Activity coefficient high ionic strength

Usually, the analytical chemist needs to determine the concentration of the ion of interest rather than its activity. The obvious approach to converting potentiometric measurements from activity to concentration is to make use of an empirical calibration curve, such as the one shown in Figure 5.3. Electrodes potentials of standard solutions are thus measured and plotted (on a semilog paper) versus the concentration. Since the ionic strength of the sample is seldom known, it is often useful to add a high concentration of an electrolyte to the standards and the sample to maintain approximately the same ionic strength (i.e., the same activity coefficient). The ionic strength adjustor is usually a buffer (since pH control is also desired for most ISEs). The empirical calibration plot thus yields results in terms of concentration. Theoretically,... 

The Debye-Hiickel methods work poorly, however, when carried to moderate or high ionic strength, especially when salts other than NaCl dominate the solute. In the theory, the ionic strength represents all the properties of a solution. For this reason, a Debye-Hiickel method applied to any solution of a certain ionic strength (whether dominated by NaCl, KC1, HC1, H2SO4, or any salt or salt mixture) gives the same set of activity coefficients, irregardless of the solution s composition. This result, except for dilute solutions, is, of course, incorrect. Clearly, we cannot rely... 

The reduced species is the radical R the activity coefficient of which, yQx, is close to unity. The oxidised species, at any rate in the organic solvents, is not the lone carbenium ion R+, but one that is part of an ion-pair because of the relatively high ionic strength... 

None of these extensions has been really satisfactory and they are not very useful at high ionic strength. The Davies equation (19) differs from the others in providing an additional term which alters the response of the activity coefficient to changes in ionic strength, particularly at higher values. The authors have had some success with this type of equation by replacing the. 2 factor in the second term with a variable. The variable can be determined by experiment at a particular set of conditions. 

In many of the published applications of thermodynamics in hydrometallurgy, activity coefficients have been either omitted or crudely estimated. No doubt, this has been due in part to the difficulties in estimating ionic activity coefficients at high ionic strengths. However, with the recent surge of developments, some of the more current studies have addressed the activity coefficient problem more realistically. Representative published applications are presented in Table HI. 

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. 

During a redox reaction, a potentiometric titration can be employed to determine a concentration of analyte rather than an activity, since we are only using the emf as a reaction variable in the accurate determination of an end point volume. For this reason, an absolute value of reference electrode need not be known, as we are only concerned with changes in emf. It is, however, advisable to titrate at high ionic strength levels in order to minimize fluctuations in the mean ionic activity coefficients. 

Despite the additional complexity, all the equations in Table 5.3 are functionally equivalent. That is, the activity coefficients approach a value of 1 as the ionic strength of the solution is decreased to 0 m. Thus, in dilute solutions, w,. In other words, the effective concentration of an ion decreases with increasing ionic strength. In contrast, the activity coefficients of uncharged solutes can be greater than 1 in solutions of high ionic strength, such as seawater. 

Numerous studies on the thermodynamics of calcium chloride solutions were published in the 1980s. Many of these were oriented toward verifying and expanding the Pitzer equations for determination of activity coefficients and other parameters in electrolyte solutions of high ionic strength. A review article covering much of this work is available (7). Application of Pitzer equations to the modeling of brine density as a function of composition, temperature, and pressure has been successfully carried out (8). 

At low ionic strength, y I for neutral compounds. At high ionic strength, most neutral molecules can be salted out of aqueous solution. That is, when a high concentration (typically > 1 M) of a salt such as NaCl is added to an aqueous solution, neutral molecules usually become less soluble. Does the activity coefficient, -yclher, increase or decrease at high ionic strength ... 

A routine procedure for measuring F- is to dilute the unknown in a high ionic strength buffer containing acetic acid, sodium citrate, NaCl. and NaOH to adjust the pH to 5.5. The buffer keeps all standards and unknowns at a constant ionic strength, so the fluoride activity coefficient is constant in all solutions (and can therefore be ignored). 

The goal of this research was to improve activity coefficient prediction, and hence, equilibrium calculations in flue gas desulfurization (FGD) processes of both low and high ionic strength. A data base and methods were developed to use the local composition model by Chen et al. (MIT/Aspen Technology). The model was used to predict solubilities in various multicomponent systems for gypsum, magnesium sulfite, calcium sulfite, calcium carbonate, and magnesium carbonate SCU vapor pressure over sulfite/ bisulfite solutions and, C02 vapor pressure over car-bonate/bicarbonate solutions. 

The second term in the DAVIES and extended DEBYE-HUCKEL equations forces the activity coefficient to increase at high ionic strength. This is owed to the fact, that ion interactions are not only based on Coulomb forces any more, ion sizes change with the ionic strength, and ions with the same charge interact. 

One advantage of PALS is that, as far as 13 is concerned, the medium appears transparent to Ps even at high concentrations of some solutes (e.g. CIO, CL, alkali cations). A promising application would be then to measure stability constants in concentrated solutions, to assess the validity of equations for the activity coefficients at high ionic strengths [111]. 

D and Y/., y, y. and y, denote their respective activity coefficients. These coefficients are present to take account of the non-ideal behaviour of real systems, but, in practice, the valufjs of Y, Yn. Y y, are difficult to measure and are not Ljsually known. In dilute solutions of high ionic strength they are often assumed to be 1 so that, to a first approximation, the value of K is defined by the concentrations of A, B, C and D alone. 

The equilibrium constant for the process shown in equation 5.5 is called a stability constant . The terms formation constant and binding constant are also sometimes used in this context. The stability constant can be defined on the basis of concentrations assuming unit activity coefficients, an assumption which is not usually too unrealistic in dilute solutions of high ionic strength. The stability constant, for the reaction shown in equation 5.5 is given by equation 5.6 ... 

With the arrival of the Pitzer method for calculating activity coefficients at high ionic strengths (si m), research by Harvie and Weare (1980) led to computations of equilibrium mineral solubilities for brines. They could calculate... 

Because of the high ionic strength of the brines, the calculations were carried out using a Pitzer ion interaction model (US DOE, 1996) for the activity coefficients of the aqueous species (Pitzer, 1987, 2000). Pitzer parameters for the dominant non-radioactive species present in WIPP brines are summarized in Harvie and Weare (1980), Harvie et al. (1984), Felmy and Weare (1986), and Pitzer (1987, 2000). For the actinide species, the Pitzer parameters that were used are summarized in the WIPP Compliance Certification Application (CCA) (US DOE, 1996). Actinide interactions with the inorganic ions H, Na, K, Mg, CU, and HCO /COa were considered. 

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