Conditional solubility product constant

Solubility product constants of 10-ll 73 and 10-22.4 have been reported (8) for uranyl carbonte and hydroxide, respectively. The hydroxide was calculated to be the stable solid phase under the conditions of our experiments. For... 

The hydroxide was expected to be the stable solid phase for Pu4+ under the conditions of our experiments. Reported and estimated solubility product constants range from 10-52 (7) to 10-62 (6). 

The model balance equation for each metal and ligand (e.g., Eqs. 2.49 and 2.52) is augmented to include formally the concentration of each possible solid phase. By choosing an appropriate linear combination of these equations, it is always possible to eliminate the concentrations of the solid phases from the set of equations to be solved numerically. Moreover, some of the free ionic concentrations of the metals and ligands also can be eliminated from the equations because of the constraints imposed by on their activities (combine Eqs. 3.2 and 3.3), which holds for each solid phase formed. The final set of nonlinear algebraic equations obtained from this elimination process will involve only independent free ionic concentrations, as well as conditional stability and solubility product constants. The numerical solution of these equations then proceeds much like the iteration scheme outlined in Section 2.4 for the case where only complexation reactions were considered, with the exception of an added requirement of self-consistency, that the calculated concentration of each solid formed be a positive number and that IAP not be greater than Kso (see Fig. 

A thermodynamic model of dissolution is presented in this chapter, which relates the solubility product constant to the thermodynamic potentials and measurable parameters, such as temperature and pressure of the solution. The resulting relations allow us to develop conditions in which CBPCs are likely to form by reactions of various oxides (or minerals) with phosphate solutions. Thus, the model predicts formation of CBPCs. 

The quantity Asp/aM i" may be regarded as a conditional solubility product, which is a function of the pH and of the reagent concentration. Equation (22-15) is also useful when one wishes to take into account the effect of hydrolysis or of masking agents that may be present. It is necessary only to make the appropriate calculation of the fraction from the hydrolysis constants [Equation (7-17)] or from the formation constants of the secondary complexes [Equation (11-16)]. 

In the WIPP performance assessment calculations, it was assumed that redox conditions would be controlled by the presence of metallic iron and that U(VI) would be reduced to U(IV). An upper bound for the solubility of U(IV) was estimated from that of Th(IV), using the oxidation state analogy. Calculations by Wall et al (2002) suggest that this is a conservative assumption— that the solubility of U(IV) is much lower than that of Th(IV). This is because the solubility product constant of Th02(am)> the solubility limiting phase in the An(IV) model, is several orders of magnitude greater than that of U02(am)-... 

In other words, equation (54) is only valid for those pH conditions for which the solubility product constant of the salt is not exceeded. 

The conditional solubility product where K sp is the conditional solubility product, similar to the conditional forma-value holds for only a specified pH. tion constant described in Chapter 9. 

In this equation lAP denotes the Ion Activity Product (in the example of gypsum or anhydrite these would be ([Ca " ] [SO/ ]). Kj,p is the solubility product constant of the respective mineral. A saturation index SI = 0 describes the condition in which the solution of the corresponding mineral is just saturated, SI > 0 describes the condition of supersaturation of the solution, SI < 0 its undersaturation. The activity [A] of a substance is calculated according to the equation ... 

The solubility product constant is a useful parameter for calculating the aqueous solubility of sparingly soluble compounds under various conditions. It may be determined by direct measurement or calculated from the standard Gibbs energies of formation AjG° of the species involved at their standard states. Thus if = [M ] ", [A ]" is the equilibrium constant for the reaction... 

The solubility product constant, K p, for calcium carbonate at room temperature is approximately 3.0 X 10 . Calculate the solubility of CaCOj in grams per liter under these conditions. 

Although the standard potentials are the fundamental values for all thermodynamic calculations, in practice, one has more frequently to deal with the so-called formal potentials. The formal potentials are conditional constants, very similar to the conditional stability constants of complexes and conditional solubility products of sparingly soluble salts (see [2c]). The term conditional indicates that these constants relate to specific conditions, which deviate from the usual standard conditions. Formal potentials deviate from standard potentials for two reasons, i.e., because of nonunity activity coefficients and because of chemical side reactions . The latter should better be termed side equilibria however, this term is not in common use. Let us consider the redox system iron(II/ni) in water ... 

Therefore, a thermodynamic equilibrium constant known as the solubility product constant K p is used for slightly soluble salts. This solubility product constant is useful for understanding the dissolution characteristics, because its value does not change in either acid or basic solutions under the same conditions of temperature, pressure and ionic strength. 

These examples illustrate the relationship between the solubility of a slightly soluble ionic compound in pure water and its solubility product constant. In the next section, you will see how the solubility product constant can be used to calculate the solubility in the presence of other ions. K p is also useful in deciding whether to expect precipitation under given conditions. 

On the other hand, the solubility of a substance is a value and not a product of values. Solubility is an equilibrium position that represents the amount of the sohd required to form a saturated solution with a specific amount of solvent It has an infinite number of possible values at a given temperature and is dependent on other conditions, such as the presence of a common ion. Another way to distinguish the two is that solubility speaks of the substance as a whole, while the solubility product constant deals with its constituent parts. 

The solubility product principle can be very useful when applied to solutions of slightly soluble substances. It cannothe applied to solutions of soluble substances. This is because the positive and negative ions attract each other, and this attraction becomes appreciable when the ions are close together. Sometimes it is necessary to consider two equilibria simultaneously. For example, if either ion hydrolyzes, the salt will be more soluble than predicted when only the solubility product constant is used. The solubility product is also sensitive to changes in solution temperature to the extent that the solubiUty of the dissolved substance is affected by such changes. All of these factors limit the conditions under which the solubility product principle can be applied. 

The notion of conditional solubility product is already an extension of the concept of conditional constants. Among other possible extensions, let s also mention the case for which in the studied complex, the metal and the hgand are combined in different ratios. For example, let s consider the case in which successive complexes ML and ML2 are forming. We ll consider that the complex under study is ML that is, it is considered the principal complex. After having adopted the same logic as that which prevailed in the adoption of conditional constants, we can write... 

Kq is termed the solubility product constant under standard conditions (SC),... 

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