Students often ask their physical chemistry instructors, "why do I need to know this?" The response by the instructors might be, "because you don't really know something until you derive it!" I can appreciate this exchange after teaching physical chemistry for over twenty years. The mathematical models we use in chemistry are based on assumptions that are usually hidden from the beginning student and it is in physical chemistry that these assumptions are unveiled. However, I think the students are asking another question, one that does not ask for justification of the derivation. I think they want to know about why in terms of where is this applied and why it is important. In other words they want relevance as one of the answers to the question.

The issue of relevance of the materials or even of the immediacy of the topics and concepts is important to students and to instructors as well. Physical chemistry needs to be relevant, it needs to engage students in understanding and solving modern chemical problems that link the subject to the wider scientific enterprise. In this commentary I introduce three Mathcad documents that respond to this call for relevance by a focus on chemical dynamics. The three documents described in the September 1999 issue of the Journal of Chemical Education use interesting and current topics to set the stage for the study of chemical reaction kinetics. The authors use chemistry to drive both the development of the mathematical models and student progress in mastering the concepts of the discipline and the software for doing the modeling.

Chemical dynamics seems like it would be an ideal place to include chemical relevance but, if we look closely, we see that this usually occurs only through sample problems or as end of chapter exercises. Although it might be necessary to use A + B --> C + D in the derivation of rate laws, modern practical examples and interesting chemical reactions should be placed at the core of instruction in physical chemistry. In other words, use the chemistry to drive both the development of the mathematical models and student progress in mastering the concepts of the discipline. In this column we present two examples that build concepts within the context of practical and chemically interesting systems. The two examples are first, the study of the ozone layer along with NO_x and HO_x stratospheric chemistry, and second, the study of oscillating reactions and chaos theory.

Stratospheric Chemistry

In the pair of Mathcad documents written by Erica Harvey and Robert Sweeney we see how context based instructional materials can focus student learning on a chemically relevant topic and the mathematics used to model that chemical system. In "Modeling Stratospheric Ozone Kinetics, Part 1" the authors provide students with materials that introduce them to the process of modeling coupled chemical reactions, i.e. the Chapman cycle. In their second document, "Modeling Stratospheric Ozone Kinetics, Part II: Addition of Hydrogen, Nitrogen and Chlorine", Harvey and Sweeney, extend the study of ozone chemistry to include the NO_x and HO_x ozone destroying molecules found in the stratosphere. More examples of using atmospheric chemistry as a system for instruction in physical chemistry are being developed and will be published in this column.

The Effective Use of Software

The Harvey-Sweeney documents demonstrate several key techniques for the effective pedagogical use of a symbolic engine like Mathcad for effective content delivery and skill building. First, the documents contain clear goals and objectives. Students know from the beginning what they are expected to be able to do after completing the material. Second, the chemistry, and mathematical formalism of the modeling process are intertwined with methods for implementing the exercise through Mathcad activities. Third, the modeling and mathematical techniques are implemented through detailed exercises. Fourth, students use embedded exercises to test their skill with each step of the modeling process. Fifth, all steps in the process of creating and working with the mathematical model for the Chapman cycle are clearly explained with respect to the way that Mathcad works. Finally, through graphs of concentration of chemical species, O, O₂, and O₃, experimentation and exploration of stratospheric chemistry are possible. Students do the experiments for themselves with the software.

Getting More out of Dynamics

The third document in the September 1999 appearance of the column was prepared by John Pojman. In this document he presents "Studying Nonlinear Chemical Dynamics with Numerical Experiments". The focus of the document is the oscillating reaction subset of the broad area of nonlinear dynamics. Oscillating reactions are diverse and wide spread throughout living systems from the cellular level up through the behavior of organs and organisms as individuals or groups. Embedded in the Pojman document is a core introduction to analytical and numerical integration. Students are led through an exploration of the methods and sources of error for this integration technique. They get introduced to modeling dynamic systems by studying the simple harmonic oscillator. The document moves students steadily along the development of the attractor concept and into models of oscillatory systems. The materials prepared by Pojman focus study by students.

In the Classroom

The three documents presented in this column are ideal additions to the active learning classroom. While they can be used as lecture presentation materials I think they will not provide as strong a learning experience when used in lecture. I personally will use these materials with my students as independent study projects. The Pojman document is sufficiently accessible for beginning physical chemistry students that they can do most of the work on their own along with group discussion during specific class periods. A valuable compliment to the Pojman document is a set of Mathcad documents created by W. T. Grubbs through which students can study the Fourier transform of molecular vibrations (1). In the Fourier documents students can explore an alternative mathematical model for molecular oscillations, i.e. bond vibrations.

The Harvey/Sweeney documents will comprise a second independent exercise. Near the end of the semester I will expect each student to present a portion of the material in seminar fashion. I expect one other outcome from the students as they study these materials. I expect that they will gain experience with using Mathcad more quickly than if I tried to lecture them on how to use the software. Physical chemistry is a hands-on discipline in both the experimental laboratory and the computer laboratory. Learning occurs best when students are actively engaged with significant concepts through well-crafted teaching materials.

Acknowledgment

We thank the NSF for support of the 1997 NSF-UFE Workshop on Numerical Methods in the Undergraduate Chemistry Curriculum Using the Mathcad Software. Additional support was provided by the NSF Division of Undergraduate Education through grant DUE #9455928.

Literature Cited

1. Grubbs, W. T. Fourier Transforms of Molecular Vibrations. J. Chem. Educ. 1999, 76, 286.