mnemonic device is named for is important for potential widespread use of this teaching aid. KEYWORDS: Analytical Chemistry, Upper Division Undergraduate, Mnemonics/Rote Learning, Electrochemistry, Oxidation/Reduction, Transport Properties (TN), is “LEO says GER” for “Loss of Electrons is Oxidation and Gain of Electrons is Reduction”.1 In this article, a new mnemonic aid is introduced for use in the field of electrochemistry. Electrochemistry is a topic that is typically introduced near the end of the general chemistry sequence. At this level, the focus is generally centered on several basic concepts: (a) balancing oxidation−reduction reactions, (b) differentiating between voltaic and galvanic electrochemical cells, (c) calculating electrochemical cell potentials, (d) using a table of standard electrode potentials, and (e) using the Nernst equation. The topic of electrochemistry is usually revisited in the quantitative analysis and instrumental analysis courses. At this level, the electrochemistry concepts that are introduced are more complex than in the general chemistry course. For example, a thorough discussion of the electrochemical techniques that are used to study dynamic electron-transfer reactions (e.g., cyclic voltammetry) would likely be taught in these upper-level courses. Also, the topic of potentiometry would likely be covered in these courses, which is a technique that is significantly different from voltammetry. In potentiometry, the potential is measured across an ion-selective membrane under the conditions of no current flow. This is how pH is measured: the potential generated is related to the hydronium ion activity of a solution. Potentiometry is considered a static electrochemical technique: continuous movement of analyte species to the electrode surface is not required. By contrast, voltammetry is performed by controlling the potential of the experiment as the electrogenerated current

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nemonic aids are used to help learn information by translating it into a form that the brain can better retain than in its original form and can be presented in several different formats, including short phrases and acronyms. For example, the acronym “HOMES” is used to recall the names of the Great Lakes (Huron, Ontario, Michigan, Erie, and Superior). Another example is the short phrase “Every Good Boy Does Fine”, which is a mnemonic aid to recall the lines of the treble clef in music (EGBDF). There have been numerous articles published in this Journal describing various chemistryrelated mnemonic devices, with a nice summary of articles provided by DeLoach in 1960.1 In his article, a popular mnemonic aid that is used to memorize the order of the colors in the visible range of the electromagnetic spectrum was discussed. In this mnemonic, which is attributed to the late Louis H. Dunlop at McKeesport (PA) High School, the imaginary name “Roy G. Biv” provides the first letter of each color (red, orange, yellow, green, blue, indigo, and violet). Other recently published mnemonic devices include the “energy pie”, which is used to provide relationships between thermodynamic potentials and related variables;2 and the word “OREO” (as in the popular cookie), which is used to recall the basic steps of classical tautomerization mechanisms in organic chemistry.3 Two of the most popular mnemonic aids that are used in electrochemistry relate to the distinguishing between oxidation and reduction processes. These tools are used by students to remember the electron transfers in oxidation−reduction reactions. The first mnemonic aid is “OIL RIG”, which stands for “Oxidation Is Loss of electrons and Reduction Is Gain of electrons”.4 The second mnemonic device, which is attributed to the late Lee Meriwether at Montgomery Bell Academy © 2013 American Chemical Society and Division of Chemical Education, Inc.

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RUN-D.M.C.: THE MNEMONIC AID Mass transfer is the movement of material from one location in solution to another. This movement stems from either differences in electrical or chemical potential at the two locations or movement of a volume element of solution. The three modes of mass transfer are as follows. Diffusion: Diffusion is the transport of a species under the influence of a gradient of chemical potential in a liquid or a gas (i.e., a concentration gradient). Migration: Migration is the transport of a charged body (e.g., ion) under the influence of an electric field (i.e., a gradient of electrical potential). For example, anions are attracted to a positively charged electrode and repelled by a negatively charged electrode. Convection: Convection is the transport of a species through the bulk motion of the solution. This motion occurs as a result of natural convection (i.e., convection generated by density gradients) and forced convection. Common methods of forced convection include stirring the solution, rotating the working electrode, or flowing the solution through a cell. The mnemonic aid to remember these three methods of mass transfer is “Run-D.M.C.” The first part of the mnemonic device (i.e., “Run”) refers to the fact that there is movement of material in the solution toward the working electrode surface. Students can think about the electroactive species as “running” to the working electrode surface. It is noted that, in doing this, the role of animism in the teaching of chemical topics arises. Research associated with the use of these personifications of inanimate objects shows that “animisms lead to better understanding thereby having a lasting motivational effect”.7 The second part of the mnemonic aid (i.e., D.M.C.) simply corresponds to the first letter of the three modes of mass transport: Diffusion, Migration, and Convection. The mnemonic’s symbol, being similar to the hip-hop group’s wellknown logo, is a useful visual tool that can be used to help with implementation of this mnemonic device.8 In electrochemistry, the measured current is directly related to the molar flux density of the analyte. In order to measure current, the unreacted analyte must physically move to the surface of the working electrode. Mass transfer to the working electrode surface is described using the Nernst−Planck equation, which is written for a one-dimensional mass transfer along the x axis

