Appreciation

As discussed in Chapter 3, at moderate pressures, vapor-phase nonideality is usually small in comparison to liquid-phase nonideality. However, when associating carboxylic acids are present, vapor-phase nonideality may dominate. These acids dimerize appreciably in the vapor phase even at low pressures fugacity coefficients are well removed from unity. To illustrate. Figures 8 and 9 show observed and calculated vapor-liquid equilibria for two systems containing an associating component. 

To illustrate calculations for a binary system containing a supercritical, condensable component. Figure 12 shows isobaric equilibria for ethane-n-heptane. Using the virial equation for vapor-phase fugacity coefficients, and the UNIQUAC equation for liquid-phase activity coefficients, calculated results give an excellent representation of the data of Kay (1938). In this case,the total pressure is not large and therefore, the mixture is at all times remote from critical conditions. For this binary system, the particular method of calculation used here would not be successful at appreciably higher pressures. 

Calculate the weighted network area Anetwork from Eq. (7.22). When the weighted h values i4>h) vary appreciably, say, by more than one order of magnitude, an improved estimate of Anetwork can be evaluated by linear programming. ... 

The list of contributors is on page 6 and I am deeply indebted to them, for it is they who originally prepared MiaU s Dictionary of Chemistry from which this Dictionary has been compiled. Errors and omissions are my responsibility and 1 would appreciate receiving notice of them. 

If an appreciable current flows between the electrode and the solution, thus disturbing the reversible thermodynamic equilibrium conditions, the electrode is said to be polarized and the system is then operating under irreversible conditions. 

Finally it is likely that attention will be focused on emissions of polynuclear aromatics (PNA) in diesel fuels. Currently the analytical techniques for these materials in exhaust systems are not very accurate and will need appreciable improvement. In conventional diesel fuels, emissions of PNA thought to be carcinogenic do not exceed however, a few micrograms per km, that is a car will have to be driven for several years and cover at least 100,000 km to emit one gram of benzopyrene for example These already very low levels can be divided by four if deeply hydrotreated diesel fuels are used. 

The basics of the method are simple. Reflections occur at all layers in the subsurface where an appreciable change in acoustic impedance is seen by the propagating wave. This acoustic impedance is the product of the sonic velocity and density of the formation. There are actually different wave types that propagate in solid rock, but the first arrival (i.e. fastest ray path) is normally the compressional or P wave. The two attributes that are measured are... 

Whereas faults displace formerly connected lithologic units, fractures do not show appreciable displacement. They also represent planes of brittle failure and affect hard... 

As is evident firom the theory of the method, h must be the height of rise above a surface for which AP is zero, that is, a flat liquid surface. In practice, then, h is measured relative to the surface of the liquid in a wide outer tube or dish, as illustrated in Fig. n-6, and it is important to realize that there may not be an appreciable capillary rise in relatively wide tubes. Thus, for water, the rise is 0.04 mm in a tube 1.6 cm in radius, although it is only 0.0009 mm in one of 2.7-cm radius. 

The next point of interest has to do with the question of how deep the surface region or region of appreciably unbalanced forces is. This depends primarily on the range of intermolecular forces and, except where ions are involved, the principal force between molecules is of the so-called van der Waals type (see Section VI-1). This type of force decreases with about the seventh power of the intermolecular distance and, consequently, it is only the first shell or two of nearest neighbors whose interaction with a given molecule is of importance. In other words, a molecule experiences essentially symmetrical forces once it is a few molecular diameters away from the surface, and the thickness of the surface region is of this order of magnitude (see Ref. 23, for example). (Certain aspects of this conclusion need modification and are discussed in Sections X-6C and XVII-5.)... 

We have considered the surface tension behavior of several types of systems, and now it is desirable to discuss in slightly more detail the very important case of aqueous mixtures. If the surface tensions of the separate pure liquids differ appreciably, as in the case of alcohol-water mixtures, then the addition of small amounts of the second component generally results in a marked decrease in surface tension from that of the pure water. The case of ethanol and water is shown in Fig. III-9c. As seen in Section III-5, this effect may be accounted for in terms of selective adsorption of the alcohol at the interface. Dilute aqueous solutions of organic substances can be treated with a semiempirical equation attributed to von Szyszkowski [89,90]... 

Although Gibbs published his monumental treatise on heterogeneous equilibrium in 187S, his work was not generally appreciated until the turn of the century, and it was not until many years later that the field of surface chemistry developed to the point that experimental applications of the Gibbs equation became important. 

If a mass of some substance were placed on a liquid surface so that initially it is present in a layer of appreciable thickness, as illustrated in Fig. IV-1, then two possibilities exist as to what may happen. These are best treated in terms of what is called the spreading coefficient. 

Spreading velocities v are on the order of 15-30 cm/sec on water [39], and v for a homologous series tends to vary linearly with the equilibrium film pressure, it", although in the case of alcohols a minimum seemed to be required for v to be appreciable. Also, as illustrated in Fig. IV-3, substrate water is entrained to some depth (0.5 mm in the case of oleic acid), a compensating counterflow being present at greater depths [40]. Related to this is the observation that v tends to vary inversely with substrate viscosity [41-43]. An analysis of the stress-strain situation led to the equation... 

Streaming potential measurements are to be made using a glass capillary tube and a particular electrolyte solution, for example, O.OIM sodium acetate in water. Discuss whether the streaming potential should or should not vary appreciably with temperature. 

There is appreciable contact angle hysteresis for many of the systems reported in Table X-2 the customary practice of reporting advancing angles has been followed. 

The extensive use of the Young equation (Eq. X-18) reflects its general acceptance. Curiously, however, the equation has never been verified experimentally since surface tensions of solids are rather difficult to measure. While Fowkes and Sawyer [140] claimed verification for liquids on a fluorocarbon polymer, it is not clear that their assumptions are valid. Nucleation studies indicate that the interfacial tension between a solid and its liquid is appreciable (see Section K-3) and may not be ignored. Indirect experimental tests involve comparing the variation of the contact angle with solute concentration with separate adsorption studies [173]. 

There is a number of very pleasing and instructive relationships between adsorption from a binary solution at the solid-solution interface and that at the solution-vapor and the solid-vapor interfaces. The subject is sufficiently specialized, however, that the reader is referred to the general references and, in particular, to Ref. 153. Finally, some studies on the effect of high pressure (up to several thousand atmospheres) on binary adsorption isotherms have been reported [154]. Quite appreciable effects were found, indicating that significant partial molal volume changes may occur on adsorption. 

Thus, to encourage wetting, 7sl and 7lv should be made as small as possible. This is done in practice by adding a surfactant to the liquid phase. The surfactant adsorbs to both the liquid-solid and liquid-vapor interfaces, lowering those interfacial tensions. Nonvolatile surfactants do not affect 7sv appreciably (see, however. Section X-7). It might be thought that it would be sufficient merely to lower ytv and that a rather small variety of additives would suffice to meet all needs. Actually it is equally if not more important that the surfactant lower 7sL> and each solid will make its own demands. 

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