Entropy basis

Dislocation theory as a portion of the subject of solid-state physics is somewhat beyond the scope of this book, but it is desirable to examine the subject briefly in terms of its implications in surface chemistry. Perhaps the most elementary type of defect is that of an extra or interstitial atom—Frenkel defect [110]—or a missing atom or vacancy—Schottky defect [111]. Such point defects play an important role in the treatment of diffusion and electrical conductivities in solids and the solubility of a salt in the host lattice of another or different valence type [112]. Point defects have a thermodynamic basis for their existence in terms of the energy and entropy of their formation, the situation is similar to the formation of isolated holes and erratic atoms on a surface. Dislocations, on the other hand, may be viewed as an organized concentration of point defects they are lattice defects and play an important role in the mechanism of the plastic deformation of solids. Lattice defects or dislocations are not thermodynamic in the sense of the point defects their formation is intimately connected with the mechanism of nucleation and crystal growth (see Section IX-4), and they constitute an important source of surface imperfection. 

It is of interest in the present context (and is useful later) to outline the statistical mechanical basis for calculating the energy and entropy that are associated with rotation [66]. According to the Boltzmann principle, the time average energy of a molecule is given by... 

Ref. 205). The two mechanisms may sometimes be distinguished on the basis of the expected rate law (see Section XVni-8) one or the other may be ruled out if unreasonable adsorption entropies are implied (see Ref. 206). Molecular beam studies, which can determine the residence time of an adsorbed species, have permitted an experimental decision as to which type of mechanism applies (Langmuir-Hinshelwood in the case of CO + O2 on Pt(lll)—note Problem XVIII-26) [207,208]. 

Water-soluble globular proteins usually have an interior composed almost entirely of non polar, hydrophobic amino acids such as phenylalanine, tryptophan, valine and leucine witl polar and charged amino acids such as lysine and arginine located on the surface of thi molecule. This packing of hydrophobic residues is a consequence of the hydrophobic effeci which is the most important factor that contributes to protein stability. The molecula basis for the hydrophobic effect continues to be the subject of some debate but is general considered to be entropic in origin. Moreover, it is the entropy change of the solvent that i... 

A second way of dealing with the relationship between aj and the experimental concentration requires the use of a statistical model. We assume that the system consists of Nj molecules of type 1 and N2 molecules of type 2. In addition, it is assumed that the molecules, while distinguishable, are identical to one another in size and interaction energy. That is, we can replace a molecule of type 1 in the mixture by one of type 2 and both AV and AH are zero for the process. Now we consider the placement of these molecules in the Nj + N2 = N sites of a three-dimensional lattice. The total number of arrangements of the N molecules is given by N , but since interchanging any of the I s or 2 s makes no difference, we divide by the number of ways of doing the latter—Ni and N2 , respectively—to obtain the total number of different ways the system can come about. This is called the thermodynamic probabilty 2 of the system, and we saw in Sec. 3.3 that 2 is the basis for the statistical calculation of entropy. For this specific model... 

Mollier diagram for potassium. Basis enthalpy = 0.0 oal/g atom at 298 K entropy = 15.8 oal/(g atom-K) at 298 K. (Aerojet-General Rep. AGN8194, vol Reproduced hy permission.)... 

The theoretical steam rate (sometimes referred to as the water rate) for stream turbines can be determined from Keenan and Keyes or Mollier charts following a constant entropy path. The theoretical steam rate is given as Ib/hr/kw which is easily converted to Ib/hr/hp. One word of caution—in using Keenan and Keyes, steam pressures are given in PSIG. Sea level is the basis. For low steam pressures at high altitudes appropriate coirections must be made. See the section on Pressure Drop Air-Cooled Air Side Heat Exchangers, in this handbook, for the equation to correct atmospheric pressure for altitude. 

The Joule-Brayton (JB) constant pressure closed cycle is the basis of the cyclic gas turbine power plant, with steady flow of air (or gas) through a compressor, heater, turbine, cooler within a closed circuit (Fig. 1.4). The turbine drives the compressor and a generator delivering the electrical power, heat is supplied at a constant pressure and is also rejected at constant pressure. The temperature-entropy diagram for this cycle is also... 

