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…

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…

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…

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…

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…

The lithium ion battery will be a reliable electrical resource for many years to come. A simple model of the lithium ions motion due to changes in concentration and voltage is presented. The battery chosen has LiCoO[subscript 2] as the cathode, LiPF[subscript 6] as the electrolyte, and LiC[subscript 6] as the anode. The concentration gradient and…

The initial interaction among student, instructor, and content on the first day of class is critical in setting the stage for the remainder of the semester. While many students would like to ease into the semester, experienced faculty realize that the first day of class provides a one-time opportunity to shape the students' first impression…

A classroom exercise is described to introduce enzyme kinetics in an undergraduate biochemistry or chemistry course. The exercise is a simulation in which a student acts as an enzyme that "catalyzes" the unscrewing of a nut from a bolt. With other students assisting, the student enzyme carries out reactions with bolt-nut substrates under different…

A mathematical model of a non-ideal solution is presented, where it is shown how and where the non-ideality manifests itself in the standard thermodynamics tableau. Examples related to the non-ideal solution thermodynamics study are also included.

The existing vector formalism method for thermodynamic relationship maintains tractability and uses accessible mathematics, which can be seen as a diverting and entertaining step into the mathematical formalism of thermodynamics and as an elementary application of matrix algebra. The method is based on ideas and operations apt to improve the…

A simplified mathematical model for the calculation of imprecision associated with the construction of a calibration line is presented. The model also aims at a discussion on variables that really affect it and to integrate the resulting imprecision with that caused by the other steps in the analytical method in order to calculate a real…

A laboratory experiment reinforces the concept of acid-base equilibria while introducing a common application of spectrophotometry and can easily be completed within a standard four-hour laboratory period. It provides students with an opportunity to use advanced data analysis techniques like data smoothing and spectral deconvolution to…

The evolution of ideas about the concept of chaos is surveyed. Discussed are chaos in deterministic, dynamic systems; order in dissipative systems; and thermodynamics and irreversibility. Included are logistic and bifurcation maps to illustrate points made in the discussion. (CW)