Activity solubility product constant

Molarity, molality, standard state and activity Solubility product constants... 

It is important to note that the solubility product relation applies with sufficient accuracy for purposes of quantitative analysis only to saturated solutions of slightly soluble electrolytes and with small additions of other salts. In the presence of moderate concentrations of salts, the ionic concentration, and therefore the ionic strength of the solution, will increase. This will, in general, lower the activity coefficients of both ions, and consequently the ionic concentrations (and therefore the solubility) must increase in order to maintain the solubility product constant. This effect, which is most marked when the added electrolyte does not possess an ion in common with the sparingly soluble salt, is termed the salt effect. 

Once the composition of the aqueous solution phase has been determined, the activity of an electrolyte having the same chemical formula as the assumed precipitate can be calculated (11,12). This calculation may utilize either mean ionic activity coefficients and total concentrations of the ions in the electrolyte, or single-ion activity coefficients and free-species concentrations of the ions in the electrolyte (11). If the latter approach is used, the computed electrolyte activity is termed an ion-activity product (12). Regardless of which approach is adopted, the calculated electrolyte activity is compared to the solubility product constant of the assumed precipitate as a test for the existence of the solid phase. If the calculated ion-activity product is smaller than the candidate solubility product constant, the corresponding solid phase is concluded not to have formed in the time period of the solubility measurements. Ihis judgment must be tempered, of course, in light of the precision with which both electrolyte activities and solubility product constants can be determined (12). 

The experimental observation that an ion-activity product is smaller than a corresponding solubility product constant by an order of magnitude or less provides no evidence as to the general mechanism of a sorption process. 

Write the equation for the slight dissolution of the insoluble compound and calculate the AG°(reaction) using Equation (6) from Chapter 2. Once the AG°(reaction) value is obtained, the K value is calculated using Equation (8) also from Chapter 2. Keeping in mind that the concentration (activity) of the insoluble compound is defined as 1, it is recognized that the K value for the dissolution of the insoluble compound is the solubility product constant, Ksp. Alternatively, the Ksp value may be available from compilations of such values as presented in Lange s Handbook of Chemistry or the CRC Handbook of Chemistry and Physics. ... 

The solubility, s, of AgCl can be determined at a given temperature and tile activity coefficient y determined at that temperature from the solubility and the solubility product constant K. Thus... 

As an alternative to laboratory solubility measurements, solubility product constants (KSp), which are derived from thermodynamic data, can be used to calculate the solubility of solids in water (Table 2.9). Each solubility product constant describes a disassociation of a solid in water and calculates the activities or concentrations of the dissolution products in the saturated solution. The solubility product constant or another equilibrium constant of a reaction may be derived from the Gibbs free energy of the reaction (AG"K) as shown in the following equation ... 

In complex solutions such as estuarine waters, where the proportion of ions in solution is commonly not the same as that in the solids from which they are derived, it is necessary to use the solubility product constant defined as KSp = [A ] [B-]. To determine the degree to which a solution is supersaturated or undersaturated, the ion activity product (IAP) can be compared to the Ksp. 

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. 

Because for a solid phase AB the activity is assumed to be constant at 1, the equilibrium constant of the mass-action law results in a solubility product constant (Ksp) or ion-activity product (IAP) as below ... 

The logarithm of the quotient of the ion activity product (IAP) and solubility product constant (KSP) is called the saturation index (SI). The IAP is calculated from activities that are calculated from analytically determined concentrations by considering the ionic strength, the temperature, and complex formation. The solubility product is derived in a similar manner as the IAP but using equilibrium solubility data corrected to the appropriate water temperature. 

Using the solubility product constants for calcite and strontianite and assuming a calcium activity of 1.6 mmol/L, a distribution coefficient of 0.8 for strontium and 0.98 for calcite, and a ratio of 50 1 (=0.02) in the solid-solution mineral, the following equation gives the activity of strontium ... 

