Entropy of Mixing of Distinguishable Particles

• Autores: Evguenii I. Kozliak
• Localización: Journal of chemical education, ISSN 0021-9584, Vol. 91, Nº 6, 2014, págs. 834-838
• Idioma: inglés
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• Resumen

  • 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, ΔH(mixing) in a reversible process—due to a change in the energy of intermolecular interactions, Δε—that is responsible for the nonzero entropy. Temperature in the Clausius equation, dSsystem = đqrev/T, normalizes the heat—different in various processes—to yield the same entropy of mixing per mole, as long as this temperature, T = Θ′(mixing), that of the reversible process, is linked to the Boltzmann characteristic temperature, Θ = Δε/k = 2Θ′ ln 2. For mixing exactly the same substances, dSsystem = đqrev = 0, and thus, Θ′(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.