Solubility product constant measurement

The general approach illustrated by Example 18.7 is widely used to determine equilibrium constants for solution reactions. The pH meter in particular can be used to determine acid or base equilibrium constants by measuring the pH of solutions containing known concentrations of weak acids or bases. Specific ion electrodes are readily adapted to the determination of solubility product constants. For example, a chloride ion electrode can be used to find [Cl-] in equilibrium with AgCl(s) and a known [Ag+]. From that information, Ksp of AgCl can be calculated. 

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). 

It has long been recognized that ferric iron is a moderately strong acid. As early as 1896, Goodwin (5) concluded from conductometric measurements that simple dilution of ferric chloride solutions led to the formation of FeOH2+. The insolubility of ferric hydroxide has of course been appreciated even longer. The best current estimate of the solubility product constant for Fe OH)s at 25° (in 3 M NaC104) is (d). 

Metastability of Hydrolyzed Iron (III) Solutions The low solubility of ferric hydroxide has been alluded to in the Introduction. Feitknecht and Michaelis (29) have observed that aU ferric perchlorate solutions to which base has been added are unstable with respect to eventual precipitation of various forms of hydrated ferric oxides. In 3 M NaC104 at 25° C the two phase system reaches an apparent equilibrium after 200 hours, according to Biedermann and Schindler (6), who obtained a reproducible solubility product constant for ferric hydroxide at varying degrees of hydrolysis. It appears that many of the solutions used in the equilibrium studies of Hedstrom (9) and Biedermann (22) were metastable, and should eventually have produced precipitates. Nevertheless, since the measured potentials were reversible, the conclusions reached about the species present in solution remain valid. 

A potentiometric method for determination of ionization constants for weak acids and bases in mixed solvents and for determination of solubility product constants in mixed solvents is described. The method utilizes glass electrodes, is rapid and convenient, and gives results in agreement with corresponding values from the literature. After describing the experimental details of the method, we present results of its application to three types of ionization equilibria. These results include a study of the thermodynamics of ionization of acetic acid, benzoic acid, phenol, water, and silver chloride in aqueous mixtures of acetone, tetrahydrofuran, and ethanol. The solvent compositions in these studies were varied from 0 to ca. 70 mass % nonaqueous component, and measurements were made at several temperatures between 10° and 40°C. 

The use of radiotracers is an excellent technique for measuring the solubility product constant of sparingly soluble salts or for making other studies of substances present in low concentrations. Another very important and classic example of the use of radiotracers is that of studying the occurrence and properties of isotopic exchange reactions—reactions of the type... 

Total salinity based on K2 (second ionization constant for carbonic acid) and Kj (solubility product constant for CaCC>3) (in practice measured as total dissolved solids)... 

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 this chapter, we will extend the concepts of equilibrium that have been discussed in previous chapters. In Chapter 10 we discussed the concept of equilibrium in relation to saturated solutions in which an equilibrium was established between solvated ions and undissolved solute. In Chapter 11 we discussed the solubility of different salts when we looked at the formation of precipitates. In this chapter you will see the connection between these two ideas with the introduction of the solubility product constant, Ksp, which is a quantitative means of describing solubility equilibria. This measure helps to predict and explain the precipitation of different salts from solution. You will also see how the common-ion effect, temperature, and pH affect solubility. 

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 solubility product constants for some ionic compounds are listed in Table 18-3. Note that they are all small numbers. Solubility product constants are measured and recorded only for sparingly soluble compounds. 

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 ... 

The foregoing example illustrates how equilibrium constants for overall cell reactions can be determined electrochemically. Although the example dealt with redox equilibrium, related procedures can be used to measure the solubility product constants of sparingly soluble ionic compounds or the ionization constants of weak acids and bases. Suppose that the solubility product constant of AgCl is to be determined by means of an electrochemical cell. One half-cell contains solid AgCl and Ag metal in equilibrium with a known concentration of CP (aq) (established with 0.00100 M NaCl, for example) so that an unknown but definite concentration of Kg aq) is present. A silver electrode is used so that the half-cell reaction involved is either the reduction of Ag (aq) or the oxidation of Ag. This is, in effect, an Ag" Ag half-cell whose potential is to be determined. The second half-cell can be any whose potential is accurately known, and its choice is a matter of convenience. In the following example, the second half-cell is a standard H30" H2 half-cell. 

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. 

A silver rod and a SHE are dipped into a saturated aqueous solution of silver oxalate, Ag2C204, at 25°C. The measured potential difference between the rod and the SHE is 0.589 V, the rod being positive. Calculate the solubility product constant for silver oxalate. 

Calcite solubility product constants range over 0.3 log units. The major tabulated differences are in the free energies of calcite and of the calcium ion. The most reliable measurement and evaluation of calcite solubility is that of Plummer and Busenberg (31). They found log Ksp = -8.48(+ 0.02) at 298.15 K which agrees excellently with the CODATA value of -8.47. The main source of error can be traced to a 2 kJ/mol difference between the CODATA and USGS values for the enthalpy of formation of calcite from the elements. The recent CODATA revisions of the calcium ion and calcite values take into account many different properties including the Plummer and Busenberg solubility value (31). Hence, they are the most reliable values for this system. 

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... 

It follows that we can determine the solubility product constants for slightly soluble materials by measuring the standard potential of the appropriate electrochemical cell. (Compare to Examples 17.6 and 17.7, Section 17.12.)... 

It is important to distinguish carefully between solubility and the solubility-product constant. The solubility of a substance is the quantity that dissolves to form a saturated solution. (Section 13.2) Solubility is often expressed as grams of solute per liter of Solution (g/L). Molar solubility is the number of moles of solute that dissolve in forming 1 L of saturated solution of the solute (mol/L). The solubility-product constant (K p) is the equilibrium constant for the equilibrium between an ionic solid and its saturated solution and is a unitless number. Thus, the magnitude of is a measure of how much of the solid dissolves to form a saturated solution. 

Physical-chemical data concerning ionic equilibria can be obtained from conductimetric studies. Con-ductimetric measurement has led to the determination of acid and base dissociation constants, stability constants, and solubility product constants. Further details may be found in modern texts of physical chemistry. 

The solubility product constants K,p = exp(—AG /KT) are 2.5x10 and 5.0 X 10 , respectively. Prior values from approaches to solubility equilibria on poorly crystallized precipitates were significantly larger (Baes and Mesmer 1976). One would expect the K°p measured from finely divided precipitates to be larger, rather than smaller, than that determined from well-crystallized solids used for calorimetry. However, Kragten and Decnop-Weever (1987) found K% [La(OH)j] = 1.6 x 10 in the most recent study of a series of lanthanide-hydroxide equilibrium studies by the precipitation borderline method. 

A student measures the molar solubility of magnesium fluoride in a water solution to be 1.19 X 10 M. Based on her data, what is the solubility product constant for this compound ... 

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