Chemical Education Today
Letters Undergraduates’ Understanding of Entropy Sözbilir and Bennett carried out an extensive investigation on undergraduates’ understanding of entropy (1). Though I agree in general with their statements that order–disorder arguments form a misleading entropy concept, I would like to make some comments with regard to a certain part of their online supplement. In Box 3 Sözbilir and Bennett wrote about two competing factors to be considered.1 The authors state in the explanation, “On one hand, there is an apparent increase of organization when the crystallization occurs but on the other hand, the temperature of the system increases during the freezing because of the energy released due to the formation of new bonds in the ice crystal since the system is thermally insulated.” I think this is unclear. What is meant by “increase of organization”? Isn’t this a hidden disorder argument in contrast to the whole contribution? Of course the number of microstates increases, but not for the reason Sözbilir and Bennett pointed out: temperature effect competing with “organization effect”. The reason for the entropy increase is different. The additivity of entropy values is restricted under certain circumstances. Kittel and Krömer wrote in their textbook (2): Die Entropie von zwei unabhängigen Systemen ist gleich der Summe der einzelnen Entropien. (Transl.: The entropy of two independent systems is the sum of the entropy values of the individual systems.) Reactants and products of a chemical reaction are not two independent individual systems. To be independent is a conditio sine qua non for the additivity of entropy. Particles, atoms of the reactants, are part of the products after the reaction. Any macrostate of the reacting system can be realized by more microstates compared with separated crystal- and solution-systems. More permutations must be calculated. It is not correct to argue that the temperature effect overcompensates the crystallization effect.
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The crystallization ends in an equilibrium state of a crystal in a saturated solution. The entropy maximum is reached, which means that the systems capacity for thermal energy—or the extent of the storage system as I wrote in ref 3—has a relative maximum. This can easily be proved by heating this equilibrium state and heating separated solution- and crystal-systems in comparison. To reach the same ∆T value for the temperature change, the equilibrium state needs more energy. This is due to Le Châteliers principle: heating the equilibrium starts the endothermic—that is, temperature decreasing—reaction. Note 1. Box 3 shows a hot saturated solution of sodium thiosulfate that is allowed to cool slowly. The solution is sealed in a thermally insulated flask and a tiny seeding crystal is dropped through a hole in the lid. Crystallization occurs spontaneously, with an apparent increase of organization. The question is asked, What do you think will happen to the entropy of the system when the crystals form?
Literature Cited 1. Sözbilir, M.; Bennett, J. M. J. Chem. Educ. 2007, 84, 1204. 2. Kittel, Ch.; Krömer, H. Thermodynamik, 5th ed.; Oldenbourg; München, 2001. 3. Jungermann, A. H. J. Chem. Educ. 2006, 83, 1686.
Supporting JCE Online Material
http://www.jce.divched.org/Journal/Issues/2008/Sep/abs1192_1.html Abstract and keywords Full text (HTML and PDF) with links to cited JCE articles Arnd H. Jungermann Department of Chemistry Markgräfler Gymnasium Müllheim, D-79379 Germany
[email protected] Journal of Chemical Education • Vol. 85 No. 9 September 2008 • www.JCE.DivCHED.org • © Division of Chemical Education
