FINDIF is a Windows application that numerically solves the one-dimensional (1D) Schrödinger equation and displays the eigenstates, eigenvalues, and probability density of the system. FINDIF accepts both nonperiodic and periodic 1D potential energy functions as input and uses the finite difference method to evaluate the energy of the quantum…

We present an algorithm for solving the time-dependent Schrödinger equation that is based on the finite-difference expression of the kinetic energy operator. Students who have some knowledge of linear algebra can understand the theory used to derive the algorithm. This is because the finite-difference kinetic energy matrix and the Hückel matrix…

This work is part of a larger project that seeks to understand how students blend (integrate) chemistry and mathematics as they work through chemical kinetics problems. Here we focus on four students from our larger sample: two students that demonstrated more instances of blending chemistry and mathematics in their interviews ("high-frequency…

In this article, we show a "very" simple algorithm for the evaluation of the character tables applicable to all finite point groups. The method uses linear combinations of the symmetry operators associated with the point group's classes as the basis set. Eigenvectors of the resulting matrix of such representations are related to the…

We present a detailed yet easy-to-follow discussion of the mathematical treatment of time-resolved spectroscopic data in a model-based approach. This is accompanied and complemented by an example of a colorful and pedagogically rich chemical reaction: the permanganate oxidation of sugars in basic aqueous media (often known as the chameleon…

Approximate mathematical treatments are commonly taught in undergraduate chemistry, but the validity ranges of these approximations have rarely been properly defined. We present error contour plots of commonly used quadratic approximations for calculating equilibrium proton concentrations of monoprotic acids. Students and instructors can easily…

This is an easy and inexpensive laboratory experiment in which undergraduate students at the Bachelor's degree level in Chemistry can measure formation constants of complexes [Ni(en)[subscript n](OH[subscript 2])[subscript 6-2n]][superscript 2]+ (n = 1, 2 or 3; en = ethylenediamine) through an acid-base titration. The background information…

The concept of relative density is introduced in the middle school and high school curricula by an intuitive approach based on the phenomena of immersion and flotation. In high school, the same concept is taught as the ratio between the masses of two bodies of the same volume. This dichotomy of the concept of relative density between the two…

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…

In this paper, we develop a general but very simple mathematical foundation for the predefined coefficient graphical method of Hückel molecular orbital theory (HMO). We first present the general solution for the recurrence relation of the coefficients of Hückel molecular orbitals (MOs). Subsequently, for all the three unbranched hydrocarbons,…

We present a modernization of the undergraduate physical chemistry laboratory experiment for determining the speed of sound in various gases from resonant frequencies in a spherical resonator. The resonator (schematic IR = 7.5 cm) is constructed by 3D printing with eco-friendly poly(lactic acid), a commercially viable alternative to traditional…

With recent curricular movements aimed at engaging students in science practices, more work is needed regarding evidence-based approaches for supporting students in developing competency in contexts such as chemistry. In this work, we focus on student engagement in constructing models related to graphical representations of reaction rate. Using…

Students beginning college chemistry are expected to arrive prepared with fundamental, prerequisite conceptual understanding and skills from high school. While some topics may be reviewed explicitly in the course, prerequisite material-including hidden prerequisites often overlooked by faculty-is typically considered assumed prior knowledge and…

Techniques from the branch of artificial intelligence known as machine learning (ML) have been applied to a wide range of problems in chemistry. Nonetheless, there are very few examples of pedagogical activities to introduce ML to chemistry students in the chemistry education literature. Here we report a computational activity that introduces…

This work describes a semester-long learning module designed to equip students with the analytical and practical skills necessary to be successful in an interdisciplinary polymer research environment. This learning module combines laboratory experiments involving both synthesis and materials characterization with lectures in polymer theory, and…