Calcium sulfate activity coefficients

In the HMW model, in contrast, Ca++ and SO4 are the only calcium or sulfate-bearing species considered. The species maintain equal concentration, as required by electroneutrality, and mirror the solubility curve in Figure 8.6. Unlike the B-dot model, the species activities follow trends dissimilar to their concentrations. The Ca++ activity rises sharply while that of SO4 decreases. In this case, variation in gypsum solubility arises not from the formation of ion pairs, but from changes in the activity coefficients for Ca++ and SO4 as well as in the water activity. The latter value, according to the model, decreases with NaCl concentration from one to about 0.7. 

The level of impurity uptake can be considered to depend on the thermodynamics of the system as well as on the kinetics of crystal growth and incorporation of units in the growing crystal. The kinetics are mainly affected by the residence time which determines the supersaturation, by the stoichiometry (calcium over sulfate concentration ratio) and by growth retarding impurities. The thermodynamics are related to activity coefficients in the solution and the solid phase, complexation constants, solubility products and dimensions of the foreign ions compared to those of the ions of the host lattice [2,3,4]. 

To be able to interpret these results and to correct for the lower calcium concentrations at high sulfate and phosphate concentrations, the partition coefficients D have been determined. These values follow from the slopes of the curves in figure 7. For 5.5 and 6.0 M HjPO a D of about 1.5 10" is obtained. A similar D-value for both acid concentrations should indeed be obtained, when the activity coefficients of the ions in solution is not strongly affected by the acid concentration. The D-value for 6.5 M H PO lies somewhat higher. This could e.g. be caused by a higher activity coefficient of cadmium compared to calcium at this acid concentration. The thermodynamic D-value cannot be determined by increasing the residence time, because a residence time of 2400 seconds already caused anhydrite formation. 

Fig. 4 to Fig. 8 show the severe divergence for activity coefficients such as given here for calcium, chloride, sulfate, sodium and water ions, calculated with different equations. The activity coefficients were calculated applying Eq. 13 to Eq. 17 for the corresponding ion dissociation theories, whereas the values for the PITZER equations were gained using the program PHRQPITZ. The limit of validity of each theory is clearly shown. 

In seawater, the differences between activities and concentrations must always be considered (cf. Sect. 15.1.1). The activity coefficients for monovalent ions in seawater assume a value around 0.75, for divalent ions this value usually lies around 0.2. In most cases of practical importance, the activity coefficients can be regarded with sufficient exactness as constants, since they are, over the whole range of ionic strengths in solution, predominately bound to the concentrations of sodium, chloride, and sulfate which are not directly involved in the calcite-carbonate-equilibrium. The proportion of ionic complexes in the overall calcium or carbonate content can mostly be considered with sufficient exactness as constant in the free water column of the ocean. Yet, this cannot be applied to pore water which frequently contains totally different concentrations and distributions of complex species due to diage-netic reactions. 

G42. Marshall, W.L., R. Slusher. "The ionization constant of nitric acid at high temperatures from solubilities of calcium sulfate in HNO3-H2O, 100-350"C activity coefficients and thermodynamic functions , J. inorg. nucl. Chem., v37, PPH91-1202 (1975)... 

G72. Yeatts, L.B. W.L. Marshall, "Apparent invariance of activity coefficients of calcium sulfate at constant ionic strength and temperature in the system CaSOH-NazSOH-NaNOs-HaO to the critical temperature of water. Association equilibria", J. Phys. Chem., v73, 1, pp81-90 (1969)... 

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