Precipitation theoretical considerations

For simplicity, the basic theoretical considerations of electrostatic precipitation are given in terms of cylindrical geometry, i.e., pipe-type electrostatic precipitation. This makes it possible to show most of the basic principles without numerical modeling. 

When our work started, the phase transitions was observed only for weakly charged networks of PAA gels swollen in the mixtures of water (good solvent) with acetone (precipitant) of different compositions. The first stage of our work was the investigation of the nature and polarity of a precipitant on the position and the amplitude of the phase transition. According to the results of theoretical consideration of Refs. [7,18,20], the transition point and the value of the jump of the volume are primarily determined by the network structure and by the parameter of polymer-solvent interaction Xns- By smoothly changing the composition of the binary solvent, it is possible to vary effective value of the Xns parameter and to convert the network to a collapsed state. In this case, the amplitude of phase transition should not depend on the nature of precipitant. 

Studies on the interaction between oppositely charged polyelectrolytes date back to 1896 when Kossel389 precipitated egg albumin with protamine. Since that time extensive studies have been made on pairs of strong polyelectrolytes, pairs of strong and weak polyelectrolytes, pairs of weak polyelectrolytes, as well as on amphoteric complexes. However, the theoretical considerations of intermacromolecular interactions between polyelectrolytes were only based on extremely simplified model systems. However, even in the case of such systems, there are many unsolved problems such as the determination of the local dielectric constant in domains of macromolecular chains, the evaluation of other secondary binding forces, especially hydrophobic interactions, and so on. 

Eriksson E (1965) Deuterium and oxygen-18 in precipitation and other natural waters some theoretical considerations. Tellus 18 498-512 Faure, G (1977) Principles of Isotope Geology. Wiley, New York... 

Only a small fractionation is associated with the precipitation of snlfates in seawater. Theoretical considerations as well as snlfur-isotope measurements in natural environments revealed an isotopic difference between seawater sulfate and... 

This convention is justified by its convenience, provided that (Section 1.4.2) there are no sudden inflection points in the neutralization curve of the must or wine at the pK of the organic acids present, as their buffer capacities overlap, at least partially. In addition to these somewhat theoretical considerations, there are also some more practical issues. An aqueous solution of sodium hydroxide is used to determine the titration curve of a must or wine, in order to measnre total acidity and buffer capacity. Sodium, rather than potassium, hydroxide is used as the sodium salts of tartaric acid are soluble, while potassium bitartrate would be likely to precipitate out during titration. It is, however, questionable to use the same aqueous sodium hydroxide solution, which is a dilute alcohol solution, for both must and wine. 

A reasonable theory of agglutination and precipitation, the framework theory (lattice theory ), was proposed in 1934 by Marrack (6), and has received strong support from the theoretical considerations and experiments of Heidelberger (9,14, 15) and Pauling (18,19, 20, 28) and their collaborators. 

Solubility of the precipitate in excess of antiserum has been reported for a few systems, such as diphtheria toxin and horse antitoxin, but not for antigen-antibody systems in general. Theoretical considerations indicate that solubility in antibody excess should occur for antigens wi small valence (such as the dihaptenic substances of Table IV) but not for antigens with large valence, which would only witii difificulty be saturated with antibody to form a soluble complex. 

Theoretical considerations indicate that the smaller nanoparticles may be more toxic due to their large specific surface areas. Thus, factors that promote coagulation and precipitation of nanoparticles in the environment will probably decrease their toxicity. 

The extent to which the solubility product must be exceeded (i.e., the amount of supersaturation) before precipitation occurs depends on several factors, such as the stability, composition, and crystal structure of the precipitating BX j, phase. For instance, if the crystal structure and lattice dimensions of BXj, are such that it can form a coherent interface with the alloy matrix, only a small amount of supersaturation is probably necessary for BX precipitation. As discussed by Gesmundo et al. (1998), the degree of supersaturation is alloy-depen-dent and can be quite large. Methods of predicting the amount of supersaturation necessary from theoretical considerations have not yet been developed. 

