Activity coefficient equations constants

TABLE 13-3 Activity-Coefficient Equations in Binary Form for Use with Parameters and Constants in Tables 13-2 and 13-4... 

The advantages of constant-pressure activity coefficients also become clear when we try to relate to one another the activity coefficients of all the components in a mixture through the Gibbs-Duhem equation (P6, P7). For variable-pressure activity coefficients at constant temperature we obtain... 

The constants in any of the activity coefficient equations can be readily calculated from experimental values of the activity coefficients at infinite dilution. For the Wilson equation ... 

At sufficiently low concentrations, the activity coefficients become constants independent of composition, and if we choose infinitely dilute solutions as our standard states, " we may equate them to unity. Under these conditions, the estimation of kn a priori is reduced to an estimate of the structural parameters of X reciuired to determine the partition function of X and an estimate of the effect of the solvent on the equilibrium constant Kx ... 

Table 13-1, based on the binary-system activity-coefficient-equation forms given in Table 13-3. Consistent Antoine vapor-pressure constants and liquid molar volumes are listed in Table 13-4. The Wilson equation is particularly useful for systems that are highly nonideal but do not undergo phase splitting, as exemplified by the ethanol-hexane system, whose activity coefficients are shown in Fig. 13-20. For systems such as this, in which activity coefficients in dilute regions may...

Thirdly, another corollary of the first limitation, is the inconsistency and inadequacy of activity coefficient equations. Some models use the extended Delbye-Huckel equation (EDH), others the extended Debye-Huckel with an additional linear term (B-dot, 78, 79) and others the Davies equation (some with the constant 0.2 and some with 0.3, M). The activity coefficients given in Table VIII for seawater show fair agreement because seawater ionic strength is not far from the range of applicability of the equations. However, the accumulation of errors from the consideration of several ions and complexes could lead to serious discrepancies. Another related problem is the calculation of activity coefficients for neutral complexes. Very little reliable information is available on the activity of neutral ion pairs and since these often comprise the dominant species in aqueous systems their activity coefficients can be an important source of uncertainty. 

In view of the neglect of the activity coefficients, the constants Ki and K2 have been replaced by ki and Ic2 which become identical with the former at infinite dilution. If q is the concentration of the quinone form, which is supposed to be a neutral substance exhibiting neither acidic nor basic properties, the oxidation-reduction potential, which according to equation (4) may be w ritten as... 

The color-change equilibrium at any particular ionic strength (where the term for activity coefficient is constant) can be expressed by the equation... 

If the solution is ideal (y, = 1) or if the activity coefficient is constant for the range of concentrations involved in the experiment, then this equation becomes... 

Substituting Equation (4.315) for results in the Gibbs-Duhem equation for activity coefficient at constant [T,p],... 

Constants for the activity coefficient equation (eqns. 12,13) B = 1.32416014E+00... 

Table II. Association reaction, stability constant, ion-activity-coefficient equation, and ion-activity-coefficient parameters for each aqueous species for the WATEQ, amended WATEQ, and fit aqueous models...

The single constant Wilson equation was fitted to experimental partition coefficient data for ethanol for the ternary systems benzene-water-ethanol (9) and n-hexane-water-ethanol (12). The partition coefficient was calculated from equation (12) using the Wilson equation to compute the activity coefficients. The constants, Xy, were chosen to give a best fit in the least squares. sense to the experimental partition coefficients. Table II shows the resulting constants. 

For the purposes of the present review, the data have been re-analysed using a version of the Lee-Wheaton equation modified so that the activity-coefficient equation matches the SIT equation usually used in the TDB project (Appendix B). At comparable temperatures, the calculated nickel sulphate association constants are slightly larger than those recalculated from the results of other conductivity studies [1895FRA], [76SHI/TSU], [79FIS/FOX]. In the present review, we estimate the uncertainty in K at 25°C to be + 20. The same uncertainty is estimated for 20 and 30°C, but for temperatures above 30°C and below 20°C, an uncertainty of 30 is estimated. 

Moderate temperature changes result in such minor changes in activity coefficient that constant-pressure data are ordinarily satisfactory for application of the various integrated forms of the Gibbs-Duhem equation. 

The activities of Aj Bj and C in the solution at K must equal those of 5, and C, respectively, in the solution at L. Lines VK and LR represent solutions of constant activity of C. Similarly, TK and LS are solutions of constant activity of B, and UK and LW those of constant activity of 4. By means of the ternary activity-coefficient equations it should be possible to locate points such as K and L where the three constant activity curves intersect. In this fashion it should be possible to locate both the tie lines and the solubility curve. 

Unfortunately, the activity-coefficient equations cannot conveniently be made explicit in terms of x, and the location of the constant activity curves on the triangular diagram is possible only by a lengthy series of interpolations. Location of the triple intersection points becomes an even more difficult trial-and-error procedure. While this can be done, for practical purposes use of the ternary activity-coefficient equations is ordinarily limited to cases where the solubility curve of the ternary liquid system is known. For such a situation, the calculations become relatively simple, since it is then merely necessary to compute activities of C along the solubility curve and to join equal values on opposite sides of the curve by the tie lines. 

For cuprous chloride in HCl-HClOii solutions, the solubility data of Hikita et al. (C6) met the requirement for data taken at multiple ionic strengths and chlorine concentrations that Fritz needed in order to solve for the stability constants and activity coefficient equation parameters. Unfortunately, this data, like many sets of solubility data, was presented as molarities without the solution densities needed to convert them to the molalities required by Pitzer s equations. Consequently Fritz replaced the molality terms of the equations with molarities. He presented the following justifications (C2) ... 

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