Jeffrey S. Wicken Behrend college of The Pennsylvania State University Erie, 16510
The Chemically Organizing Effects of Entropy Maximization
All physicochemical behavior is governed in some way by the constraints provided by the second law of thermodynamics. Our understanding of this extremelv. i m.~ o r t a nand t ubiquitous law has enlarged tremendously sincc it6 original formulation by Carnot, who shuwed that one cannot ohrain n complete cmwrsion ot heat energy to mechanical u,ork. Since the converse of this finding, namely the comdete convertibility of mechanical energy to heat, was knbwn from Joule's experiments, Carnot's statement provided the first real statement that energy-transforming processes involved a certain direction in time, and that they progressed toward the gradual accumulation of heat a t the expense of more "useful" forms of energy. Clausius further developed and formalized this concept of temporal irreversibility by defining the entropy function and showing that an increase in the value of this parameter accompanied all naturally occurring (irreversible) processes. Time was thus shown to he an objective, "real" coordinate axis whose measure consisted in universal entropic changes. The evolution of the second law culminated in its statistical interpretation by Bolkmann, in which the entropy of a system was related to its degree of randomness. As pointed out by Denhigh,' tbis correlation has often been construed to the effect that naturally occurring processes inevitably act to impose disorder or disorganization on the universe. This limited understanding of the randomizing process has tended to obfuscate its creative influence in evolution. Biologists, for example, are constantly confronted with the problem of rationalizing the evolutionary emergence of complex molecular structures and systems within the randomizing constraints imposed by the second law. One way of sidestepping this problem has been to acknowledge, correctly, that the exceedingly improbable distribution of matter seen in living organisms is maintained a t the expense of chemical reactions which impose disorder on the environment (the conversion of carbohydrates to carbon dioxide and water, for example), so that the overall requirement of entropic increase is not actually violated by living systems. This formulation still avoids confronting the necessity of some thermodynamic organizing principle that might account for the emergence of these structures and svstems in the first lace. 'I'he stvond law h ~generally s heen regarded as a disorganir~ne le but this is not entirelv correct. If also ".~ r ~ n c iin~ nature. promotes the development of localized regions of chemical oreanization, as manifested in chemical bond formation. Hellre elahorating on this aratement. I would like to digress 3 hit on Bdtrmann'i ntatistical int~.r~retation ot the entronv function, using an example provided by Denhigh.2 suppose that one juxtaposes two hypothetical microcrystals, one consisting of four atoms of element A and the other consisting of four atoms of element B, so that a slow diffusion of atoms can occur across the houndary between the crystals. If we assume that A and B are sufficiently similar in electronic configuration that they can participate in each other's lattice structure equally well as in their own, what will he the most probable arrangement of atoms with respect to the original boundary once equilibrium has been reached? The initial configuration will he
-
As diffusion occurs across this boundary, other configurations will emerge, such as A A
B / A A I B
B
I
There are 8!/4!/4!= 70 possihle configurations for this system. Only one corresponds to the original arrangement. On the other hand, there are 16 possible ways of achieving a 3A + B:A 3B distribution, and 36 possible configurations contributing to the 2A 2B:2A 2B distribution, with respect to the original boundary. If each of these 70 configurations is equally probable (one of the basic postulates of statistical mechanics), then the latter arrangement is 36 times as likely to occur as the original at any time after equilibrium has been reached. What makes statistical mechanics such a powerful tool to apply to physicochemical systems is the enormous number of molecules that participate in any such system. Suppose that instead of four, there are ten atoms of each type. Now, there are 67 X 10'O possible configurations for the system, of which only one corresponds to the (~riginalunmixed state. When numbers of reasonable magnitudes are used in these calculations, the chances of an unmixed configuration occurring at any time become vanishinelv - .small. Hence. mixin~occursto produce homogeneous solutions, in tbis modkl, aimay because there are so vastly manv more mixed confirmrations of matter than segrepated 0 where AS, is the change in universal entropy, and where AS, and AS, are the entropy changes associated with the chemical svstem and with the reservoir.. rewectivelv. that the . . Suppose -reactions in the system are exothermic and that an amount of heat.. Q,. . . is released to the reservoir. Under isothermal conditions the entropy increase of the reservoir is
AS, = Q,/T Qr represents that amount of the potential energy of the chemical svstem that has been converted to the randomized kinetic energy of heat. Under these conditions the second law may he stated as
AS, = AS. + Q,IT > 0 The entropy change of the system consists, as before, of chances in its distribution of matter and enerw. -" Since AS. is only one term in the overall entropy expression, it may eitier increase or decrease without violating the second law. The thermal energy of a chemical system is partitioned among translational, rotational, and vibrational modes. The transl&ional contribution to the thermal entropy of a system is generally affected most by changes in chemical organization, because it is directly dependent on the number of molecules through which translational energy can be spread, while having a relatively small dependency on molecular weight. Therefore, dissociative processes are favored principally by maximizing translational entropy.
The configurational entropy of a system, on the other hand, depends on the number of different molecular species comprising the system, as well as on the total number of molecules. This contribution therefore favors the generation of chemical diversity, as indicated earlier, as a vehicle for matter-randomization. The entropy transferred to the reservoir, QJT, is due to energy-randomization. Since Q, is provided by potential energy changes occurring within the system, i t can he expressed in terms of state functions of the system itself. At constant pressure AH, = -Q,
where AH, is the change in enthalpy of the system. Under these conditions, a statement of the second law is AS, = AS,
- AHJT > 0
The above equation states that for systems in thermal contact with their surroundings, changes in the magnitudes of two state functions bring about the entropic increase required of irreversible processes. The first of these changes is an increase in the entropy of the system itself, and involves
both configurational and thermal factors. Both factors are generally disorganizing in their effects. However, since configurational entropic increases attend the formation of new molecular species, this factor also promotes the generation of chemical novelty. In this sense, it constitutes a creative force in chemical evolution, increasing variety and diversity in the universe. The second term contributing to the overall entropic increase is a decrease in enthalpy (or internal energy) of the system, achieved through the formation of chemical bonds. (It should be emphasized that changes in enthalpy or internal enerav Droceed accordina to the ~ r i n c i ~ lof e senerrv conseru a t i & ~ h e y do not constitute b o c e s i laws and can only he used to rationalize the behavior of a ~hysicochemicalsystem under the specific conditions that a ieduction in their Galues appears as the energy-randomization term in the second law formulation.) A maximization of chemical bonding is thus favored in order to make potential energy available for soreadine as heat. This second contribution to entronv." maximization, particularly with reference to the photochemical sources of electronic ootential enerev. ".. has a distinctlv organizing effect on matter and is of decided importance in chemical evolution.
Volume 53, Number 10, October 1976 / 625
