Although voltammetry is one of the most widely used electrochemical techniques, the mathematical foundations of its characteristic current responses are rarely available in a didactic and self-contained form. As a consequence, students and researchers often make use of inadequate equations and approaches without a clear comprehension of the conditions under which they are valid. This work addresses this educational gap by providing a thorough, step-by-step, illustrated derivation of voltammetric current profiles. Starting from first principles and physical intuition, the main assumptions necessary to model a voltammetric experiment are presented, along with the key mathematical tools that are employed throughout the text. The paradigm system studied is a reversible electrochemical reaction on a macroelectrode in a semi-infinite domain, in which mass transport occurs only through diffusion. The derivation follows a six-step procedure, progressing from the partial differential equations that describe mass transport to the voltammetric current expression. Each of the six steps can be adapted and applied to solve different physical problems in electrochemistry. After deriving the current profiles, they are thoroughly examined to yield peak current (Randles–Ševčík) and peak potential equations, which are discussed in detail using intuitive terms. Finally, the six-step method is applied to chronoamperometry and finite kinetics electrochemical reactions, showcasing its wide applicability. By making explicit the logical structure behind electrochemical models, this work aims to provide students and researchers with tools needed to critically interpret voltammograms and adapt theoretical models to new electrochemical systems.
This paper explains basic liquid–liquid equilibrium calculations for binary systems, the isoactivity and tangent-line methods for the coexistence compositions, plus the plotting of spinodal lines and the estimation of the critical temperature. The ternary liquid–liquid equilibrium is also covered due to its industrial importance as the reduction of experimental data to models and the multicomponent formulation. The reader can reproduce and extend the examples, which are included in computational Jupyter Python notebooks.
The chemistry of the atmosphere, with a focus on its transition from gas to particle phases, is described. Emphasis is placed on how our understanding of this chemistry has evolved over time, reaching the current point, where every atmospheric compartment can be modeled, helping to tackle the emergent issues of air pollution and climate change. The main reactions occurring in the different compartments and contributing to the final observed aerosol compositions are presented. The different possible pathways of compounds, from their emission to their presence in aerosol particles, passing through an interface to reach a bulk aqueous phase, are pedagogically described. The goal is to provide the reader with the opportunity to understand key aspects of this important field of chemistry and to offer insights into how it has evolved over the years, also touching on new and still little-explored facets, such as surface reactions.
In many languages, element names are phonetic borrowings. By contrast, Chinese element names are single-syllable logographs, typically phono-semantic compounds: a radical that signals a broad material class ((sic) metal, (sic) stone, (sic) gas, (sic) water) paired with a component that hints at the pronunciation. This radical-based encoding of physical state is a distinctive advantage of the Chinese system, providing immediate chemical information that is absent from most European element names. This article reviews the historical development from early descriptive gas names through the X & uacute;-Fryer standardization, the shift to single-character transliterations, and later refinements. The architecture of all element characters is comprehensively analyzed, highlighting noteworthy examples and groups of elements. A printable and scalable periodic table, annotated with modern Chinese names and translations, is provided as a reference resource. Practical challenges of homophones, regional variants, and the modern naming of superheavy elements are also discussed. Chinese element names offer a window into how scientific knowledge was transmitted across cultural and linguistic boundaries during the nineteenth and twentieth centuries.Level: Undergraduate and above.AbstractIn many languages, element names are phonetic borrowings. By contrast, Chinese element names are single-syllable logographs, typically phono-semantic compounds: a radical that signals a broad material class ((sic) metal, (sic) stone, (sic) gas, (sic) water) paired with a component that hints at the pronunciation. This radical-based encoding of physical state is a distinctive advantage of the Chinese system, providing immediate chemical information that is absent from most European element names. This article reviews the historical development from early descriptive gas names through the X & uacute;-Fryer standardization, the shift to single-character transliterations, and later refinements. The architecture of all element characters is comprehensively analyzed, highlighting noteworthy examples and groups of elements. A printable and scalable periodic table, annotated with modern Chinese names and translations, is provided as a reference resource. Practical challenges of homophones, regional variants, and the modern naming of superheavy elements are also discussed. Chinese element names offer a window into how scientific knowledge was transmitted across cultural and linguistic boundaries during the nineteenth and twentieth centuries.Level: Undergraduate and above.
