Chemical Education Today
Letters State Functions vs State Governments I found the discussion by Leonard, Rossini, and Wójcik of the validity of thermodynamic anthropomorphisms (1, 2) to be quite fascinating. Leonard presented an excerpt from the 1971 Priestley Medal Address given by F. D. Rossini, in which he likened entropy to personal freedom (cf. molecular motional freedom) and enthalpy to personal security (cf. bond formation and a more stable or “secure” system). Wójcik, in his response letter, warned against anthropomorphizing science: Models that work well in explaining experimental observations are not meant to shed light on the human condition. In fact, it can be dangerous to assume that they do. The rise of Social Darwinism in the late 19th century and eugenics in the early 20th century are just two examples of scientific theories that were mistakenly extended into misguided social policies. Although Wójcik’s point is well-taken, I do not agree that such “loose thinking” should be “purged” from science altogether. A well-drawn analogy between two surprisingly dissimilar concepts can not only be helpful in the classroom, it can be pleasing and instructive on its own merits, as long as one is cognizant of its limitations. On the surface, Rossini’s analogy relating enthalpy, entropy, and the equilibrium constant to freedom and security in the modern nation-state seems like a good example of an unusual and instructive comparison. I was initially intrigued. Using the thermodynamic conclusion that (a) a reaction’s spontaneity (or Keq) increases when either ∆H gets more negative (stronger security) or ∆S gets more positive (more freedom), Rossini analogized that (b) “One cannot have a maximum of freedom and a maximum of security at the same time.” Sadly, point (a), although true, does not support point (b), not even in the limited realm of chemical thermodynamics, much less in the broader realm of political governance. Unfortunately, two errors lurk within Rossini’s exposition. The first is a simple typo: The final part of the last equation should read –(∆H°/RT) + ∆S°/R = ln(Keq) not –RTln(Keq). More importantly, Rossini’s point (b) from above is that in any thermodynamic system, a negative ∆H or a positive ∆S can be maximized, but never both. This conclusion is only true, however, if Keq is constant; of course Keq (and ∆G°) are only constant if reactants and products and all reaction conditions are identical. Rossini does not specify, in his political governance thermodynamic system, the “reactants” and “products”. Let us assume, for argument’s sake, that the “reactants” are citizens living under an initial system (i) of political governance, and the “products” are citizens living under a final system (f) of political governance. Then Rossini’s argument is that for different final systems of governance (f1, f2, f3, etc.), ∆H° and ∆S° for the change in political systems can vary, but always in opposite directions: If, relative to political system i, f features increased personal
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freedom (positive ∆S°), then f must also feature decreased security (positive ∆H°). Conversely, if f features increased security (negative ∆H°), then f must also feature decreased personal freedom (negative ∆S°). In other words, Rossini seems to believe that ∆H° and ∆S° must have the same sign. This conclusion may make a certain amount of political sense, but it is flawed from a purely thermodynamic perspective. Although it is true that ∆H ° and ∆S° are the same sign for many reactions (especially homogeneous reactions with no phase changes), this is by no means always the case. To present just two common counter-examples, for the combustion of solid glucose, ∆H ° = ᎑2803 kJ mol᎑1 and ∆S° = +260. J mol ᎑1 K᎑1; for the disproportionation of aqueous hydrogen peroxide (to dioxygen and water), ∆H ° = ᎑95 kJ mol᎑1 and ∆S° = +29 J mol᎑1 K᎑1. So to take Rossini’s analogy to its final conclusion, based on his own thermodynamic analysis, there could well be a political system out there that maximizes both personal freedom and security. From a chemical perspective, there does not have to be a tradeoff between security (negative ∆H ) and freedom (positive ∆S ). Although Rossini’s analogy is amusing and entertaining and makes some political sense, unfortunately, its thermodynamic conclusions are flawed. Literature Cited 1. Leonard, H. J. Chem. Educ. 2006, 83, 39. 2. Wójcik, John F. J. Chem. Educ. 2006, 83, 39. Todd P. Silverstein Department of Chemistry Willamette University Salem, OR 97301
[email protected] The author replies: I was pleased to see the response by T. P. Silverstein to my letter (1). I support his conclusions completely, especially the “well drawn analogy between two surprisingly dissimilar concepts cannot only be helpful in the classroom, it can be pleasing and instructive on its own merits, as long as one is cognizant of its limitations”. We can assume that Rossini may have used this analogy in his teaching, as I did for over 30 years, as well as in his Priestley Medal Address. Literature Cited 1. Leonard, H. J. Chem. Educ. 2006, 83, 39. Harold Leonard 3441A E Lake Rd Skaneateles, NY 13152-9000
[email protected] Vol. 83 No. 6 June 2006
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Journal of Chemical Education
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