Student Deployed Compu-Graphical Methods for Electrochemistry Education
Authors: Parr Daniel Lee , Leddy Johna 
Published: February 2020

Spreadsheets enhance student acquisition of electrochemical concepts at both undergraduate and graduate levels. The interactive nature of compu-graphical methods allows students more rapid and therefore extensive exploration of electrochemical concepts in thermodynamics, kinetics, and electrochemical methods. Here, several instructional tools are described with focus on the potential axis.

Potential Axis - A Spreadsheet for Thermodynamics, Voltammetry, and Electrolysis

For reactions A + ne ⇌ B at standard potential EA⁰ and C + me⇌D at EC⁰, calculation of standard cell potential Ecell⁰ = EA⁰ -EC⁰ for net reaction mA + nD ⇌ mB + nC yields thermodynamic information of standard free energy for the reaction ΔGcell⁰ = -nmFEcell⁰. In turn, ΔGcell⁰ identifies spontaneity when ΔGcell⁰ < 0 and equilibrium when ΔGcell⁰ = 0. When more than two reactions are possible or when pH changes for proton dependent reactions or oxygen is present or not, developing chemical intuition about the system and identifying stable species and thermodynamic reaction energies is more complicated. By plotting the reactions on a potential axis, thermodynamic assessment is readily obtained.
Under IUPAC conventions with positive potential E to the right, reaction A + ne ⇌ B is plotted as B|A at potential EA⁰ on the potential axis. On addition of a second reaction C + me ⇌ D where EA⁰ < EC⁰, a simplified potential axis is B|A........D|C where potential is positive to the right. When chemical species are on the outside of the E⁰ lines, reaction is spontaneous. For example, if the axis for the A B couple and the C D couple is B|A........D|C , B and C react to form A and D spontaneously. Any other combinations of species are thermodynamically stable (B+A+D and C+D+A).
A potential axis is shown below for several copper species at pH = 0. Because Cu and O₂ are outside the E⁰ vertical axes at 0.34 and 1.23 V vs NHE, Cu reacts spontaneously with O₂ based on thermodynamic potentials ECu²⁺|Cu⁰ and EO₂|H₂O⁰. Several other observations about copper electrochemistry are of note. Copper metal Cu is stable in strong acid. Cu⁺ is not observed in water because Cu⁺ is outside the vertical E⁰ lines for Cu⁺|Cu²⁺ and Cu|Cu⁺, so Cu⁺ reacts spontaneously with itself (disproportionation) to form copper metal and cupric cation. Cu is stable in HCl but not oxidizing HNO₃. Nickel metal and Zn metal (Zn|Zn²⁺ not shown at -0.76 V vs NHE) react spontaneously with both HCl and HNO₃.
Potential axes are also useful for mapping voltammetry and identifying the sequence of electrolysis steps. Consider a system that contains Cu, Cu²⁺ and Cl⁻ in an aqueous system that is not degassed (contains O₂) at pH = 0. Based on the reactions plotted on the potential axis for copper, the species that are present and can be oxidized will be oxidized in sequence as potential E is swept from negative to positive. Species are oxidized in the sequence Cu then H₂O; because water is the solvent, chloride will not be accessible for oxidation to chlorine. Species that are present and can be reduced, are reduced in ranked in order for E swept from positive to negative as O₂, Cu²⁺, and H⁺. If pH changes, the formal potentials E⁰' for O₂, H⁺, and NO₃⁻ will also shift and the order of reactions can change. Note that as shown, neither concentrations other than standard conditions nor metal ions precipitated as oxides and hydroxides are not included but can be introduced.
Several other ideas will be discussed briefly.

Compu-graphical finite difference simulations for cyclic voltammetry for use at the undergraduate and graduate levels. (Thanks to Alanah Fitch who first suggested the form for undergraduates.)

Useful ideas to convey include:

• the concept of flux as number per area per time
• electrochemical systems are circuits composed of electron and ion conductors
• relationship between measurement rates and kinetic rates
• difference between equilibrium (thermodynamics) and steady state (kinetics)
• diffusion length ℓ² ≈ Dt (diffusion coefficient and time) and use in characterizing micro- and nano-structures on electrodes
......

Figure 1