Teaching vapor–liquid equilibrium in real fluid systems is often difficult because students must connect abstract thermodynamic relations with numerical calculations and engineering interpretation. This study presents a computational teaching case based on the binary CO2–H2S system to illustrate how fugacity-based equilibrium can be analyzed using the Peng–Robinson equation of state (EOS) in a commercial process simulator. The purpose of the work is not to generate new experimental thermodynamic data but to provide an instructional bridge between textbook thermodynamics and simulation-based engineering analysis. The methodology was applied as a guided modeling exercise for third-year undergraduate chemical technology students within the course Modeling of Chemical Technological Processes. By combining phase equilibrium theory, fugacity relations, and pressure-dependent flash calculations, the approach enables learners to interpret non-ideal vapor–liquid behavior in terms of equilibrium criteria, vapor fraction, and p–x–y relations, rather than treating simulator outputs as black-box results. The results show that the proposed framework can be used to explain how pressure influences phase splitting and composition in an acid gas mixture while preserving the thermodynamic meaning of the calculations. Instructor-based classroom observations indicated improved student engagement when the topic was taught through an industrially relevant simulation case instead of theory and hand calculations alone. Limited classroom performance data also suggested improved student outcomes after implementation of the simulator-based activity, although the present work does not constitute a full controlled educational study. Overall, the study shows that industrially relevant simulation exercises can support conceptual understanding of real-fluid thermodynamics and provide an effective pedagogical link between equilibrium theory and engineering practice.
A guided, stepwise thermodynamic analysis of the ammonia synthesis reaction is presented in the form of a multipart student problem with an accompanying guided computational solution. The activity is designed to strengthen student understanding of chemical potentials (µ), Gibbs (G), and Helmholtz (A) free energies, and their quantitative connection to chemical equilibrium under different thermodynamic constraints. The problem is organized into pedagogically sequenced tasks involving the calculation and interpretation of µ, G, and A as functions of the reaction extent, together with the determination of the equilibrium position (reaction extent) and the equilibrium constant, under conditions of constant temperature–pressure and constant temperature–volume. The influence of pressure and temperature on free energy profiles and equilibrium position is examined quantitatively. A computer-assisted approach is employed to allow students to focus on conceptual understanding rather than extensive numerical calculations or algebraic manipulation. A Wolfram Mathematica notebook is provided to facilitate calculations and visualization of results, supporting the integration of thermodynamic concepts within a unified problem-solving framework applied to a reaction of industrial relevance.
The global challenges of the twenty-first century compel contemporary scientific research to address Complex Systems, including all living organisms, natural ecosystems, urban environments, human societies, the global economy, the climate, and Earth's geology. At first glance, these systems appear very different from one another and are traditionally studied by well-distinct disciplines. However, interdisciplinary investigations of these systems, initiated as early as the eighteenth century and becoming systematic since the 1980s in several research groups worldwide, have revealed that they share common features. Chemical research also contributes to the study of such systems, playing a central role in describing biological and physicochemical systems. It is therefore important to understand the behavior of Complex Systems, the limitations of scientific research in studying them, and promising methodologies for deepening their comprehension. This lecture illustrates how the global challenges of the twenty-first century, together with the methodologies proposed to address them, are fostering a third revolutionary cultural event in humanity’s journey to uncover the secrets of nature—an event that also involves chemistry itself. Chemistry is essential both for understanding and for contributing to this third revolutionary cultural event. A promising synergy between chemistry and the science of Complex Systems is claimed.
Lithium-ion batteries (LIBs) dominate the electrochemical energy storage field currently, yet undergraduate materials science and engineering students often encounter LIB technology primarily via classroom studies. Despite having a fundamental knowledge of electrochemistry, still hands-on experience with cell construction, testing, and performance analysis is missing. This article describes a structured, short-term laboratory module, allowing students to apply fundamental electrochemical principles by assembling and evaluating lithium-ion coin cells. Students construct CR2032 coin cells with graphite anodes and lithium oxide-based cathodes (particularly lithium cobalt oxide or lithium manganese oxide) and test their electrochemical performance under controlled cycling settings. This report shows the analysis of six basic charts, assisting the discussion of important performance metrics such as capacity retention and coulombic efficiency. The subject is purposely comprehensive and analytical, pushing students to use theoretical knowledge, while gaining also practical understanding of experimental constraints and design choices. In addition, general battery-related difficulties and future prospects are raised to encourage additional theoretical and experimental research. This hands-on teaching approach is straightforward, versatile, and easily adaptable to various battery chemistries or extended testing of performance deterioration during cycling.
