51/ paradox

Discuss the paradox in the wettability of a fractal surface (Eq. X-33). A true fractal surface is infinite in extent and a liquid of a finite contact angle will trap air at some length scale. How will this influence the contact angle measured for a fractal surface ... 

Irreversible adsorption discussed in Section XI-3 poses a paradox. Consider, for example, curve 1 of Fig. XI-8, and for a particular system let the equilibrium concentration be 0.025 g/lOO cm, corresponding to a coverage, 6 of about 0.5. If the adsorption is irreversible, no desorption would occur on a small dilution on the other hand, more adsorption would occur if the concentration were increased. If adsorption is possible but not desorption, why does the adsorption stop at 6 = 0.5 instead of continuing up to 0 = 1 Comment on this paradox and on possible explanations. 

XVIII-11 (the paradox of desorption heat exceeding adsorption heat is explainable in terms of a partial irreversibility of the adsorption-desorption process). 

Process 2, the adsorption of the reactant(s), is often quite rapid for nonporous adsorbents, but not necessarily so it appears to be the rate-limiting step for the water-gas reaction, CO + HjO = CO2 + H2, on Cu(lll) [200]. On the other hand, process 4, the desorption of products, must always be activated at least by Q, the heat of adsorption, and is much more apt to be slow. In fact, because of this expectation, certain seemingly paradoxical situations have arisen. For example, the catalyzed exchange between hydrogen and deuterium on metal surfaces may be quite rapid at temperatures well below room temperature and under circumstances such that the rate of desorption of the product HD appeared to be so slow that the observed reaction should not have been able to occur To be more specific, the originally proposed mechanism, due to Bonhoeffer and Farkas [201], was that of Eq. XVIII-32. That is. 

A first glimmer of tire resolution to the paradox of how control fields can control purity content is obtained by... 

The paradox involved here ean be made more understandable by introdueing the eoneept of entropy ereation. Unlike the energy, the volume or the number of moles, the entropy is not eonserved. The entropy of a system (in the example, subsystems a or P) may ehange in two ways first, by the transport of entropy aeross the boundary (in this ease, from a to P or vice versa) when energy is transferred in the fomi of heat, and seeond. 

The recurrence paradox is easy to refiite and was done so by Boltzmaim. He pointed out that the recurrence... 

Diatomic molecules have only one vibrational mode, but VER mechanisms are paradoxically quite complex (see examples C3.5.6.1 and C3.5.6.2). Consequently there is an enonnous variability in VER lifetimes, which may range from 56 s (liquid N2 [18]) to 1 ps (e.g. XeF in Ar [25]), and a high level of sensitivity to environment. A remarkable feature of simpler systems is spontaneous concentration and localization of vibrational energy due to anhannonicity. Collisional up-pumping processes such as... 

The molecular electronic polarizability is one of the most important descriptors used in QSPR models. Paradoxically, although it is an electronic property, it is often easier to calculate the polarizability by an additive method (see Section 7.1) than quantum mechanically. Ah-initio and DFT methods need very large basis sets before they give accurate polarizabilities. Accurate molecular polarizabilities are available from semi-empirical MO calculations very easily using a modified version of a simple variational technique proposed by Rivail and co-workers [41]. The molecular electronic polarizability correlates quite strongly with the molecular volume, although there are many cases where both descriptors are useful in QSPR models. 

The reliability of the in silico models will be improved and their scope for predictions will be broader as soon as more reliable experimental data are available. However, there is the paradox of predictivity versus diversity. The greater the chemical diversity in a data set, the more difficult is the establishment of a predictive structure-activity relationship. Otherwise, a model developed based on compounds representing only a small subspace of the chemical space has no predictivity for compounds beyond its boundaries. 

In a Lewis-acid catalysed Diels-Alder reaction, the first step is coordination of the catalyst to a Lewis-basic site of the reactant. In a typical catalysed Diels-Alder reaction, the carbonyl oxygen of the dienophile coordinates to the Lewis acid. The most common solvents for these processes are inert apolar liquids such as dichloromethane or benzene. Protic solvents, and water in particular, are avoided because of their strong interactions wifti the catalyst and the reacting system. Interestingly, for other catalysed reactions such as hydroformylations the same solvents do not give problems. This paradox is a result of the difference in hardness of the reactants and the catalyst involved... 

