Idealized composition

Batch reactors often are used to develop continuous processes because of their suitabiUty and convenient use in laboratory experimentation. Industrial practice generally favors processing continuously rather than in single batches, because overall investment and operating costs usually are less. Data obtained in batch reactors, except for very rapid reactions, can be well defined and used to predict performance of larger scale, continuous-flow reactors. Almost all batch reactors are well stirred thus, ideally, compositions are uniform throughout and residence times of all contained reactants are constant. 

The only commercial ore, chromite [1308-31-2], which is also called chromite ore, chrome ore, and chrome, has the ideal composition Fe0-Cr2 03, ie, 68 wt % Cr202, 32 wt % FeO, or ca 46 wt % chromium. Actually the Cr Fe ratio varies considerably and the ores are better represented as (Fe,Mg)0-(Cr,Fe,Al)203. Table 1 gives the classification of chromite ores. 

Gaseous SO2 is readily soluble in water (3927 cm SO2 in lOOg H2O at 20°). Numerous species are present in this aqueous. solution of sulfurous acid" (p. 717). At 0° a cubic clathrate hydrate also forms with a composition S02.6H20 it.s dissociation pressure reaches I atm at 7.1°. The ideal composition would be SO2.55H2O (p. 627). 

Noble gas hydrates are formed similarly when water is frozen under a high pressure of gas (p. 626). They have the ideal composition, [Gg(H20)46], and again are formed by Ar, Kr and Xe but not by He or Ne. A comparable phenomenon occurs when synthetic zeolites (molecular sieves) are cooled under a high pressure of gas, and Ar and Kr have been encapsulated in this way (p. 358). Samples containing up to 20% by weight of Ar have been obtained. 

Oxides of the actinides are refractory materials and, in fact, Th02 has the highest mp (3390°C) of any oxide. They have been extensively studied because of their importance as nuclear fuels. However, they are exceedingly complicated because of the prevalence of polymorphism, nonstoichiometry and intermediate phases. The simple stoichiometries quoted in Table 31.5 should therefore be regarded as idealized compositions. 

At a given ideal composition, two or more types of defects are always present in every compound. The dominant combinations of defects depend on the type of material. The most prominent examples are named after Frenkel and Schottky. Ions or atoms leave their regular lattice sites and are displaced to an interstitial site or move to the surface simultaneously with other ions or atoms, respectively, in order to balance the charge and local composition. Silver halides show dominant Frenkel disorder, whereas alkali halides show mostly Schottky defects. 

There seem to be many binary metallic systems in which there are phases of this sort. In the sodium-lead system there are two such phases. One of them, based on the ideal structure Na3Pb, extends from 27 to 30 atomic percent lead, with its maximum at about 28 atomic percent lead and the other, corresponding to the ideal composition NaPb3, extends from 68 to 72 atomic percent lead, with maximum at about 70 atomic percent. The intensities of X-ray reflection have verified that in the second of these phases sodium atoms occupy the positions 0, 0, 0, and the other three positions in the unit cell are occupied by lead atoms isomorphously replaced to some extent by sodium atoms (Zintl Harder, 1931). These two phases are interesting in that the ranges of stability do not include the pure compounds Na8Pb and NaPb3. 

The ideal composition CrYI does not seem to be attained in all cases (see Table XII). Whether this is due to the existence of extended phases (e.g., CrSIi j) or represents an individual phase is not known. The compounds are described as black, and sensitive to air. Additional work should be done for the chromium system. 

The ideal composition of Prussian blue is Fe(III)4[Fe(II)(CN)g]3.15H2O. The crystal structure is cubic. All Fe(III) lattice sites are occupied, whereas those of Fe(II) are only 75% occupied. At low temperatures the paramagnetic Fe(III) ions order ferromagnetically (T = 5.6 K). Finally we note that upon replacing Fe(II) by Ru(II) or Os(II) the color properties are not drastically influenced. 

