Sulfate activity coefficients

The activity of any ion, a = 7m, where y is the activity coefficient and m is the molaHty (mol solute/kg solvent). Because it is not possible to measure individual ionic activities, a mean ionic activity coefficient, 7, is used to define the activities of all ions in a solution. The convention used in most of the Hterature to report the mean ionic activity coefficients for sulfuric acid is based on the assumption that the acid dissociates completely into hydrogen and sulfate ions. This assumption leads to the foUowing formula for the activity of sulfuric acid. 

To calculate the open circuit voltage of the lead—acid battery, an accurate value for the standard cell potential, which is consistent with the activity coefficients of sulfuric acid, must also be known. The standard cell potential for the double sulfate reaction is 2.048 V at 25 °C. This value is calculated from the standard electrode potentials for the (Pt)H2 H2S04(yw) PbS04 Pb02(Pt) electrode 1.690 V (14), for the Pb(Hg) PbS04 H2S04(yw) H2(Pt) electrode 0.3526 V (19), and for the Pb Pb2+ Pb(Hg) 0.0057 V (21). 

The saturated solution of silver sulfate in water at 25°C has a molality equal to 0.02689, and the activity coefficient y of tho solute in this saturated solution is 0.533. 

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. 

With an aqueous fluid phase of high ionic strength, the problem of obtaining activity coefficients may be circumvented simply by using apparent equilibrium constants expressed in terms of concentrations. This procedure is recommended for hydro-metallurgical systems in which complexation reactions are important, e.g., in ammonia, chloride, or sulfate solutions. 

Worked Example 3.11. We know the concentration of copper sulfate to be 0.01 mol dm from other experiments, and so we also know (from suitable tables) that the mean ionic activity coefficient of the copper sulfate solution is 0.404. The measured electrode potential was Ec j+ — 0.269 V and = 0.340 V. We will calculate the... 

The mean ionic activity coefficient, of copper sulfate decreases to 0.158 when the concentration was raised from 0.01 to 0.1 mol dm" . By using the Nemst equation, calculate the electrode potential, for the following situations ... 

Similarly, the same method and the same mean salt furnish values of individual ionic activity coefficients for other ions—e.g., the sulfate group SO " ... 

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. 

Letcher, T.M. et al.. Activity coefficients at infinite dilution measurements for organic solutes in the ionic liquid l-butyl-3-methylimidazolium 2-(2-methoxyethoxy)ethyl sulfate using glc at T = (298.15, 303.15 and 308.15) K, /. Chem. Thermodyn., 37, 587, 2005. 

A better method for studying the alkali metal cation-soap anion interaction on the surface, according to Weil (58), is to assume a similarity between surface behavior and solution behavior and to use the activity coefficient of the solute in the solution as the parameter to account for surface behavior. By plotting activity coefficients as a function of the molality for the salts of the alkali metals (7, 26), the resulting order of the curves of the weak acids (formates, acetates, hydroxides) is the reverse of that found for the strong acids (chlorides, bromides, nitrates, chlorates, sulfates). The activity curves of the acetate salts can be used as the counterparts for the long-chain fatty acid salts, while those for the chlorides can be the analogs of the alkyl sulfates. The scheme is speculative in that the fatty acid and alkyl sulfate salts micellize, and acetate and chloride do not. 

Both associated and nonassociated electrolytes exist in sea water, the latter (typified by the alkali metal ions U+, Na-, K+, Rb+, and Cs-) predominantly as solvated free cations. The major anions. Cl and Br, exist as free anions, whereas as much as 20% of the F in sea water may be associated as the ion-pair MgF+. and 103 may be a more important species of I than I-. Based on dissociation constants and individual ion activity coefficients the distribution of the major cations in sea water as sulfate, bicarbonate, or carbonate ion-pairs has been evaluated at specified conditions by Garrels and Thompson (19621. 

The Gibbs phase rule is the basis for organizing the models. In general, the number of independent variables (degrees of freedom) is equal to the number of variables minus the number of independent relationships. For each unique phase equilibria, we may write one independent relationship. In addition to this (with no other special stipulations), we may write one additional independent relationship to maintain electroneutrality. Table I summarizes the chemical constituents considered as variables in this study and by means of chemical reactions depicts independent relationships. (Throughout the paper, activity coefficients are calculated by the Debye-Hiickel relationship). Since there are no data available on pressure dependence, pressure is considered a constant at 1 atm. Sulfate and chloride are not considered variables because little specific data concerning their equilibria are available. Sulfate may be involved in a redox reaction with iron sulfides (e.g., hydrotroilite), and/or it may be in equilibrium with barite (BaS04) or some solid solution combinations. Chloride may reach no simple chemical equilibrium with respect to a phase. Therefore, these two ions are considered only to the... 

