Chemical Education Today
Letters Regarding Entropy Analysis
The author replies:
Hearty congratulations to Thomas Bindel (1) for his pioneering efforts at introducing entropy in terms of probability and microstates to high school students. It is especially nice to see such a clear discussion of the entropy changes in the surroundings. I am very impressed that Bindel can bring first-year high school chemistry students to such a sophisticated understanding in just three weeks time. What a whirlwind tour! (Our tour at St. Olaf College takes about 20 days to accomplish the same with first-year college students, albeit at a more quantitative level—see ref 2.) One minor criticism I have regards ∆Suniv not involving entropy effects of concentration and pressure. It seems strange to involve only ∆S° and not (∆S° – R ln Q) in a definition of ∆Suniv in eqs 19, 31, and 32. This results in odd derivations leading to “∆Suniv = R ln K ” and “–T∆Suniv = ∆rG°”. It would be more proper (as is given in Table 3 of ref 1) to label ∆Suniv in these equations as ∆S°univ, indicating “standard states”, although that certainly diminishes its significance. A better solution would be to use ∆rS instead of ∆rS° in eq 19. This then leads to the more common expressions
I would like to thank Robert Hanson for his kind remarks concerning my recent article (1). The print version of the article deals largely with teaching entropy analysis to the first-year high school level with some material intended for more advanced students. A large portion of the material presented in the supplement is for advanced students (classes) and teacher enhancement. In the first-year course, I do not present concentration effects or pressure effects. Pressure and concentration effects are discussed in the supplement on pages 17–19 (S = S° – R ln P and ∆rS = ∆rS° – R ln Q), as they are much more advanced topics. Additionally, on page 19 of the supplement, Q < K is discussed as a condition for the spontaneous conversion of reactants to products and likewise, Q > K is a condition for the spontaneous conversion of products into reactants. There is a problem with the symbol “∆Suniv” as it does not indicate whether the reactive system is in standard state or not. If the system is in standard state, then the numerical value for ∆Suniv can be used to directly calculate K, otherwise not. The use of ∆S°univ to denote that the reactive system is under standard state conditions is not ideal, as there are no standard states for the universe. Craig (2) has stated that there is a degree of “awkwardness” associated with the use of the standard state designation in this way. Unfortunately, this led to the use of ∆Suniv = –R ln K and –T∆Suniv = ∆rG°. Perhaps a new symbol could be devised, such as, ∆Suniv(sys°).
∆Suniv = R ln K兾Q and –T∆Suniv = ∆rG (So if Q < K, then ∆Suniv > 0, ∆rG < 0, and the forward reaction is favored; if Q > K, then ∆Suniv < 0, ∆rG > 0, and the reverse reaction is favored.) Thus, the sign of ∆Suniv is generally not taken as a measure of whether or not a reaction ends up favoring products or reactants at equilibrium (K > 1 or K < 1, respectively) as Bindel states but, rather, whether or not a particular mixture of reactants and products will naturally proceed, based on simple principles of chance, to form more products (Q < K ) or to form more reactants (Q > K ). Bindel is correct in stating that “for spontaneous changes, ∆Suniv > 0 and since T > 0, ∆G < 0”.
Literature Cited 1. Bindel, T. H. J. Chem Educ. 2004, 81, 1585. 2. Craig, N.C. Entropy Analysis; VCH: New York, 1992. Thomas H. Bindel Pomona High School Arvada, CO 80005
[email protected] Literature Cited 1. Bindel, T. H. J. Chem. Educ. 2004, 81, 1585. 2. Index of /depts/chemistry/imt/days. http://www.stolaf.edu/depts/ chemistry/imt/days (accessed Apr 2005). Robert M. Hanson Department of Chemistry St. Olaf College Northfield, MN 55057
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Vol. 82 No. 6 June 2005
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Journal of Chemical Education
839
