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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

J. Chem. Educ., 2005, 82 (11), p 1703

DOI: 10.1021/ed082p1703

Publication Date (Web): November 1, 2005

Section:

History, Education, and Documentation

Abstract

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).

Keywords (Audience):

Upper-Division Undergraduate

Keywords (Domain):

Physical Chemistry

Keywords (Feature):

Advanced Chemistry Classroom and Laboratory

Keywords (Pedagogy):

Textbooks / Reference Books

Keywords (Subject):

IR Spectroscopy

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This article has been cited by 3 ACS Journal articles (3 most recent appear below).

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Received: August 03, 2009

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Article

Determination of the Rotational Barrier in Ethane by Vibrational Spectroscopy and Statistical Thermodynamics