thumbnail /ketchel Entropy and Its Role in Introductory Chemistry Franklin R. Blckford Tompkins Cortland Community College Dryden, NY 13053
A broad definition of entropy is that it is a measure of randomness or disorder which can also be internreted in terms of probability; a state of disorder is more probable than a state of order. For example, when ice melts to liquid water, there is an increase in the disorder of the water molecules. Instead of being constrained to the highly ordered arrangement of the ice crystal, molecules in liquid water are freer to move about. The molecules are now able to move through the entire liquid region instead of being confined to vibrating about rather fixed positions. and their disorder or randomness is increased. We say that the entropy of the water is increased upon melting. A similar, but more extensive, increase in entropy occurs when liquid water is vaporized. Vaporization generally involves an increase in volume by a factor of about 1000, and thus the molecules are fartherapart and even less ordered than in the liquid state. For the same substance, entropy always increases upon melting and also upon vaporization: The phase change illustration of entropy can be regarded as a particle randomness aspect of entropy. That is, as the physical position of the molecules becomes more disordered, the entropy increases. However, there is more to entropy than particle randomness. The particle randomness illustration implies that all gases a t the same temperature and pressure have the same entropy, but this is not the case. Another asnect of entronv is that of enerw randomness. Energy randomness can bTunderstood by cbnsidering the auantum nature of enerev. Particle randomness is explained by the disorder of discregparticles of matter, and analogously enerm -" randomness can be explained by the disorder of discrete quanta of energy. All energy is quantized in a manner analoeous to the auantization of the electron enerw levels in an atom. In addition to electron energy, moleculeshave other ways of distributing energy. They can move from one position t o another (translate), stretch or bend their chemical bonds (vibrate), and rotate. All of these kinds of energy--electronic, translational, vibrational, and rotational-are quantized. Different molecules differ in the number of ways they can distribute energy quanta and thus differ in entropy. In addition to electronic energy levels, which are not significant to entropy considerations a t 25'C, a monatomic molecule possesses only one other kind of energy-translation. A diatomic molecule. however. oossesses rotational and vibrational enerw in additidn to transfation, and a polyatomic molecule possess& more modes of vibration. The enerw auantacan be dispersed among the different kinds of ene&(translation, rotation, vibration, and electronic), and the more ways there are of dispersing the energy, the greater is the energy randomness or entropy. In general, for comparable molecules like the halogens, entropy increases with increasing mass. This is due to the fact that more massive molecules have their energy levels more closely spaced, and thus the energy quanta can be more randomly distributed among them. This can be illustrated by an analogy. Consider randomly throwing a bucketful of pennies at each of two sets of stairs, each staircase of the same total height but differing in the height of the steps. The steps on one set of stairs are spaced only one centimeter apart while the second set has the more normal spacing of 15 cm apart. Since
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MARY
there will be more steps available on the staircase with the more closely spaced steps, the pennies will be more randomly distributed and the entropy will be greater. Another factor that affects entropy is molecular complexity; the more atoms there are in a mol&ule, the more complex i t is and thus there are more ways that the molecule can vibrate. For molecules of comparable mass, entropy increases with increasing complexity because more complex molecnles have more wavs of distributine enerev auanta. A diatomic carbon monoxide molecule has only &e mode of vibration, that of stretching. An ethylene molecule, C2Ha, of the same molecular weight as CO but containing more atoms has 12 modes of vibration. The ethylene molecule thus has more ways of distributing the energy quanta and has greater entropy. In chemical reactions there is almost alwavs an increase in entropy if the reaction produces an increase in the number of moles of gas. This is so because gases, being much more disordered than solids or liquids, generally have greater entropy. In reactions that do not involve eases but result in an increase in the total number of moles, there is generally an increase in entropy also. ~ i k e v o l u m and e mass, entropy is a fundamental property of a substance or system, and like volume and mass it is an extensive property. That is, the entropy of two moles of a wt).;tance ia twice that of one mole. IJnfnrtunately, although entrupy is adefinite propertvol'matter, there is nodirect way to measure it.'l'his is 1053). that thwe is nu type uf instrument into which we can