Solubility plot

Unlike the crystalline cycloamylose complexes, combining ratios of host to guest in solution are usually 1 1. A notable exception is the interaction of the cycloamyloses with long chain aliphatic carboxylic acids. Solubility plots suggest that as many as four cycloheptaamylose molecules may interact with a single molecule of dodecanoic acid (Schlenk and Sand, 1961). In analogy to the crystalline state, cycloamyloses may form channels in solution in order to accomodate extended chains. 

Fig. 6 Phase solubility plot for an impure solute consisting of 75% of the analyte substance and 25% of an impurity.

Fig. 7 Phase solubility plot resulting from a positive solute interaction between the analyte substance and an impurity.

Polyhydroxyfullerenes, 72 251 Poly(hydroxystearic acid), solubility plots, S 685t... 

The solubility plots for lepidocrocite, ferrihydrite and hematite (Fig. 9.2) and for goethite, ferrihydrite and soil-Fe (Fig. 9.3) show only the total Fe activity. They were obtained in the same way as that for goethite using the appropriate constants from Tables 9.1, 9.2 and 9.4. 

As demonstrated by the pH - solubility plot generated with citric acid / citrate buffered solutions of indinavir free base monohydrate, the aqueous solubility of indinavir free base monohydrate increases with decreasing pH. The data points of this study aie given in Table 4, and plotted in Figure 9. 

For a weakly acidic compound at pHc pKa (e.g., by 2 units), the solubility is practically independent of pH and remains constant pKa, the solubility increases exponentially with pH, where the excess solid phase in equilibrium with the saturated solution is the free acid. At certain pH value, the log-linear relationship of solubility with pH abruptly ends, and the solubility plots enter a nearly constant range, where the excess solid phase is the salt. The pH value where the log-linear relationship ends and near constant solubility starts is the pH of maximum solubility pHmax- Forcompounds containing bothacidicand basic functional groups, the solubility of zwitterion (internal salt pair) at the isoelectric point is typically the lowest over the entire pH range. 

The model simulates an experimentally observed trend (25) that the solubility of chains in a SCF shows a strong inverse dependence on the molecular mass of the polymer. Figure 5 shows that changing the molecular weight of the chain molecule from 100 to 700 causes a reduction in solubility of nearly 6 orders of magnitude. The model also shows that all the solubility plots tend to flatten out around 300 bar, as observed in experiments (25). Classical EOS like a modified cubic EOS (2JD > when applied to such systems, produce solubility curves which tend to show a sharp maximum around 200 bar. For polymer-SCF systems, therefore, the lattice EOS is believed to be superior to modified cubic EOS. 

Figure 7. Solubility plot also showing the supersolubility curve.

Fig. 3.5 Fractions of the KjO, NajO, KjO + NajO (molar) and SO, that are water soluble, plotted against the molar ratio of total SO, to (total K,0 + total NbjO) for production clinkers (circles) and laboratory clinkers (squares). Recalculated from the data of Pollitt and Brown (P2).

All such points formed smooth curves when plotted on the three-component triangular graphs used for each system investigated except that of the potassium chloride-water-THF system. In the latter case, two solubility curves appeared which met in an invariant point. The solubility plots are shown in Figures 1, 2, and 3. 

The solubility plots shown in Figure 6.5-1 illustrate how the effect of temperature on solubility can vary from system to system. Increasing the temperature from 0°C to 100°C barely changes NaCl solubility but increases the solubility of KNO3 by more than a factor of 10. For Na2S04, solubility increases up to about 40°C and decreases thereafter. 

The effect of pKa on cocrystal solubility, plotted using a K p = 1 X 10 and pKa values of 5 and 2, is shown in Fig. 18. This plot shows that by lowering the pKa of the acid, higher cocrystal solubilities are achieved at lower pH. 

Fig. 1 illustrates that solubilization by ionization can be very efficient for a mono acidic or basic drug. The linear solubilization slope corresponds to a 10-fold increase in solubility for a one-unit change in pH. Zwitterionic compounds, which have both acidic and basic functional groups, will have a pH solubility plot... 

The. solubility of kaolinite in terms of ZAl(aq) versus pH, can be derived and graphed in the same way we have developed the AKOH) solubility plot, except that we must fix the concentration of dissolved silica. Thus, for example, we write ... 

As dissolution is usually an endothermic process, an increase in the solubility of solids with a rise in temperature is the general rule. Therefore, most graphs of solubility plotted against temperature show a continuous rise, but there are exceptions, for example, the solubility of sodium chloride is almost invariant, while that for calcium hydroxide falls slightly from a solubility of 0.185 g/mL at 0°C to 0.077 g/mL at 100°C. 

A schematic of change in the type of microemulsion with the salinity is shown in Figure 7.8, and a volume fraction diagram of the data presented in Table 7.2 is shown in Figure 7.9. The volume fraction information can also be represented by a solubility plot, as shown in Figure 7.10 (see page 254). We will see later that the solubilization ratio is a very important parameter in interfacial tension calculation. 

T is temperature, Ak is the change in compressibility caused by the reaction, V indicates partial molal volume, and sub- scripts refer to pressure in atmospheres. Determination of AV would allow calculation of stCOYOACaa) quantity necessary for predicting the direction of tne pressure effect for several geochemical reactions which are difficult to investigate experimentally, for exaniple, mineral formation at sea floor conditions. However, this calculation demands accuracy in knowledge of the atmospheric pressure solubility, and confidence in the reproducibility of the pressure versus solubility plots. 

Extracted pitch behavior is also dependent on the pltch/solvent ratio used for the separation. Altering ratios will affect both the weight percent dissolved, and the properties of an extract. Increasing the pltch/solvent ratio of a polar or hydrogen bonded solvent can decrease their effectiveness and shift and reduce the size of the enhanced solubility region on solubility plots. In this way an over-effective solvent can be moderated so it extracts a mesophase forming sample. 

Solubility Plots To investigate solubilities of oxides in molten salts as a function of melt basicity, experiments were carried out by Rapp and coworkers in molten Na2S04 at 1200 K [13]. The melt basicity was fixed by variation of the gas atmosphere containing p(S02) and p 02) and by addition of Na202 to the molten... 

Fig. 8 Solubility plots of various oxides in molten Na2S04 at 1200 K as a function of melt basicity a(Na20).

Fig. 9 Solubility plot of NiO in a (Lio.62Ko.38)2C03 mixture as a function of p(C02) in the gas phase at temperatures of 923 to 023 K.

There is still considerable merit, however, in favour of equation 3.7 because of its simple form and its usefulness in the graphical estimation of transition points. Conventional solubility plots, such as those shown in Figure 3.1, can prove unreliable for this purpose when only a few data points are available, especially when the points lie on one or more different curves. Solubilities plotted in accordance with equation 3.7 are shown in Figure 3.2. Mole fraction concentrations x are recorded on the logarithmic abscissa and values of 10 T ... 

Figure 2.6 Diagrammatic representation of a polymer solubility plot based on Hansen s parameter system. The dotted circles represent projections of the sphere of solubility . A specific example of these projections is shown in Figure 2.7.

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