Gentle Reader, forgive me if the title - Connecting Acid-Base and Redox Connections (CABARC) - is redundant, but the connections between acid-base and redox reactions already exist, and it is my hope that we as instructors can parlay these connections into easier, better, and deeper understanding of both topics.
KEYWORDS for this blog post: acid-base, Brønsted acid-base, redox, buffer, electron buffer, potentiometric titration, ½ reaction, conjugate acid-base pair
Consider the two overlapping graphs in Figure 1 (Overlapping graphs with unlabeled y-axis). As the graph does not have a label on the y-axis, it is flawed, and yet the data looks familiar. The shape of the two data plots has the look of titrations. But are they acid/base titrations? As it turns out, they are both potentiometric titrations using a standard calomel electrode (SCE) and a platinum flag spanning about +450 mV to 1200 mV vs. the SCE.
Figure 1: Overlapping graphs with unlabeled y-axis
Figure 2 shows the y-axis. The titrations are a part of an analysis of the oxidation state of a mixed valent vanadium compound that will be covered in the next of these blog posts in "The Most Brutal Stoichiometry Problem Ever," and a follow-up to my previous blog, "Water Tower Analogyi". But, for now, lest us stick with CABARC.
Figure 2: Overlapping graphs of potentiometric titrations. Green: Fe(II) solution standardization with Ce(IV) primary standard. Multicolor: Regions of titration for analysis of LixV2O5 sample.
The familiarity in shape between acid-base and potentiometric titrations is not coincidental, and this realization can lead us down a path that connects the transfer reaction classes: proton transfer (Brønsted/Lowry acid-base) and electron transfer (redox) reactions. The method here is to compare and borrow from the language of acid-base and redox, and vice versa. Using the unified idea, "transfer," the instructor and student can benefit from fruitful conceptual and language connections that make both topics more manageable by linking them. And, as with other of my blogs, there is a MS PowerPoint presentation with useful slides, some of these taken from a talk I gave at a recent ACS Meetingii.
The link between acid-base and redox transfer reactions is long-standing, but has not been utilized in General Chemistry textbooks. Typically, in the first semester there is a chapter on reaction types. Acid-base and redox reaction are in separate sections, though they may both be described as transfer reactions. Separated into sections, the opportunity to make connections between the two is lost. In the second semester, as they are in unrelated chapters, the separateness of the discussions of the two transfer reactions are only reinforced by the one time they are connected: the necessarily sequential steps to balance mixed proton-electron transfer reactions.
Your humble servant wrote an article about 30 years ago that provided concrete classroom exercises to create a tactile, visual for students to learn about transfer reactions, "Kinetic Classroom"iii, which YOU can use in class. Plugging my paper notwithstanding, once revealed (mentioned?), the most obvious connection is seen in in the parallels between the Henderson-Hasselback (HH) and Nernst Equations as shown below. Let's look.
The HH equation is in fact derivable from the Nernst equation, but I will leave it to both of you who are interested to go through the math. Once laid out as above, we can see the heart of both are their standard state terms, pKa and Eo, respectively. The logarithmic perturbation from the standard state, results in a measurable value, pH and E, respectively. Seen in this way, we should not be surprised that the plot of a potentiometric titration has a frighteningly similar look to that of an acid-base titration. The idea here is to unify the acid-base and redox under "transfer reactions," and define both by following what is transferred, proton and electron, respectively. And just as Deep Throat during Watergate said, "Follow the money," we follow what is transferred, and then we naturally appropriate the pre-existing language of both acid-base and redox chemistry.
Strictly, pH is only used for aqueous systems, so a Brønsted/Lowry proton transfer approach is appropriate, where there is a base that either has a proton (acid) or can accept a proton (base). Correspondingly, in a one-electron redox half-reaction (for simplicity of discussion) there is a species that has an electron (reducing agent/reducer/fuel) and the same species that can accept an electron (oxidizing agent/oxidizer). Or, if you will, givers (acid and reducer) and getters (base and oxidizer).
Having appropriated language to describe the transfer reactions, we can transfer, appropriately, language from one reaction class to the other. Specifically, let's go back to our friends HH and Nernst and look at their Logarithmic Perturbations. Okay, there is a sign change because of the way that each is defined, but that does not change their fundamental similarities. In fact, if the two perturbations both had a positive sign, the getters would be in the numerator and the givers would be in the denominator, but, we are stuck with history, so we won't dwell on that. Instead, let us dwell on the ratio, getters/givers, and recall in acid-base chemistry, when this ratio is between 1:10 and 10:1, we have the canonical conditions for a pH buffer, "A solution that resists changes when acids or bases are added to it; typically, a solution of a weak acid and its conjugate base." In a titration, this is seen flanking the standard state, pKa, where graphically the ΔpH/ΔV slope is shallow.
Take another look at Figure 2, and you will see the solution resisting change upon addition of the reducing agent, Fe2+; the ΔE/ΔV slope is shallow. Each shallow part reflects a solution that is an Electron Buffer. Figure 3 adds labels for each of the three half-reaction Electron Buffer (Equations 3, 4 and 5) from the potentiometric titration:
Figure 3: For clarity the vanadium half-reaction is shown with oxidation states rather than aqueous species.
