The Potential Energies of Cohesion of a Crystalline Organic Enantiomer and the Racemate; on the Energy for the Liquid Racemate [1] |
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Authors: | Francisco Ros Pilar Jiménez María Victoria Roux |
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Affiliation: | (1) Instituto de Qu?mica M?dica, CSIC, Juan de la Cierva 3, E-28006 Madrid, Spain |
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Abstract: | The cohesion potential energy of the crystal of one enantiomer of ethyl 3-cyano-3-(3,4-dimethyloxyphenyl)-2,2,4-trimethylpentanoate, −47.7 ± 0.1 kJ mol−1 (0–90°C), was found out from the heat of sublimation (123.2 ± 5.1 kJ mol−1, 78.6°C) and the kinetic energies for the gas phase and the crystal. It was found that the entropy function of Debye’s theory of solids mathematically agreed with the vibrational entropy of the gas (variationally obtained), allowing to disclose the vibrational energy using the Debye energy function (E vib 835.0 kJ mol−1 (78.6°C), E 0 included). E kin for the crystal (771.1 kJ mol−1 (78.6°C)) was obtained by Debye’s theory with the experimental heat capacity. The cohesion energy represented a moderate part of the sublimation energy. The cohesion energy of the racemic crystal, −44.2 kJ mol−1, was obtained by the heat of formation of the crystal in the solid state (3.0 kJ mol−1, 83.3°C) and E kin for the crystal (by Debye’s theory). The decrease in cohesion on formation of the crystal accounted for the energy of formation. The change in potential energy on liquefaction of the racemate from the gas state was disclosed obtaining added-up E vib + rot for the liquid in the way as to E vib for the gas, the Debye entropy function being increasedly suited for the liquid (E vib + rot 763.4 kJ mol−1 (115.4°C)). Positive ΔE pot, 13.0 kJ mol−1, arised from the increase in electronic energy (Δ l νmean − 154.3 cm−1, by the dielectric nature of the liquid), added to the cohesion energy. |
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