Activity mean molal

When the measured pH is used, the following conditions prevail (1) the individual-ion activities and individual-ion activity coefficients again depend on choice of scale (regardless of the inconsistency of the measured pH (2) the mean-activity coefficients are independent of the measured pH and, thus, independent of scale, and (3) the calculated mean activities, mean molalities, ion-activity products, saturation indices and CO2 partial pressure are not independent of scale. This dependency of thermodynamic properties on scale when the measured pH is used in calculations is particularly acute in the carbonate... 

The following data (for 25°C) were obtained at the pzc for the Hg-aqueous NaF interface. Estimate and plot it as a function of the mole fraction of salt in solution. In the table,/ is mean activity coefficient such that a = f m , where m is mean molality. 

Table 21.9 Stoichiometric mean molal activity coefficients (7,) for aqueous inorganic...

Of course, (4.9) cannot be used at higher ionic strengths. A more precise procedure is then required, such as the Robinson-Stokes equation for the mean molal activity coefficient [11] (see also [86a], chapter 1)... 

In equation 3 the terms of fNa+ and 7H + are the rational activity coefficients of exchanging cations in the zeolite phase and the terms yNa+ and XM + are the molal single ion activity coefficients in the solution phase. Equation 4 can be rewritten as equation 5 when the two salts, NaX and MX2 have a common anion. The mean molal activity coefficients usually can be estimated from literature data. The corrected selectivity coefficient includes a term that corrects for the non-ideality of the solution phase. Thus any variation in the corrected selectivity coefficient is due to non-ideality in the zeolite phase (see equation 3). 

In the concentration range regarding the ED processes, the effective diffusion coefficient (Z>B) can be predicted via the Gordon relationship (Reid et al, 1987), which accounts for the partial derivative of the natural logarithm of the mean molal activity coefficient (y+) with respect to molality (m) and solvent relative viscosity (rjr) ... 

FIG. 2 Effect of solute molality (m) on the mean molal activity coefficient (y ) for sodium chloride (O), sodium acetate (O), and sodium propionate ( ) at 25°C, as extracted from Robinson and Stokes (2002). The continuous lines were calculated using Eq. 9 and the empirical coefficients At extracted from Fidaleo and Moresi (2005a,b, 2006). 

The reference state of the electrolyte can now be defined in terms of thii equation. We use the infinitely dilute solution of the component in the solvent and let the mean activity coefficient go to unity as the molality or mean molality goes to zero. This definition fixes the standard state of the solute on the basis of Equation (8.184). We find later in this section that it is neither profitable nor convenient to express the chemical potential of the component in terms of its molality and activity. Moreover, we are not able to separate the individual quantities, and /i . Consequently, we arbitrarily define the standard chemical potential of the component by... 

Determine the mean molal activity coefficient at 25°C for A12(S04)3 present at 2 x 10-4 m concentration in a solution also containing a 10-4 m Na3P04. 

Two additional observations should be made. First, the methods used here treat each of the ionic types as a separate species that influences the thermodynamic properties of solutions very strongly by virtue of its associated charge. Second, it is instructive to examine the dependence of the mean molal activity coefficient for several different electrolytes as a function of the molality. Representative examples are shown in Fig. 4.3.1. One sees at first a very steep drop in as m is increased, and then either a gradual or a very sharp... 

FIGURE 4.3.1 Variation of mean molal activity coefficient as a function of molality for several salts in aqueous solutions. 

Determine the mean molal activity coefficient for LiCi at the concentrations c - 10-2, 3.3 x 10-2, 10 1 mol/liter. 

One notes that a knowledge of the mean molal activity of HCi in a solution of molality m and the tabulation of standard emfs enables one to calculate the value for the schematized cell. Normally, however, the procedure is used in reverse i.e., from a measurement of emfs the mean activity coefficients for ions in solution may then be determined. The procedure is now... 

Determine the equilibrium constant for the dissociation of Hg2Ci2 into ionic constituents. Determine both the mean molal activity coefficient and molality of the ions in equilibrium with the undissolved salt at 25°C. 

Table VI. Mean Ionic Activity Coefficients (Molality Scale) of HBr in H20/NMA Solvent Mixtures at 25°C...

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. 

Figure 2. Mean molal activity coefficients of macrocomponent salts as a function of ionic strength for sea water concentrates. Normalized molar composition ratios Na = 1.00 = 0.021 Mg = 0.136 Ca Cd Fh Zn = 0.001 CU...

Considering the assumptions incorporated into the carbonate subroutine and in using the mole-fraction statistical model for the partitioning of the mean molal activity coefficients into single Ion activity coefficients, the agreement between predicted and measured trace metal concentrations in GSL brine was better than expected. 

In this equation is the experimentally determined selectivity coefficient, m is the molality of each ion, y is the activity coefficient of the ion in the gel phase and y- is the mean molal activity coefficient of the electrolyte in the external solution phase. 

Here it is a plot of P vs. [(v+y+(v-y-m P ] that is linear and that can be used to read off the desired mean molal activity coefficient. As earlier, P refers to the extrapolated pressure reached in Henry s Law plot for the component in pure form. 

If one specifies the activities of the solids as described in Section 3.7 (ordinarily very close to unity) then a measurement of the cell emf yields the mean molal activity coefficient of ZnCla in solution. 

The product 7 + 7- is experimentally measurable. The quantity (7 referred to as the mean molal activity coefficient The mean ionic molality is defined as im+mJ) and is simply m for a univalent-univalent electrolyte. Summarizing these definitions for a nonideal, univalent-univalent solution, where the solute is component 2. 

Table 2.1. Molal Concentrations of Aqueous NaCl, Water Activity, and Mean Molal Activity Coef ient of NaCl in Water...

A similar expression can be obtained for the symmetric and the unsymmetric mole fraction activity coefficient. In a completely dissociated solution of n mol Na2S04, the mean molal activity coefficient is... 

The mean activity coefficient of a sparingly soluble salt in any solution, containing other electrolytes, can thus be evaluated provided the solubility product and the mean molality of the ions of the salt in the given solution are known. In order to obtain X, the values of are determined from the experimentally observed solubilities of the sparingly soluble salt in the presence of various amounts of other electrolytes, and the results are extrapolated to infinite dilution (Fig. 27). In the latter case the activity coefficient is unity, in accordance with the chosen standard state, and hence, by equation (39.71), KV"" is equal to the extrapolated value of... 

Values of electrolyte activities, as measured by osmotic pressures, freezing point depression, and other experimental methods are in the literature (References 5 and 6, for example) or one can calculate activity coefficients based on models of molecular-level interactions between ions in electrolyte solutions. For illustrative purposes, mean molal activity coefficients for various salts at different aqueous molal (mj concentrations at 25°C are listed in Table 26.3 [7]. 

Mean Molal Activity Coefficients (y ) of Aqueous Salt Solutions at 25°C... 

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