The concept of oxidation number (oxidation state) of an atom in a molecule with AxBy formula is discussed according to a new simple equation that links the concepts of oxidation number, formal charge, and effective charge through the notion of electronegativity equalization. First-year undergraduate chemistry students do not find it easy to understand and distinguish these concepts. The proposed equation, named the heuristic equation, could have a significant pedagogical and didactic value. The heuristic equation can also be applied to simple AxOy solid oxides. The extension of the heuristic equation to AxBy molecules and solids with complex structures or containing more than two atoms, out of the aim of this contribution, is reported as Supplementary Information.
This article offers a vision of the current state of the art in the research and professional practice of textile heritage conservation. Fundamental aspects of the chemistry of textile materials are reviewed, as well as the main alteration processes associated with the causal agents, which are also described. Current analytical methods for fiber identification, some of which have been inherited from microscopy and spot-testing techniques from past centuries, are reviewed, along with instrumental techniques, and standard and ad hoc methods for characterizing fibers, yarns, and fabrics, and their alterations. The primary methods and materials used in conserving textiles, namely, cleaning, conditioning, stabilization, loss compensation, and disinfection and disinfestation are presented. Special emphasis is placed on providing a current overview of this field, including the most recent methods based on nanosciences, nanotechnologies, and nanomaterials.
The ideal gas approximation is usually associated with low-pressure conditions, while high pressures are generally expected to lead to significant deviations from ideality. However, the behavior of many chemically relevant systems remains nearly ideal even at high pressures. An example is the mixture of N2, H2, and NH3 used in the Haber–Bosch process, which shows deviations of less than 10% from unity in the compressibility factor under typical operating conditions ( 673.15-773.15 K and 150-250 bar) . This behavior is rarely explained from first principles in chemical thermodynamics textbooks, which often treat pressure as the main driver of non-ideality. Therefore, in this work, we provide a statistical-mechanical rationale based on Mayer functions to clarify this apparent contradiction. We show that the system operates above the Boyle temperature of the equilibrium mixture, where the high thermal energy of the molecules weakens attractive spatial correlations, allowing short-range repulsive forces to dominate and result in near-ideal behavior. Combined with experimental results for the equilibrium conversion of ammonia synthesis and estimated values of the virial coefficients, these findings demonstrate that pressure alone is not a sufficient metric for gas non-ideality, which is governed by the interplay among pressure, temperature, composition, and intermolecular interactions. Beyond bridging the gap between thermodynamic theory and industrial practice by providing a theoretical foundation for the near-ideal behavior of gas mixtures at high temperatures and pressures, the results of this work should be helpful for researchers interested in teaching chemical thermodynamics at the undergraduate and graduate levels.
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.
