No abstract

No abstract

Linear least squares fitting of experimental data is a corner stone of data analysis in general chemistry and physical chemistry laboratory programs. Even when nonlinear data are available, students are routinely taught to linearize it and apply linear least squares fitting to extract chemically significant information. This approach is becoming even more strongly entrenched with the availability of spreadsheet programs that are able to linearize data and generate a linear least squares fit with only a few key strokes.There are several reasons why the linearization approach may be inappropriate. First, the power of spreadsheets like Excel and mathematical engines like Mathcad make it possible to extract information directly from minimally processed data through the use of nonlinear curve fitting. These tools permit modeling of the data without introducing the biases implicit in linearizing nonlinear data. Second, the power of the new computer tools available to chemists and chemistry students alleviates the need to depend on techniques that were essential before the advent of the routine use of PCs in the laboratory. Third, students are capable of learning and using nonlinear curve fitting techniques. While younger students may need to use templates, physical chemistry students are ready to program many of these techniques for themselves, especially when using an equation engine, and should be taught to do so.Reduction of kinetic data through nonlinear curve fitting will be the focus of this paper. The methods described can be applied to other types of nonlinear data commonly obtained from the routine use of laboratory instruments. Although the theoretical basis for the approach taken in this paper is not new, the discussion of it is scattered throughout the literature and is not in a form that would be useful to the majority of students in college courses. The summary in this paper should make the theory accessible to junior and senior students and their professors. This is important because as teachers and students implement the statistical features in commercial software, they need to have some experience with the underlying theory of the applications found in these products. DiscussionChemical kinetics is taught to undergraduate chemistry students in a way that often does not correspond to modern practice. In particular, the determination of the order of a chemical reaction is frequently done using the standard linear forms, namely, ln(B 0 /B) or 1/B -1/B 0 is plotted as a function of time for first-and second-order reactions, respectively. Students are advised to make plots corresponding to the expected linearized forms of the kinetic models for the reaction, and then choose the one that appears linear or the one with the best correlation coefficient. The rate constant is then extracted from the slope of the best straight line as determined from visual or linear least squares fitting procedures.A good example of the inadequacy of this technique can be found in the text by Noggle (p 527) (1), where 1st-order,...

Structures and relative energies were obtained for the hydrogen bonded dimers of formamide and formamidic acid using the 3-21G basis set. A double proton transfer transition state is claimed to link these two dimers. While the structure of the transition state was intermediate between those of the two dimers, the energy was only 7.6 kJ/mol greater than the less stable formamidic acid dimer. The activation energy from the formamide dimer side of the reaction was found to be 125 kJ/mol of dimer. A similar transition state was found for the amidine dimer system. The activation energy for this model reaction was found to be 66.9 kJ/mol of dimer.

Ab initio molecular orbital calculations at SCF level with the 3-21G, 6-31G, and 6-31G** basis sets and CI level with the 6-31G basis set have been carried out for an isoelectronic series HX-CH=Y and X=CH-YH, where X, Y can be CH2, NH, and 0. Optimized structures (3-21G and 6-31G**) for both tautomers and the 1,3 hydrogen shift transition states are reported. The relative stabilities of the isomers and the barriers of the 1,3 shift are discussed in terms of proton affinities and bond orders. It is shown that both the relative stabilities of the tautomers and the relative barrier heights can be explained qualitatively using simple proton affinity arguments and that the barrier heights are quantitatively related to bond orders.