is measured. For this to occur, analyte must be transported continuously to the working electrode surface. This dynamic technique gives the experimenter control over what reactions will take place in a system under study instead of merely measuring existing potentials in an electrochemical cell (static methods). For a typical voltammetry experiment, the oxidation or reduction of an electroactive molecule occurs at the interface between the solution and the working electrode. Because of this, molecules dissolved in solution must be transported to the working electrode for the electron transfer process to occur. Therefore, the movement of molecules from the bulk solution of the electrochemical cell to the working electrode surface is an important part of electrochemical techniques. The movement of material in an electrochemical cell is called mass transport. In electrochemical analysis, there are three mass transport processes of importance: diffusion, migration, and convection. An explanation of the processes that are occurring at the working electrode surface is important because these processes influence the measured faradaic current when using voltammetric techniques. In this article, a mnemonic aid is presented to help students understand the process of mass transfer in electrochemical systems. Although voltammetry is a dynamic technique, it may be somewhat confusing to students in terms of what is occurring during the experiment. Most analytical techniques that students learn in an upper-level course can be considered static in nature. For example, in a typical absorption spectroscopy experiment, the analyte solution is irradiated with a source of light and the quantity of light that is transmitted is detected. In this type of spectroscopy, the analyte is static: there is no impact on the movement of the sample solution on the measured transmittance. Voltammetry, in contrast, is a technique that is dynamic in nature: the movement of analyte species to the working electrode surface is required for the electrochemical study of a particular system.

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RUN-D.M.C.: THE MUSIC GROUP The mnemonic aid mentioned here is derived from the name of a historically and culturally significant music group in the United States. Run-D.M.C. is a hip-hop group from Hollis, Queens, New York, founded in 1981 by Joseph “Run” Simmons, Darryl “D.M.C.” McDaniels, and Jason “Jam Master Jay” Mizell.5 Run-D.M.C. is widely acknowledged as one of the most influential groups in the history of hip-hop music and culture. Arguably, their best known single, “Walk This Way” (1986), was a collaborative effort with the hard rock group Aerosmith. This song ultimately reached #4 on the Billboard Hot 100 list. Run-D.M.C. was the first group in the hip-hop genre to have a gold album (Run-D.M.C., 1984) and to be nominated for a Grammy Award. Other accomplishments by Run-D.M.C. in relation to hip-hop music include the following: first to earn a platinum record (King of Rock, 1985), first to earn a multiplatinum certification (Raising Hell, 1986), first to make a music video appearance on the MTV (Music Television) cable network, and first to appear on the cover of Rolling Stone magazine. The group was recognized as “The Greatest HipHop Group of All Time” by MTV News and “Greatest Hip-hop Artist of All Time” by VH1.6 In 2009, Run-D.M.C. was inducted into the Rock and Roll Hall of Fame, becoming only the second hip-hop group in history to receive this prestigious honor.