place n sample and ohtain a direct reading of i t s entropy. Instead. entropy values must be calculated based on other measurements. This lack of dirpct measurability, hmverer, dues not lessen the significance of entropy as a l'undamenrd property, althnugh it dues add to cont'usinn in understanding it. There is, though, a familiar analogy-that of densitv. Densitv is renerallv not measured directlv, and, in fact, cannot be for &any substances. I t is calculated from other measurements. Although entropy can be defined in a broad way as a measure of randomness, i.e., probability, it does have a precise definition. In fact, it has two very precise definitions; one was arrived a t over a hundred years ago from a study of the macroscopic properties of heat, and the other was derived from the microscopic consideration of the probability distribution of energy quanta among molecules. Unfortunately, both of these definitions are too complex, in concept if not in mathematical formulation. to consider in an introductorv course. Instead, we can consider the change in entropy of asibstance or system under the special condition of constant temperature. Under this special condition, the change in entropy, denoted as AS, is equal to the amount of heat ( q ) absorbed or evolved divided by the absolute temperature (T).; A S = q/T. For example, the entropy increase accompanying .. the vaporization uf I mole if waterat 100°C and 1 atm 01' pressure is equal to the molar heat of vaporization (3,720 calories) di\ided hy the absolute temperatnri, 313OK. This computes to be an entropy increase of 26.1 caloriesldegree. The most sienificant reason whv entronv is of concern to chemists is that fundamentally there are only two reasons why chemical reactions occur; one is the tendency to achieve lower ~
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Brief descriptions of phenomena, topics, facts. mc.. which chemical educators have found to be of interest in their teachmg, are presented in a "note type" format througham the JOURNAL.
Volume 59
Number 4
April 1982
317
energy and the other is the tendency to achieve maximum randomness. Whether a reaction will occur a t a given temperature depends on the balance of these two tendencies. Although almost all spontaneous chemical reactions that occur a t 250C and one atmosphere of pressure are exothermic and thus the tendency to lower energy is the driving force, entrow is the driving force behind manv"ohvsical . . chanees in chem&y. The physkd processes discussed in chemistr; that are best explained in terms of entropy, even from a qualitative consideration of entropy, include the change in boiling point and freezing point of a solution compared to the pure solvent, the diffusion of gases, solubility, osmosis, and the melting of ice. When a nonvolatile solute is dissolved in a liquid like water, the basic reason that the boiling point is raised and the freezing point is lowered is that the solution represents a higher state of entropy than the pure liquid. Since a tendency toward maximum randomness is one of the fundamental tendencies in nature, the solution is favored, for generally a mixture of solute and solvent is a more disordered condition than pure solute and pure solvent. Both boiling and freezing effect a seoaration of solute and solvent. The mamitude of the entropy c k g e that occurs upon boiling a solution is less than for boiling the pure solvent because the entropy value of the solution is greater than for the pure liquid. Thus, for the solution, the entropy driving force of boiling is lessened and a higher temperature is required. The freezing point of a solution is lower than that of the pure solvent because freezing a
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solution involves a greater decrease in entropy than freezing the pure liquid. There is a greater entropy driving force to retain the liquid state for the solution than for the pure liquid. Gases always diffuse into each other because the mixture is more disordered. The process of dissolving a solid in a liquid is almost always endothermic. The reason that i t occurs spontaneously is that the nrocess of solution results in an entrow . increase. Osmosis can be understood best as occurring because of the drivina force to achieve aeater entrow. ." The water molecules spont&eously move through the semipermeable membrane to dilute the solution and increase entropy. If the water moved from the solution into the pure water, it would effect a separation of solute and solvent and this would decrease the randomness The melting of ice above O°C occurs simply because the water is moving in the direction of greater randomness. Clearly the process of melting ice does not occur to achieve a lower energy state; it absorbs heat. I t must then be due to the randomness tendency. A more thorough explanation of entropy can he found in W. G. Davies' paperback, "Introduction to Chemical Thermodynamics: A Non-Calculus Approach," (W. B. Saunders, Philadelphia, 1972) and G . C. Pimentel and R. D. Spratley's paperback, "Understanding Chemical Thermodynamics," (Holden-Day, Inc., San Francisco, 1969).
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