Solubility equilibria relative solubilities

Indole itself forms a dimer or a trimer, depending on experimental conditions the dimer hydrochloride is formed in aprotic solvents with dry HCl, whereas aqueous media lead to dimer or trimer, or both. It was Schmitz-DuMont and his collaborators who beautifully cleared up the experimental confusion and discovered the simple fact that in aqueous acid the composition of the product is dictated by the relative solubilities of the dimer and trimer hydrochlorides/ -This, of course, established the very important point that there is an equilibrium in solution among indole, the dimer, the trimer, and their salts. It was furthermore demonstrated that the polymerization mechanism involves acid catalysis and that in dilute solution the rate of reaction is dependent on the concentration of acid. 

Cr(VI).Other remediation processes for Cr(VI) contaminated soils include H2S injection, aqueous Fe(II) injection, and the use of reduced Fe solids. Aqueous-phase Cr(VI)-Fe(II) redox reactions may be significant if Fe2+ concentrations are in equilibrium with relatively soluble, ferric hydroxide-like phases (Tokunaga et al., 2003). The overall interactions involving microbial activity, organic carbon degradation, Fe2+, and mineral surfaces control the net rates of Cr(VI) reactions in soils. 

It should be noted that constant temperature and pressure are assumed, and that A must exist in exactly the same form in both phases. Equilibrium is established when the chemical potentials (free energies) of the solute in the two phases are equal and is usually achieved within a few minutes by vigorous shaking. The value of KD is a reflection of the relative solubilities of the solute in the two phases. 

Le Chatelier s principle is a powerful tool for explaining how a reaction at equilibrium shifts when a stress is placed on the system. In this experiment, you can use Le Chatelier s principle to evaluate the relative solubilities of two precipitates. By observing the formation of two precipitates in the same system, you can infer the relationship between the solubilities of the two ionic compounds and the numerical values of their solubility product constants (K ). You will be able to verify your own experimental results by calculating the molar solubilities of the two compounds using the Ksp for each compound. 

The relative solubilities reported are very crude estimates based on equilibrium solubility products. These estimates do not take into account variations in solubility as a function of pH, ionic strength, activities of various solution species (e.g., HCO "), redox state, particle size, surface defect types and concentrations, the concentration of various types of adsorbates, including natural organic matter, on mineral surface, or the presence of different types of bacteria or microbial biofilms on mineral surfaces. 

The solubility and surface tension results itemized in Table XVII confirm that there is a larger interaction between ethanol and the TAA salts as the size of the cation or organic portion increases. The data show that in spite of the R4NBr salts becoming more soluble in water as the cation size increases, their solubility increases much more rapidly in ethanol, in fact by a factor of 10 greater in ethanol than in water as the salt series of the present investigation is ascended. As a result, the two highest members of the series, the tetrapropyl and tetrabutyl salts, are actually more soluble in ethanol than in water, while the reverse is true for the lower three. Consequently, on the basis of relative solubilities of the salts studied in both ethanol and water, trends in the salt effect parameters similar to those of this work, based on the vapor-equilibrium studies listed in Table XVIII would be observed. 

Sampling and Measurements. The determination of dissolved actinide concentration was started a week after the preparation of solutions and continued periodically for several months until the solubility equilibrium in each solution was attained. Some solutions, in which the solubilities of americium or plutonium were relatively high, were spectrophotometrically analyzed to ascertain the chemical state of dissolved species. For each sample, 0.2 to 1.0 mL of solution was filtered with a Millex-22 syringe filter (0.22 pm pore size) and the actinide concentration determined in a liquid scintillation counter. After filtration with a Millex-22, randomly chosen sample solutions were further filtered with various ultrafilters of different pore sizes in order to determine if different types of filtration would affect the measured concentration. The chemical stability of dissolved species was examined with respect to sorption on surfaces of experimental vials and of filters. The experiment was performed as follows the solution filtered by a Millex-22 was put into a polyethylene vial, stored one day, filtered with a new filter of the same pore size and put into another polyethylene vial. This procedure was repeated twice with two new polyethylene vials and the activities of filtrates were compared. The ultrafiltration was carried out by centrifugation with an appropriate filter holder. The results show that the dissolved species in solution after filtration with Millex-22 (0.22 ym) do not sorb on surfaces of experimental materials and that the actinide concentration is not appreciably changed with decreasing pore size of ultrafilters. The pore size of a filter is estimated from its given Dalton number on the basis of a hardsphere model used in the previous work (20). 