∂C(x) ∂ϕ(x) zF − DC + Cv(x) ∂x RT ∂x diffusion migration convection

J ( x )= − D

(1)

where J(x) is the molar flux density [mol/(s cm )] at distance x from the surface, D is the diffusion coefficient (cm2/s), ∂C(x)/ ∂x is the concentration gradient at distance x, ∂φ(x)/∂x is the potential gradient, z is the charge, C is the concentration (mol/ cm3), and v(x) is the velocity (cm/s) with which a volume element in solution moves along the axis. Note that the three terms on the right-hand side in this equation represent the contributions to the molar flux density of diffusion, migration, and convection, respectively. Molar flux density is defined as the number of molecules penetrating a unit area of an 2

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temperature and pressure. Diffusion coefficients are typically determined experimentally and presented in corresponding reference tables.11 Diffusion coefficients can be calculated using a variety of equations. The first equation of interest is the Einstein−Smoluchowski equation, which is in the general form of

imaginary plane in a unit of time. The sign associated with molar flux density identifies the direction of motion: positive toward and negative away from the plane. The relative contributions of diffusion and migration to the molar flux density of an electroactive species differ at a particular time for different locations within a solution. In the bulk solution (i.e., far away from the electrode surface), concentration gradients are typically small, and the total current is carried primarily by migration. However, near the working electrode surface, an electroactive species is transported by both processes.9 It can be emphasized to students that eq 1 is complex, where calculation of a molar flux density is typically difficult when all three forms of mass transfer are in effect. Students are typically taught that, to reduce this complexity, electrochemical systems are usually designed so that one or more of these contributions to mass transfer are negligible. For instance, convection can be eliminated by preventing stirring and vibrations of the electrochemical cell. Also, natural convection, which is due to thermal gradients, is a possible contribution to mass transfer. However, conditions are typically selected where this movement is negligible (e.g., isothermal environment). Migration can be reduced to minute levels by addition of an excess of nonelectroactive ions (a supporting electrolyte) at a concentration that is significantly larger than that of the electroactive species (e.g., electrolyte concentration = 100 × analyte concentration). This will simplify the mathematical treatment of electrochemical systems by elimination of the ∂φ(x)/∂x term in eq 1. The presence of a supporting electrolyte decreases the solution resistance between the working and reference electrodes in an electrochemical system. This reduces the uncompensated resistance drop, which improves the accuracy of the working electrode’s potential. The supporting electrolyte also ensures that the nonfaradaic (e.g., charging) current will be small compared to the faradaic current. It is feasible to restrict the contributions to mass transfer of an electroactive species near the working electrode surface to only diffusion by using a supporting electrolyte and operating in a quiescent (i.e., unstirred) solution. Diffusion can be described using Fick’s laws, which relates the molar flux density of an electroactive species and its concentration as functions of time and position.10 Fick’s laws are as follows. Fick’s first law states that the molar flux density is proportional to the concentration gradient (i.e., movement from regions of higher concentrations to regions of lower concentration) and is expressed as

J (x ) = − D

∂C(x) ∂x

D = μkBT

where μ is the mobility [cm /(V s)], kB is Boltzmann’s constant (8.617 × 10−5 eV/K), and T is the temperature (K). If the particles of interest are spherical and diffusing through a liquid with a low Reynolds number, then the Stokes−Einstein equation can be used to calculate the diffusion coefficient:

D=

kBT 6πηr

(5) −23

where kB is Boltzmann’s constant (1.381 × 10 J/K), η is viscosity [kg/(cm s)], and r is the radius of the spherical particle (cm).

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ELECTROCHEMICAL TECHNIQUES Cyclic voltammetry (CV) is the most common technique used in the field of electrochemistry. In CV, a triangular potential waveform (i.e., voltage as a function of time) is applied to a solution containing an electroactive species. As the potential is scanned, the resulting current is measured. In most instances, CV is conducted with a stationary working electrode. Under these experimental conditions, the generated current is governed by the Randles−Sevcik equation (at 25 °C): i p = (2.69 × 105)n3/2ACD1/2ν1/2

