Equilibrium solubility analysis

When a precipitate has been formed during the qualitative analysis of the ions present in a solution, it may be necessary to dissolve the precipitate again to identify the cation or anion. One strategy is to remove one of the ions from the solubility equilibrium so that the precipitate will continue to dissolve in a fruitless chase for equilibrium. Suppose, for example, that a solid hydroxide such as iron(IIl) hydroxide is in equilibrium with its ions in solution ... 

Predicting sorption coefficients and hence the mobility of organic pollutants in aqueous-solid systems requires complete knowledge and analysis of various physical and chemical properties of such pollutants. This includes properties such as solubility, equilibrium vapor pressure, Henry s law constant, partition coefficient, as well as pKa and pKb values. Such properties can initially help determine the sorption-desorption behavior of organic pollutants once they are released, directly and/or indirectly, to the aqueous environment and then are in direct contact with solid phases. The following sections briefly summarize these properties. 

A convenient method of interpreting water analysis for the purpose of determining the calcium carbonate solubility equilibrium conditions is embodied in the Langelier equation. The Langelier equation can be used to... 

Liquid-phase extraction is a procedure by which some fraction of a solute is taken out of solution by shaking the solution with a different solvent (in which the solute usually has greater solubility). The analysis of this process assumes that the shaking is sufficient so that equilibrium is established for the solute, i, between the two solutions. At equilibrium, the chemical potentials of the solute in the two solutions are equal. Assuming ideally dilute solutions, we can write... 

Chukhlantsev [56CHU] prepared copper selenite by mixing 0.1 M solutions of copper sulphate and sodium selenite in the cold. The product was aged for 24 hours. Chemical analysis confirmed the 1 1 ratio between Cu(ll) and Se(lV). The solubility of the specimen in dilute solution of nitric or sulphuric acid was measured at 293 K. No X-ray diffraction measurements were performed and the solubility equilibrium will be written on the assumption that the composition of the solid phase is CuSe03-2H20 ... 

Ripan and Vericeanu [68R1P/VER] studied the solubility of CuSe03-2H20(s) by conductivity measurements as described in Appendix A. An equilibrium analysis performed as outlined there on the total concentrations provided in the paper, about 1.8 X 10 M, leads to the conclusion that almost 80% of the copper(II) would be present as hydroxo complexes at equilibrium. Hence, a conductivity measurement is unsuitable for the determination of the solubility of copper selenite and no reliable value of the solubility product can be calculated from the data in [68R1PA ER]. Masson et al. [86MAS/LUT] calculated log (, = - (7.49 0.10) from the data neglecting hydrolysis of Cu. ... 

The study of the variation of the solubility with the selenite concentration is stated to have been carried at the constant ionic strengths 0.01 and 0.3 M. How this was accomplished was not clear from the information in the paper. The data in the tables rather seem to indicate that the ionic strength varied and reached 0.03 and 0.5 M, respectively, in the solution with the highest selenite concentrations. The analysis of the data was made with an equilibrium model that comprised the solubility equilibrium and the formation of the complex 0(8003)2 T us the formation of CoSe03(aq) was not included in the model. The analysis led to values of the solubility product at the two ionic strengths that appear to be inconsistent with the value obtained from the solubility in water. This result together with the improbable model made the review reject the outcome of the equilibrium analysis. 

The design of the experiment is not well suited for an equilibrium analysis, but definitely showed that Ag2Se03(cr) is dissolved by an excess of SeOj. No equilibrium constants were derived in the paper from these data. The review calculated ((A.22), 298.15 K) from the data at the lowest total selenite concentration and pH < 6. The protonation constants from the first series were used in the calculation. The result was log Ai, ((A.22), 298.15 K) = - (15.20 + 0.15). Hence there is a significant difference between the values of the solubility product determined by the two techniques, which cannot be accounted for and apparently not observed by the authors. 

As previously stated, leaching is another extraction process in which a liquid is used to remove soluble matter from its mixture with an inert solid. With a few extra considerations, the equilibrium analysis of leaching is the same as for liquid extraction. Several assumptions are made in designing leaching processes. These can be rendered correct with the proper choice of solvent. It is assumed that the solid is insoluble in the solvent (dirt will not dissolve in water) and the flowrate of solids is essentially constant throughout the process. The solid, on the other hand, is porous and will often retain a portion of the solvent. 

In the present section, the general outline of the different EoS considered will be first recalled then we report the basic results of the non-equilibrium analysis leading to their proper extension to glassy phases. It is not the aim of this section to offer an exhaustive presentation of the characteristics of the different models and of their detailed properties, but rather to point out the model relevant parameters and how they can be retrieved from pure component and mixture properties, independent of solubility isotherms. For further details, the reader is referred to the cited original papers. 

Morral" has criticized the Wagner analysis and argued that concentration profiles such as that shown in Figure B1 violate principles of local equilibrium and that solute enrichment in the zone of internal oxidation is not possible for the case of zero solubility product. Analysis of this issue is beyond the scope of this book but it should be remarked that many experimental observations are consistent with conclusions based on Wagner s model. 

Briefly describe each of the following ideas, methods, or phenomena (a) common-ion effect in solubility equilibrium (b) fractional precipitation (c) ion-pair formation (d) qualitative cation analysis. 

