Ion, activity product

Fig. 6-4. The dissolution rate as a function of the saturation index, omega-1, where omega = co3s cas/csat is the ion activity product divided by the saturation value.

Since, from the definitions of the ion activity product and equilibrium constant (Chapter 3),... 

Solubilities of the Mg-caldte as a function of MaCOn constant. The solubility is expressed in line with Eq. (8.11) as lAP g-calcite = (Ca2 1 ) (Mg2+) CO 2). The solid curves represent the general trend of results on dissolution of biogenic and synthetic Mg-calcites. The curve fitting the data of Plummer and Mackenzie (1974) is dashed. The various points refer to the results of different researches. (For the origin of the data see Morse and Mackenzie, 1990.) (IAP = ion activity product.)... 

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. 

Ion-Activity Products. As in the determination of the amount sorbed through Equation 2, the characterization of surface precipitates often utilizes measurements made solely on the aqueous solution phase. Solubility studies limited in this way run a risk of being ambiguous as to mechanism because of the lack of direct information about the solid phase (10). In respect to the aqueous solution phase, ambiguity can be minimized if equilibrium is approached both from supersaturation and from undersaturation if the equilibration time is varied... 

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 difficulty here is that the ion-activity product includes not only the Gibbs energy change in a solid dissolution process but also the activity of the solid itself. Consider, as a simple example, the dissolution of CdCOjis), for which the ion-activity product (IAP) is (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. 

Large concentrations of Fe + develop in the soil solution in the weeks following flooding, often several mM or tens of mM (Figure 4.5). Calculations with chemical equilibrium models show that the ion activity products of pure ferrous hydroxides, carbonates and other minerals are often exceeded 100-fold (Neue and Bloom, 1989). Evidently precipitation of these minerals is inhibited, probably as a result of adsorption of foreign solutes, such as dissolved organic matter and phosphate ions, onto nucleation sites (Section 3.7). However, once a sufficient supersaturation has been reached there is a rapid precipitation of amorphous solid phases, which may later re-order to more crystalline forms. Only a small part of the Fe(II) formed in reduction remains in solution the bulk is sorbed in exchangeable forms or, eventually, precipitated. 

The ion activity product (lAP) is a measure of the activity of ions present in the solvent. By definition, the activity of a mineral phase (if present) is unity. Thus the amount of precipitate does not affect the reaction between the solid and the... 

The comparison of the ion activity product (lAP) of the dissolved constituent ions (e.g. for goethite, Fe " and OH ) with JQo of a Fe oxide provides an indication of whether the oxide will precipitate or dissolve in a particular solution. If the lAP exceeds Kso> the solution is supersaturated with respect to the oxide and precipitation takes place. If lAP = K o, the system is in equilibrium and if lAP < K o, the oxide will dissolve until equilibrium is reached. Interference with nudeation may retard or even inhibit predpitation in a supersaturated solution and prevent true equilibrium from being attained. 

Fig. 4. Calculated estimate of the long-term stability of hydrotalcite in seawater at 60 C (a) log ions activity product/equilibrium constant (log IAP/K) (b) quantity of minerals formed (c) magnesium concentration in solution.

If the aluminate ion is a component in the chemical affinity term, then the activity of dissolved silica, by itself, cannot describe the change in rate with changes in chemistry of the contacting fluid. A number of attempts have been made to explicitly include Al activity in the chemical affinity term. Gin (1996) suggested that glass dissolution could be modelled using a mixed Si/Al term for the ion activity product ((2) ... 

This expression describes what is known as the Donnan equilibrium. It does not say that the activity of M+ and/or X is the same on both sides of the membrane, but that the ion activity product is constant on both sides of the membrane. In the sense that an ion product is involved, the Donnan equilibrium clearly resembles all other ionic equilibria. 

A parameter indicating the flux of Fe2+ and H2S would be the measured ion activity product, IAP (52). A low pIAP value, corresponding to amorphous FeS, does not necessarily mean that other, more stable, solid FeS phases do not exist (the system would be supersaturated with respect to these phases), but it may indicate that the formation rate of both Fe2+ and H2S is high. At low net fluxes, other solid phases have time to form. Consequently, inverse gradients can be observed in systems where the net fluxes of Fe2+ and H2S are high (pIAP increases with depth) and in systems where the net fluxes of Fe2+ and H2S are low at the sediment-water interface (pIAP decreases with depth) (cf. ref. 52). 

