The value of the constant identifies the degree to which the compound can dissociate in water. It is influenced by surroundings. A saturated solution is in a state of equilibrium between the dissolved, dissociated, undissolved solid, and the ionic compound. Austin State University with contributing authors. Introduction Recall that the definition of solubility is the maximum possible concentration of a solute in a solution at a given temperature and pressure.
Calculation of K sp from Equilibrium Concentrations We began the chapter with an informal discussion of how the mineral fluorite is formed. Again, the equation can be simplified. This approximation is also valid, since only 0. Fluoride is more effective than calcium as a common ion because it has a second-power effect on the solubility equilibrium. Boundless vets and curates high-quality, openly licensed content from around the Internet. This particular resource used the following sources:.
JPG Wikimedia Public domain. Skip to main content. Acid-Base Equilibria. The precipitate of nickel dimethylglyoximate, NiL 2 , has soluble counterpart with the same formula, i.
Moreover, it is a predominant component in expression for s in alkaline media, see Figure 8. This pH range involves pH of ammonia buffer solutions, where NiL 2 is precipitated from NiSO 4 solution during the gravimetric analysis of nickel; the expression for solubility. The effect of other, e. The presence of citrate does not affect significantly the solubility of NiL 2 in ammonia buffer media, i. Solubility of HL in water, equal 0. However, the aqueous-ethanolic medium is thus formed, where equilibrium constants are unknown.
To avoid it, lower C Ni and C L values were applied in calculations. The equilibrium data were taken from Ref. The soluble complex having the formula identical to the formula of the precipitate occurs also in other, two-phase systems.
In some pH range, concentration of this soluble form is the dominant component of the expression for the solubility s. As stated above, such a case occurs for NiL 2. Then one can assume the approximation. Similar relationship exists also for other precipitates. By differentiation of Eq. In this case, the solubility s and then theoretical accuracy of gravimetric analysis does not change with temperature.
The core is a cluster of elements with defined composition expressed by its chemical formula and external charge that remains unchanged during the chemical process considered, e. For modeling purposes, the closed systems, composed of condensed phases separated from its environment by diathermal freely permeable by heat walls, are considered; it enables the heat exchange between the system and its environment.
Any chemical process, such as titration, is carried out under isothermal conditions, in a quasistatic manner; constant temperature is one of the conditions securing constancy of equilibrium constants values. An exchange of the matter H 2 O, CO 2 , O 2 ,… between the system and its environment is thus forbidden, for modeling purposes.
GEB is fully compatible with charge balance ChB and concentration balances F Y g , formulated for different elements and cores.
Both approaches I and II to GEB were widely discussed in the literature [ 7 — 12 , 14 , 15 , 17 , 18 , 34 , 52 — 74 ], and in three other chapters in textbooks [ 75 — 79 ] issued in within InTech. The GEB is perceived as a law of nature [ 9 , 10 , 17 , 67 , 71 , 73 , 74 ], as the hidden connection of physicochemical laws, as a breakthrough in the theory of electrolytic redox systems. The GATES refers to mono- and polyphase, redox, and nonredox, equilibrium and metastable [ 20 , 21 — 23 , 78 , 79 ] static and dynamic systems, in aqueous, nonaqueous, and mixed-solvent media [ 69 , 72 ], and in liquid-liquid extraction systems [ 53 ].
Summarizing, Approach II to GEB needs none prior information on oxidation numbers of all elements in components forming a redox system and in the species in the system thus formed.
This property distinguishes redox and nonredox systems of any degree of complexity. A detailed consideration of complex electrolytic systems requires a collection and an arrangement of qualitative particular species and quantitative data; the latter ones are expressed by interrelations between concentrations of the species. The interrelations consist of material balances and a complete set of expressions for equilibrium constants.
Our further considerations will be referred to a titration, as a most common example of dynamic systems. The redox and nonredox systems, of any degree of complexity, can be resolved in analogous manner, without any simplifications done, with the possibility to apply all prior, preselected physicochemical knowledge involved in equilibrium constants related to a system in question.
This way, one can simulate imitate the analytical prescription to any process that may be realized under isothermal conditions, in mono- and two-phase systems, with liquid-liquid extraction systems included. The system considered in this section is related to iodometric, indirect analysis of an acidified H 2 SO 4 solution of CuSO 4 [ 14 , 64 ].
It is a very interesting system, both from analytical and physicochemical viewpoints. This method consists of four steps. To follow the changes occurring in particular steps of this analysis, we assume that the corresponding reagents in particular steps are added according to the titrimetric mode, and the assumption of the volumes additivity is valid. The balances written according to Approach I to GEB, in terms of molar concentrations, are as follows:.
Concentrations of the species in the equations are interrelated in 35 independent equilibrium constants:. In the calculations made in this system according to the computer programs attached to Ref. This precipitate appears in the initial part of titration with KI C 3 solution Figure 8a and further it accompanies the titration, also in stage 4 Figure 8b.
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. For more details see text. Plots of E versus V for a stage 3 and b stage 4. The course of the E versus V relationship within the stage 3 is worth mentioning Figure 10a. Precipitation of CuI starts after addition of 0.
Subsequently, the curve in Figure 10 a increases, reaches a maximum and then decreases. Solubility s of CuI within stage 3 a and stage 4 b. 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 two-phase electrolytic systems was still rudimentary. However, the earlier arrangements persisted in subsequent generations [ 81 ], and little has changed in the meantime [ 82 ]. In the meantime, Meites et al.
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. 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.
In calculations of s, all the species formed by defined element are involved, not only the species from the related reaction notation. 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 K sp values in the relevant tables were obtained in a manner worthy of the recognition, i. 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.
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 The studies of complexes formed by simple ions started only from the s; these studies were related both to mono- and two-phase 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 o spreadsheets 2 o iterative calculation methods. In 1 o , 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. Moreover, K sp is not necessarily the product of ion concentrations, as indicated in formulas 4 , 5 , and In some numerous instances of sparingly soluble species, e.
In some instances, e. 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.
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