Activity coefficients tables

Values for many properties can be determined using reference substances, including density, surface tension, viscosity, partition coefficient, solubihty, diffusion coefficient, vapor pressure, latent heat, critical properties, entropies of vaporization, heats of solution, coUigative properties, and activity coefficients. Table 1 Hsts the equations needed for determining these properties. 

Earlier, when discussing historical development, we mentioned that different workers have used different equations to describe the Debye-Hiickel constant (A, Eq. 2.35) as a function of temperature. For example, at 0°C, the value of this constant is 0.3781, 0.3764, and 0.3767 kg1/2 mol-1/2 for the FREZCHEM, Archer and Wang (1990), and Pitzer (1991) models, respectively. At NaCl = 5 m and 0 °C, the calculated mean activity coefficients using these three parameters evaluated with the FREZCHEM model are 0.7957, 0.7995, and 0.7988, respectively. The largest discrepancy is 0.48%, which is within the range of model errors for activity coefficients (Table 3.5). 

Furthermore, if one takes the experimental values of the activity coefficient (Table 3.6) at extremely low electrolyte concentration and plots log versus I curves, it... 

Substituting the interface mole fractions into the Margules equation for activity coefficients (Table D.2) gives the following results ... 

The ions charges play a very important role in the electric interactions and therefore in the values of the activity coefficients. Table 3.2 illustrates this property by giving values for ionic strength and mean activity coefficients (calculated from the previous equations) for different types of electrolytes in a concentration equal to 10 mol L . 

To account for nonideal vapor-hquid equilibrium and possible vqxjr-liquid-liquid equilibrium (VLLE) for these quaternary systems, the NRTL model or UNIQUAC model is used for activity coefficients. Table 7.2 provides the model parameters for these five quaternary systems where the EtAc, IPAc, and AmAc systems are described by the NRTL model and MeAc and BuAc systems are represented using the UNIQUAC model. Because of the near atmosphaic pressure, the only vapor phase nonideality considered is the dimerization of acetic acid as described by the Hayden-O CoimeU second virial coefficient model. The Aspen Plus built-in association parameters are used to compute fiigacity coefficients. 

Table 3 shows results obtained from a five-component, isothermal flash calculation. In this system there are two condensable components (acetone and benzene) and three noncondensable components (hydrogen, carbon monoxide, and methane). Henry s constants for each of the noncondensables were obtained from Equations (18-22) the simplifying assumption for dilute solutions [Equation (17)] was also used for each of the noncondensables. Activity coefficients for both condensable components were calculated with the UNIQUAC equation. For that calculation, all liquid-phase composition variables are on a solute-free basis the only required binary parameters are those for the acetone-benzene system. While no experimental data are available for comparison, the calculated results are probably reliable because all simplifying assumptions are reasonable the... 

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 8.1 Individual Activity Coefficients of Ions In Water at 25°C 8.3...

Table 8.4 Individual Ionic Activity Coefficients at Higher Ionic Strengths at...

Values for the activity coefficients of ions in water at 25°C are given in Table 8.1 in terms of their effective ionic radii. 

At moderate ionic strengths a considerable improvement is effected by subtracting a term bl from the Debye-Hiickel expression b is an adjustable parameter which is 0.2 for water at 25°C. Table 8.4 gives the values of the ionic activity coefficients (for Zi from 1 to 6) with d taken to be 4.6A. 

Terminal activity coefficients, 7°, are noted in Figure 3. These are often called infinite dilution coefficients and for some systems are given in Table 1. The hexane—heptane mixture is included as an example of an ideal system. As the molecular species become more dissimilar they are prone to repel each other, tend toward liquid immiscihility, and have large positive activity coefficients, as in the case of hexane—water. 

Table 1. Terminal Activity Coefficients at Atmospheric Pressure ...

Concentrated, Binary Mixtures of Nonelectrolytes Several correlations that predict the composition dependence of Dab. re summarized in Table 5-19. Most are based on known values of D°g and Dba- In fact, a rule of thumb states that, for many binary systems, D°g and Dba bound the Dab vs. Xa cuiwe. CuUinan s equation predicts dif-fusivities even in hen of values at infinite dilution, but requires accurate density, viscosity, and activity coefficient data. 

Table 13-1, based on the binary-system activity-coefficient-eqnation 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 snown in Fig. 13-20. For systems such as this, in which activity coefficients in dilute regions may...

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

The values given in this table are only approximate, but they are adequate for process screening purposes with Eqs. (16-24) and (16-25). Rigorous calculations generally require that activity coefficients be accounted for. However, for the exchange between ions of the same valence at solution concentrations of 0.1 N or less, or between any ions at 0.01 N or less, the solution-phase activity coefficients prorated to unit valence will be similar enough that they can be omitted. 

Table 8-8 gives some nonelectrolyte transfer free energies, and Table 8-9 lists single ion transfer activity coefficients. Note especially the remarkable values for anions in dipolar aprotic solvents, indicating extensive desolvation in these solvents relative to methanol. This is consistent with the enhanced nucleophilic reactivity of anions in dipolar aprotic solvents. Parker and Blandamer have considered transfer activity coefficients for binary aqueous mixtures. 

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

As an example, take the molecule aminoazobenzene, one of the solutes listed in Table 39. When colorimetric measurements were made at room temperature on very dilute aqueous solutions of HC1, containing a trace of this substance, it was found that neutral molecules and (BH)+ ions were present in equal numbers when the concentration of the HCl was 0.0016 molal.1 At this low concentration the activity coefficient of the HCl is very near unity, and we may use (216) to find how far the vacant proton level provided by the aminoazobenzene molecule in aque-... 

Values of the distance of closest approach derived from experimental values of the activity coefficients are given in column 2 of Table 40. It will be seen that for the lithium and sodium salts the value is greater than the crystal-lattice spacing (given in column 4) by rather more than 1 angstrom, as is expected. For the salts of cesium, rubidium, and potassium, on the other hand, the distance of closest approach... 

TABLE I.a Comparison of Observed Activity Coefficients of Cu and Au with Values Calculated from Observed Short-Range Order Parameters by the First-Order Quasi-Chemical Theory... 

Table 6.2 Activity coefficient relationships for electrolyte solutions (single electrolyte)... 

Table 7.1 Debye-Hiickel parameters for the activity coefficient, volume, enthalpy, and...

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