Solubility product— evaluation

STRATEGY First, we write the chemical equation for the equilibrium and the expression for the solubility product. To evaluate Ksp, we need to know the molarity of each type of ion formed by the salt. We determine the molarities from the molar solubility, the chemical equation for the equilibrium, and the stoichiometric relations between the species. We assume complete dissociation. 

Sol id Sol utions. The aqueous concentrations of trace elements in natural waters are frequently much lower than would be expected on the basis of equilibrium solubility calculations or of supply to the water from various sources. It is often assumed that adsorption of the element on mineral surfaces is the cause for the depleted aqueous concentration of the trace element (97). However, Sposito (Chapter 11) shows that the methods commonly used to distinguish between solubility or adsorption controls are conceptually flawed. One of the important problems illustrated in Chapter 11 is the evaluation of the state of saturation of natural waters with respect to solid phases. Generally, the conclusion that a trace element is undersaturated is based on a comparison of ion activity products with known pure solid phases that contain the trace element. If a solid phase is pure, then its activity is equal to one by thermodynamic convention. However, when a trace cation is coprecipitated with another cation, the activity of the solid phase end member containing the trace cation in the coprecipitate wil 1 be less than one. If the aqueous phase is at equil ibrium with the coprecipitate, then the ion activity product wi 1 1 be 1 ess than the sol ubi 1 ity constant of the pure sol id phase containing the trace element. This condition could then lead to the conclusion that a natural water was undersaturated with respect to the pure solid phase and that the aqueous concentration of the trace cation was controlled by adsorption on mineral surfaces. While this might be true, Sposito points out that the ion activity product comparison with the solubility product does not provide any conclusive evidence as to whether an adsorption or coprecipitation process controls the aqueous concentration. 

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. 

Mattil (36) emphasized the difference in amino acid composition within the two classifications for commercial products. He pointed out that some of the differences are deliberate a high solubility isolate could well have a different amino acid composition than an isolate with low solubility. Mattil evaluated isolate PER s, which ranged from... 

Probably other equilibria would serve just as well. Using an equilibrium constant of 103 for this reaction and a solubility product of 1.73 X 10 3 for sodium ethoxide, the constants kx = 8 X 10 3 sec. 1 and (k2/kz) = 6 X 103 were evaluated. The value for kx is fairly firm (and agrees with NMR data which indicate that the rate constant is less than 10 sec. 1), but the value of (k2/kz) is dependent on an arbitrary choice, within limits, of the EtOHOEt equilibrium constant and the sodium ethoxide solubility product. In fact, the kinetic data are consistent with any value for... 

Using the carbamazepine-nicotinamide cocrystal system, a mathematical model has been developed to predict the solubility of cocrystals [41], The model predicted that the solubility of a solid cocrystal is determined by the solubility products of the reactant species and solution complexa-tion constants that could be obtained from the performance of solubility studies. In addition, graphical methods were developed to use the dependence of cocrystal solubility on ligand concentration for evaluation of the stoichiometry of the solution-phase complexes that are the precursor to the crystalline cocrystal itself. It was proposed that the dependence of cocrystal solubility on solubility product and complexation constants would aid in the design of screening protocols, and would provide guidance for systems where crystallization of the cocrystal did not take place. 

Obviously one could measure the pH of a known concentration of a weak acid and obtain a value of its hydronium ion activity, which would permit a direct evaluation of its dissociation constant. However, this would be a one-point evaluation and subject to greater errors than by titrating the acid halfway to the equivalence point. The latter approach uses a well-buffered region where the pH measurement represents the average of a large number of data points. Similar arguments can be made for the evaluation of solubility products and stability constants of complex ions. The appropriate expression for the evaluation of solubility products again is based on the half-equivalence point of the titration curve for the particular precipitation reaction [AgI(OH2)2h represents the titrant] ... 

The solubility product depends on the activity of the lattice ions in solution. If the solution contains other ions or molecules either as impurities, additional chemicals or the result of reactions within the solution phase, then this must be taken into account in the evaluation of KB. At least four separate effects on the solubility may be identified. 

Chantooni and Kolthoff " derived equations which permit the calculation of hydration constants of cations and anions from the solubility products of slightly soluble salts in solutions of acetonitrile with various concentrations of water. The ionic solubility of a salt was determined by measuring the conductance. The water concentration of the acetonitrile solution was always less than 1 M. The total ionic solubility product was expanded in powers of the water concentration. The coefficients are related to the individual ionic hydration constants and were evaluated by... 