Figure 5. Profiles of ion activity products (pIAP values) of FeS measured in Lake Kinneret sediments after the end of an algae bloom (May 30, 1988), during the stratification period (October 24, 1988), and after overturn (January 5, 1989). Straight lines correspond to solubility products of various FeS phases according to the reaction FeS + H+ Fe2+ + HS. (Based on data...

The activities of Mg++ and Ca++ obtained from the model of sea water proposed by Garrels and Thompson have recently been confirmed by use of specific Ca++ and Mg++ ion electrodes, and for Mg++ by solubility techniques and ultrasonic absorption studies of synthetic and natural sea water. The importance of ion activities to the chemistry of sea water is amply demonstrated by consideration of CaC03 (calcite) in sea water. The total molality of Ca++ in surface sea water is about 10 and that of COf is 3.7 x 1C-4 therefore the ion product is 3.7 x 10 . This value is nearly 600 times greater than the equilibrium ion activity product of CaCO of 4.6 x 10-g at 25°C and one atmosphere total pressure. However, the activities of the free 10ns Ca++ and COj = in surface sea water are about 2.3 x 10-3 and 7.4 x 10-S, respectively thus the ion activity product is 17 x 10 which is only 3,7 rimes greater than the equilibrium ion activity product of calcite. Thus, by considering activities of sea water constituents rather than concentrations, we are better able to evaluate chemical equilibria in sea water an obvious restatement of simple chemical theory but an often neglected concept in sea water chemistry. 

Our procedure was to follow the changes in concentrations and ionic strength as the water is evaporated, and by correcting ion molalities by activity coefficients, keep track of the ion activity products of the various... 

Table VIII. Calculated Ion Activity Products of Various...

The next step is to determine whether or not the water as a result of the pH change has become saturated with respect to any of the solid phases considered (Table VII). For this, ion activity products are computed for each phase and compared with the equilibrium value (Table VIII). The calculation for calcite is given to illustrate the procedure. The ion activity product is... 

Consequently, because the equilibrium value of the ion activity product is 10 8-35, the water is slightly undersaturated with respect to calcite, its Ca2+ content is fixed by C02 pressure and pH in other words, because the product of aCa2+ and aCo32 is a constant, aCa2+ and hence mca2+ can be expressed as a negative term on the right side of the electrical balance equation. After sepiolite precipitates, it can be handled similarly. The... 

Nonlinear Precipitation of Secondary Minerals from Solution. Most of the studies on dissolution of feldspars, pyroxenes, and amphiboles have employed batch techniques. In these systems the concentration of reaction products increases during an experiment. This can cause formation of secondary aluminosilicate precipitates and affect the stoichiometry of the reaction. A buildup of reaction products alters the ion activity product (IAP) of the solution vis-a-vis the parent material (Holdren and Speyer, 1986). It is not clear how secondary precipitates affect dissolution rates however, they should depress the rate (Aagaard and Helgeson, 1982) and could cause parabolic kinetics. Holdren and Speyer (1986) used a stirred-flow technique to prevent buildup of reaction products. 

The product Meh+ a La h in a solution is known as the ion activity product (IAP). The IAP is a useful concept in chemical modelling and can be used to test whether certain solutions are supersaturated with respect to a particular solid phase. For implementation into computer models a saturation index is calculated using the expression ... 

A basic premise of solubility considerations is that a solution in contact with a solid can be in an equilibrium state with that solid so that no change occurs in the composition of solid or solution with time. It is possible from thermodynamics to predict what an equilibrium ion activity product should be for a given mineral for a set of specified conditions. As will be shown later in this chapter, however, it is not always possible to obtain a solution of the proper composition to produce the equilibrium conditions if other minerals of greater stability can form from the solution. It shall also be shown that while it is possible to calculate what mineral should form from a solution based on equilibrium thermodynamics, carbonate minerals usually behave in a manner inconsistent with such predictions. 

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