Estimation from mean activity coefficient data

1 Estimation from mean activity coefficient data Example B.l  

The ion interaction coefficient e(H, Cl ) can be obtained from published values of r ,HCi Whci  

By plotting (log, jj, , + D) versus Whci a straight line with the slope 

2 Estimations based on experimental values of equilibrium constants at 

The linear regression is done as described in Appendix C. The following results are obtained  

1 Estimation from mean activity coefficient data 

By plotting (log, ,q + )) versm m a a straight line with the slope s(H, Cl ) is obtained. The degree of linearity should in itself indicate the range of validity of the specific ion interaction approach. Osmotic coefficient data can be treated in an analogous way. 

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The individual-ion activity coefficient for OH in the WATEQ model was not derived from mean activity-coefficient data. Instead, the coefficient was calculated by Equation 2, which is limited to solutions with low ionic strengths. The amended WATEQ model used mean activity-coefficient data from CsOH solutions to estimate individual-ion activity coefficients for OH . Neither the WATEQ model nor the amended WATEQ model were able to reproduce the mean activity coefficients of OH solutions for the cations Ba, K, Li" ", and Na" ". The amended WATEQ model, but not the WATEQ model, reproduced the experimental data for CsOH. Even with a different formulation for the individual-ion activity coefficient of OH , the amended WATEQ model calculated mean activity coefficients that were discrepant with the experimental data. The WATEQ model actually produced more accurate values than the amended WATEQ model for solutions of OH salts except KOH, for which both models produced inaccurate values. The fit model, by including additional OH complexes, reproduced the experimental data for all OH salts considered. 

Mean activity-coefficient data at concentrations sufficient to estimate stability constants through the fitting process are available only for a few OH salts. Hence, most OH complexes in the fit model were obtained from WATEQ, with the exception of the OH complexes of Ba, K" ", Li, and Na, which were fitted to the experimental data. 

The extension of ideal phase analysis of the Maxwell-Stefan equations to nonideal liquid mixtures requires the sufficiently accurate estimation of composition-dependent mutual diffusion coefficients and the matrix of thermodynamic factors. However, experimental data on mutual diffusion coefficients are rare, and prediction methods are satisfactory only for certain types of liquid mixtures. The thermodynamic factor may be calculated from activity coefficient models such as NRTL or UNIQUAC, which have adjustable parameters estimated from experimental phase equilibrium data. The group contribution method of UNIFAC may also be helpful, as it has a readily available parameter table consisting of mam7 species. If, however, reliable data are not available, then the averaged values of the generalized Maxwell-Stefan diffusion coefficients and the matrix of thermodynamic factors are calculated at some mean composition between x0i and xzi. Hence, the matrix of zero flux mass transfer coefficients [k ] is estimated by... 

What is the Macinnes convention, what is its justification, and how is it used to estimate individual ion activity coefficients from mean salt data ... 

The stability constants at 298.15 K have been recalculated from the original data by the review with the accepted value of log, A h = 1 -75 and various expressions for the estimate of the activity coefficients. The calculations resulted in mean values close to those reported in the paper but suggested that the uncertainty should be increased. 

Eq. (B.l) will allow fairly accurate estimates of the aetivity coefficients in mixtures of electrolytes if the ion interaction coefficients are known. Ion interaction coefficients for simple ions can be obtained from tabulated data of mean activity coefficients of strong electrolytes or from the corresponding osmotic coefficients. Ion interaction coefficients for complexes can either be estimated from the charge and size of the ion or determined experimentally from the variation of the equilibrium constant with the ionic strength. 

Deviations from predicted behaviour are here interpreted in terms of solvation, but other factors such as ion association may also be involved. Ion association leads to deviations in the opposite direction and so compensating effects of solvation and ion association may come into play. The deviations may also be absorbing inadequacies of the Debye-Hiickel model and theory, and so no great reliance can be placed on the actual numerical value of the values emerging. This major method has now been superseded by X-ray diffraction, neutron diffraction, NMR and computer simulation methods. The importance of activity measurements may lie more in the way in which they can point to fundamental difficulties in the theoretical studies on activity coefficients and conductance. The estimates of ion size and hydration studies could well provide a basis for another interpretation of conductance and activity data, or to modify the theoretical equations for mean activity coefficients and molar conductivities. 

The components of an ion-association aqueous model are (1) The set of aqueous species (free ions and complexes), (2) stability constants for all complexes, and (3) individual-ion activity coefficients for each aqueous species. The Debye-Huckel theory or one of its extensions is used to estimate individual-ion activity coefficients. For most general-purpose ion-association models, the set of aqueous complexes and their stability constants are selected from diverse sources, including studies of specific aqueous reactions, other literature sources, or from published tabulations (for example, Smith and Martell, (13)). In most models, stability constants have been chosen independently from the individual-ion, activity-coefficient expressions and without consideration of other aqueous species in the model. Generally, no attempt has been made to insure that the choices of aqueous species, stability constants, and individual-ion activity coefficients are consistent with experimental data for mineral solubilities or mean-activity coefficients. 

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). 

From this log value we estimated by means of a Quantitative Structure-Activity Relationship (QSAR) of Mackay [345] a BCFw for musk xylene of about 3,800 and a BCFl of 79,200 for this compound in fish [346]. The predicted BCFw of musk ketone (log K(, = 4.20 [344]) was 760 and the BCFl 15,800 [346]. These data, the chemical structures, n-octanol/water partition coefficients (log Ko s)... 

It should be noted that the Maxwell-Stefan D calculated from Eq. 4.1.5 can be quite sensitive to the model used to compute T, an observation first made by Dullien (1971). One of the reasons for this sensitivity is that E involves the first derivative of the activity coefficient with respect to composition. Activity coefficient model parameters are fitted to vapor-liquid equilibrium (VLE) data (see, e.g., Prausnitz et al., 1980 Gmehling and Onken, 1977). Several models may provide estimates of In % that give equally good fits of the vapor-liquid equilibrium data but that does not mean that the first derivatives of In % (and, hence, E) will be all that close. To illustrate this fact we have calculated the thermodynamic factor, E, for the system ethanol-water with several different models of In %. The results are shown in Figure 4.3 a). The interaction parameters used in these calculations were fitted to one set of VLE data as identified in the figure caption. Similar illustrations for other systems are provided by Taylor and Kooijman (1991). 

In order to examine the predictions of the model with respect to experimental data, one must estimate the mean molar activity coefficient. On the basis of equation (3.6.17), this can be obtained from the relationship... 

The vapor-liquid interface data must be estimated under transfer conditions. The ketone behaves like an hydrophobic material and tends to be rejected from the water phase by preferentially concentrating on the surface. In such a case the bulk concentrations are very different from the surface concentrations and so are the activity coefficients (19-). it is reasonable to suppose that in vapor pressure relations for mixtures, surface compositions play a more important role than bulk compositions. That is why we have correlated the vapor phase compositions to the surface concentrations by mean of the UNIFAC method of activity coefficients determination (20) and by the relation of Tamura et al (21) giving the surface tension for aqueous mixtures. 

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