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Consistent Application of the Boltzmann Distribution to Residual Entropy in Crystals

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Evguenii I. Kozliak

Department of Chemistry, University of North Dakota, Grand Forks, ND 58202-9024

J. Chem. Educ., 2007, 84 (3), p 493

DOI: 10.1021/ed084p493

Publication Date (Web): March 1, 2007

Section:

History, Education, and Documentation

Abstract

Four different approaches to residual entropy (the entropy remaining in crystals comprised of nonsymmetric molecules like CO, N₂O, FClO₃, and H₂O as temperatures approach 0 K) are analyzed and a new method of its calculation is developed based on application of the Boltzmann distribution. The inherent connection of all four methods (based on combinatorics, thermodynamics, mixing, or statistical mechanicsâ€“probabilities) to one another is shown. They yield the same numerical value of residual entropy when the â€œfrozen-inâ€ energy difference between the possible intermolecular interactions for different molecular arrangements (configurations) is negligible as compared to k_BT_fusion.

Keywords (Audience):

Upper-Division Undergraduate

Keywords (Domain):

Physical Chemistry

Keywords (Feature):

Research: Science and Education

Keywords (Pedagogy):

Textbooks / Reference Books

Keywords (Subject):

Statistical Mechanics

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

The Misinterpretation of Entropy as “Disorder”
Frank L. Lambert
Journal of Chemical Education2012 Article ASAP
- The Misinterpretation of Entropy as “Disorder”
  Frank L. Lambert
  Journal of Chemical Education2012 Article ASAP
  This letter supports the goal of the article “Entropy: Order or Information” (DOI: 10.1021/ed100922x), showing that the article’s presentation only of Shannon’s measure of information can be strengthened by linking it to energy-based thermodynamics in ...
  Abstract | Full Text HTML | Hi-Res PDF | PDF w/ Links
Overcoming Misconceptions about Configurational Entropy in Condensed Phases
Evguenii I. Kozliak
Journal of Chemical Education2009 86 (9), 1063
- Overcoming Misconceptions about Configurational Entropy in Condensed Phases
  Evguenii I. Kozliak
  Journal of Chemical Education2009 86 (9), 1063
  Configurational and thermal entropy yield identical numerical values for ΔS only when the system's "dimensionless" energy gaps (Δε /kT ) between the accessible quantized energy levels are minimized by temperature to nearly infinitesimal values so that the ...
  Abstract | Hi-Res PDF | PDF w/ Links
Configurational Entropy Revisited
Frank L. Lambert
Journal of Chemical Education2007 84 (9), 1548
- Configurational Entropy Revisited
  Frank L. Lambert
  Journal of Chemical Education2007 84 (9), 1548
  Entropy change is categorized in some prominent general chemistry textbooks as being either positional (configurational) or thermal. In those texts, the accompanying emphasis on the dispersal of matter—independent of energy considerations and thus in ...
  Abstract | Hi-Res PDF | PDF w/ Links