Mathematical Modeling in Secondary Chemistry Education: Chromatography

Thomas Kraska^1,

¹Department of Physical Chemistry, University of Cologne, Cologne, Greinstraße 4-6, D-50939, Germany

Cite this paper

Thomas Kraska. Mathematical Modeling in Secondary Chemistry Education: Chromatography. World Journal of Chemical Education. 2020; 8(3):114-121. doi: 10.12691/WJCE-8-3-3

Abstract

The rapid advance in information technology requires further developments in all areas of education. In this context, one should think about going beyond the use of digital media for the mere presentation of scientific content. Interactive computer simulations allow quasi-experimental investigations of scientific phenomena but for students they usually remain black-box approaches. For a deeper understanding of phenomena, it is desirable to go one step further and set up computer codes based on a given microscopic model as part of the chemical education. Such approach allows teaching the scientific topic in more depth, fosters the awareness of the relevance of mathematics and computing in chemistry, and lastly supports the self-directed investigation of a scientific phenomenon. In addition, it gives students the opportunity to learn in general about modelling which has become an important contribution to chemistry and other natural and engineering sciences. Here we discuss basic chromatography with a simplistic stochastic simulation method suitable for upper secondary education. In addition, the analytical solution of the processes is given at the level of secondary mathematics. Chromatography itself is potentially treated in secondary education at various levels from paper chromatography to gas chromatography. This general knowledge makes it more accessible to students as a subject for deepening by modeling and simulation.

Keywords

chromatography, stochastic simulation, diffusion, molecular interaction, computer algorithm