The method can be illustrated by reference to a classical 1933 study of the defects present in wilstite, iron monoxide. Wustite adopts the sodium chloride (NaCl) structure, and the unit cell should contain 4 Fe and 4 O atoms in the unit cell, with an ideal composition FeOi.o, but in reality the composition is oxygen rich and the unit cell dimensions also vary with composition (Table 1.1). Because there is more oxygen present than iron, the real composition can be obtained by assuming either that there are extra oxygen atoms in the unit cell (interstitial defects) to give a composition FcO 1 +v, or that there are iron vacancies present, to give a formula Fci-JD. It is... 

Uranium oxides are of importance in the nuclear industry, and for this reason considerable effort has been put into understanding their nonstoichiometric behavior. The dioxide, U02 crystallizes with the fluorite structure with an ideal composition MX2 (Fig. 4.7a) but is readily prepared in an oxygen-rich form. In this state it is... 

The spinel blocks in (3-alumina are related by mirror planes that mn through the conduction planes that is, the orientation of one block relative to another is derived by a rotation of 180°. A second form of this compound, called (3"-alumina, has similar spinel blocks. However, these are related to each other by a rotation of 120°, so that three spinel block layers are found in the unit cell, not two. The ideal composition of this phase is identical to that of (3-alumina, but the unit cell is now rhombohedral. Referred to a hexagonal unit cell, the lattice parameters are a = 0.614 nm, c = 3.385 nm. The thickness of the spinel blocks and the conduction planes is similar in both structures.3... 

Continuous stirred tank reactor (CSTR) an agitated tank reactor with a continuous flow of reactants into and products from the agitated reactor system ideally, composition and temperature of the reaction mass is at all times identical to the composition and temperature of the product stream. 

Minerak Composition (Idealized) Composition (unit cell) Framework Density (g/cc) Dimensions of Main Channel Ways (nm) ... 

Point defects are also highly prominent in the Tl,Pb,Bi/Ba,Sr,-Ca/Cu/O superconductors. Cation vacancies frequently occur. Some T1 is found on Ca sites, and there is evidence for Ca on the Sr/Ba site. Some Bi is found on both Sr and Ca sites. Both oxygen interstitials and vacancies apparently can occur. Present evidence suggests that compounds with the ideal structures and compositions would not be metallic or superconducting. There are also strong indications that these materials at their ideal compositions are in fact too unstable to be prepared. 

For other minerals, such as pyrrhotite (and, in Table 4, an ideal composition of FeS is assumed, rather than the more realistic Fc 1 AS), galena or sphalerite, the following equations may apply ... 

The most important effects of the fiber tensile stress falling away to zero at the ends are rednctions in the axial tensile modnlns and strength of the composite. Consider the idealized composite shown in Figure 5.94, where the short fibers are in parallel, and an imaginary (dash) fine is drawn across the composite at right angles to the fibers. It can be shown that the stress carried by the composite, cti, is given by... 

Calculate the overall Ca and Si contents (expressed as CaO and Si02) of a Portland cement clinker that has 55% alite, 30% belite, 5% alumi-nate phase, and 10% ferrite (assume ideal compositions for the latter two). Would you expect this to behave as a fast or a slow setting cement ... 

Figure 1. Representation of the ideal compositions of some major phyllosilicate phases in the MR - 2R - 3R coordinates. M = muscovite, paragonite P - phlogopite Py = pyrophyllite Kaol = kaolinite S serpentine T = talc Chlor = chlorite, 14 8 or aluminous 7 8 polymorphs Ce = celadonite F = feldspar.

As we have seen in the previous section, the bulk chemical compositions of montmorillonites taken from the literature are dispersed over the field of fully expandable, mixed layered and even extreme illite compositions. Just what the limits of true montmorillonite composition are cannot be established at present. We can, nevertheless, as a basis for discussion, assume that the ideal composition of beidellite with 0.25 charge per 10 oxygens and of montmorillonite with the same structural charge do exist in nature and that they form the end-members of montmorillonite solid solutions. Using this assumption one can suppose either solid solution between these two points or intimate mixtures of these two theoretical end-member fully expandable minerals. In either case the observable phase relations will be similar, since it is very difficult if not impossible to distinguish between the two species by physical or chemical methods should they be mixed together. As the bulk chemistry of the expandable phases suggests a mixture of two phases, we will use this hypothesis and it will be assumed here that the two montmorillonite... 

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