The Chernobyl nuclear disaster of April 1986 released significant radioactive contamination by means of radionuclides across Europe, presenting unprecedented challenges to environmental, radiochemistry, human and veterinary medicine. Among the most effective countermeasures developed was ammonium iron hexacyanoferrate, a Prussian blue compound that efficiently binds radiocesium in the digestive tract of animals. This compound prevented the absorption and bioaccumulation of dangerous radionuclides such as cesium-134 and cesium-137, significantly reducing contamination in the food chain. In German-speaking countries and Scandinavia, this compound became known as Giese salt after Werner Giese, the veterinarian and physicist who pioneered its application after Chernobyl. This article examines the chemistry of this remarkable compound and its classification among Prussian blue compounds, the role of radiocesium in the ecosystem, food safety and agricultural countermeasures, the history and applications of Giese salt in veterinary medicine such as powder, lickstones, and granulates, and its vital role in mitigating one of the worst nuclear disasters in history.
The quasi-steady-state approximation of chemical kinetics consists of equating to zero the time derivatives of the concentrations of intermediate species in the rate equations. It is remarkably successful in simplifying those equations, but that does not imply that any conclusions drawn are correct. Singular-perturbation theory has proved effective in deciding such questions, but is not easily accessible to non-mathematicians. It is therefore valuable to explore whether other methods can usefully contribute to our understanding of the (sometimes nonlinear) differential equations arising in chemical kinetics.
Galvani postulated the existence of animal electricity in 1791 after observing that touching the nerves and muscles of a skinned frog with an arc made of two different metals (e.g. Ag and Zn) caused convulsive movement. Alessandro Volta attributed the generation of electricity to the potential difference that arises when different metals come into contact (metallic electricity, 1796). On the basis of this hypothesis, Volta built his pile by placing discs of zinc and silver, on top of each other, separated by discs of wet cardboard (1800). However, as early as 1793, the Florentine chemist and agronomist Giovanni Fabbroni observed that, when two dissimilar metals (e.g. silver and zinc) were in contact in an aqueous solution, the oxidation of zinc occurred. Fabbroni proposed that this chemical process was responsible for generating electricity (chemical interpretation of galvanism). Fabbroni’s observations were confirmed by numerous scientists throughout the nineteenth century. However, a complete interpretation of how galvanic cells work only became possible after the discovery of the electron (Thomson in 1897). Over the following years, chemists clarified that oxidation–reduction reactions involve the transfer of electrons from the reducing agent to the oxidising agent, and that a galvanic cell can be obtained from each redox reaction by keeping the oxidant and the reductant in two separate half-cells that are connected electrically.
This article explores the historical case of the Pine Institute in Aquitaine (France) to examine whether resin chemistry between 1900 and 1970 can be regarded as a precursor to modern green and sustainable chemistry. By situating the Institute’s activities within broader scientific, economic, and ecological contexts, the study challenges the common perception that sustainability in chemistry emerged only recently. The analysis reveals that resin chemistry at the Pine Institute exhibited many traits now associated with sustainable practices: it focused on renewable, bio-sourced materials; prioritized waste valorization and minimal molecular intervention; and operated with strong regional engagement, particularly with labour unions and small producers. Though it lacked formalized sustainability metrics, resin chemistry reflected an integrative approach to science, emphasizing landscape preservation, resource circularity, and social responsibility. The decline of the field of resin chemistry in the 1970s coincided with the broader displacement of natural products by petrochemicals and a shift toward disciplinary fragmentation. By revisiting this forgotten scientific tradition, the article suggests that sustainability in chemistry can emerge from deeply embedded socio-environmental contexts. This historical perspective highlights the potential of regionally rooted, socially responsive science as a foundation for future sustainable research paradigms.