A suite of both oxidized and reduced iron minerals has been found as efflorescences and precipitates in or near the acid mine water of Iron Mountain. The dominant minerals tend to be melan-terite (or one of its dehydration products), copiapite, jarosite and iron hydroxide. These minerals and their chemical formulae are listed in Table III from the most ferrous-rich at the top to the most ferric-rich at the bottom. These minerals were collected in air-tight containers and identified by X-ray diffractometry. It was also possible to check the mineral saturation indices (log Q(AP/K), where AP = activity product and K = solubility product constant)of the mine waters with the field occurrences of the same minerals. By continual checking of the saturation index (S.I.) with actual mineralogic occurrences, inaccuracies in chemical models such as WATEQ2 can be discovered, evaluated and corrected (19), provided that these occurrences can be assumed to be an approach towards equilibrium. 

The mean activity coefficient of a sparingly soluble salt in any solution could thus be evaluated provided the solubility product (K ) and the mean concentration of the... 

Electrode Potentials and Solubility Product.—The solubility product is an equilibrium constant, namely for the equilibrium between the solid salt on the one hand and the ions in solution on the other hand, and methods are available for the evaluation of this property from e.m.f. measurements. 

The solubility product is useful for evaluating the influence of other species on the solubility of salts of low aqueous solubility. Some values of solubility products are quoted in Table 5.7. 

The mean activity coefficient of a sparingly soluble salt in any solution, containing other electrolytes, can thus be evaluated provided the solubility product and the mean molality of the ions of the salt in the given solution are known. In order to obtain X, the values of are determined from the experimentally observed solubilities of the sparingly soluble salt in the presence of various amounts of other electrolytes, and the results are extrapolated to infinite dilution (Fig. 27). In the latter case the activity coefficient is unity, in accordance with the chosen standard state, and hence, by equation (39.71), KV"" is equal to the extrapolated value of... 

Another important use of standard potentials is for the determination of sdubility products, for these are essentially equilibrium constants ( 39j). If M Al, is a sparingly solvble salt, a knowledge of the standard potentials of the electrodes M, M, A, (s), A - and M, M + permits the solubility product to be evaluated. A simple example is provided by silver chloride Ifor which the standard (oxidation) potential of the Ag, AgCl( ), Cl electrode is known to be — 0.2224 volt at 25 C. The activity of the chloride ion in the standard electrode is unity, and hence the silver ion activity must be equal to the solubility product of silver chloride. The value of Oa may be derived from equation (45.13), utilizing the standard potential of silver thus Eu i — 0.22 volt, E for silver is — 0.799, and z is 1, so that at 25 C,... 

As indicated previously, AH° can be determined in various ways, and Ss for the solid salt can be obtained from heat capacity measurements, based on the third law of thermodynamics. There remains the evaluation of AF to be considered. If the solubility product K, is known in terms of activities, either by extrapolation of solubility measurements ( 39j) or from electrode potentials ( 45i), AF can be obtained directly, since it is equal to — FT In K as stated above. When the activity solubility product is not available, use may be made of equation (39.70) for the solubility product, i.e.,... 

Numerical values for solubility-product constants, dissociation constants, and formation constants are conveniently evaluated through the measurement of cell potentials. One important virtue of this technique is that the measurement can be made without appreciably affecting any equilibria that may be present in the solution. For example, the potential of a silver electrode in a solution containing silver ion, cyanide ion, and the complex formed between them depends on the activities of the thiee species. It is possible to measure this potential with negligible current. 

In the aqueous phase, Umland and Wallmeier [80UML/WAL] attempted to determine the solubility product of Sb2Se3(cr) by the polarographic method outlined in Appendix A. Their result, log (Sb2Sc3, cr, 298.15 K) = - (113 2), is not accepted since the measurements were conducted in presence of 0.5 M tartaric acid and, therefore, the conditions for the evaluation of the constant from the measurements are not fulfilled. 

Aleksandrovich and Serebrennikov [62ALE/SER] measured the solubility of Sm2(Se03)3(s) at (298.15 + 0.05) K in HCI, HNO3, and H2SO4 of unspecified concentration. The experiments and the evaluation of the solubility product of the reaction ... 

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