Hypothetical solubility

FIGURE 1 Hypothetical solubility diagram of eutectic-forming system. 

FIGURE 4 Hypothetical solubility diagram of mixture without a eutectic at constant pressure x, solid y, liquid z, combined. 

The constant K s represents the slope of the graph, and the constant /S is given by the point of intersection of the straight line with the vertical axis and represents the logarithm of a hypothetical solubility at zero electrolyte concentration. 

If in equation 12 0/, < 1 (AG is negative), CaC03(s) will dissolve if Q/ Ks > 1, CaC03 will precipitate. The saturation test may often be made by simply comparing the activity (or concentration) of an individual reaction component, for example, in equation 12, with the activity (or concentration) this component would have if it were in hypothetical solubility equilibrium. Thus the state of saturation of CaC03(s) may be interpreted in the following way ... 

The quasi-equilibrium approximation relies on the assumption that there is a single rate-determining step, the forward and reverse rate constants of which are at least 100 times smaller than those of all other reaction steps in the kinetic scheme. It is then assumed that all steps other than the rds are always at equilibrium and hence the forward and reverse reaction rates of each non-rds step may be equated. This gives simple potential relations describing the varying activity of reaction intermediates in terms of the stable solution species (of known and potential-independent activity) that are the initial reactants or final products of the reaction. The variation of the activities of reaction intermediates is, however, restricted by either the hypothetical solubility limit of these species or, in the case of surface-confined reactions and adsorbed intermediates, the availability of surface sites. In both these cases, saturation or complete coverage conditions would result in a loss of the expected... 

Fig 6 Correlation between complex dissociation constant, (lOO-lOOOO) dissolution volume (10-1000 ml), and dissolved drug in % (Free + complexed). Hypothetic solubility of the complex 10" mol/l. Black area free dissolved drug, vertically hatched area dissolved complexed drug. 

Since the number known data of hypothetical solubilities is quite limited, SVR should be the suitable method to find the mathematical model describing the relationship between the hypothetical solubilities and the molecular parameters of solvents. 

By SVR-based feature selection, it has been found that a feature set consisting of 8, n and p can be used for mathematical modeling of the hypothetical solubility of Ceo in various solvents [144], Figure 7.2 illustrates the correlation between the values of hypothetical solubility and the values calculated by SVR using the above-mentioned three parameters,... 

Fig. 7.2 Correlation between the values of hypothetical solubility and the values calculated by SVR.

Antimony trioxide is insoluble in organic solvents and only very slightly soluble in water. The compound does form a number of hydrates of indefinite composition which are related to the hypothetical antimonic(III) acid (antimonous acid). In acidic solution antimony trioxide dissolves to form a complex series of polyantimonic(III) acids freshly precipitated antimony trioxide dissolves in strongly basic solutions with the formation of the antimonate ion [29872-00-2] Sb(OH) , as well as more complex species. Addition of suitable metal ions to these solutions permits formation of salts. Other derivatives are made by heating antimony trioxide with appropriate metal oxides or carbonates. 

Solubility. Sohd—Hquid equihbrium, or the solubiHty of a chemical compound in a solvent, refers to the amount of solute that can be dissolved at constant temperature, pressure, and system composition in other words, the maximum concentration of the solute in the solvent at static conditions. In a system consisting of a solute and a solvent, specifying system temperature and pressure fixes ah. other intensive variables. In particular, the composition of each of the two phases is fixed, and solubiHty diagrams of the type shown for a hypothetical mixture of R and S in Figure 2 can be constmcted. Such a system is said to form an eutectic, ie, there is a condition at which both R and S crystallize into a soHd phase at a fixed ratio that is identical to their ratio in solution. Consequently, there is no change in the composition of residual Hquor as a result of crystallization. 

When speculating about the hypothetical structure of interfaces with minimal free energy, the diffuse interfaces formed by the properly grafted water-soluble... 