Considering any fuel from an engineering standpoint, a few physicochemical properties with the utmost importance are the density, natural stable state, volatility, calorific value, and tendency to resist autoignition, i.e., octane rating. Petroleum-based fuels, be that gasoline, diesel, or aviation turbine fuel, are majorly composed of hydrocarbons, and in particular, the concentration of paraffins and isoparaffins outweighs other classes of hydrocarbons. Readily available resources present data for the aforementioned characteristics for a wide range of paraffins and isoparaffins, but only a few discuss the fundamental understanding behind the correlation between their significant variation and the molecular structure and/or molecular weight. This paper compiles several proven and accepted scientific theories for these variations and attempts to explain the crux of the same in a simpler way. This aids in obtaining a deeper understanding of the commonly known facts, such as why methane and butane naturally exist in a gaseous while pentane occurs in a liquid phase, why n-octane has an octane rating below zero while the value for isooctane is 100, and why branching in paraffins leads to differences in density, calorific value, volatility, and octane rating.
Resorcin[4]arenes and related cavitands are bowl-shaped macrocyclic compounds possessing rigid cavities that enable highly selective molecular recognition. In this lecture text, we describe their structural principles, conformational behavior, and electronic properties, alongside key functional applications. Special attention is given to the resorcin[4]arene-based framework, which forms the cornerstone of modern cavitand design. The dynamic vase–kite equilibrium is discussed as a central conformational feature, influencing the host–guest interactions. Through selected examples, we illustrate how fine-tuning the cavitand structure leads to diverse and controllable recognition profiles, underlining their importance in the broader context of supramolecular chemistry.
The use of videos to illustrate advances in the chemical sciences offers numerous benefits that range from enhanced reproducibility of reported findings through to enhanced reader attention and understanding. The nearly concomitant advent of the World Wide Web and of digital photography has long made the publication of laboratory videos accessible at low cost to virtually all researchers. Yet, the use of videos to illustrate advances in chemical research remains low. Besides identifying requirements to create effective chemistry research videos, this study shows why videos in chemistry papers are a crucial resource to enhance the reader’s interest in the hypercompetitive context of the digital era of today’s research in which attention has long become a scarce resource.
Catalytic methods for determination of inorganic ions are frequently labelled as catalymetry. It is the analogue of enzymatic methods of analysis. This short lecture text will be most easily understandable for everybody who is already acquainted with the basics of enzymatic analysis. Catalymetry is based on measuring the rate of catalytic chemical reactions in homogeneous solutions, and it can also be performed by measuring the currents on electrodes, when these are caused by catalysts dissolved in solutions. These two variants of analysis are in the focus of this paper. Substrates dissolved in solution can be determined, when the catalyst is immobilised on the electrode surface. Such electrocatalytic systems using immobilized enzymes, are most popular as biosensors, e.g., glucose sensors.
Statistical design of experiments (DoE) is a key method for the systematic planning, execution, and analysis of experiments. In academia, it enables efficient scientific study design, particularly in the natural and engineering sciences, by identifying complex relationships between variables while reducing experimental effort. In industry, especially in the chemical, pharmaceutical, and manufacturing sectors, DoE is used to optimize processes, identify critical parameters, ensure quality, and meet regulatory standards. It supports resource conservation, shortens development times, enhances product quality, and reduces costs. This laboratory practical is offered to Master’s students in the Chemical Technology and Biotechnology program. It aims to lower the cost of a glucose assay while ensuring a robust response signal that enables the safe detection of 0.125 mM d-glucose by employing an enzyme activity model. Students first design an efficient experimental plan using DoE software, followed by hands-on implementation of the experiments and statistical evaluation of the results. Through this process, they learn to apply DoE for optimizing complex, multivariable systems, and will develop a comprehensive understanding of the effect that various factors and their interactions have on the response signal. The skills and insights gained are broadly transferable to a range of experimental and industrial challenges, particularly in the natural sciences.
