Coefficient solid hydrate

Later Fajans and Karagunis (64) showed that for alkali halides, enthalpies of solution, osmotic coefficients, and the tendency to form solid hydrates follow gradations rather analogous to those of the solubilities. 

C. Formation of Chlorine Hydrate. Because of the presence of traces of water in compressed chlorine, the chlorine hydrate discussed in Section 9.1.3.5 again becomes a problem. As chlorine condenses, some of the water accompanies it. Depending on the temperature, a certain amount of water is soluble in the chlorine. So long as this solubility is not exceeded, the condensate remains homogeneous and solid hydrate does not form. Below we develop an estimate of the solubility of water in liquid chlorine and show that, because of its very low solubility in chlorine and therefore its very high activity coefficient in solution, it behaves as a volatile component. The practical effect of this is that water tends to concentrate in the gas phase in most first-stage liquefiers. 

Many ionic compounds can have water molecules incorporated into their solid structures. Such compounds are called hydrates. To emphasize the presence of discrete water molecules in the chemical structure, the formula of any hydrate shows the waters of hydration separated from the rest of the chemical formula by a dot. A coefficient before H2 O indicates the number of water molecules in the formula. Copper(II) sulfate pentahydrate is a good example. The formula of this beautiful deep blue solid is C11SO4 5 H2 O, indicating that five water molecules are associated with each CuSOq unit. Upon prolonged heating, CuSOq 5 H2 O loses its waters of hydration along with its color. Other examples of hydrates include aluminum nitrate nonahydrate, A1 (N03)3 9 H2 O,... 

In principle, Gibbs free energies of transfer for trihalides can be obtained from solubilities in water and in nonaqueous or mixed aqueous solutions. However, there are two major obstacles here. The first is the prevalence of hydrates and solvates. This may complicate the calculation of AGtr(LnX3) values, for application of the standard formula connecting AGt, with solubilities requires that the composition of the solid phase be the same in equilibrium with the two solvent media in question. The other major hurdle is that solubilities of the trichlorides, tribromides, and triiodides in water are so high that knowledge of activity coefficients, which indeed are known to be far from unity 4b), is essential (201). These can, indeed, be measured, but such measurements require much time, care, and patience. 

Fig. 5A The dependence on pH of the deuterium isotope effect in the hammerhead ri-bozyme-catalyzed reaction. Black circles show rate constants in H2O gray circles show rate constants in D2O. Solid curves are experimentally determined curves. The apparent plateau of cleavage rates above pH 8 is due to disruptive effects on the deprotonation of uridine and guanosine residues. Dotted lines are theoretical lines calculated from pKa values of hydrated Mg ions of 11.4 in H2O and 12.0 in D2O and on the assmnption that there is no intrinsic isotope effect (a=kH2o/kD2o=l is the coefficient of the intrinsic isotope effect). The following equation was used to plot the graph of pL vs log(rate) log kobs=log(kmax)-log(l+10

Just as an increase in solids-not-fat increases milk density, so does the removal of water by processing. If there were no changes in physical state or chemical activity coefficients (e.g., hydration of proteins or insolubilization of salts), the density of the concentrated milk could be calculated from an equation derived by Jenness (1962) and presented in the second edition of this book. Data presented by Mojonnier and Troy (1922) conform to the equation but lack sufficient precision to indicate the small changes associated with some of the changes in physical state. 

The initial predictive method by Wilcox et al. (1941) was based on distribution coefficients (sometimes called Kvsi values) for hydrates on a water-free basis. With a substantial degree of intuition, Katz determined that hydrates were solid solutions that might be treated similar to an ideal liquid solution. Establishment of the Kvsj value (defined as the component mole fraction ratio in the gas to the hydrate phase) for each of a number of components enabled the user to determine the pressure and temperature of hydrate formation from mixtures. These Kysi value charts were generated in advance of the determination of hydrate crystal structure. The method is discussed in detail in Section 4.2.2. 