Fig. 5 Dissolution profiles obtained from the solubility determination of two polymorphic forms of the same drug substance. A is the stable form with solubility 31 mg/mL. B is the profile of the metastable form with solubility 46 mg/mL. This solubility (circles) is not achieved in many instances, and precipitation of the stable form occurs at a point beyond the solubility of A, and the trace becomes B. C is the hypothetical profile of the metastable form. 

Inferred from this model is the relative independence of the effects of solubility and partitioning. For each property there is a characteristic threshold above which the log of the flux increases more slowly than below it, and the value of the threshold for one variable is not very dependent on the value of the other variable. This tabletop perspective has led to the name mesa model. The relative independence signifies that neither property can totally compensate for a deficiency in the other. This is not to say that these properties are independent of one another in a chemical sense—quite the contrary. However, in the hypothetical sense that if one property were varied independently of the other, then the consequences on flux are relatively independent. Clearly dependence... 

Oxidation-reduction electrodes. An inert metal (usually Pt, Au, or Hg) is immersed in a solution of two soluble oxidation forms of a substance. Equilibrium is established through electrons, whose concentration in solution is only hypothetical and whose electrochemical potential in solution is expressed in terms of the appropriate combination of the electrochemical potentials of the reduced and oxidized forms, which then correspond to a given energy level of the electrons in solution (cf. page 151). This type of electrode differs from electrodes of the first kind only in that both oxidation states can be present in variable concentrations, while, in electrodes of the first kind, one of the oxidation states is the electrode material (cf. Eqs 3.1.19 and 3.1.21). 

In modern terms, asphaltene is conceptually defined as the normal-pentane-insoluble and benzene-soluble fraction whether it is derived from coal or from petroleum. The generalized concept has been extended to fractions derived from other carbonaceous sources, such as coal and oil shale (8,9). With this extension there has been much effort to define asphaltenes in terms of chemical structure and elemental analysis as well as by the carbonaceous source. It was demonstrated that the elemental compositions of asphaltene fractions precipitated by different solvents from various sources of petroleum vary considerably (see Table I). Figure 1 presents hypothetical structures for asphaltenes derived from oils produced in different regions of the world. Other investigators (10,11) based on a number of analytical methods, such as NMR, GPC, etc., have suggested the hypothetical structure shown in Figure 2. 

As was discussed earlier in Section 1.2.8 a complication arises in that two of these properties (solubility and vapor pressure) are dependent on whether the solute is in the liquid or solid state. Solid solutes have lower solubilities and vapor pressures than they would have if they had been liquids. The ratio of the (actual) solid to the (hypothetical supercooled) liquid solubility or vapor pressure is termed the fugacity ratio F and can be estimated from the melting point and the entropy of fusion. This correction eliminates the effect of melting point, which depends on the stability of the solid crystalline phase, which in turn is a function of molecular symmetry and other factors. For solid solutes, the correct property to plot is the calculated or extrapolated supercooled liquid solubility. This is calculated in this handbook using where possible a measured entropy of fusion, or in the absence of such data the Walden s Rule relationship suggested by Yalkowsky (1979) which implies an entropy of fusion of 56 J/mol-K or 13.5 cal/mol-K (e.u.)... 

Figure 18.16 Hypothetical model for the metallobiology of AP in Alzheimer s disease. (From Bush, 2003. Copyright 2003, with permission from Elsevier.) The proposed sequence of events (1) concentration of iron and copper increase in the cortex with aging. There is an overproduction of APP and AP in an attempt to suppress cellular metal-ion levels. (2) Hyper-metallation of AP occurs which may facilitate H202 production. (3) Hyper-metallated AP reacts with H202 to generate oxidized and cross-linked forms, which are liberated from the membrane. (4) Soluble AP is released from the membrane and is precipitated by zinc which is released from the synaptic vesicles. Oxidized AP is the major component of the plaque deposits. (5) Oxidized AP initiates microglia activation. (6) H202 crosses cellular membranes to react with Cu and Fe, and generate hydroxyl radicals which oxidize a variety of proteins and lipids.

FIGURE 12.8 A graph showing how the solubility of a substance (in a hypothetical solvent) can change with temperature. 

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