Following the green data points is a standardization of the titrant Fe2+ solution with pipetted primary standard Ce4+ solution, before the endpoint there is a Ce4+/Ce3+, and after the endpoint is found Fe3+/Fe2+ buffer. The second curve is from an analysis of a mixed valent V5+/V4+ solid dissolved in an excess of Ce4+ solution, and has an additional intermediate (in potential and position in the titration) buffer region VO2+/VO2+ in the strong acid solution. Wait a second, these regions are only there because of reaction with electrons of Fe2+. Can you really call them "Electron Buffers"? Why, the oxidizer (right side of equations 3-5) resists the effect on potential of the reducer Fe2+, and if we took the solution at any one point its range, the Electron Buffer would resist the effect of added strong oxidizer. Hold on, part of the definition of an acid-base buffer is that it is a solution with a dissolved weak conjugate acid/base pair. So, what does that make the reducer and oxidizer? It makes them an electron conjugate pair, and by the way, it makes the following an acetic acid/acetate acid-base ½ reaction (Equation 6).
CH3COO⁻(aq) + H+(aq) ⇌ CH3COOH(aq) 6
Finally, let's look at the end of the titration where the region is labeled Fe3+/Fe2+ Buffer. Here, excess Fe3+ is in solution as a product of oxidation with the excess added Fe2+ solution. If we were to follow the logic of this parallelism, this would be like the strong acid titrant of an acid-base titration. Now, I certainly remember teaching that a strong acid cannot a buffer make. Something does not fit; either Fe3+/Fe2+ cannot be an Electron Buffer, or hydrochloric acid can be called an acid-base buffer.
An Aside: I recall being told by a biologist that a certain hydrochloric acid solution can buffer against base, and in my mind, I condescendingly thought, "What a Rube! Come on, you need a weak acid/base pair for a buffer." I credited my superior chemistry training to catching the "error," and left it at that. But now, to kick the hornet's nest, I contend that then I was in error and the pair hydronium/water has a weak base (water) and, at the other end of the spectrum, water/hydroxide has a weak acid (again water). That being said, honestly, the distinction found in the conventional definition is darned useful, and I contend it should be maintained. But back then I missed a teaching moment for myself because of undue professional arrogance, and instead, humility would have been a quicker path to deeper knowledge on my part.
I can think of two widely different system types that could benefit from this useful transfer terminology:
1) Do you ever wonder why batteries, particularly solid-state ones, can be labeled with a specific voltage? It is because they have two linked Electron Buffer systems that hold the potential reasonably constant until their buffer capacity is emptied and the battery dies.
2) Electron shuttles in biological systems such as photosystems are profoundly complex, but much of their behavior can be understood as a series of linked Electron Buffers. In the Comment Section, Gentle Readers, I would welcome further examples of Electron Buffers.
Understanding transfer in any endeavor, whether it is in accounting, logistics or chemistry, is a challenge. Figure 4 summarizes the bifurcation of language seen between acid-base and redox chemistry, and the unification of these ideas under the broad tent of transfer reactions.
Figure 4: Summary of Acid-Base and Redox Parallelisms, and how these are united under the idea of Transfer Reactions.
It is my contention that teaching twice, teaches better and more deeply. Perhaps, think of it as taking two points of view, acid-base and redox, and triangulating to the deeper idea, transfer. Examining and borrowing from each leg of the triangle reinforces understanding and lets you see each point of view better and deeper. Perhaps my contention at the beginning that this method would be easier is aspirational, but it is my aspirational hope that you will take some or all of this to the classroom and begin creating connections and transferring ideas and language not only in transfer reactions, but between you, your students and beyond.
CITATIONS:
(1) Lomax, Joseph F. "Water Tower Reservoir Analogy of a Buffer" In Chem Ed XChange, online, 2022; Vol. 2023.
(2) Lomax, Joseph F. "Redox intercalation chemistry: A superhero advanced laboratory illustrating non-stoichiometry and electron buffers with implications for the general chemistry classroom", ACS Fall 2023 Abstract 3906812-CHED, August 16, 2023.
(3) Lomax, Joseph F. "Kinetic Classroom: Acid-Base and Redox Demonstrations with Student Movement" J. Chem. Educ. 1994, 71, 5, 428. https://doi.org/10.1021/ed071p428
ACKNOWLEDGEMENTS: Dr. Suzanne Q. Lomax for encouragement and assistance in manuscript preparation.
iLomax, Joseph F. "Redox intercalation chemistry: A superhero advanced laboratory illustrating non-stoichiometry and electron buffers with implications for the general chemistry classroom", ACS Fall 2023 Abstract 3906812-CHED, August 16, 2023.
iiLomax, Joseph F. "Kinetic Classroom: Acid-Base and Redox Demonstrations with Student Movement" J. Chem. Educ. 1994, 71, 5, 428. https://doi.org/10.1021/ed071p428
iiiLomax, J. F. "Water Tower Reservoir Analogy of a Buffer" In ChemEd XChange, online, 2022; Vol. 2023.
