Solubility equilibrium calculations

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. 

Two different approaches have been taken by researchers to determine the secondary mineralogy of CCBs (1) direct observation, which is accomplished via analysis of weathered ash materials, and (2) prediction, based on chemical equilibrium solubility calculations for ash pore-waters and/or experimental ash leachate or extractant solutions. Because the secondary phases are typically present in very low abundance, their characterization by direct analysis is difficult. On the other hand, predictions based on chemical equilibrium modelling or laboratory leaching experiments may not be reliable indicators of element leachability or accurately indicate the secondary phases that will form under field conditions (Eighmy et al. 1994 Janssen-Jurkovicova et al. 1994). 

The results obtained in the previous section permit calculation of penetrant solubility in a glassy polymer as a function of temperature, penetrant fugacity and polymer density. Contrary to the situation for the equilibrium solubility calculation, the polymer density under pseudo- uilibrium conditions must be known in order to calculate the corresponding penetrant content. For pure penetrants, the comparison of model predictions with experimental isotherms is rather satisfactory for the cases in which volume dilation data are also available (i, 13),... 

McFarland et al. recently [1] published the results of studies carried out on 22 crystalline compounds. Their water solubilities were determined using pSOL [21], an automated instrument employing the pH-metric method described by Avdeef and coworkers [22]. This technique assures that it is the thermodynamic equilibrium solubility that is measured. While only ionizable compounds can be determined by this method, their solubilities are expressed as the molarity of the unionized molecular species, the intrinsic solubility, SQ. This avoids confusion about a compound s overall solubility dependence on pH. Thus, S0, is analogous to P, the octanol/water partition coefficient in both situations, the ionized species are implicitly factored out. In order to use pSOL, one must have knowledge of the various pKas involved therefore, in principle, one can compute the total solubility of a compound over an entire pH range. However, the intrinsic solubility will be our focus here. There was one zwitterionic compound in this dataset. To obtain best results, this compound was formulated as the zwitterion rather than the neutral form in the HYBOT [23] calculations. 

Since [Fe(lll)]jojaj [Fe " ], the formation of ion pairs and complexes is greatly enhancing the equilibrium solubility of ferrihydrite. This is called the salting-in effect and illustrates why mineral solubility calculations in seawater must take ion speciation into consideration. 

This simplified calculation is used to illustrate basic computational techniques. It assumes that all of the Fe(OH)3(aq) is a true solute. The quality of this assumption is a matter of debate as at pH 8, Fe(OH)3(aq), tends to form colloids. Thus, laboratory measurements of ferrihydrite solubility yield results highly dependent on the method by which [Fe(lll)]jQ(gj is isolated. Ultrafiltration techniques that exclude colloids from the [Fe(lll)]jQjgj pool produce very low equilibrium solubility concentrations, on the order of 0.01 nM. This is an important issue because a significant fraction of the iron in seawater is likely colloidal, some of which is inorganic and some organic. In oxic... 

The equilibrium solubility of an Fe oxide can be approached from two directions -precipitation and dissolution. The first method involves precipitating the oxide from a supersaturated solution of ions with stepwise or continuous addition of base und using potentiometric measurements to monitor pH and calculate Fej- in equilibrium with the solid phase until no further systematic change is detected. Alternatively the oxide is allowed to dissolve in an undersaturated solution, with simultaneous measurement of pH and Fejuntil equilibrium is reached. It is essential that neither a phase transformation nor recrystallization (formation of larger crystals) occurs during the experiment this may happen with ferrihydrite which transforms (at room temperature) to a more condensed, less soluble phase. A discussion of the details of these methods is given by Feitknecht and Schindler (1963) and by Schindler (1963). 

For mote about equilibrium calculations, see W. B. Guenther, Unified Equilibrium Calculations (New York Wiley, 1991) J. N. Butler. Ionic Equilibrium Solubility and pH Calculations (New York Wiley, 1998) and M. Meloun, Computation of Solution Equilibria (New York Wiley, 1988). For equilibrium calculation software, see http //www.micromath.com/ and http //www.acadsoft.co.uk/... 

From Chapters 4, 5 and 6 thermodynamic data and predictions, the maximum methane concentration (solubility) occurs in the aqueous liquid at equilibrium with hydrates. In order for methane to exsolve the liquid, the solubility must change rapidly as the water rises with corresponding decreases in pressure and temperature. Solubility calculations (Handa, 1990) indicate a change in methane concentration too gradual to account for a significant hydrate amount. Solubility data are needed at conditions of hydrate formation, in order to confirm this model. Preliminary solubility data are available from Besnard et al. (1997). 

A. Calculate the equilibrium solubilities in the liquid and solid at 0.2 atmosphere H2. Express your answer in STP. 

Nitric acid is a strong electrolyte. Therefore, the solubilities of nitrogen oxides in water given in Ref. 191 and based on Henry s law are utilized and further corrected by using the method of van Krevelen and Hofhjzer (77) for electrolyte solutions. The chemical equilibrium is calculated in terms of liquid-phase activities. The local composition model of Engels (192), based on the UNIQUAC model, is used for the calculation of vapor pressures and activity coefficients of water and nitric acid. Multicomponent diffusion coefficients in the liquid phase are corrected for the nonideality, as suggested in Ref. 57. 

