On entropy

Equation (3.16) shows that the force required to stretch a sample can be broken into two contributions one that measures how the enthalpy of the sample changes with elongation and one which measures the same effect on entropy. The pressure of a system also reflects two parallel contributions, except that the coefficients are associated with volume changes. It will help to pursue the analogy with a gas a bit further. The internal energy of an ideal gas is independent of volume The molecules are noninteracting so it makes no difference how far apart they are. Therefore, for an ideal gas (3U/3V)j = 0 and the thermodynamic equation of state becomes... 

As known, SEC separates molecules and particles according to their hydro-dynamic volume in solution. In an ideal case, the SEC separation is based solely on entropy changes and is not accompanied with any enthalpic processes. In real systems, however, enthalpic interactions among components of the chromatographic system often play a nonnegligible role and affect the corresponding retention volumes (Vr) of samples. This is clearly evident from the elution behavior of small molecules, which depends rather strongly on their chemical nature and on the properties of eluent used. This is the case even for... 

Similar observations hold for solubility. Predominandy ionic halides tend to dissolve in polar, coordinating solvents of high dielectric constant, the precise solubility being dictated by the balance between lattice energies and solvation energies of the ions, on the one hand, and on entropy changes involved in dissolution of the crystal lattice, solvation of the ions and modification of the solvent structure, on the other [AG(cryst->-saturated soln) = 0 = A/7 -TA5]. For a given cation (e.g. K, Ca +) solubility in water typically follows the sequence... 

However, solubility, depending as it does on the rather small difference between solvation energy and lattice energy (both large quantities which themselves increase as cation size decreases) and on entropy effects, cannot be simply related to cation radius. No consistent trends are apparent in aqueous, or for that matter nonaqueous, solutions but an empirical distinction can often be made between the lighter cerium lanthanides and the heavier yttrium lanthanides. Thus oxalates, double sulfates and double nitrates of the former are rather less soluble and basic nitrates more soluble than those of the latter. The differences are by no means sharp, but classical separation procedures depended on them. 

Edmister, W, G., Application of Thermodynamics to Hydrocarbon Processing, Pet. Refiner, Part XVI, Effect of Pressure on Entropy and Enthalpy, Feb. (1949). 

Notice from the figure that the effect of temperature on entropy is due almost entirely to phase changes. The slope of the curve is small in regions where only one phase is present. In contrast, there is a large jump in entropy when the solid melts and an even larger one when the liquid vaporizes. This behavior is typical of all substances melting and vaporization are accompanied by relatively large increases in entropy. 

Data on entropies and heat capacities, which are available only for dimethyl sulfoxide and dimethyl sulfone, can be found elsewhere19. 

Chapter 9, on entropy and molecular rotation in crystals and liquids, is concerned mostly with statistical mechanics rather than quantum mechanics, but the two appear together in SP 74. Chapter 9 contains one of Pauling s most celebrated papers, SP 73, in which he explains the experimentally measured zero-point entropy of ice as due to water-molecule orientation disorder in the tetrahedrally H-bonded ice structure with asymmetric hydrogen bonds (in which the bonding proton is not at the center of the bond). This concept has proven fully valid, and the disorder phenomenon is now known to affect greatly the physical properties of ice via the... 

The steric environment of the atoms in the vicinity of the reaction centre will change in the course of a chemical reaction, and consequently the potential energy due to non-bonded interactions will in general also change and contribute to the free energy of activation. The effect is mainly on the vibrational energy levels, and since they are usually widely spaced, the contribution is to the enthalpy rather than the entropy. When low vibrational frequencies or internal rotations are involved, however, effects on entropy might of course also be expected. In any case, the rather universal non-bonded effects will affect the rates of essentially all chemical reactions, and not only the rates of reactions that are subject to obvious steric effects in the classical sense. 

Work can be completely converted to heat, but—and this is important—a complete conversion of heat to work is not possible in an isothermal system. This problem is dealt with by the second law of thermodynamics, with its statement on entropy The entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium. ... 

Kline, S.J. (1999). The Low Down on Entropy and Interpretative Thermodynamics. DCW Industries, Inc., Palm Drive, CA... 

The ring size (degree of oligomerization x) and conformation of M-E heterocycles strongly depends on steric effects of the substituents (repulsive interactions), ring strain effects and on entropy factors. This was shown for instance by Beachley and Racette for several heterocyclic aminoalanes [R2A1NR2]X97 and confirmed by our own results. However, predictions whether four- or six-membered heterocycles will be formed are... 