Paradoxically, compounds incorporating bonds with noble gases are difficult to model. This is because a very accurate method is needed in order to correctly... 

It may seem, at first sight, paradoxical that a competition reaction carried out under conditions in which the measured rate is independent of the concentration of the aromatic can tell us about the relative reactivities of two aromatics. Obviously, the measured rate has nothing to do with the rate of the product-determining step, and what is important in determining relative reactivities is the ratio of the values of ( 3.2.4) for two compounds. The criteria to be met for a correct application of the competitive method are well understood. ... 

The future use of lead may be decided by the resolution of an environmental paradox. Some markets for lead are being phased out because of environmental concerns, eg, the use of tetraethyllead as a gasoline additive. However, a 1990 State of California law and similar laws in nine eastern U.S. states require that 2% of new cars meet 2ero-emission standards in 1998. By 2003 this requirement rises to 10% of new vehicles. Zero emission vehicles are generally accepted to mean electric, ie, battery powered cars, and there is considerable research effort to bring suitable electric vehicles to market by 1998. 

Regulating Pesticides in Food The De/anej Paradox, Report of Board on Agriculture, Committee on Scientific and Regulatory Issues Underlying Pesticide Use Patterns and Agricultural Innovation, U.S. National Research Council, National Academy Press, Washington, D.C., 1987, 272 pp. 

Paradoxically, even rapid lowering of demand may cause rapid cost escalation this was the case in New Jersey during a 1981 drought when conservation caused substantial shrinking of demand and private water companies had to double their water prices. The continued increase of demand and reduction of supply portend real and relendess water-cost increases in every part of the United States in the future. One possible way to assure at least adequate suppHes, and possibly to moderate these cost increases, is through water reuse. 

Paradoxically, the thia2ides are efficacious, especially if combined with a prostaglandin synthetase inhibitor such as indomethacin or aspirin, in the treatment of nephrogenic diabetes insidipus, in which the patient s renal tubules fail to reabsorb water despite the excessive production of ADH (28). Thia2ides can decrease the urine volume up to 50% in these patients. 

There is also evidence for stable 3,4-adducts from the X-ray analysis of 2-amino-4-ethoxy-3,4-dihydropteridinium bromide, the nucleophilic addition product of 2-aminopteridine hydrobromide and ethanol (69JCS(B)489). The pH values obtained by potentiometric titration of (16) with acid and back-titration with alkali produces a hysteresis loop, indicating an equilibrium between various molecular species such as the anhydrous neutral form and the predominantly hydrated cation. Table 1 illustrates more aspects of this anomaly. 2-Aminop-teridine, paradoxically, is a stronger base than any of its methyl derivatives each dimethyl derivative is a weaker base than either of its parent monomethyl derivatives. Thus the base strengths decrease in the order in which they are expected to increase, with only the 2-amino-4,6,7-trimethylpteridine out of order, being more basic than the 4,7-dimethyl derivative. 

Leading Examples Electrodialysis has its greatest use in removing salts from brackish water, where feed salinity is around 0.05-0.5 percent. For producing high-purity water, ED can economically reduce solute levels to extremely low levels as a hybrid process in combination with an ion-exchange bed. ED is not economical for the produc tion of potable water from seawater. Paradoxically, it is also used for the concentration of seawater from 3.5 to 20 percent salt. The concentration of monovalent ions and selective removal of divalent ions from seawater uses special membranes. This process is unique to Japan, where by law it is used to produce essentially all of its domestic table salt. ED is very widely used for deashing whey, where the desalted product is a useful food additive, especially for baby food. 

This case history illustrates the paradox so often encountered in microbiologically influenced corrosion. Clearly, two corrosion mechanisms were operating in the system, namely, acid attack and microbiologically influenced corrosion. To what degree each mechanism contributed to wastage is difficult to quantify after the fact. This was especially the case here, since other areas of the rolling oil system were attacked by a predominantly acidic form of corrosion. 

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