8. Final comments

addition of 0.795 mL of 2.0 mol/L KI (Figure 11a). Subsequently, the curve in Figure 10a increases, reaches a maximum and then decreases. At a due excess of the KI (C3) added on

(a) (b)

**E**

Figure 9. The speciation plots for indicated Cu-species within the successive stages. The V-values on the abscissas correspond to successive addition of V mL of: 0.25 mol/L NH3 (stage 1); 0.75 mol/L CH3COOH (stage 2); 2.0 mol/L KI

> 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6

> > 0 5 10 15 20

**V**

C) is not

the stage 3 (V<sup>K</sup> = 20 mL), solid iodine (I2(s), of solubility 0.00133 mol/L at 25<sup>o</sup>

0 5 10 15 20

**V**

precipitated.

0.53 0.54

Figure 10. Plots of E versus V for (a) stage 3 and (b) stage 4.

0.55 0.56 0.57

**E**

0.58 0.59

(stage 3); and 0.1 mol/L Na2S2O3 (stage 4). For more details see text.

124 Descriptive Inorganic Chemistry Researches of Metal Compounds

The solubility and dissolution of sparingly soluble salts in aqueous media are among the main educational topics realized within general chemistry and analytical chemistry courses. The principles of solubility calculations were formulated at a time when knowledge of the twophase electrolytic systems was still rudimentary. However, the earlier arrangements persisted in subsequent generations [81], and little has changed in the meantime [82]. About 20 years ago, Hawkes put in the title of his article [83] a dramatic question, corresponding to his statement presented therein that "the simple algorithms in introductory texts usually produce dramatic and often catastrophic errors"; it is hard not to agree with this opinion.

In the meantime, Meites et al. [84] stated that "It would be better to confine illustrations of the solubility product principle to 1:1 salts, like silver bromide (…), in which the (…) calculations will yield results close enough to the truth." The unwarranted simplifications cause confusion in teaching of chemistry. Students will trust us enough to believe that a calculation we have taught must be generally useful.

The theory of electrolytic systems, perceived as the main problem in the physicochemical studies for many decades, is now put on the side. It can be argued that the gaining of quantitative chemical knowledge in the education process is essentially based on the stoichiometry and proportions.

Overview of the literature indicates that the problems of dissolution and solubility calculation are not usually resolved in a proper manner; positive (and sole) exceptions are the studies and practice made by the authors of this chapter. Other authors, e.g., [13, 85], rely on the simplified schemes (ready-to-use formulas), which usually lead to erroneous results, expressed by dissolution denoted as s\* [mol/L]; the values for s\* are based on stoichiometric reaction notations and expressions for the solubility product values, specified by Eqs. (1) and (2). The calculation of s\* contradicts the common sense principle; this was clearly stated in the example with Fe(OH)3 precipitate. Equation (27) was applied to struvite [50] and dolomite [86], although these precipitates are nonequilibrium solid phases when introduced into pure water, as were proved in Refs. [20–23]. The fact of the struvite instability was known at the end of nineteenth century [49]; nevertheless, the formula s\* = (Ksp) 1/3 for struvite may be still encountered in almost all textbooks and learning materials; this problem was raised in Ref. [15]. In this chapter, we identified typical errors involved with s\* calculations, and indicated the proper manner of resolution of the problem in question.

The calculations of solubility s\* , based on stoichiometric notation and Eq. (3), contradict the calculations of s, based on the matter and charge preservation. In calculations of s, all the species formed by defined element are involved, not only the species from the related reaction notation. A simple zeroing method, based on charge balance equation, can be applied for the calculation of pH = pH0 value, and then for calculation of concentrations for all species involved in expression for solubility value.

The solubility of a precipitate and the pH-interval where it exists as an equilibrium-solid phase in two-phase system can be accurately determined from calculations based on charge and concentration balances, and complete set of equilibrium constant values referred to the system in question.

In the calculations performed here we assumed a priori that the Ksp values in the relevant tables were obtained in a manner worthy of the recognition, i.e., these values are true. However, one should be aware that the equilibrium constants collected in the relevant tables come from the period of time covering many decades; it results from an overview of dates of references contained in some textbooks [31, 85] relating to the equilibrium constants. In the early literature were generally presented the results obtained in the simplest manner, based on Ksp calculation from the experimentally determined s\* value, where all soluble species formed in solution by these ions were included on account of simple cations and anions forming the expression for Ksp. In many instances, the Ksp\* values should be then perceived as conditional equilibrium constants [87]. Moreover, the differences between the equilibrium constants obtained under different physicochemical conditions in the solution tested were credited on account of activity coefficients, as an antidote to any discrepancies between theory and experiment.

First dissociation constants for acids were published in 1889. Most of the stability constants of metal complexes were determined after the announcement 1941 of Bjerrum's works, see Ref. [88], about ammine-complexes of metals, and research studies on metal complexes were carried out intermittently in the twentieth century [89]. The studies of complexes formed by simple ions started only from the 1940s; these studies were related both to mono- and twophase systems. It should also be noted that the first mathematical models used for determination of equilibrium constants were adapted to the current computing capabilities. Critical comments in this regard can be found, among others, in the Beck [90] monograph; the variation between the values obtained by different authors for some equilibrium constants was startling, and reaching 20 orders of magnitude. It should be noted, however, that the determination of a set of stability constants of complexes as parameters of a set of suitable algebraic equations requires complex mathematical models, solvable only with use of an iterative computer program [91–93].

The difficulties associated with the resolution of electrolytic systems and two-phase systems, in particular, can be perceived today in the context of calculations using (1<sup>o</sup> ) spreadsheets (2o ) iterative calculation methods. In (1<sup>o</sup> ), a calculation is made by the zeroing method applied to the function with one variable; both options are presented in this chapter.

The expression for solubility products, as well as the expression of other equilibrium constants, is formulated on the basis of mass action law (MAL). It should be noted, however, that the underlying mathematical formalism contained in MAL does not inspire trust, to put it mildly. For this purpose, the equilibrium law (EL) based on the Gibbs function [94] and the Lagrange multipliers method [95–97] with laws of charge and elements conservation was suggested lately by Michałowski.

From semantic viewpoint, the term "solubility product" is not adequate, e.g., in relation to Eq. (8). Moreover, Ksp is not necessarily the product of ion concentrations, as indicated in formulas (4), (5), and (11). In some (numerous) instances of sparingly soluble species, e.g., sulfur, solid iodine, 8-hydroxyquinoline, dimethylglyoxime, the term solubility product is not applied. In some instances, e.g., for MnO2, this term is doubtful.

One of the main purposes of the present chapter is to familiarize GEB within GATES as GATES/GEB to a wider community of analysts engaged in electrolytic systems, also in aspect of solubility problems.

In this context, owing to large advantages and versatile capabilities offered by GATES/GEB, it deserves a due attention and promotion. The GATES is perceived as a step toward reductionism [19, 71] of chemistry in the area of electrolytic systems and the GEB is considered as a general law of nature; it provides the real proof of the world harmony, harmony of nature.
