Temperature-solubility relations

As with conventional detergents, bile salt-aqueous mixtures exhibit a typical temperature (CMT) which transforms the system into a clear micellar phase [3,5,6]. For most of the common bile salts (an account of the phase relations of common bile 

Bile salts carry extensive hydrophobic (hydrocarbon) portions in each molecule that attempt to reduce their contact with water (4). This is reflected in rapid, dynamic association-dissociation equilibrium to form self-aggregates or micelles as the total concentration of bile salt solute is increased (the CMC) [2-6]. Experimentally, micelles are undetectable in dilute solutions of the monomers, and are detected in increasing numbers and often size above the CMC [98]. Because bile salt micelles are often small (i.e., dimers) [5], and since self-aggregation continues to proceed in many cases with increasing concentration above the CMC [17,18,20,52,98], the detection of the lowest concentration at which the first aggregates form depends particularly upon the sensitivity of the experimental probes employed [98] and the physical-chemical conditions [3-5]. 

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The above set of equations can be solved numerically given input parameters, including surface tension a, temperature, solubility relation, D and p as a function of total H2O content (and pressure and temperature), initial bubble radius ao, initial outer shell radius Sq, initial total H2O content in the melt, and ambient pressure Pf. For example. Figure 4-14 shows the calculated bubble radius versus time, recast in terms of P versus t/tc to compare with the Avrami equation (Equation 4-70). 

The complicated solubility relations, rates of hydrolysis, sclf-disproportionation and intcrcon-version with other phosphates depends sensitively on pH, eoncentration, temperature and ihc presence of impurities.Though of great interest academically and of paramount imporlaree industrially these aspects will not be further considered Triphosphates such as... 

For the purpose of investigating solubility relations at a given temperature in three-component systems of the type discussed above, the proportion of nonsolvent which must be added to produce incipient precipitation may be observed as a function of the polymer concentration. Isothermal phase diagrams like that shown in Fig. 123 may... 

Apart from the qualitative observations made previously about suitable solvents for study, the subject of solvates has two important bearings on the topics of thermochemistry which form the main body of this review. The first is that measured solubilities relate to the appropriate hydrate in equilibrium with the saturated solution, rather than to the anhydrous halide. Obviously, therefore, any estimate of enthalpy of solution from temperature dependence of solubility will refer to the appropriate solvate. The second area of relevance is to halide-solvent bonding strengths. These may be gauged to some extent from differential thermal analysis (DTA), thermogravimetric analysis (TGA), and differential scanning calorimetry (DSC) solvates of "aprotic solvents such as pyridine, tetrahydrofuran, and acetonitrile will give clearer pictures here than solvates of "protic solvents such as water or alcohols. 

Dodson, C.R. and Standing, M.B. Pressure, Volume, Temperature and Solubility Relations for Natural Gas-Water Mixtures, Drill, and Prod. Prac., API (1944) 173-179. 

Filtration of warm mixtures always proceeds more rapidly than the filtration of cold mixtures, because the viscosity is lower at higher temperatures. Hence, warm filtration is to be preferred if the stability of the material and the solubility relations are favorable. 

Dodson, C. R., and M. B. Standing, Pressure-Volume-Temperature and Solubility Relations for Natural-Gas-Water Mixtures, API Drilling and Production Practice, p. 173, 1944. 

This paper describes the results of an experimental study of condensed phase equilibria in the system MoFe-UFo carried out by thermal analysis and x-ray diffraction analysis. A temperature-composition phase diagram is constructed from the temperatures of observed thermal arrests in MoFe-UFe mixtures, and the basis for the formation of this particular type of diagram is traced to the physical properties of the pure components. The solid-solubility relations indicated by the diagram are traced to the crystal structures of the pure solids. 

Information of solubility of gases in oils is rather limited. Vegetable oils readily dissolve between 4% and 10% of their own volume of air and other gases at ambient temperature. All gases, with exception of carbon dioxide, increase in solubility with increasing temperature. The relation between solubility (S) and temperature (t) can be expressed by following linear equations (30) ... 

Sodium sulfadiazine and sulfafurazole diolamine in therapeutic doses (1 mg) added to 5% dextrose and 5% dextrose and saline solution have been found to be compatible, yet when added to commercial polyionic solutions (such as Abbott lonosol B, Baxter electrolyte No.2) both rapidly form heavy precipitates. pH and temperature are two vital parameters, but the pH effect is not simply a solubility-related phenomenon. Polyionic solutions of a lower initial pH (4.4-4.6) cause crystallisation of sulfafurazole at room temperature within 2.5 h, the pH values of the admixtures being 5.65 and 5.75 respectively. Other solutions with slightly higher initial pH levels (6.1-6.6) formed crystals only after preliminary cooling to 20°C at pH values from 4.25 to 4.90. If the temperature remains constant, the intensity of precipitation varies with the composition and initial pH of the solution used as a vehicle. 

Molality is expressed as the number of moles of solute dissolved per kilogram of solvent, and is therefore independent of temperature since all of the quantities are expressed on a temperature-independent weight basis. The molality of a solution is useful in describing solubility-related phenomena at various temperatures, and as the concentration unit of colligative property studies. When the density of the solvent equals unity, or in the case of dilute aqueous solutions, the molarity and the molality of the solution would be equivalent. 

For any case in which F is zero, a definite reproducible solubility equilibrium can be reached. Complete representation of the solubility relations is accomplished in the phase diagram, which gives the number, composition, and relative amounts of each phase present at any temperature in a sample containing the components in any specified proportion. Solubilities may therefore be expressed in any appropriate units of concentration, such as the quality of the solute dissolved (defined mass, number of moles) divided by the quantity either of the solvent (defined mass, volume, or number of moles) or of the solution (defined mass, volume, or number of moles). Jacques et al. (1981) have provided a compilation of the expressions for concentration and solubility. 

The solubility relations of sodium sulphate illustrate very clearly the importance of the solid phase for the definition of saturation and supersaturation. Since the solubility curve of the anhydrous salt has been followed backwards to a temperature of about 18 , it is readily seen, from Fig. 73, that at a temperature of, say, 20 , three different saturated solutions of sodium sulphate are possible, according as the anhydrous salt, the heptahydrate or the decahydrate, is present as the solid phase. Two of these solutions, however, would be metastable and supersaturated with respect to the decahydrate. 

In the preceding chapter we considered the changes in the solubility of double salts and of mixtures of their constituent salts with the temperature noting, more especially, the relationships between the two systems at the transition point. It is now proposed to conclude the study of the three-component systems by discussing very briefly the solubility relations at constant temperature, or the isothermal solubility curves. In this way fresh light will be thrown on the change in the solubility of one component by the addition of another component, and also on the conditions of formation and stable existence of double salts in solution. With the help of these isothermal curves, also, the phenomena of crystallisation at constant temperature—phenomena which have not only a scientific interest but also an important bearing on the industrial pieparation of double salts— will be more clearly understood. ... 

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