Information • Textbooks • Media • Resources
JCE Online: Mathcad in the Chemistry Curriculum
edited by
Theresa Julia Zielinski Monmouth University West Long Beach, NJ 07764
Making Physical Chemistry Relevant with Modern Chemical Dynamics For as long as I can remember, the mathematical emphasis in physical chemistry, especially the derivations, and the amount of required work have been the dominant reasons why students think physical chemistry is hard. Some faculty colleagues claim that the difficulty of physical chemistry, a coalescence of chemistry, mathematics, and physics, is a hurdle that causes lower enrollment in the chemistry major. It is interesting to juxtapose these two statements with the often-heard faculty complaints that students don’t know enough mathematics or don’t work hard enough. The poignant student question “Why do I need to know this?” focuses the light sharply on a significant issue in teaching physical chemistry. 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 column I introduce three Mathcad documents that respond to this call for relevance. The focus of this column is chemical dynamics. Chemical dynamics usually garners only a fraction of the physical chemistry curriculum. It is often taught as one third of the semester devoted to quantum mechanics or as a bridge between the thermodynamics and quantum mechanics semesters with a foot in each semester. Sometimes it takes up an entire semester or quarter of instruction. The significance of chemical dynamics is supported by its own American Chemical Society examination. Chemical dynamics would seem to 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 endof-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 (i) the study of the ozone layer along with NOx and HOx stratospheric chemistry and (ii) the study of oscillating reactions and chaos theory. Stratospheric Chemistry Stratospheric chemistry is ripe for development as the medium through which to merge chemistry and mathematical models. Mathcad is a tool that makes the link feasible. In the pair of Mathcad documents written by Erica Harvey and Robert Sweeney we see how the software can focus student learning on a chemically relevant topic. In “Modeling Stratospheric Ozone Kinetics, Part I” the authors provide students with materials that introduce the process of modeling coupled chemical reactions (i.e., the Chapman cycle). The close linkage between chemistry and modeling is shown through the 1308
W
four performance objectives for the document. Students are expected to be able to “write differential rate expressions for species involved in a series of chemical reactions; understand how to set up and numerically solve systems of differential equations to show the time evolution of a chemical system; determine the effects of varying rate constants and initial concentrations; and recognize and understand the Chapman cycle that controls ozone concentrations in the stratosphere.” 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 NOx and HOx ozone-destroying molecules found in the stratosphere. Added to the list of performance objectives are the abilities to add reactions and complexities to a model, to recognize trade-offs in modeling chemical systems, and to understand and discuss the relative importance of YOx cycles to ozone chemistry. The Effective Use of Software The Harvey–Sweeney documents demonstrate several key methods for using 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. Students will simultaneously learn the chemistry, the modeling, and how to use the software. Third, the modeling and mathematical techniques are implemented through detailed exercises through which students can discover how to do the tasks leading to the mastery of content. 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, students experiment and explore stratospheric chemistry with the near-instantaneous feedback required for learning about complex coupled reactions. Students are not just told what happens, they actually do it for themselves with the software. If students do nothing in chemical kinetics but this one Mathcad document they will have learned sufficient content and developed ample skills to enable independent study and mastery of most of the traditional concepts in chemical kinetics. If students complete both documents they will have learned a lot of chemistry and mathematics and discovered the power of models to obtain better understanding of complex systems. Getting More out of Dynamics Of course students can and should do more. They should savor some of the other exciting aspects of chemical kinetics
Journal of Chemical Education • Vol. 76 No. 9 September 1999 • JChemEd.chem.wisc.edu
Information • Textbooks • Media • Resources
and chemical dynamics models. John Pojman presents an interesting approach in “Studying Nonlinear Chemical Dynamics with Numerical Experiments”. The focus of the Pojman document is the oscillating reaction subset of the broad area of nonlinear dynamics. Oscillating reactions are diverse and widespread 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 are 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. Rabbits and lynxes provide concrete images for developing skills with the numerical integration methods in Mathcad. All the introductory material leads systematically toward the Brusselator model for chemical reactions and the Oregonator model for the Belousov–Zhabotinsky oscillating reaction. Previous work in the document permits the presentation at this point to be more concise. Students can fill in documentation as they study the material. Throughout the document student exercises focus study. The document ends with an extensive list of references for oscillating reactions. In the Classroom
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, that is, 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 wellcrafted 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’s Division of Undergraduate Education through grant DUE #9455928. Note
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
W The complete articles and Mathcad documents described in these abstracts are available from JCE Online at http:// JChemEd.chem.wisc.edu/JCEWWW/Columns/McadInChem/
Literature Cited 1. Grubbs, W. T. J. Chem. Educ. 1999, 76, 286; http:// jchemed.chem.wisc.edu/JCEWWW/Columns/McadInChem/Mcad007/.
JChemEd.chem.wisc.edu • Vol. 76 No. 9 September 1999 • Journal of Chemical Education
1309