Copyright

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References

[1]	Tedre, M. and Denning, P. J., “The Long Quest for Computational Thinking”, Proceedings of the 16th Koli Calling Conference in Computing Education Research, 120-127. 2016.
[2]	Wing, J., “Computational Thinking”, Comm. ACM, 49 (3). 33-35. 2006.
[3]	Aho, A. V., “Ubiquity symposium: Computation and Computa¬tional Thinking”, Ubiquity, January 2011.
[4]	Yasar, O., “The Essence of Computational Thinking”, Comput. Sci. Eng., 19 (4). 74-82. July/August 2017.
[5]	Grover, S., Pea, R., “Computational Thinking in K-12: A Review of the State of the Field”, Educ. Researcher, 42 (1). 38-43. January 2013.
[6]	Giddings, J.C., Eyring, H., “A Molecular Dynamic Theory of Chromatography”, J. Phys. Chem. 59(5). 416-421, May 1955.
[7]	Felinger, A., “Review Molecular dynamic theories in chromato¬graphy”, J. Chromatogr. A 1184. 20-41. 2008.
[8]	Wernekenschnieder, M., Zinn, P., “Monte-Carlo Simulation of Gas Chromatographic Separation for the Prediction of Retention Times and Peak Half Widths Chromatographia 28. (5/6). Sept. 1989.
[9]	Felinger, A., Cavazzini, A., Remelli, M., Dondi, F., “Stochastic-Dispersive Theory of Chromatography” Anal. Chem. 71. 4472-4479. 1999.
[10]	Dondi, F., Cavazzini, A., Pasti, L., “Chromatography as Lévy Stochastic process”, J. Chromatogr. A 1126. 257-267. 2006.
[11]	Zhao, J., Sun, Y., Gao, Y., “Theoretical simulation of chromatographic separation based on random diffusion in the restricted space”, Sci China Chem. 59(7). 824-829. July 2016.
[12]	Ehrenfest P., Ehrenfest, T., “Über zwei bekannte Einwände gegen das Boltzmannsche H-Theorem”, Phys. Z., 8. 311-314. 1907.
[13]	Balaji, S., Mahmoud, H., Ting, Z., “Phases in the diffusion of gases via the Ehrenfest urn model”, J. Appl. Prob. 47. 841-855. 2010.
[14]	Casas, G.A., Nobre, F.D., Curado, E.M.F., “Nonlinear Ehrenfest’s urn model”, Phys. Rev. E 91. 042139. 2015.
[15]	Gaucher, G. M., “An Introduction to Chromatography”, J. Chem. Educ. 46(11). 729-733. Nov. 1969.
[16]	Harsch G., (1984). Kinetics and Mechanism - A Games Approach, J. Chem. Edu. 61, 1039-1043.
[17]	Harsch, G. (1985). Vom Würfelspiel zum Naturgesetz. Simulation und Modelldenken in der physikalischen Chemie. Verlag Chemie VCH, Weinheim.
[18]	Smith, C.A., Warren Villaescusa, F., “Simulating Chromatographic Separations in the Classroom”, J. Chem. Educ. 80(9). 1023-1025. Sept. 2003.
[19]	Smith, C.A., “Checkerboard Chromatography”, J. Chem. Educ. 81(3) 384A-.384B March 2004.
[20]	Hunt, E.A., Deo, S.K., “Board-Game Gel Filtration and Affinity Chromatography”, J. Chem. Educ. 86(1). 19-20. Jan. 2009.
[21]	Brunauer, L.S., Davis, K.K., “Size Exclusion Chromatography: An Experiment for High School and Community College Chemistry and Biotechnology Laboratory Programs”, J. Chem. Educ. 85(5) 683-685. May 2008.
[22]	Samide, M.J., “Separation Anxiety: An In-Class Game Designed To Help Students Discover Chromatography”, J. Chem. Educ. 85 (11). 1512-1514. Nov. 2008.
[23]	Rafferty J.L., Siepmann, I., Schurec, M.R., “The effects of chain length, embedded polar groups, pressure, and pore shape on structure and retention in reversed-phase liquid chromatography: Molecular-level insights from Monte Carlo simulations” J. Chromatogr. A 1216. 2320-2331. 2009.
[24]	Brown, R., A brief account of microscopical observations made in the months of June, July and August 1827, on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies”, Phil. Mag. 4(21). 161-173. 1828.
[25]	Fick, A., “Über Diffusion“. Annalen der Physik, 94 (1). 59-86. 1855.
[26]	Einstein, A., “Über die von der molekulartheoretischen Theorie der Wärme geforderte Bewegung in ruhenden Flüssigkeiten suspendierten Teilchen”, Ann. Phys. 17. 549-560. 1905.
[27]	Galton, F., Natural Inheritance, Macmillan and Co. London 1894, 63-66. https://archive.org/details/naturalinherita01galtgoog/page/n8/mode/2up (retrieved on April 2nd 2020)
[28]	Taylor, G.I., “Dispersion of soluble matter in solvent flowing slowly through a tube”, Proc. R. Soc. London 219(1137). 186-203. Aug. 1953.
[29]	Alizadeh, A., Nieto de Castro. I C. A., Wakeham, W. A., “The Theory of the Taylor Dispersion Technique for Liquid Diffusivity Measurements”, Int. J. Thermophys., 1(3). 243-284. 1980.
[30]	Levelt-Sengers, J.M.H., Deiters, U.K., Klask, U., Swiderski, P., Schneider, G.M., “Application of the Taylor dispersion method in supercritical fluids“, Int. J. Thermophys. 14(4). 893-922. 1993.
[31]	Choguill, C.L. "Gas Chromatography", Trans. Kansas Acad. Sci. 61, 253-255. 1958.
[32]	Cowan, P. J., Sugihara, J. M. "A Gas Chromatography Demon¬stration Apparatus", J. Chem. Educ. 36(5). 246-247. 1959.
[33]	McLean, J., Pauson, P.L. "A Gas Chromatography Demonstration Apparatus", J. Chem. Educ. 40(10). 539-540. 1963.
[34]	Kappenberg, F. “Gaschromatographie in der Schule” (in German) http://www.kappenberg.com/pages/lowcost-chromatographie/ gaschromatographen.html (retrieved on April 2nd 2020).
[35]	Lorke J., Sommer, K. "Teaching chromatography in secondary school - an investigation concerning grade, context, content, experiments and media", Problems of Education in the 21st Century 19. 63-69. 2010.