Carson and Katz noted that their experimental hydrate composition changed at different temperatures and pressures in a manner indicative of a solid solution of mixtures, rather than segregated macroscopic quantities of pure hydrocarbons within the hydrate. The concept of a solid solution enabled the notion of the mole fraction of a guest component in the solid phase hydrate mixture, on a water-free basis. Carson and Katz defined a vapor-solid distribution coefficient (KVSi) for each component as... 

For immobilized lipase preparations, a more complex mechanism is expected to occur since esterification efficiency is also highly dependent on the hydration state of the enzyme preparation, which can be greatly modified by the nature of the substrate and the support (1,4)- In the case of butyl butyrate synthesis, analysis of substrate polarity measured as partition coefficient (Table 1) showed a higher value for butanol than for butyric acid, favoring butanol migration to the solid phase (immobilized lipase). Thus, there should be more alcohol than acid at the active site of the immobilized lipase, requiring an excess of acid in the reaction medium to provide equimolar amounts of reactants and satisfactory yields (7). 

Here A//adS is the enthalpy of adsorption, T is the temperature, and AAads is the entropy change associated with the adsorption of the protein onto the surface. Protein adsorption will take place if AGads < 0. Considering a complex system, where proteins are dissolved in an aqueous environment, and are brought into contact with an artificial interface, there are a vast number of parameters that impact AGads due to their small size (i.e., large diffusion coefficient), water molecules are the first to reach the surface when a solid substrate is placed in an aqueous biological environment. Hence, a hydrate layer is formed. With some delay, proteins diffuse to the interface and competition for a suitable spot for adsorption starts. This competition... 

One of the most successful applications of crystal field theory to transition metal chemistry, and the one that heralded the re-discovery of the theory by Orgel in 1952, has been the rationalization of observed thermodynamic properties of transition metal ions. Examples include explanations of trends in heats of hydration and lattice energies of transition metal compounds. These and other thermodynamic properties which are influenced by crystal field stabilization energies, including ideal solid-solution behaviour and distribution coefficients of transition metals between coexisting phases, are described in this chapter. 

Zone chromatography is a variant of the zone melting method, in which the mixture being separated is introduced into a column with a solid solvent and a molten zone is passed repeatedly along the length of the column to separate mixtures into separate bands of their components. Zone chromatography has been used for the separation of mixtures of lanthanides for preparative and analytical purposes The chelates used were mixtures of hydrated / -diketonates and their adducts with 2,2 -bipyridyl (bipy) and acety-lacetonimines. The distribution coefficients of different chelates and binary mixtures have been determined . 

Pure solid + fluid phase equilibrium calculations are challenging but can, in principle, be modeled if the triple point of the pure solid and the enthalpy of fusion are known, the physical state of the solid does not change with temperature and pressure, and a chemical potential model (or equivalent), with known coefficients, for solid constituents is available. These conditions are rarely met even for simple mixtures and it is difficult to generalize multiphase behavior prediction results involving even well-defined solids. The presence of polymorphs, solid-solid transitions, and solid compounds provide additional modeling challenges, for example, ice, gas hydrates, and solid hydrocarbons all have multiple forms. 

By treating the Krafft point as the melting point of the hydrated solid surfactant, the partition coefficient of the solute can be calculated from its effect on the Krafft point. Simple thermodynamic considerations lead to the following relationship at low mole fractions of solute in the micellar phase ... 

Figure 2 shows a representation of the resin-solvent-solute components of a column chromatographic system. The column is filled with resin beads of the solid stationary phase packed together with the voids between the beads filled with solvent. The phases of interest are (i) the liquid phase between the resin beads, (ii) the liquid phase held within the resin beads and (Hi) the solid phase of the polymeric matrix of the resin beads. When the feed solution is placed in contact with the hydrated resin in the chromatographic column, the solutes distribute themselves between the liquid inside the resin and that between the resin beads. The distribution for component i is defined by the distribution coefficient,... 

Table 21.2. Specific conductivity a, proton self-diffusion coefficient D, and residence time between reorientations v esfor some hydrated solid state protonic conductors... 

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