In the Classroom edited by
Applications and Analogies
Ron DeLorenzo Middle Georgia College Cochran, GA 31014
Energy as Money, Chemical Bonding as Business, and Negative ∆H and ∆G as Investment Evguenii I. Kozliak Department of Chemistry, University of North Dakota, Grand Forks, ND 58202; *
[email protected] Many freshmen, particularly non-majors, struggle with conceptual thinking in general or introductory chemistry (1– 3). One of the notoriously difficult topics is thermodynamics (4–6); thus, a number of approaches and analogies have been suggested to illustrate the concepts of equilibrium, entropy, and free energy (from the standpoint of statistics) and to facilitate enthalpy calculations (5–8). In my experience, the root of the difficulty lies in the sign convention and the implication of the sign of ∆H and ∆G on spontaneity. Wynn suggested viewing reaction heat as cash and associating the “system” with an ATM machine; “surroundings” would be the customer’s pocket (9). This excellent analogy provides an illustration of heat versus potential energy and the sign convention. I suggest modifying Wynn’s analogy to take it one step further. In my experience, simple analogies that are applicable to a single topic always teach students how to obtain correct numerical answers but do not necessarily develop the understanding of fundamental concepts. To build a network of logic in the student’s mind, an analogy or metaphor should appeal to the student emotionally and be applicable to a number of related topics. In my analogy, “each of us” is a system. We interact with the surroundings by either gaining or losing money. If a person’s wealth grows, for instance, from $100 to $110, the final value is greater than the initial value by $10. Therefore, as defined by Wynn (9), ∆ (money) is positive. I add that this makes sense emotionally, because gaining money is a positive experience. Conversely, if the final amount of money is lower than the original value, a person loses money. In this case ∆ is negative, and losing money is emotionally negative for the individual. Applying the abstract concept of system to themselves makes the difference for many non-majors. Most seem to understand what “negative gain” is in terms of money. A similar analogy helps explain the sign of ∆H for forming and breaking chemical bonds between single atoms: negative sign for any stable bond formation and positive sign for bond breakup. People will combine (enter a business partnership) only if they expect the concurrent release of a profit. Once the profit is released, it will be transferred to a different account or invested elsewhere. Therefore, ∆ for the formation of a business from people (atoms) is negative despite the fact that it is profitable (this is what students usually do not understand about negative ∆H). Conversely, breaking a stable business relationship requires outside cash, a buyout, and, thus, positive ∆ for the process to occur (i.e., money has to flow into the business). What is the price of this
buyout? Obviously, as much money as the people had gained by creating their relationship (since the profit has gone elsewhere). This example can also be used to discuss energy conservation. The analogy also illustrates positive values of ionization energy by the necessity of providing energy (paying money) to end the relationship of an electron (an employee) with the attractive nucleus (place of employment, as in an incentive package). Then it may be applied to lattice enthalpy (a difficult concept for the students). Forming molecules of ionic compounds (small businesses) requires energy (outside cash) for several steps, such as vaporization, atomization, and ionization (breaking stable interatomic relationships in free elements). However, their mergers to create a larger company with a regular interpersonal business network (ionic crystal) result in a significant release of profit, that is, energy. The analogy may also be expanded to free energy, ∆G. The abstract idea that negative ∆G is beneficial for any process can be illustrated in business terms, such as gross profit or total investment. Since negative ∆H is considered as net profit or investment in the surroundings, positive ∆S (considering that ∆G = ∆H − T∆S ) may be viewed as internal investment to make positive changes within the business. Significant positive changes within the system can balance the loss of money (for endothermic reactions) and vice versa, depending on the climate of the market, that is, temperature. The more free energy released, that is, the more negative its change, the better the business. Market evaluation of no-profit (endothermic), high-tech companies in 2000 provides a good example: when the market was hot, their stock prices were rising (reflecting negative ∆G and, thus, meaning that business was great). Once the temperature decreased, the stocks plunged (positive ∆G, poor business). The metaphor for ∆S further illustrates the statistical significance of entropy as a measure of randomness (or more precisely, energy flow toward dissipation, ref 10). Reinvesting profit back into the business is much more disorderly than simply collecting the cash dividend. The reinvested money gets scattered in many microstates and may even be lost due to uncertain statistical factors affecting business. However, despite the risk and uncertainty, reinvestment is the firstchoice option in business. Thus, increasing entropy is favorable. A number of my students noted that the suggested model provides a connection between chemistry and classes in business and accounting traditionally taken by many non-science majors.
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In the Classroom
Acknowledgments The author thanks Bush Foundation for partial funding within the Bush Scholarship program; T. A. Ballintine (UND Chemistry) for excellent advice, and A. J. Borgerding, and K. A. Thomasson (UND Chemistry) for reading and discussion of the manuscript. Literature Cited 1. Webster, T. J.; Hooper, L. J. Chem. Educ. 1998, 75, 328–331.
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Journal of Chemical Education • Vol. 79 No. 12 December 2002 • JChemEd.chem.wisc.edu
