Abstract:

In this work, an interactive application (App) developed to explain differential equations is presented. The App has been developed by our group based on Mathematica software and it is aimed at undergraduate students of first-year of Pharmacy, Biotechnology or Biomedicine. To help clarifying the mathematical concept, differential equations have been contextualized by solving a chemical problem. In particular, the proposed chemical problem is the kinetics study of a set of elemental reactions that can be considered individually or combined. This way, the understanding of differential equations is expected to be clearer for the students. From the point of view of mathematics, the kinetics of a chemical reaction is defined by differential equations that correlate the concentration and the reaction rates. Thanks to the app, the students can see the results of the differential equations associated to the selected reactions by displaying the evolution of the different involved concentrations with time.

The App shows a set of predefine elemental reactions that can be selected individually or by sets. In the case of set of reactions, the resulting system can be coupled (the reactions share chemical species) or not coupled systems (the reactions do not have any chemical species in common), leading to different chemical regimens that, in turn, results in different evolution time of the involved chemical species.

The App presents a graphic interactive interface where the students can control the different parameters involved in the reactions. Once the single or the set of reactions is chosen, the App shows the corresponding differential equations. This way the students can make a direct correlation between the mathematical notation and the problem they are solving (independent variable: time, dependent variable: concentrations, derivative: reaction rate and initial conditions: reactant concentration). The App solves the selected problem and shows the solution by the displaying the resulting equation and the following graphics: i) the plotting of the concentration of reagents and products as a function of time and ii) a parametric representation of the chemical species evolution.

As previously mentioned, the student can simulate only one or a set of simultaneous equations that could be coupled or not depending on the existence of common chemical species. This widens the resulting chemical regimens that can be achieved, so many chemical concepts can be introduced and studied: kinetics-equilibrium, oscillatory regimens, limiting and excess reagent, chemical efficiency…

In summary, thanks to the correlation between differential equations and chemical kinetics, the students can learn the previous mentioned concepts by a direct application of such a complicate mathematical idea. Besides, the App allows the cross study of two different subjects.

References:
[1] Atkins, P. & Paula, J. de. Physical Chemistry. Freeman, W. H. & Company (2014).
[2] Pilling, S., Seakins, P. W. & Pilling, M. J. Reaction Kinetics. Oxford Science Publications, (1996).
[3] Field, R. J. & Schneider, F. W. Oscillating chemical reactions and nonlinear dynamics. J. Chem. Educ., 66 (3), 195 (1983).
[4] A Universal Integrated Rate Equation for Chemical Kinetics J. Phys. Chem. A, 2018, 122 (16), pp 4009–4014

Keywords:

Virtual learning, differential equations, chemical kinetics.