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ERIC Number: EJ1032430
Record Type: Journal
Publication Date: 2014-Jun
Pages: 5
Abstractor: As Provided
Reference Count: 24
ISSN: ISSN-0021-9584
Entropy of Mixing of Distinguishable Particles
Kozliak, Evguenii I.
Journal of Chemical Education, v91 n6 p834-838 Jun 2014
The molar entropy of mixing yields values that depend only on the number of mixing components rather than on their chemical nature. To explain this phenomenon using the logic of chemistry, this article considers mixing of distinguishable particles, thus complementing the well-known approach developed for nondistinguishable particles, for example, ideal gases and solutions. The result is a simple quantitative treatment based on the Boltzmann distribution using the Gibbs paradox as a case study to define a macroscopic thermodynamic criterion of distinguishability. It is the presence of nonzero, albeit often small, ?H(mixing) in a reversible process--due to a change in the energy of intermolecular interactions, ?e--that is responsible for the nonzero entropy. Temperature in the Clausius equation, dS[subscript system] = dq[subscript rev]/T, normalizes the heat--different in various processes--to yield the same entropy of mixing per mole, as long as this temperature, T = T'(mixing), that of the reversible process, is linked to the Boltzmann characteristic temperature, T = ?e/k = 2T' ln 2. For mixing exactly the same substances, dS[subscript system] = dq[subscript rev] = 0, and thus, T'(mixing) is undefined as a 0/0 uncertainty; the process can occur reversibly for any amount at any temperature. Two cases of negative entropy of mixing/expansion validate the suggested approach.
Division of Chemical Education, Inc and ACS Publications Division of the American Chemical Society. 1155 Sixteenth Street NW, Washington, DC 20036. Tel: 800-227-5558; Tel: 202-872-4600; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education; Postsecondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A