Chapter 3.1: Visualization of the Nernst Equation Via 3-D Topo Surfaces: E⁰ Plateaus, Left-Hand Bluffs, Front Cliffs and Reaction Paths

A new 3-D graphical representation of oxidation–reduction (redox) processes in aqueous solutions has been developed utilizing a composition grid for which the x-axis carries the activity of the reduced form of the redox couple and the y-axis carries the activity of the oxidized form. The Nernst equation potential corresponding to the redox couple’s activities at each grid point is plotted above it as a z-coordinate. This creates a 3-D trend surface (a topo) over the grid. The topos typically have a steep left-hand bluff and a precipitous front cliff that are encountered when one or the other of the redox couple species is near depletion. In between these two features, much of the topo is a broad plateau with an elevation near the E0 for the half-reaction. Discharge paths during the operation of a galvanic cell appear as oppositely-trending, angled paths across a pair of vertically-separated surfaces. The cell dies when the two reaction paths achieve the same potential, i.e., identical z-coordinates. Redox TOPOS, a free downloadable Microsoft Excel workbook, generates 1681-point (41 x 41) 3-D topos once a redox couple has been identified and all Nernst equation parameters have been entered. Also included are a set of PowerPoint lecture slides and a document “Teaching with Redox TOPOS” containing sections for use in lecture and exercises for homework or discussion for introductory college courses and upper division or graduate physical chemistry, analytical chemistry, biochemistry, and geochemistry courses.https://scholarworks.umt.edu/topos/1007/thumbnail.jp

Chapter 1.3: 3-D Topo Surface Visualization of Acid-Base Species Distributions: Corner Buttes, Corner Pits, Curving Ridge Crests and Dilution Plains

This chapter adds 3-D species distribution topos to earlier surfaces that showed pH (Chapter 1.1) and buffer capacity behavior (Chapter 1.2) during titration and dilution procedures. It constructs trend surfaces by plotting computed alpha distribution coefficients above a composition grid with “mL of NaOH” as the x-axis and overall system dilution (log C) as the y-axis. The systematic shift from protonated to deprotonated forms is clearly visualized on a linear z-axis. Because pH and buffer capacity surfaces accompany the species topos, it is easy to see their interrelationships. On the basis of their graphical appearance, features on species topo surfaces have been named corner buttes, corner pits, curving ridge crests, curving canyons and dilution plains. Ramps connecting surface features are linear when tied to additions of NaOH and logarithmic when followed on the log C dilution axis. The amphiprotic behavior of water is demonstrated through dilution procedures. Systems examined include acetic acid, CH3COOH (a weak monoprotic acid); carbonic acid, H2CO3 (a weak diprotic acid), and phosphoric acid, H3PO4 (a weak triprotic acid). For comparative purposes, species topos are depicted for a set of three acids with hypothetical pKas of 4.0, 7.0, and 10.0. Supplementary files include the Species TOPOS software, a macro-enabled Excel workbook that quickly generates pH, buffer capacity and alpha surfaces for any mono-, di-, or triprotic acid desired. Only the acid dissociation constants, the Ka values, are needed as inputs. Also included are a set of PowerPoint lecture slides and a document “Teaching with Species TOPOS” with sections for lecture, practice exercises, and suggested laboratory activities for introductory college courses and upper-division or graduate courses in analytical chemistry, biochemistry and geochemistry.https://scholarworks.umt.edu/topos/1003/thumbnail.jp

Chapter 1.2: Visualization of Buffer Capacity with 3-D Topos: Buffer Ridges, Equivalence Point Canyons and Dilution Ramps

The BufCap TOPOS software generates 3-D topographic surfaces for acid-base equilibrium studies that portray pH and buffer capacity behavior during titration and dilution procedures. Topo surfaces are created by plotting computed pH and buffer capacity values above a composition grid with volume of NaOH as the x-axis and overall system dilution as the y-axis. What emerge are surface features that correspond to pH and buffer behaviors in aqueous solutions. Topo surfaces are created for pH, log buffer capacity and linear buffer capacity. Equivalence point breaks become pH cliffs and logarithmic buffer capacity canyons that grow shallower with dilution. Areas of high buffer capacity become rounded ridges. Dilution alone generates 45° ramps. Example systems include acetic acid, CH3COOH (a weak monoprotic acid); hydrochloric acid, HCl (a strong acid); oxalic acid, HOOCCOOH (a weak diprotic acid) and L-glutamic acid hydrochloride, C5H9NO4·HCl (a weak triprotic acid). The Supplementary files include a copy of the interactive BufCap TOPOS program as a downloadable Excel workbook. Its macro-enabled spreadsheets quickly generate surfaces for any mono-, di-, or triprotic acid. Only acid dissociation constants, Ka values, need be changed. Other materials include a PowerPoint lecture, materials/suggested laboratory activities for teaching with BufCap TOPOS, and derivation of new equations that permit the calculation of buffer capacities for titration/dilution composition grid points.https://scholarworks.umt.edu/topos/1002/thumbnail.jp

Chapter 4.1: Visualizing the Solubility of Salts Via 3-D Topo Surfaces: Pyramids with Ridges and Plateaus