The present article deals with the working principles of regenerative wet photovoltaic cells compared to n-p-type junction dry photovoltaic cells and photo-electrochemical cathodic protection short-circuited cells from thermodynamic and electrokinetic aspects with a pedagogical motivation. Additionally, it introduces two hypothetical regenerative hydrogen/oxygen photovoltaic cells conceptually designed for the first time to our knowledge. Their working mechanisms are discussed in terms of the single shifts of the redox Fermi level to the flat band Fermi level, (E_F, fb^n-E_F^redox) , in the negative potential direction and (E_F, fb^p-E_F^redox) in the positive potential direction during illumination. These negative and positive single shifts are directly responsible for the generation of photo emf (electromotive force) and occurrence of both the negative inverse overvoltage, η_h^n, l<0 , for photosensitized anodic oxidation by the valence band (VB) minority holes in the n-type anode and the positive inverse overvoltage, η_e^p, l>0 , for photosensitized cathodic reduction by the conduction band (CB) minority electrons in the p-type cathode, respectively, on the energy band diagram as well as the photocurrent I vs voltage V polarization curve. The splitting of one unique equilibrium Fermi level E_F , at which chemical potentials of majority and minority carriers overlap in the dark, has been detailed between the two quasi-Fermi levels of majority and minority carriers, (nE_F-pE_F) , which is a measure of the departure from thermodynamic equilibrium ( (nE_F=pE_F) at equilibrium), where the mass action law no longer applies. Both single shifts of the Fermi level during illumination are confirmed to be almost equal in value regarding the difference between the two quasi-Fermi levels, (nE_F-pE_F) . This parameter (the diffusion [contact] potential multiplied by electronic charge at the dry photovoltaic cell) can be regarded as the light quanta energy gain stored in photoexcited minority carrier holes and electrons, which provides the thermodynamic affinity (driving force) necessary for the photo-sensitized anodic and cathodic transfer. This can never contradict the second law of thermodynamics. The negative single shift of the equilibrium potential, V_eq^redox , of a redox couple to the flat band potential, V_fb , driven by the photoexcited VB minority holes in the n-type anode, allows us, relative to the positive single shift of the V_eq^redox to the V_fb , caused by the photoexcited CB minority electrons in the p-type cathode, to qualitatively predict the photo-I vs -V polarization curves. These I–V curves are analogous to the electrochemical I–V curves of any self-driven galvanic cell in the dark. The expected photo-I–V curves are qualitatively justified by some experimental data published in other literature. The negative/positive inverse overvoltages, i.e., negative/positive single shifts of V_eq^redox to V_fb , are confirmed to be the limiting photo emfs in value. In short, the single shift of the Fermi level is divided by the electronic charge, {-(E_F, fb^n-E_F^redox)/e} and {-(E_F, fb^p-E_F^redox)/e} , which are named the negative and positive inverse overvoltages (zero inverse overvoltage at equilibrium in the dark), η_h^n, l<0 and η_e^p, l>0 , which again mean the limiting photo emfs, (V_oc^n, l<0) regarding the counter cathode for the n-type-based photovoltaic cell inclusive the photo-electrochemical cathodic protection cell and (V_oc^p, l>0) regarding the counter anode for the p-type-based photovoltaic cell, respectively. The formation of an electron-depleted space charge region of the n-type anode is confirmed to be adequate for migration of the majority electron and minority hole across the transition region into the surface prior to producing photosensitized reduction and oxidation currents as well as photovoltages, respectively, at both the regenerative wet photovoltaic cell and the photo-electrochemical cathodic protection cell. The same is true of a hole-depleted space charge region of the p-type cathode. By comparison, the presence of a depleted space charge region is well suited for the photoexcited minority EHP (electron-hole pair) to migrate (drift) across the transition region into the n-type and p-type regions, respectively, before recombining there and finally delivering a photocurrent as well as a photovoltage at the dry photovoltaic cell inclusive the n/p junction. The presence of a depletion region, as opposed to an enriched space charge region, is a key requirement for all three types of cells to function effectively.
We give here a brief and relatively simple derivation of the mean relative speed of two gas molecules moving according to the kinetic theory of an ideal gas. This account avoids both a lengthy or involved derivation and the plausibility argument used in some textbooks. We discuss also the extension to real gases that is possible in view of recent work.
This lecture text introduces the Bohr model of the hydrogen atom in a historical context. Danish physicist Niels Henrik David Bohr introduced this model in a series of three scientific articles in 1913. The model was originally formulated on the basis of five explicit assumptions, which have been re-formulated as two postulates in modern chemistry textbooks. This contribution points out that the assumption of the absence of electromagnetic radiation in a system containing moving charges was a direct violation of Maxwell equations but, in fact, simply stated what had already been firmly established in experimental observations. The quantization condition, which said that the angular momentum of the electron is an integer multiple of h/(2π), was validated in the model by demonstrating that this leads to a theoretical prediction of the atomic spectrum of hydrogen that is in full agreement with the experimental results. In hindsight, this postulate seems to be the core achievement and was later justified in three independent discoveries: the wave–particle duality of de Broglie, the uncertainty principle of Heisenberg, and the direct detection of the angular momentum of the photon by Raman and Bhagavantam.
