Configurational Entropy Revisited

1548 Journal of Chemical Education • Vol. 84 No. 9 September 2007 • www.JCE.DivCHED.org Entropy change is categorized in some prominent general chemistry textbooks as being either positional (configurational) or thermal. Positional entropy focuses on the number of positions in space that can be occupied by the molecules of a system. Then, to the extent that more positions exist after a process than before, the greater is the entropy increase in the system. Configurational (positional) entropy has a distinguished history. Developed from classical statistical mechanics, it was the basis of Pauling’s 1935 determination of the residual entropy in ice (1), Bent’s brilliantly simple development of the entropy of mixing in 1965 (2), and more recently, such publications as Craig’s use of the cell model in presenting entropy change in mixing (3). There is no question about the correct values obtained from such calculations via configurational entropy change, the facile steps in the procedure, or its being the only practical method for calculating entropy change in some complex areas of thermodynamics. However, positional entropy as presented in several widelyused and influential general chemistry texts has two serious conceptual flaws in introducing beginners to entropy change.1 When positional entropy is emphasized, it strongly implies that matter can spread out without any involvement of the energy associated with its mobile molecules. Equally misleading, the undue focus on the difference between “energy-unrelated” positional entropy change and thermal entropy change discounts the shared aspects of their fundamental relationship. One text states (and several others agree substantially), “[there are] two basic types of spontaneous physical process: 1. Matter tends to become dispersed. 2. Energy tends to become dispersed.”1 With “1” as positional entropy and “2” as thermal entropy, there are a number of questions for students both within the thermodynamics chapters and at the chapter ends. Unfortunately, this reinforces the idea of discriminating between “types of entropy” rather than focusing on the common foundation of entropy increase, energy spreading out. A fundamental problem engendered by general chemistry texts employing positional entropy (and in others not emphasizing that expression) is that gas expansion or fluid mixing is due to “the driving force2 of probability”, as one textbook states. Certainly probability, in the sense of a spatially broader and thus of a probably greater distribution for the motional energy of each constituent’s molecules, is an essential consideration in mixing or expansion, but this is not the interpretation of probability given in texts employing positional entropy.3