The great importance of the solubility product concept lies in its bearing upon precipitation from solution, which is, of course, one of the important operations of quantitative analysis. The solubility product is the ultimate value which is attained by the ionic concentration product when equilibrium has been established between the solid phase of a difficultly soluble salt and the solution. If the experimental conditions are such that the ionic concentration product is different from the solubility product, then the system will attempt to adjust itself in such a manner that the ionic and solubility products are equal in value. Thus if, for a given electrolyte, the product of the concentrations of the ions in solution is arbitrarily made to exceed the solubility product, as for example by the addition of a salt with a common ion, the adjustment of the system to equilibrium results in precipitation of the solid salt, provided supersaturation conditions are excluded. If the ionic concentration product is less than the solubility product or can arbitrarily be made so, as (for example) by complex salt formation or by the formation of weak electrolytes, then a further quantity of solute can pass into solution until the solubility product is attained, or, if this is not possible, until all the solute has dissolved. 

AB diblock copolymers in the presence of a selective surface can form an adsorbed layer, which is a planar form of aggregation or self-assembly. This is very useful in the manipulation of the surface properties of solid surfaces, especially those that are employed in liquid media. Several situations have been studied both theoretically and experimentally, among them the case of a selective surface but a nonselective solvent [75] which results in swelling of both the anchor and the buoy layers. However, we concentrate on the situation most closely related to the micelle conditions just discussed, namely, adsorption from a selective solvent. Our theoretical discussion is adapted and abbreviated from that of Marques et al. [76], who considered many features not discussed here. They began their analysis from the grand canonical free energy of a block copolymer layer in equilibrium with a reservoir containing soluble block copolymer at chemical potential peK. They also considered the possible effects of micellization in solution on the adsorption process [61]. We assume in this presentation that the anchor layer is in a solvent-free, melt state above Tg. The anchor layer is assumed to be thin and smooth, with a sharp interface between it and the solvent swollen buoy layer. 

Special care has to be taken if the polymer is only soluble in a solvent mixture or if a certain property, e.g., a definite value of the second virial coefficient, needs to be adjusted by adding another solvent. In this case the analysis is complicated due to the different refractive indices of the solvent components [32]. In case of a binary solvent mixture we find, that formally Equation (42) is still valid. The refractive index increment needs to be replaced by an increment accounting for a complex formation of the polymer and the solvent mixture, when one of the solvents adsorbs preferentially on the polymer. Instead of measuring the true molar mass Mw the apparent molar mass Mapp is measured. How large the difference is depends on the difference between the refractive index increments ([dn/dc) — (dn/dc)A>0. (dn/dc)fl is the increment determined in the mixed solvents in osmotic equilibrium, while (dn/dc)A0 is determined for infinite dilution of the polymer in solvent A. For clarity we omitted the fixed parameters such as temperature, T, and pressure, p. 

It is important to ascertain whether the solid phase of the solute changes during equilibration to produce a different polymorph or solvate, by analyzing the solid phase (using either chemical or thermal analysis, or x-ray diffraction). If a solid-solid phase transition occurs during equilibration, the measured equilibrium solubility will be that of the new solid phase of the solute. Methods of circumventing this problem have been proposed and evaluated [26]. 

Phase solubility analysis is a technique to determine the purity of a substance based on a careful study of its solubility behavior [38,39]. The method has its theoretical basis in the phase mle, developed by Gibbs, in which the equilibrium existing in a system is defined by the relation between the number of coexisting phases and components. The equilibrium solubility of a material in a particular solvent, although a function of temperature and pressure, is nevertheless an intrinsic property of that material. Any deviation from the solubility exhibited by a pure sample arises from the presence of impurities and/or crystal defects, and so accurate solubility measurements can be used to deduce the purity of the sample. 

To make contact with atomic theories of the binding of interstitial hydrogen in silicon, and to extrapolate the solubility to lower temperatures, some thermodynamic analysis of these data is needed a convenient procedure is that of Johnson, etal. (1986). As we have seen in Section II. l,Eqs. (2) et seq., the equilibrium concentration of any interstitial species is determined by the concentration of possible sites for this species, the vibrational partition function for each occupied site, and the difference between the chemical potential p, of the hydrogen and the ground state energy E0 on this type of site. In equilibrium with external H2 gas, /x is accurately known from thermochemical tables for the latter. A convenient source is the... 

Are the equilibrium constants for the important reactions in the thermodynamic dataset sufficiently accurate The collection of thermodynamic data is subject to error in the experiment, chemical analysis, and interpretation of the experimental results. Error margins, however, are seldom reported and never seem to appear in data compilations. Compiled data, furthermore, have generally been extrapolated from the temperature of measurement to that of interest (e.g., Helgeson, 1969). The stabilities of many aqueous species have been determined only at room temperature, for example, and mineral solubilities many times are measured at high temperatures where reactions approach equilibrium most rapidly. Evaluating the stabilities and sometimes even the stoichiometries of complex species is especially difficult and prone to inaccuracy. 

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. 

For the purpose of this case study we will select Isopropyl alcohol as the crystallization solvent and assume that the NRTL-SAC solubility curve for Form A has been confirmed as reasonably accurate in the laboratory. If experimental solubility data is measured in IPA then it can be fitted to a more accurate (but non predictive) thermodynamic model such as NRTL or UNIQUAC at this point, taking care with analysis of the solid phase in equilibrium. As the activity coefficient model only relates to species in the liquid phase we can use the same model with each different set of AHm and Tm data to calculate the solubility of the other polymorphs of Cimetidine, as shown in Figure 21. True polymorphs only differ from each other in the solid phase and are otherwise chemically identical. 

---