(6)

where ip is the peak current (cathodic or anodic), n is the number of electrons transferred, A is the area of the electrode surface (cm2), C is the concentration (mol/cm3), D is the diffusion coefficient (cm2/s), and ν is the scan rate (V/s). In this equation, the only variable associated with the mass transport of the electroactive species is the diffusion coefficient. The other modes of mass transport (migration and convection) are negligible if the experimental conditions include a significant concentration of supporting electrolyte and a quiescent solution.9 A good series of electrochemistry-based experiments for the instrumental analysis laboratory have been published by the Pine Instrument Company.12 One of the experiments employs an iron chloride solution to study the basics of cyclic voltammetry. In this experiment, the Randles− Sevcik equation is used to calculate the diffusion coefficient of the analyte. There are some recent examples where the Randles−Sevcik equation is employed as part of the solution to a research problem. For instance, this equation was used in comparing ten room temperature protic ionic liquids (RTPILs), which are “green” solvents that can be used as substitutes for common organic solvents. In this research investigation, the behavior of the RTPILs were compared using well-established redox molecules (i.e., ferrocene, cobaltocene).13 Cyclic voltammetry can be performed when the working electrode is stationary or when it is rotated. The modes of mass transport involved when the working electrode is rotated are convection and diffusion. Whereas convection is now incorporated into the experiment, a different equation is used to describe electrochemical systems that are studied using rotated disk electrodes. The limiting current (iL) generated

(2)

Note that the negative sign is implemented in this equation because the net molar flux density is from a region of high concentration to one of low concentration. Fick’s second law predicts how diffusion causes the concentration to change with time. For a one-dimensional system, Fick’s second law is expressed as ∂ 2C(x) ∂C(x) =D ∂t ∂x 2

(4) 2

(3)

The diffusion coefficient (D) is the proportionality factor in Fick’s laws of diffusion. The diffusion coefficient is a measure of the rate at which molecules move randomly through a concentration gradient. It is a physical constant that is dependent on the size of the molecule, as well as the 1651

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is approximately 10−3 cm. Here, this line of demarcation is called the “Margin”. (Note that the “M” here is not “migration”, as in the earlier use of the mnemonic device.) At regions extending from the working electrode surface (beyond the margin), the primary mode of mass transport is convection. Therefore, this region is called the “Convection layer”.15 This is another way to use the Run-D.M.C. mnemonic aid, with the three regions extending from the working electrode surface being represented in the mnemonic (D = diffusion layer, M = margin, C = convection layer).

from an electrochemical experiment with a rotated disk electrode is governed by the Levich−Koutecky equation (at 25 °C): iL = (0.62)nFACD2/3ν−1/6ω1/2

(7)

where n is the number of electrons transferred, F is the Faraday constant [96485 C/(mol e−)], A is the area of the electrode surface (cm2), C is the concentration (mol/cm3), D is the diffusion coefficient (cm2/s), ν is the scan rate (V/s), and ω is the angular frequency of rotation (= 2π × rotation rate).7 From this equation, it is observed that the quantity of analyte transported to the electrode surface is controlled by the rates of diffusion (D) and convection (ω). For use in the instrumental analysis laboratory, one of the experiments from the Pine Instrument Company employs rotated disk voltammetry to investigate a potassium ferricyanide solution.12 With respect to recent research efforts, rotated disk voltammetry has been used to determine the diffusion coefficient in modified metallic catalysts.14 In this example, calculation of the diffusion coefficients informed the researchers if a dimer was formed upon reduction of the catalysts. To further explain the mass transfer processes that occur in an electrochemical experiment involving a rotated disk electrode, one needs to focus on what occurs at the working electrode surface. For example, consider a reduction where the oxidized species (O) is converted to its reduced form (R) at the working electrode surface (assume that the applied potential is sufficient for rapid reduction). The concentration of the electroactive species in its oxidized form can be represented as CO, and CR in its reduced form. In the bulk solution, the concentration of the oxidized species is dominant. However, when the oxidized species nears the working electrode surface, CO begins to decrease (with a corresponding increase in CR). This is represented in Figure 1, which shows the concentration profile of the oxidized species near the working electrode surface. The region where CO begins to decrease is called the “Diffusion layer”. At the diffusion layer, the only mode of mass transport that takes place is diffusion. In most electrochemical systems, the thickness of the diffusion layer (represented by δ)

