J. A. Campbell Harvey Mudd College Claremont. CA 9171 1
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Paradigms and Paradoxes
Most students of 40 years ago learned that "A catalyst is a substance which increases the rate of a reaction without entering into it." I taught this myself for a few years, so thorouahlv had I been educated (?,or trained, or conditioned) to it. k n d remarkably, I still find the statement in an occasional text. Yet very simple logic clearly shows the statement to be nonsense. F i r how can any system affect a property of some other system without affecting it and being affected itself. Few teachers use this paradigm today, yet we retain others of even wider use and similar inexactitude. Let us consider a few. "Systems Tend to a Minimum In Potentlal Energy" (Really?) Since potential energies in closed and open systems can increase easily, this statement must apply (if to anything) only in an isolated system. Shortly after giving this statement, many texts ~ r o c e e dto "The sum of the kinetic and potential energy in an isolated system is constant." Then they later discuss orocesses such as "crvstalline ammonium chloride dissdves in water and cools showing that its kinetic energy has been convertcd to potential energy in the system," or "water ewporates in an isolated system cuoling as it converts kinetic into potential energy." Has the potential energy in these systems decreased? No, it has increased, and in an isolnted system. A little thought shows that, even in mechanical systems. systems do not necessarily tend to a potential energy minimum: pendulums oscillate between minima and maxima, so do vihratina molecules. Roth spend a minimum amount of time at the potential energy minimum. The pendulum only goes to a minimum potential energy if it minimizes hoth its potential and kinetic energy. The minimization of the potential energyof the tntal isdated system (hnth f w pendulums and vibrating molecules) is readily interpreted in terms of converting the larger quanta assnciated with vihratinnal potential enereies to the smaller quanta associated with translational kinetic energies. ~ n e r i yis more spread out in the latter, the entropy is maximized. Many sources of the errnnenus potential energy statement proceed to provide the student options on stating "tendencies," optio& which are hoth more useful and more accurate. Two are- "In an isolated system the entropy increases in all net changes," and "In a closed system a t constant temperature and pressure the Gihbs free energy decreases in all net ehnnees." Mv exoerience is that both of these functions are -, easier to evaluate, use, and understand than is potential energy, when it comes to predicting the direction of change. T o repeat, the fact that onecan use the potential energy argument a t all is mainly due t o the higher entropy associated with the smaller quanta of thermal kinetic energy compared to the larger quanta associated with molecular potential energy. This is also the principal factor validating "energy tends to degrade to heat." Pendulums, and other mechanical systems. "tend to a potential energy minimum" by increasing the entropy of the svstem throuah aeneratina heat. ~ a x i m i z a t i o nof entropy, by the spreading out of energy and/or mass, can account for both "directions" in which any chemical reaction mav occur. or for anv other chan~es-for . example, holh evaporation and condensatinn. Can ."kinimiaat ion of potential energy" dl, thesamen increaze in entrnpv ~
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(AS > 0) is a general criterion for change in all known isolated systems. Decrease in potential energy is a very limited criterion and needs to have those limitations clearly expressed. It is of doubtful usefulness in chemistry. "The Entropy of a Shuffled Deck of Cards Is Greater than that of a New Deck" (True?) T h e statement in this subtitle (or a similar one about a child's room, or a set of dominoes, or wind-blown leaves, or a crowd after a public event) is usually followed by A S = k In ( W ~ I W I ) .
But note that while it is true there is only one way to have a new deck (that is, however it comes), there is alsoonly one way to have it after shuffling. Similarly, dominoes are arranged in one way before the game. and only one way after the game. T h e leaves have one pattern before and a single different pattern after the wind blows. So also with the people a t any moment a t and after a public event. In each case the entropy change of the system is zero so long as one compares a single non-dynamic initial state and a single non-dynamic final state: A S = k In ( W21W~)= k In 1 = 0. Of course, if one counts all the states of the dynamic crowd a t and after a public event, A S is positive for the crowd as a system. And A S for the universe is unquestionably positive in all cases. Our intuitive acceptance of the usual argument followsfrom the human tendency to define a particular, regular array as ordered, and all other arrays together as disordered. Using these concepts the "ordered" array is scarcer (though it ma\' ~ e r s i sfor t a Innp time), and if the system then moves through all the "disord&edn arrays the entropy increases. But note that the states classed as disordered must he accessible and nttnined., otherwise thev cannot be counted. If states are accessihle hut not nttnined, for example most electronic states at low temperatures, the states ha\,e neyligihle effect on the entropy. Thus the very nature of statistical entropy usually involves dynamism and movement through all the available states. The human conceDts of reaularitv, simplicity, or order need to include a dynamic con&neni when applied to discussions of entrow. It is the actual changes (or lack 1hereof) in the sysvm which ;]elp determine the entropy of a system and its change. A Newtonian ideal gas (molecules evenly spaced, repelling with an inverse square law, and exhibiting equal partition of eneray) . . would statistically have zero molar entropy a t all conditions and, hence,zerochange withany changes in P, V. and,or T since there w d d Ilr a single unique itnte at every set uf P, V , T values, just as there is for an ideal crystal at 0' Kelvin. The fact that entropy does vary is nneof the best hits of evidence for the existence of molecules and the validity of the kinetic theory. Entropy measures the extent to which atoms and energy have spread out in the availahle volume and in the availahle quantum states.
"Energy Is the Abitlty lo do Work" (1s it?) This statement is found in many books. It is often followed in short order by "The energy of an isolated system is constant." Later on one mav read. "The abilitv of an isolated system to do work decreases w&h time and becomes zero ar equilil~rium."Andthe students faithfully repeat all threeon ~
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Volume 57. Number 1. January 1980 1 41
demand (though, if they want full credit, not in the same answer). S U D D OaSstudent ~ reasoned. "Energy is the ability of a system do work. An equilibrium system can do no work. So, an equilibrium system has no energy." How would we judge him? The patent absurdity of "Energy is the ability to do work" in liaht of the accurate second and third statements above might &ow the case against it to rest here, but I leave it as an exercise for the reader to explore this further. There are surely other paradigmi passed on in science as
42 1 Journal of Chemical Education
imperfect as the three mentioned here, and, like them, capable of restatement in terms less paradoxical, much more accurate, and no more difficult to comprehend. We should seek such inadequacies and replace them. But perpetuation of proved fallacy persists, and I expect to be reading all three of the above subtitles for some years to come. Small wonder students are confused by our rules and prefer to memorize them rather than to understand them.
