Thermodynamic equilibrium constant solubility product

In Chapter 6 we defined the thermodynamic equilibrium constant written in terms of activities to account for the effects of inert electrolytes on equilibria. The presence of diverse salts will generally increase the solubility of precipitates due to the shielding of the dissociated ion species. (Their activity is decreased.) Consider the solubility of AgCl. The thermodynamic solubility product K p is... 

Since there are two singly charged ions both in the numerator and in the denominator of this equilibrium concentration quotient and thi ionic concentration never exceeds 0.1 mole 1 , we assume that th. value of is equal, within about 10%, to that of the (thermodynamic < equilibrium constant for the reaction. Dmding this constant by thf solubility product of silver iodide, we obtain the equilibrium constant K - Q s ... 

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. 

Another important application is the use of potentio-metric measurements for the evaluation of thermodynamic equilibrium constants. In particular, the dissociation constants for weak acids and weak bases in a variety of solvents are evaluated conveniently with a pH electrode measuring system. The most precise approach is to perform an acid-base titration such that the titration curve can be recorded. Obviously, one could measure the pH of a known concentration of a weak acid and obtain a value of its hydronium-ion activity which would permit a direct evaluation of its dissociation constant. However, this would be a one-point evaluation and subject to greater errors than by titrating the acid halfway to the equivalence point. The latter approach uses a well-buffered region where the pH measurement represents the average of a large number of data points. Similar arguments can be made for the evaluation of solubility products and stability constants of complex ions. 

One of the most basic requirements in analytical chemistry is the ability to make up solutions to the required strength, and to be able to interpret the various ways of defining concentration in solution and solids. For solution-based methods, it is vital to be able to accurately prepare known-strength solutions in order to calibrate analytical instruments. By way of background to this, we introduce some elementary chemical thermodynamics - the equilibrium constant of a reversible reaction, and the solubility and solubility product of compounds. More information, and considerably more detail, on this topic can be found in Garrels and Christ (1965), as well as many more recent geochemistry texts. We then give some worked examples to show how... 

Sol id Sol utions. The aqueous concentrations of trace elements in natural waters are frequently much lower than would be expected on the basis of equilibrium solubility calculations or of supply to the water from various sources. It is often assumed that adsorption of the element on mineral surfaces is the cause for the depleted aqueous concentration of the trace element (97). However, Sposito (Chapter 11) shows that the methods commonly used to distinguish between solubility or adsorption controls are conceptually flawed. One of the important problems illustrated in Chapter 11 is the evaluation of the state of saturation of natural waters with respect to solid phases. Generally, the conclusion that a trace element is undersaturated is based on a comparison of ion activity products with known pure solid phases that contain the trace element. If a solid phase is pure, then its activity is equal to one by thermodynamic convention. However, when a trace cation is coprecipitated with another cation, the activity of the solid phase end member containing the trace cation in the coprecipitate wil 1 be less than one. If the aqueous phase is at equil ibrium with the coprecipitate, then the ion activity product wi 1 1 be 1 ess than the sol ubi 1 ity constant of the pure sol id phase containing the trace element. This condition could then lead to the conclusion that a natural water was undersaturated with respect to the pure solid phase and that the aqueous concentration of the trace cation was controlled by adsorption on mineral surfaces. While this might be true, Sposito points out that the ion activity product comparison with the solubility product does not provide any conclusive evidence as to whether an adsorption or coprecipitation process controls the aqueous concentration. 

The thermodynamic feasibility of a reaction with precipitating products can be assessed by comparing the mass action ratio to the equilibrium constant of a reaction. This requires estimation of solubilities, using melting points of reactants in combination with the reaction equilibrium constant [39]. 

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 ... 

This is a dissolution equilibrium that is governed by the thermodynamic constant called Ksp (solubility product, see Example 2.1). To calculate the K3p value, we now use the A G/° values from the table. First we use them to calculate the A G° for this reaction and we then use this value to calculate the numerical value for Ksp. Because [Al3+] is given, we are able to calculate [OH-] and thus the pH. Mathematically speaking ... 

Solubility products, like other equilibrium constants, are thermodynamic quantities. They tell us nothing about how fast a given reaction occurs, only whether it can occur under specified conditions. 

Electrochemical cells can also be used to determine other thermodynamic parameters such as equilibrium constants. For example, the solubility product for the sparingly soluble salt AgCl may be determined by comparing the properties of the silver silver chloride electrode (9.2.23) with those of the silver silver ion electrode (9.2.39). The potentials of these electrodes are equal when they are in a saturated solution of AgCl, that is, when the activities of these ions are those given by equilibrium (9.2.40). Therefore, under these conditions... 

Thermodynamics The equilibrium constant for dissolving an ionic substance is known as the solubility product. It is related to a Gibbs free energy change that depends on a balance of lattice energy and solvation energies, together with an entropy contribution. 

The available thermodynamic data are of two types stabihty constants, enthalpy and entropy of reaction for the formation of soluble complexes Th(S04) " " and solubihty data for various solid phases. The two sources are linked because the solubility of the solid phases depends on the chemical speciation, i.e., the sulphate complexes present in the aqueous phase. The analysis of the experimental stability constants has been made using the SIT model however, this method cannot be used to describe the often very high solubility of the solid sulphate phases. In order to describe these data the present review has selected a set of equilibrium constants for the formation of Th(S04) and Th(S04)2(aq) at zero ionic strength based on the SIT model and then used these as constants in a Gibbs energy minimisation code (NONLINT-SIT) for modelling experimental data to determine equilibrium constants for the formation of Th(S04)3 and the solubility products of different thorium sulphate solids phases. 

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