P322: Geometry in chemistry: Learning sequences for incorporation into undergraduate chemistry courses
Coverage of molecular and solid state structures in two- and three- dimensions is ubiquitous in traditional chemistry curricula. It starts with atomic packing and hybridization in general chemistry, continues as conformational analysis and stereochemistry in organic chemistry, and reappears in upper division courses under the guise of normal mode analysis, group theory, and transition metal complex structures. Arguably, basic geometry skills enrich students’ spatial abilities and facilitate understanding of these topics. Spatial abilities are often considered as a success factor not only in chemistry, but across STEM majors. This suggests that the development of a series of exercises aimed at practicing geometry in the context of chemistry is an important task. This presentation introduces two learning sequences at the intersection of chemistry and geometry. Each sequence consists of several conceptually related problems aimed at exploring the relationships between ideas of chemistry, geometry, and mathematics. The aim of the first sequence is evaluation of distances between hydrogens attached to adjacent carbons in eclipsed and staggered conformations of ethane molecules. The second sequence includes estimation of the volume of a fullerene molecule and the density of a fullerite solid. Problems within each sequence require calculations of the dimensions of various molecules and conic solids based on these molecules. Besides providing a connection between chemistry and geometry, these sequences highlight the reductionist’s approach to complex problems and illustrate order-of-magnitude estimates on the submicroscopic level.