Partition coefficients are used to describe the distribution of nonpolar organic compounds between water and organisms. It can be viewed as a partitioning process between the aqueous phase and the bulk organic matter present in biota (Schwarzenbach et al. 1993). The premise behind the use of equilibrium models is that accumulation of compounds is dominated by their relative solubility in water and the solid phases, respectively. Equilibrium models, therefore, rely on the following assumptions (Landrum et al. 1996) ... 

The dimensionless partition coefficient K = cp/cl = Sr, also known as a relative solubility coefficient, is defined as the ratio of the concentration of a substance in the polymer cP to that in the liquid (food) cLat equilibrium. While D is practically independent of the liquid phase in contact with the polymer in these measurements, the K values are determined by the nature of the polymer and liquid contact phases. From the definition Sr = K, a relative peremeability coefficient can be calculated, Pr = Sr D, with the dimension D. Here, accordingly to Eq. (9-2) and the solubility constant in the polymer and in the liquid phases expressed as SP = cP/p and Sl = C Jp, respectively, the following relationship results between the absolute and relative permeability coefficients ... 

Cyclopentadienyltin(II) chloride and bromide can be made by the exchange reaction shown in Eq. (2) (79). This is apparently an equilibrium system, and the product is determined by the relative solubility of the reagents present. It is not possible to synthesize the iodide this way because it is too soluble in THF (31). 

Although the presence of mixed bridging ligands may favour the formation of high nuclearity assemblies, it remains difficult to pinpoint the factors that give rise to these unusual cyclic products. In accordance with the previous discussion, it seems likely that these multi-component species may exist in solution in equilibrium with related oligomeric species their isolation will thus be influenced by both the position of the equilibrium as well as by the relative solubilities of the respective species in the chosen reaction solvent. 

As is to be expected from relative solubility, the first minerals to form from concentrating waters are the alkaline-earth carbonates. The equilibrium precipitation of calcite also illustrates... 

Calcium Sulfite Deposition. Calcium sulfite (CaS03 %H20) is formed in the scrubber under those conditions that favor sulfite formation. These conditions are apparent when one considers the sulfite-bisulfite equilibrium and compares the relative solubilities of the corresponding calcium salts. As seen in Figure 2, extremely soluble bisulfite in solution changes to relatively insoluble sulfite when the solution pH shifts from 4 to 10. When SO2 is absorbed, the scrubber solution is usually between pH 4 and 6 and, therefore, the predominant species is... 

It has been established that the He/ He ratio has values characteristic of the source of the gas. Deep oceanic waters over rift zones and sea-floor spreading centres are found not only to be enriched in total He, relative to the solubility equilibrium with the atmosphere. 

Phase Behavior. The surfactant formulations for enhanced oil recovery consist of surfactant, alcohol and brine with or without added oil. As the alcohol and surfactant are added to equal volumes of oil and brine, the surfactant partitioning between oil and brine phases depends on the relative solubilities of the surfactant in each phase. If most of the surfactant remains in the brine phase, the system becomes two phases, and the aqueous phase consists of micelles or oil-in-water microemulsions depending upon the amount of oil solubilized. If most of the surfactant remains in the oil phase, a two-phase system is formed with reversed micelles or the water-in-oil microemulsion in equilibrium with an aqueous phase. 

The solubility measure describes the concentration reached in solution, when a pure phase of the material is allowed to dissolve in the solvent for a defined period of time, at a defined temperature (and pressure). Most often for pharmaceutical purposes, the pure phase is a solid, ideally a crystalline solid, and the liquid is water or a buffered aqueous solution, at a controlled temperature (often 25 or 37 °C) and ambient pressure. The purity of the solid can have a large effect on measured solubility. Solubility can be measured in water or in pH-controlled buffers. In water, the extent of solubility for ionizable compounds will depend upon the p fCa values and the nature of the counterion. In pH-controlled aqueous buffered solution, at equilibrium, the solubility will depend upon the compound s intrinsic solubility, its plQ, and the ionic strength. It may also depend upon the relative solubility of the initial added compound and the solubility of the salt formed by the compound with the buffer salts, with which the solid may equilibrate. In any buffer or solvent system, the measured solubility may depend on the time of sampling, as solubility kinetics... 

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. 

As discussed earlier in the Thermodynamics section of this chapter, the difference in free energy between solid phases (i.e. polymorphs and solvates) is directly proportional to their relative solubilities (Equation 2). Therefore, a saturated solution of a less stable (more soluble) phase is super-saturated with respect to a more stable (less soluble) phase. Since super-saturated solutions are metastable, a more stable phase will eventually crystallize in order to establish equilibrium and remove supersaturation. According to Ostwald s (1897) Law... 

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