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SUMMARY Dynamic electrochemical methods are used in laboratories around the world to study a variety of research problems. For example, cyclic voltammetry is used in the field of bioenergetics, which is a subdiscipline of biochemistry that involves the study of energy flow in living systems. Here, the electrochemical properties of biomolecules (e.g., cytochrome c) can be examined to learn how they affect the energy flow in living organisms. To prepare students that may perform research in these areas, a better understanding of the concepts related to dynamic electrochemistry is needed. An explanation of the processes that are occurring at the working electrode surface is an important part of the discussion of voltammetric techniques in upper-level chemistry courses. For electron transfer to take place, the electroactive species must interact with the working electrode surface. In other words, to continuously measure current, the unreacted analyte must be continuously moved to the surface of the working electrode. Having a good idea of how material can move in an analyte solution to the working electrode surface is essential to understanding electrochemistry at a detailed level. There are three modes of mass transport to the working electrode surface: diffusion, migration, and convection. This concept can be challenging for students because it is a different mode of thinking about measuring electrochemical systems (dynamic vs static). Using the mnemonic aid “Run-D.M.C.” helps students recall these three processes. This mnemonic device also aids in the interpretation of a typical concentration profile near the working electrode surface. The popularity of the hip-hop music group that this mnemonic aid is named for will undoubtedly help students recall this information when needed.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The author would like to thank Michael C. Leopold from the University of Richmond and Amanda S. Harper-Leatherman from Fairfield University for thoughtful discussions. The author would also like to thank the reviewers for helpful comments.

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REFERENCES

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Figure 1. Concentration profile at the working electrode surface. The solid line () is the actual concentration gradient, the long dashed line (− − −) is a linear approximation of the gradient, and the short dashed line (- - -) is the “margin” that defines the diffusion layer. 1652

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(3) Stephens, C. E. A Simple Mnemonic for Tautomerization Mechanisms in Organic Chemistry. J. Chem. Educ. 2010, 87 (11), 1186−1187. (4) Glynn, S. M.; Koballa, T. R.; Coleman, D. Mnemonic Methods. Sci. Teach. 2003, 70 (9), 52−55. (5) Run-D.M.C. Wikipedia site. http://en.wikipedia.org/wiki/Run-D. M.C. (accessed Oct 2013). (6) (a) MTV News: The Greatest Hip Hop Groups of All Time. http://www.mtv.com/bands/h/hip_hop_week/2007/groups/ index11.jhtml (accessed Oct 2013). (b) VH1: 50 Greatest Hip Hop Artists. http://www.rockonthenet.com/archive/2003/vh1hiphop.htm (accessed Oct 2013). (7) Puettschneider, M.; Lueck, G. The Role of Animism in the Mediation of Chemical Topics. CHEMKON 2004, 11, 167−174. (8) Cassette Culture. Run-D.M.C. logo. http://www. cassetteculturemusic.co.uk/2012/08/17/keeping-it-simple-the-4-bestband-logos-in-the-universe-the-stories-behind-them/ (accessed Oct 2013). (9) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications, 2nd ed.; John Wiley & Sons: New York, 2001. (10) Brett, C. M. A.; Brett, A. M. O. Electrochemistry: Principles, Methods, and Applications; Oxford University Press: New York, 1993. (11) Mostinsky, I. L. Diffusion Coefficient. http://www.thermopedia. com/content/696/ (accessed Oct 2013). (12) Pine Instrument Company. Educator’s Reference Guide for Electrochemistry. http://www.pineinst.com/echem/files/LMCBPPROF1.pdf (accessed Oct 2013). (13) Lu, X.; Burrell, G.; Separovic, F.; Zhao, C. Electrochemistry of Room Temperature Protic Ionic Liquids: A Critical Assessment for Use as Electrolytes in Electrochemical Applications. J. Phys. Chem. B 2012, 116 (30), 9160−9170. (14) Smieja, J. M.; Sampson, M. D.; Grice, K. A.; Benson, E. E.; Froehlich, J. D.; Kubiak, C. P. Manganese as a Substitute for Rhenium in CO2 Reduction Catalysts: The Importance of Acids. Inorg. Chem. 2013, 52 (5), 2484−2491. (15) Kissinger, P. T.; Preddy, C. R.; Shoup, R. E.; Heineman, W. R. Fundamental Concepts of Analytical Electrochemistry. In Laboratory Techniques in Electroanalytical Chemistry, 2nd ed.; Kissinger, P. T., Heineman, W. R., Eds.; Marcel Dekker: New York, 1996.

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