A new 3-D graphical representation for the solubility of sparingly soluble salts in aqueous solutions has been developed utilizing a new composition grid. In this case, the x-axis carries the concentration of the salt’s cation (usually a metal) and the y-axis holds the concentration of the salt’s anion. Plotted above the grid are a salt’s solubility, individual species concentrations or distribution coefficients. Three levels of sophistication in the descriptive chemistry are discussed. In Case 1, the only dissolved species included are the cation and anion present in the salt’s solubility product expression, the Ksp. Case 2 adds the possibility of ion pairs or neutral complexes. Finally, Case 3 encompasses all complexes for which thermodynamic constants are available. Example systems include the 1:1 AgCl and the 1:2 PbI2 salts. The composition grid approach addresses not only the solubility of a solid salt in pure water, but essentially all other feasible conditions in which one or the other of the component ions is present in the dissolving liquid phase. Case 1 gives rise to 3-D solubility surfaces (topos) that have a pyramidal shape. Case 2 possesses plateaus under saturated conditions where the concentration of the ion pair or neutral complex dominates. Case 3 can add extra ramps under saturated conditions when other complexes become important. A comparison of the topos from all three cases for a given salt allows the user to see the effects of incompletely capturing the possible chemical processes that contribute to solubility. The Case 3 solubility maximum can be significantly larger than that for Case 1. In the AgCl system, for example, the maximum solubility was 12.5 times greater than that predicted for Case 1. Included as supplementary files for the chapter are the downloadable Solubility TOPOS software (an Excel workbook), a PowerPoint lecture, teaching materials, a detailed description of the formulas and algorithms used to solve for solubility, and a Visual Basic code listing.https://scholarworks.umt.edu/topos/1009/thumbnail.jp

Chapter 2.1: Visualization of Metal Ion Buffering Via 3-D Topo Surfaces of Complexometric Titrations

This chapter examines 1:1 metal-ligand complexometric titrations in aqueous media. It presents surfaces that plot computed equilibrium parameters above a composition grid with titration progress (mL of ligand) as the x-axis and overall system dilution (log C ) as the y-axis. The sample systems in this chapter are restricted to EDTA as a ligand. Other chelating ligands that form exclusively 1:1 complexes could also be modeled with this software. The surfaces show the quality of the equivalence point break under various conditions. More importantly, they develop the phenomenon of metal ion buffering. They clearly distinguish the difference between “pseudo-buffering” and “true buffering”. They introduce terminology for two different forms of metal ion buffering: 1) mass action metal ion buffering under excess ligand conditions; and 2) precipitate metal ion buffering when hydroxide precipitates are present under excess metal ion conditions. Systems modeled are EDTA titrations of Cu2+, Ca2+ and Mg2+. A final section demonstrates a second type of topo that helps evaluate the optimal pH for an EDTA titration. Supplemental files include the Complexation TOPOS software, an Excel workbook that generates topo surfaces in under 20 seconds, and teaching suggestions. Required inputs are: 1) stability constants for the metal-ligand complex; 2) acid dissociation constants for the ligand, 3) stability constants for hydroxy complexes from of the metal cation; and 4) a Ksp value and stoichiometry for hydroxide precipitates. Many of these constants are contained in a workbook tab. Also included are a PowerPoint lecture and teaching materials (for lecture, homework, and pre-laboratory activities) that are suitable in general chemistry courses or third-year and graduate courses in analytical chemistry, biochemistry and geochemistry.https://scholarworks.umt.edu/topos/1004/thumbnail.jp

Prologue: An Overview to Water Topos: A 3-D Trend Surface Approach to Viewing and Teaching Aqueous Equilibrium Chemistry

The “topo” approach to viewing and teaching aqueous equilibrium through 3-D trend surfaces is introduced. A list of the pedagogical resource categories that accompany each chapter is provided. We describe the “composition grids” that form the foundation for the trend surfaces. A roadmap for the subsequent chapters follows. Finally, a brief statement about the Excel-based computer software is provided.https://scholarworks.umt.edu/topos/1000/thumbnail.jp

Chapter 3.2: Why Batteries Deliver a Fairly Constant Voltage Until They Suddenly Die: An Application of Nernst Topo Surfaces

Two characteristics of batteries, their delivery of nearly constant voltage and their rapid failure, are explained through a visual examination of the Nernst equation. Two Galvanic cells are described in detail: (1) a wet cell involving iron and copper salts and (2) a mercury oxide dry cell. A complete description of the wet cell requires a three-dimensional Nernst surface because the potential is a function of two variables: the activities of both the oxidized and reduced forms in each redox couple. Dry cell potentials, which utilize solid or pure liquid species, are functions of only one variable and can be described by a pair of traces in a traditional plot. Plots of the Nernst potential are relatively flat for most activities, but they exhibit bluffs and cliffs under extreme conditions. The flat plateaus are responsible for the fairly constant voltage that batteries deliver; the bluffs and cliffs explain why batteries fail so quickly as they wear down. This chapter, an expansion of ideas introduced in Chapter 3.1, focuses on a familiar real-world application.https://scholarworks.umt.edu/topos/1008/thumbnail.jp