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Previously in this Journal (1), I made an attempt to uncover the hidden musical talents of a variety of chemical processes, including first-order reactions using model reactions, as well as some real chemical reactions based on the equations that describe the rate of disappearance of reactants and the rate of formation of products. Since then, I have explored the musical artifacts of second-order reactions based on model functions as well as three real chemical reactions: namely, isobutyl bromide and sodium ethoxide reaction; dimerization of butadiene; and hydrolysis of ethyl nitrobenzoate. Study of these model reactions reveals that the concentration at time zero (c0) and the second-order rate constant (k2) influence both amplitude and timbre, unlike those of the first-order reactions where c0 has been found to manipulate only the amplitude. Similar to first-order reactions, these reactions also seem to produce music characteristic of their nature, type of reaction, and kind of species involved in the reaction. The music created by these reactions is certainly quite distinct compared to that of first-order reactions. The online supplement to this letter outlines a brief methodology for extracting amplitudes and frequencies from second-order reactions using discrete Fourier transformation (DFT) presented in the form of spectral analysis figures for model functions and real chemical reactions. The frequencies thus generated fall in the infrasound region not audible to the human ear (<20 Hz) and hence are magnified using techniques described elsewhere (1). The magnified frequencies are further transformed into musical notes using principles of music theory (data provided in tables) for model functions and real second-order reactions, respectively. Grand staves with notation playable on an instrument such as the piano are shown for model functions and real second-order reactions. The online supplement also contains figures that describe the rate of change of concentration as a function of time for three chosen models functions, as well as for three real second-order reactions. This material contains tables listing the frequencies, the amplitudes, and the phases derived from the DFT analysis for model functions, and real chemical reactions. Six sound files in mp3 format are included for three model functions and three real second-order reactions; four sound files in midi format are also available Literature Cited- Kumbar, M. J. Chem. Educ. 2007, 84, 1933.
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