Four fundamental problems encountered in the education of chemists at the undergraduate and graduate levels are presented, with insightful solutions using mathematics as an important tool. The binomial theorem and the use of tree diagrams are applied to the prediction of the mass spectral molecular ion isotope pattern for molecules containing any combination of elements; the concept of integration is applied to the Lorentzian line shape of NMR signals; analytical geometry of parabolas is applied to the derivation of the simple Marcus equation; and simple concepts of probability are applied to the prediction of the multiplicity of products in single-encounter bimolecular and multimolecular photoreactions with known multiplicities of reactants.
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