Despite the fact that the few studies on such systems which have been made [12-16] suggest that the entropy term is not unimportant for the position of the equilibrium, the lack of information on entropy obliges us to use Equation (3) in order to obtain a first approximation for these systems. However, although a major contribution to the overall AS0 for reactions such as those in Equations (iv) and (v) arises from the solvation of the ions [17], this is in fact incorporated in the AHB calculated below by the use of a calculated AG0sol [9]. 

Check out the video clip giving more information on entropy at www. brightredbooks.net... 

It was thought for some time that central peaks were due to impurities, defects and other such extrinsic or intrinsic factors. A number of models and mechanisms based on entropy fluctuations, phonon density fluctuations, dielectric relaxation, molecular... 

The first objection, that of uonequilibriuni, has received a partial rebuttal from Rodebush (R5, R6, R7). The motions of translation and rotation tend to stabilize a cluster, as can be shown by considerations of the entropy of these two effects. It is also pointed out that water is an unusual material because the liquid molecules in the bulk material have a tetrahedral arrangement. Thus a tiny bubble will be surrounded by unsatisfied hydrogen bonds in the curved liquid surface. The effect on entropy of the interfacial organization probably means that the use of a constant molecular heat of vaporization X as used by Bernath and others is in error. 

Students often state the laws of thermodynamics this way. You cant win because you cant get any more energy out of a system than you put into it. You can t break even because no matter what you do, some of your energy will be lost as ambient heat. Lastly, you cant get out of the game because you depend on entropy-increasing processes, such as solar nuclear fusion or cellular respiration, to remain alive. 

As can be expected, the creation of the Third Edition allowed for further improvements in the readability of the text and for the correction of inaccuracies appearing in earlier editions. Content changes were also made. The most significant of these changes include a reworking of the presentation of the scientific method as found in Chapter 1. For Chapter 9, the section on entropy was greatly revised. For Chapter 10, Lewis acids and bases are now discussed, and for Chapter 17 a new section on gas laws was added. The topical chapters of this textbook, Chapters 13—19, were also updated to reflect current events. 

Using an argument based on entropy production, what can be concluded about the algebraic sign of the electrical conductivity ... 

Fig. 8. Effect of thermodynamic buffering on entropy production, (a) Plot of Su versus x [equations (8) and (15) with LAK = 0]. The plots were normalized with Lp = L = X2 = I. The other values in the plot As = 8.5 kcal/mole, AGak = 0.15 kcal/mole, P, = 0.008 M, and M = 0.005. LJ was varied between 0.0 and 0.9 in steps of 0.1. Thin line, rop, for q%c broken tine, loci of steady states.

The mechanisms by which liquid crystals influence reaction rates need further study. Presumably, one important factor is the effect of ordering on entropy changes of various steps of the reaction. Bacon (44) has considered this factor in connection with the ability of thermotropic liquid crystals to increase the polymerization rate of phenylacetylene. 

The rule of Price and Hammett has been found to hold in several other kinetic studies. However, it has been shown to fail in oxime formation under conditions identical with those of the semicarbazone study (Fitzpatrick and Gettler, 1956). This is perhaps not surprising in view of the known complexity of semicarbazone and oxime formation, but it should serve as a warning that the effect of structure on entropy is by no means well understood. 

Baughman concluded that while none of the three methods examined was markedly superior, lack of data limits the use of equations dependent on entropies. 

At this point the need arises to become more explicit about the nature of entropy generation. In the case of the heat exchanger, entropy generation appears to be equal to the product of the heat flow and a factor that can be identified as the thermodynamic driving force, A(l/T). In the next chapter we turn to a branch of thermodynamics, better known as irreversible thermodynamics or nonequilibrium thermodynamics, to convey a much more universal message on entropy generation, flows, and driving forces. 

The main problem with predictions of kinetic preferences based on force-field calculations of relative stabilities of reaction intermediates arises from the fact that the energies of the competing intermediate structures usually differ by amounts smaller than the accuracy of the energy calculations. These calculations are inherently inexact, since the force-field parameters for the intermediates are mostly unknown (high-level ab initio calculations would be needed to determine them). Moreover, the probability that a reaction passes via a given intermediate depends not only on its enthalpy, but also on entropy thus, a dynamic description of the solvated intermediate would be required. Finally, even if we knew the structure of a reaction intermediate perfectly, it would always remain an approximation for the geometry of the transition state, whose free energy is the real determinant of the reaction kinetics. 

In Table 2 the data on entropy are presented, as well as data on enthalpy of compounds of titanium with a solution of an acid on a surface of a particle. 

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