On the basis of the values of AS° derived in this way it appears that the chelate effect is usually due to more favourable entropy changes associated with ring formation. However, the objection can be made that and /3l-l as just defined have different dimensions and so are not directly comparable. It has been suggested that to surmount this objection concentrations should be expressed in the dimensionless unit mole fraction instead of the more usual mol dm. Since the concentration of pure water at 25°C is approximately 55.5 moldm , the value of concentration expressed in mole fractions = cone in moldm /55.5 Thus, while is thereby increased by the factor (55.5), /3l-l is increased by the factor (55.5) so that the derived values of AG° and AS° will be quite different. The effect of this change in units is shown in Table 19.1 for the Cd complexes of L = methylamine and L-L = ethylenediamine. It appears that the entropy advantage of the chelate, and with it the chelate effect itself, virtually disappears when mole fractions replace moldm . ... 

Hcuts et a .,64 while not disputing that penultimate units might influence the activation energies, proposed on the basis of theoretical calculations that penultimate unit effects of the magnitude seen in Ihe S-AN and other systems (i.e. 2-5 fold) can also be explained by variations in the entropy of activation for the process. They also proposed that this effect would mainly influence rate rather than specificity. 

In equation (1.17), S is entropy, k is a constant known as the Boltzmann constant, and W is the thermodynamic probability. In Chapter 10 we will see how to calculate W. For now, it is sufficient to know that it is equal to the number of arrangements or microstates that a molecule can be in for a particular macrostate. Macrostates with many microstates are those of high probability. Hence, the name thermodynamic probability for W. But macrostates with many microstates are states of high disorder. Thus, on a molecular basis, W, and hence 5, is a measure of the disorder in the system. We will wait for the second law of thermodynamics to make quantitative calculations of AS, the change in S, at which time we will verify the relationship between entropy and disorder. For example, we will show that... 

The transition obtained under stress can be in some cases reversible, as found, for instance, for PBT. In that case, careful studies of the stress and strain dependence of the molar fractions of the two forms have been reported [83]. The observed stress-strain curves (Fig. 16) have been interpreted as due to the elastic deformation of the a form, followed by a plateau region corresponding to the a toward [t transition and then followed by the elastic deformation of the P form. On the basis of the changes with the temperature of the critical stresses (associated to the plateau region) also the enthalpy and the entropy of the transition have been evaluated [83]. 

On the basis of the evidence presented above as well as some other pertinent data (e.g. negative entropies of activation), Darwish and Braverman have suggested that the rearrangement of allylic 2,6-dimethylbenzenesulfinates (6a-f) to corresponding sulfones (7a-f) proceeds by a cyclic intramolecular mechanism involving a five-membered transition state which may be represented by a resonance hybrid (8) of the following resonance structures. 

The Hg/dimethyl formamide (DMF) interface has been studied by capacitance measurements10,120,294,301,310 in the presence of various tetraalkylammonium and alkali metal perchlorates in the range of temperatures -15 to 40°C. The specific adsorption of (C2H5)4NC104 was found to be negligible.108,109 The properties of the inner layer were analyzed on the basis of a three-state model. The temperature coefficient of the inner-layer potential drop has been found to be negative at Easo, with a minimum at -5.5 fiC cm-2. Thus the entropy of formation of the interface has a maximum at this charge. These data cannot be described... 

Next, an exploration of thermodynamics and equilibrium, based on a conceptual understanding of entropy and Gihbs free energy. This integrated presentation lays a common foundation for these concepts and provides a basis for understanding the origin and form of the equilibrium constant and the behavior of equilibrium systems. 

Why Do We Need to Know This Material The second law of thermodynamics is the key to understanding why one chemical reaction has a natural tendency to occur bur another one does not. We apply the second law by using the very important concepts of entropy and Gibbs free energy. The third law of thermodynamics is the basis of the numerical values of these two quantities. The second and third laws jointly provide a way to predict the effects of changes in temperature and pressure on physical and chemical processes. They also lay the thermodynamic foundations for discussing chemical equilibrium, which the following chapters explore in detail. 

On the basis of the structures of each of the following molecules, predict which ones would be most likely to have a residual entropy in their crystal forms at T = 0 (a) CO, ... 

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