The discussion in the previous sections concerning solvated species indicates that a complete knowledge of the chemical reactions that take place in a system is not necessary in order to apply thermodynamics to that system, provided that the assumptions made are applied consistently. The application of thermodynamics to sulfuric acid in aqueous solution affords another illustration of this fact. We choose the reference state of sulfuric acid to be the infinitely dilute solution. However, because we know that sulfuric acid is dissociated in aqueous solution, we must express the chemical potential in terms of the dissociation products rather than the component (Sect. 8.15). Either we can assume that the only solute species present are hydrogen ion and sulfate ion (we choose to designate the acid species as hydrogen rather than hydronium ion), or we can take into account the weak character of the bisulfate ion and assume that the species are hydrogen ion, bisulfate ion, and sulfate ion. With the first assumption, the effect of the weakness of the bisulfate ion is contained in the mean activity coefficient of the sulfuric acid, whereas with the second assumption, the ionization constant of the bisulfate ion is involved indirectly. 

Figure 6.11. A. Saturation state of seawater with respect to aragonite as a function of sulfate reduction. Based on general model of Ben-Yaakov (1973), updated by using pK a values and total ion activity coefficients of Millero (1982). B. Observed saturation state of Mangrove Lake, Bermuda pore waters with respect to calcite.

P.-C. Zhang and D. L. Sparks, Kinetics and mechanisms of sulfate adsorption/desorption on goethite using pressure-jump relaxation, Soil Sci. Soc. Am. J. 54 1266 (1990). The rate coefficients inEq. 4.44c need not be modified by the model surface-species activity coefficients adopted in this paper. 

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. 

Davies CW (1938) The extent of dissociation of salts in water. VIII. An equation for the mean ionic activity coefficient of an electrolyte in water, and a revision of the dissociation constant of some sulfates.- Jour.Chem.Soc. pp.2093-2098... 

The Mean Molal Activity Coefficient Calculation for the Macro-Component Salts. The mean molal activity coefficients for the macro-component chloride and sulfate salts are given in Figures 2a and 2b, respectively. Because of the unavailability of measured activity coefficient data in brines, validation of the results presented in Figures 2a and 2b was not possible. 

The activity coefficient 7caso.,c = 1> because CaSO is not dissociated, /so is the activity coefficient of the sulfate ion. 

A raw water containing 140 mg/L of dissolved solids is subjected to coagulation treatment using ferric sulfate. The optimum pH was determined to be equal to 8.2 at a temperature of 25°C. Assume that all parameters to solve the problem can be obtained from the given conditions except the activity coefficient FeOH. Calculate the activity coefficient of FeOH ... 

EXAMPLE 2-1 Using the DHLL, calculate the activity coefiScients of each of the ions and the mean activity coefficient of the salt in a 10 m solution of potassium sulfate. 

Figure 15-2 (left) depicts several titration curves of Fe(II) with permanganate. Beyond the end point the experimental curves differ from the theoretical shape, which is nearly flat beyond the end point (5-equivalent reduction). The essential symmetry of the curves suggests that the potential is determined by the Mn(III)-Mn(II) couple beyond the end point. Evidence for this behavior can be seen in solutions containing sulfate or phosphate, which tend to stabilize Mn(III) (Section 17-1). That sulfuric and phosphoric acids have about the same effect before and after the end point is consistent with the similarity of the behavior of the Mn(III)-Mn(II) and the Fe(III)-Fe(II) systems with respect to changes in activity coefficients as well as with respect to hydrolysis and complex formation. 

In this case the formal potential includes correction factors for activity coefficients, acid-base phenomena (hydrolysis of Fe " to FeOH " ), complex formation (sulfate complexes), and the liquid junction potential used between the reference electrode and the half-cell in question. Although the correction is strictly valid only at the single concentration at which the potential has been determined, formal potentials may often lead to better predictions than standard potentials because they represent quantities subject to direct experimental measurement. 

Figure 2. The Henry constant of oxygen in aqueous solutions of sodium sulfate at 25 °C (O) experimental data (a) the Henry constant calculated with eq 24 using for the mean activity coefficient of dissolved salt the Debye-Hiickel equation (b) the Henry constant calculated with eq 24 using for the mean activity coefficient of dissolved salt the extended Debye-Hiickel equation (c) the Henry constant calculated with eq 24 using for the mean activity coefficient of dissolved salt the Bromley equation (d) the Henry constant calculated with eq 15.

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