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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

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

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

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 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 coeffi-

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 com-

cients, as an antidote to any discrepancies between theory and experiment.

1/3 for struvite may be still encountered in

, based on stoichiometric notation and Eq. (3), contradict the

century [49]; nevertheless, the formula s\* = (Ksp)

126 Descriptive Inorganic Chemistry Researches of Metal Compounds

manner of resolution of the problem in question.

involved in expression for solubility value.

The calculations of solubility s\*

in question.

puter program [91–93].

Anna Maria Michałowska-Kaczmarczyk<sup>1</sup> , Aneta Spórna-Kucab<sup>2</sup> and Tadeusz Michałowski<sup>2</sup> \*

\*Address all correspondence to: michalot@o2.pl

1 Department of Oncology, The University Hospital in Cracow, Cracow, Poland

2 Faculty of Chemical Engineering and Technology, Cracow University of Technology, Cracow, Poland
