The utilization of modeling tools has gained significant attention recently. These models typically involve a series of partial differential equations, which can be challenging for novice modelers. This paper presented an approach in practical teaching of modeling tools for ion-exchange chromatography with three parts: model introduction, model…

The process of diffusion is intimately related to random molecular displacement and is central to many problems in chemistry. Here, we provide an intuitive derivation of the diffusion equation based on the analysis of the random trajectories of particles generated and plotted by simple MATLAB and Python scripts. The codes are very simple and…

When learning chemistry, students must learn to extract chemical information from mathematical expressions. However, chemistry students' exposure to mathematics often comes primarily from pure mathematics courses, which can lead to knowledge fragmentation and potentially hinder their ability to use mathematics in chemistry. This study examines how…

Simple mathematical models can serve to reveal the essence of experimental phenomena and scientific concepts. The particle in a box (PIB), for example, is widely used in undergraduate programs to teach the quantum mechanical principles behind the UV--vis spectra of conjugated polyenes and polyynes. In this work, the particle on a ring (POR) and…

An educational lattice model is proposed for the investigation of the influence of the density and indirectly of the pressure on the chemical equilibrium of the ideal gas phase reaction A [equilibrium] 2B. The model can be introduced by a board game simulating a stochastic process. This game can also be used to set up a corresponding computer…

Upper-division undergraduate students are introduced to polymer processing using material extrusion fused filament fabrication 3D printing to make poly(lactic acid) (PLA) mechanical testing specimens. Computer aided design and slicing software packages are used to demonstrate the process of preparing 3D computer models for printing. Following the…

Metamodeling ideas move beyond using a model to solve a problem to consider the nature and purpose of a model, such as reasoning about a model's empirical basis and understanding why and how a model might change or be replaced. Given that chemistry relies heavily on the use of models to describe particulate-level phenomena, developing…

Excluded-volume interactions are ubiquitous to modeling the average size of polymers in solution. This paper shows how simulations can be used by students to explore the emergence of mathematical scaling relations from excluded-volume interactions. Simulations provide robust visual representations of the system, and can be used to investigate a…

One of the unique advantages of electrochemistry is that the relationship between thermodynamics and kinetics is quantitative, which is the basis of voltammetry. Mathematical models of electrochemical systems take advantage of this relationship to predict the effect of changing a system property (e.g., concentration, scan rate, or rate constant)…

Colorimetry allows every color to be defined as a combination of three values, known as "color coordinates." Color coordinates allow researchers to universalize and standardize their color measurements, and nowadays, determining the color coordinates of samples is a routine method applied by organic and analytical chemists, students, and…

Understanding the nature and purpose of models, including mathematical models, is critical to enabling undergraduate chemistry students to use models to predict and explain phenomena. However, students often do not have systematic conceptions about different kinds of models. To gain a sense of how students understand different models in the…

Here, we present an interdisciplinary educational project intended for high school chemistry that is focused on the establishment of a mathematical model to describe the relationship between conductivity and concentration, while linking chemistry to mathematics with the help of computer software. The project was designed to help high school…

Introductory chemistry students encounter the concept of hybrid orbitals as a transition from atomic orbitals to molecular bonding. The principal purpose of learning hybridization in the undergraduate curriculum is to impart an understanding of the origins of molecular bonding and geometry. Physical models of both individual hybrid orbitals and…

Quantum dots (QDs) are useful for demonstrating the particle-in-a-box (PIB) model utilized in quantum chemistry, and can readily be applied to a discussion of both thermodynamics and kinetics in an undergraduate laboratory setting. Modifications of existing synthetic procedures were used to create QDs of different sizes and compositions (CdS…

In undergraduate physical chemistry, Schrödinger's equation is solved for a variety of cases. In doing so, the energies and wave functions of the system can be interpreted to provide connections with the physical system being studied. Solving this equation by hand for a one-dimensional system is a manageable task, but it becomes time-consuming…