Abstract
In this chapter, original methods for determining thermodynamic properties such as the equilibrium activity product or solubility product of sparingly soluble compounds and the stability constants of complexes are described. Methods for determining concentration product and solubility are based solely on pH measurements of the saturated aqueous solutions for a known initial composition of the heterogeneous mixture and the equilibrium constants of an arbitrary set of possible side reactions in the solution. In the case of sparingly soluble acids or hydroxides, the determination of the solubility (Sol) and solubility product (KS) is also possible in the presence of other acids and bases of known concentrations. Sol and KS were calculated from known experimental pH data for a series of hydroxides, acids, neutral and acidic salts MmHxAy(S), as well as basic/mixed salts Mm(OH)xAy(S) of arbitrary composition.
TopIntroduction
We describe the original method for determining thermodynamic characteristics in multicomponent heterogeneous systems such as the equilibrium activity product (
) or solubility product, equilibrium concentration product (KS) of sparingly soluble compounds, and the stability constants of complexes. The methods for KS and solubility (Sol) determining are based solely on pH measurements of saturated aqueous solutions for a known initial composition of the heterogeneous mixture and the equilibrium constants of an arbitrary set of possible side reactions in the solution. In the case of sparingly soluble acids or hydroxides, the determination of the solubility Sol and solubility product KS is also possible in the presence of other acids and bases of known concentrations. The quantities of Sol and KS have been calculated from the known experimental pH data for a series of hydroxides, acids, neutral salts MmAy(S), acidic salts MmHxAy(S) and basic/mixed salts Mm(OH)xAy(S) of arbitrary composition. The elaborated methods for determining the solubility and solubility product of slightly soluble compounds of different nature and arbitrary composition based on pH-metric data allow an essential simplification of the experimental measurement procedure.
The research of the thermodynamic characteristics of complex chemical equilibria and the thermodynamic properties of substances provokes a continuous interest and attracts attention, because the thermodynamic data have both scientific and practical importance (Bénézeth et al., 2018; Gácsi et al., 2016; Sandeepa et al., 2018; Scholz & Kahlert, 2015). Their reciprocal relations with different physicochemical properties constitute the basis for the systematization of experimental material, the substantiated search for the optimal conditions of technological processes or the repression of unwanted or unknown laws, as well as for solving other practical or theoretical tasks. Thus, for example, the regulation of thermodynamic parameters allows to turn the different processes in the desired direction and to synthesize the substances with certain properties. At the same time, for optimal realization of process and the regulation of the composition of a system, it is necessary that in the field of optimal concentrations it would have a minimum sensitivity and high buffering action in relation to the substance in force (Tenno et al., 2018; Zhang et al., 2015). The thermodynamics of equilibrium processes play an essential role in the design of technological schemes for the synthesis and purification of substances (Pohl, 2020). Due to the complexity and large volume of experiments, a current task is to develop and apply the thermodynamic research methods to describe the complex experiments and predict them in those cases where the experiment is impossible or difficult to perform.
The solubility method is one of the oldest research methods of the processes of complexes formed in solution. The general methods for measuring solubility are well described in the literature (Pazukhin & Kudryavtsev, 1990; Schwertmann, 1991). The exact composition of precipitate must be known in the solubility method and remain unchanged during the experiment. Although the measurement of solubility usually includes the analysis of saturated solution, the experiments were also performed to mix the solutions of known concentration with the subsequent determination of the mass of precipitate formed (Pazukhin & Kudryavtsev, 1990). The composition and stability of insoluble and soluble species are determined by the mathematical analysis of the solubility curve.
In the general case, two types of experimental data were used: a) solubility as a function of the initial concentrations of substances in solution or b) measurement of solubility is accompanied by the determination of one or several additional functions of the solution composition, more commonly pH. The determination of the solubility product is essentially simplified if, at the same time as the solubility, the pH of the saturated solution is measured. This variant of determining the solubility product has been used in a number of works (Bergström & Avdeef, 2019; Bulatov, 1974; Dyatlova et al., 1988; Hsieh et al., 2015; McBride et al, 2019; Sa‘ib, 2015).
Key Terms in this Chapter
Homogenous Mixture: Mixture of substances blended so thoroughly that you cannot see individual substances. Every sample of the mixture will show the same amounts of each substance. Homogeneous mixtures can be solid, liquid, gas, or plasma mixtures.
Equilibrium: State where reactants and products reach a balance - no more solute can be dissolved in the solvent in the set conditions (temperature, pressure). Such a solution is called a saturated solution.
Sparingly Soluble Compound: It precipitates up to reaching equilibrium between the produced solid phase and its ions in the solution.
Residual Concentration: The difference between the initial concentration of species in the solution and its quantity in mol in the solid phase per one liter of saturated solution. After reaching the equilibrium state in the heterogeneous mixture, the solid phase is separated from the liquid one, and then the residual concentration is measured.
Solubility Product: Of a compound at a given temperature is equal to the product of the concentrations of its ions in the saturated solution, with each concentration term raised to the power to the number of ions produced on dissociation of one mole of the substance.
Heterogenous Mixture: Mixture with a non-uniform composition. The composition varies from one region to another with at least two phases that remain separate from each other, with clearly identifiable properties.
Stoichiometric Coefficient: Number written in front of atoms, ions, and molecules in a chemical reaction to balance the number of each element on both the reactant and product sides of the equation. Though the stoichiometric coefficients can be fractions, whole numbers are frequently used and often preferred.
Solubility: The ability of a solid, liquid, or gaseous chemical substance (referred to as the solute) to dissolve in solvent (usually a liquid) and form a solution. The solubility of a substance fundamentally depends on the solvent used, as well as temperature and pressure. The solubility of a substance in a particular solvent is measured by the concentration of the saturated solution. A solution is considered saturated when adding additional solute no longer increases the concentration of the solution.