The possibility to fractionally precipitate ions as a function of the solution s pH value is important in qualitative as well as quantitative analysis. Indeed, by a judicious adjustment of the solution s pH (with the help of the theoretical considerations... 

We must be convinced here that we have given theoretical considerations. From a practical standpoint, a local excess of hydroxide ions in the solution may appear during the addition of a strong base (delivered in order to precipitate and separate the metallic hydroxide). The local excess may be the cause of the hydroxide precipitation, although, theoretically, it is soluble in these conditions. Some metallic ions may be trapped in it as a result. This is the reason why the alkali must be added slowly and with homogenization. It must also be known that the equilibrium between the hydroxide preeipitate and the solution is often slowly attained because of the slow evolution of the precipitate. It is sometimes possible to quantitatively describe this parasitic phenomenon by handling several solubility products according to the state of the precipitate. As a result, several solubility eurves exist. 

Representative Method The best way to appreciate the importance of the theoretical and practical details discussed in the previous section is to carefully examine the procedure for a typical precipitation gravimetric method. Although each method has its own unique considerations, the determination of Mg + in water and waste-water by precipitating MgNH4P04 6H2O and isolating Mg2P20y provides an instructive example of a typical procedure. 

Iron Precipitation. Rich sulfide ore or Hquated antimony sulfide (cmde antimony) is reduced to metal by iron precipitation. This process, consisting essentially of heating molten antimony sulfide ia cmcibles with slightly more than the theoretical amount of fine iron scrap, depends on the abihty of iron to displace antimony from molten antimony sulfide. Sodium sulfate and carbon are added to produce sodium sulfide, or salt is added to form a light fusible matte with iron sulfide and to faciHtate separation of the metal. Because the metal so formed contains considerable iron and some sulfur, a second fusion with some Hquated antimony sulfide and salt foHows for purification. 

Several reported chemical systems of gas-liquid precipitation are first reviewed from the viewpoints of both experimental study and industrial application. The characteristic feature of gas-liquid mass transfer in terms of its effects on the crystallization process is then discussed theoretically together with a summary of experimental results. The secondary processes of particle agglomeration and disruption are then modelled and discussed in respect of the effect of reactor fluid dynamics. Finally, different types of gas-liquid contacting reactor and their respective design considerations are overviewed for application to controlled precipitate particle formation. 

An increased hydrogen ion concentration, that is a considerably greater amount of acid than the theoretical two equivalents of Scheme 2-1, is necessary in the diazotization of weakly basic amines. The classic example of this is the preparation of 4-nitrobenzenediazonium ions 4-nitroaniline is dissolved in hot 5-10 m HC1 to convert it into the anilinium ion and the solution is either cooled quickly or poured onto ice. In this way the anilinium chloride is precipitated before hydrolysis to the base can occur. On immediate addition of nitrite, smooth diazotization can be obtained. The diazonium salt solution formed should be practically clear and should not become cloudy on standing in the dark. Some practice is necessary, and details can be found in the books emphasizing preparative aspects (Fierz-David and Blangey, 1952 Saunders and Allen, 1985 in Houben-Weyl, Vol. E 16a, Part II, the chapter written by Engel, 1990). These books give a series of detailed prescriptions for specific examples and a useful review of the principal variations of the methods of diazotization. Such reviews have also been written by Putter (1965) and Schank (1975). 

After the last precipitation, the fra-nitrocinnamic acid is washed with a little water and then sucked as dry as possible (Note 5). The product, which still contains considerable water, is dissolved in 250-300 cc. of boiling 95 per cent alcohol from which the nitrocinnamic acid crystallizes on cooling. The yield amounts to 47-49 g. (74—77 per cent of the theoretical amount). 

The Si02/Al203 ratios vary from 84 100 (Ross and Kerr, 1934, report a low value of 74 100) to 197 100. Most values are considerably lower than the theoretical value 200 100 of the kaolinite minerals. It appears that when silica and alumina precipitate, alumina is usually in excess of that required for a stable 1 1 structure. 

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