For the species in solution (SOLUTIONSPECIES, Table 23), listed in the top row with current number, solubility constant log k and enthalpy delta h are given in kcal/mol or kJ/mol at a temperature of 25 °C. Using the sub-key-word gamma parameters for the calculation of the activity coefficient y according the WATEQ-DEBYE-HUCKEL ion dissociation theory (compare to chapter 1.1.2.6.1) are given. With the sub-key-word analytical , coefficients At to A5 are defined to calculate the temperature dependence of the solubility-product constant. 

A suite of both oxidized and reduced iron minerals has been found as efflorescences and precipitates in or near the acid mine water of Iron Mountain. The dominant minerals tend to be melan-terite (or one of its dehydration products), copiapite, jarosite and iron hydroxide. These minerals and their chemical formulae are listed in Table III from the most ferrous-rich at the top to the most ferric-rich at the bottom. These minerals were collected in air-tight containers and identified by X-ray diffractometry. It was also possible to check the mineral saturation indices (log Q(AP/K), where AP = activity product and K = solubility product constant)of the mine waters with the field occurrences of the same minerals. By continual checking of the saturation index (S.I.) with actual mineralogic occurrences, inaccuracies in chemical models such as WATEQ2 can be discovered, evaluated and corrected (19), provided that these occurrences can be assumed to be an approach towards equilibrium. 

Chemistry is a very wide field however, only a very small portion, indeed, of this seemingly complex subject is used in this book. These include equivalents and equivalent mass, methods of expressing concentrations, activity and active concentration, equilibrium and solubility product constants, and acids and bases. This knowledge of chemistry will be used under the unit processes part of this book. 

Note the pair of braces denoting activity. Because is a solid, its activity is unity. For this reason, the product K AJi,] is a constant and is designated as K p. Ksp is called the solubility product constant of the equilibrium dissolution reaction. Equation (11) now transforms to... 

After speciation and activities have been calculated for all the free ions, ion pairs, triplets, etc., a mineral saturation index can be computed. The saturation index, SI, is defined as the logarithm of the ratio of the ion-activity product, lAP, to the solubility product constant,... 

Calcium sulfite and calcium sulfate scaling in the system can be a problem for the lime/limestone wet scrubber systems. Scaling occurs when the solutions are supersaturated to a point where heterogeneous crystallization (crystallization on foreign surfaces such as the scrubber walls, overfiow pots, marbles) takes place, resulting from nucleation. The ratios of the products of the activities (A) of Ca and S04 " or to their solubility product constants Kgp) as a measure of the degree of supersaturation are ... 

Laboratory experiments have shown that heterogeneous crystallization is not significant until the ratio of the activity product to the solubility product constant reaches about 1.5 for calcium sulfate and about 7 for calcium sulfite. 

Numerical values for solubility-product constants, dissociation constants, and formation constants are conveniently evaluated through the measurement of cell potentials. One important virtue of this technique is that the measurement can be made without appreciably affecting any equilibria that may be present in the solution. For example, the potential of a silver electrode in a solution containing silver ion, cyanide ion, and the complex formed between them depends on the activities of the thiee species. It is possible to measure this potential with negligible current. 

In equilibria that involve slightly soluble compounds in water, the equilibrium constant is called a solubility product constant, The activity of the solid BaSO is one (Section... 

For aqueous systems, a unit activity is expected for the solid species (i.e., we assume that the chemical reactivity of a solid in water is unchanging as long as there is solid in equilibrium with the solution). Also, for dilute concentrations, we assume that the activities are equal to the concentrations of the species. With these assumptions, we can reduce the solubility product constant equation to... 

In the usual consideration for sparingly soluble salts, the activity coefficients Ym+ and Ya would each equal unity, and the solubility product constant can be derived using only the concentrations of the ions. 

Figure 1. Activity of CaSOi when MgSOt is added to a 0.01 M CaSOf solution at 50°C as calculated from the Bechtel-modified Radian Equilibrium Program and from the Pitzer equations in this chapter. The horizontal line shows the solubility-product constant of CaSOt.

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 ... 

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