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2005
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Research: Science and Education
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Advanced Chemistry Classroom and Laboratory
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Determination of the Rotational Barrier in Ethane by Vibrational Spectroscopy and Statistical Thermodynamics
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Gianfranco Ercolani
Dipartimento di Scienze e Tecnologie Chimiche, Università di Roma Tor Vergata, 00133 Roma, Italy
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November 2005
Vol. 82 No. 11
p. 1703
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| Abstract |
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In a previous article in this Journal (J.
Chem. Educ. 2000, 77, 1495) we introduced
a numerical method, namely, the finite-difference boundary-value method, for
the solution of the one-dimensional Schrödinger equation and illustrated
its application to the evaluation of energy levels and wave functions for hindered
internal rotations. Here the method is used to determine, in combination with
vibrational spectroscopy and statistical thermodynamics, the torsional potential
in ethane. In particular two distinct approaches have been exploited: the first
approach is based on the experimental frequency of torsional mode, and the second,
less direct but historically more relevant, approach is based on the experimental
heat capacity of ethane at various temperatures and on the frequencies of the
other normal modes of vibration. The two approaches provide energy barriers in
good agreement with each other, 12.35 and 11.74 kJ mol–1, respectively,
and with the literature values. It is shown that the finite-difference boundary-value
method, providing a great number of accurate energy levels, is ideally suited
for the calculation of both energy transitions and the partition function for
internal rotation. The latter is used to calculate the contribution of torsional
mode to thermodynamic functions, such as heat capacity, entropy, and enthalpy.
The results are in excellent agreement with those obtained from the tables of
Pitzer (Lewis, G. N.; Randall, M.; Pitzer, K. S.; Brewer, L. Thermodynamics,
2nd ed.; McGraw-Hill: New York, 1961; Chapter 27).
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| More Information |
 Citation |
Ercolani, Gianfranco. J. Chem. Educ. 2005 82 1703.
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Keywords |
Alkanes / Cycloalkanes; Conformational Analysis; Graduate Education / Research; Heat Capacity; IR Spectroscopy; Molecular Properties / Structure; Physical Chemistry; Quantum Chemistry; Statistical Mechanics; Textbooks / Reference Books; Thermodynamics; Upper-Division Undergraduate
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History |
Created:
Last Updated: |
9/22/2005
9/29/2005
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