The thermodynamic equilibrium is calculated with the Henry coefficients corrected for the electrolyte influence. As nitric acid is a strong electrolyte, the solubilities of nitrogen oxides in water [81] must be recalculated according to [20] to account for the non-ideal electrolyte behavior. 

J. N. Butler, Ionic Equilibrium Solubility and pH Calculations, Wiley Interscience, New York, 1998. 

The experimental technique involves batch gas absorption (by surface aeration) in a liquid. The pressure of the enclosed gas phase in the reactor decreases with time because of the absorption. This decrease in pressure with time allows the estimation of the mass-transfer rate and the volumetric mass-transfer coefficient, kLaL. The total pressure decrease until equilibrium is reached gives the equilibrium solubility C. The relevant equations for the calculations of C and kLaL are derived by Albal et al. (1983), Deimling et al. (1985), and Karandikar et al. (1986). These can be expressed as... 

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. 

Because of the interactive nature of aqueous solute specia-tion calculations, it would be desirable to enter at once into the chemical model the reactions and thermodynamic data for all elements whose inclusion might affect the computed activity or equilibrium solubility of other solute species. However, our experience is that the greatest reliability is obtained by adding only the data for one element, or for one ligand group, at a time then test data sets and real world water sample analyses are run before making further additions to or changes in the model. 

Solubility calculations were added for two allophanes, for which the equilibrium constants and formulae are a function of pH. Paces (74) found cold ground waters collected from springs in granitic rocks of the Bohemian Massif of Czechoslovakia to be supersaturated with respect to kaolinite while being unsaturated with respect to amorphous silica. He interpreted this as an indication that a metastable aluminosilicate more soluble than kaolinite was controlling the concentrations of alumina and silica in these waters. This aluminosilicate was further hypothesized to be of varied chemical composition, controlled by the mole... 

In equation 9, x is the mole fraction of silica and is equal to 1.24 - 0.135pH. This expression describes the linear variation between pure amorphous hydrous alumina and silica as a function of pH (75). The equilibrium constant for this substance was calculated by combining two endmember constants from the literature and incorporating the pH-dependence equation into the resulting expression, yielding an expression for the equilibrium solubility (75) of ... 

The computerized aqueous chemical model of Truesdell and Jones (, 3), WATEQ, has been greatly revised and expanded to include consideration of ion association and solubility equilibria for several trace metals, Ag, As, Cd, Cu, Mn, Ni, Pb and Zn, solubility equilibria for various metastable and(or) sparingly soluble equilibrium solids, calculation of propagated standard deviation, calculation of redox potential from various couples, polysulfides, and a mass balance section for sulfide solutes. Revisions include expansion and revision of the redox, sulfate, iron, boron, and fluoride solute sections, changes in the possible operations with Fe (II, III, and II + HI), and updating the model s thermodynamic data base using critically evaluated values (81, 50, 58) and new compilations (51, 26 R. M. Siebert and... 

White (1995) found that the apparent thermodynamic supersaturation of silicate minerals in most soil pore waters resulted from excessive values for total dissolved aluminum. In reality, much of this aluminum is complexed with dissolved organics in shallow soils and does not contribute to the thermodynamic saturation state of silicate minerals. Solubility calculations involving low dissolved organic concentrations in deeper soil horizons and in groundwater appear to produce much clearer equilibrium relationships (Paces, 1972 Stefansson and Amorsson, 2000 Stefansson, 2001). 

Vapour-phase calibration (VPC) is based on the principle that the concentration of the volatile analyte in the gas phase can be determined by external-standard calibration. If the total amount present in the vial is known, the concentration in the sample phase at equilibrium is calculated from the difference. This technique, where the distribution of a volatile compound between two phases in a headspace vial is determined by using a pure vapour as reference, was originally implemented by Kolb using automated head-space equipment to determine distribution coefficients in gas-liquid [77] and gas-solid systems [78], and later by Schoene et al. [79] to determine solubility coefficients in vapours of both solid and liquid polymers. Although these investigations focused on... 

As in a thermodynamic system description used for a normal solubility equilibrium calculation, the system contains a gas phase, if considered relevant for the problem at hand, an aqueous solution phase (external to the fibres), and a number of solid phases, which appear either with fixed stoichiometry or as solid solutions. The fibres are described as a separate aqueous phase. The thermodynamic data and stoichiometry for the solute species inside the fibre phase are identical to those describing the species in the external solution volume, with the exception that the charge of the species in the two aqueous phases must be defined separately. This will ensure that, given valid input values, charge neutrality will apply to both aqueous phases individually in the equilibrium composition calculated by Gibbs energy... 

So, by thinking of a process logically, one can almost formulate the equation. Noyes and Whitney did this for us, and precisely, although each equation operates only under certain boundary conditions. Nevertheless, from the Noyes-Whitney equation one can predict accurately what the effect on dissolution will be if the solubility of the dmg in the medium is increased, for example, by a change in pH. There are other equations for calculating the effect of pH on the equilibrium solubility, so this helps us get a quantitative view of the world. 

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